The Nuclear Energy Density Functional Formalism
NASA Astrophysics Data System (ADS)
Duguet, T.
The present document focuses on the theoretical foundations of the nuclear energy density functional (EDF) method. As such, it does not aim at reviewing the status of the field, at covering all possible ramifications of the approach or at presenting recent achievements and applications. The objective is to provide a modern account of the nuclear EDF formalism that is at variance with traditional presentations that rely, at one point or another, on a Hamiltonian-based picture. The latter is not general enough to encompass what the nuclear EDF method represents as of today. Specifically, the traditional Hamiltonian-based picture does not allow one to grasp the difficulties associated with the fact that currently available parametrizations of the energy kernel E[g',g] at play in the method do not derive from a genuine Hamilton operator, would the latter be effective. The method is formulated from the outset through the most general multi-reference, i.e. beyond mean-field, implementation such that the single-reference, i.e. "mean-field", derives as a particular case. As such, a key point of the presentation provided here is to demonstrate that the multi-reference EDF method can indeed be formulated in a mathematically meaningful fashion even if E[g',g] does not derive from a genuine Hamilton operator. In particular, the restoration of symmetries can be entirely formulated without making any reference to a projected state, i.e. within a genuine EDF framework. However, and as is illustrated in the present document, a mathematically meaningful formulation does not guarantee that the formalism is sound from a physical standpoint. The price at which the latter can be enforced as well in the future is eventually alluded to.
Faber, C; Boulanger, P; Attaccalite, C; Duchemin, I; Blase, X
2014-03-13
Many-body Green's function perturbation theories, such as the GW and Bethe-Salpeter formalisms, are starting to be routinely applied to study charged and neutral electronic excitations in molecular organic systems relevant to applications in photovoltaics, photochemistry or biology. In parallel, density functional theory and its time-dependent extensions significantly progressed along the line of range-separated hybrid functionals within the generalized Kohn-Sham formalism designed to provide correct excitation energies. We give an overview and compare these approaches with examples drawn from the study of gas phase organic systems such as fullerenes, porphyrins, bacteriochlorophylls or nucleobases molecules. The perspectives and challenges that many-body perturbation theory is facing, such as the role of self-consistency, the calculation of forces and potential energy surfaces in the excited states, or the development of embedding techniques specific to the GW and Bethe-Salpeter equation formalisms, are outlined. PMID:24516185
Weatherbee, Andrew; Sugita, Mitsuro; Bizheva, Kostadinka; Popov, Ivan; Vitkin, Alex
2016-06-15
The distribution of backscattered intensities as described by the probability density function (PDF) of tissue-scattered light contains information that may be useful for tissue assessment and diagnosis, including characterization of its pathology. In this Letter, we examine the PDF description of the light scattering statistics in a well characterized tissue-like particulate medium using optical coherence tomography (OCT). It is shown that for low scatterer density, the governing statistics depart considerably from a Gaussian description and follow the K distribution for both OCT amplitude and intensity. The PDF formalism is shown to be independent of the scatterer flow conditions; this is expected from theory, and suggests robustness and motion independence of the OCT amplitude (and OCT intensity) PDF metrics in the context of potential biomedical applications. PMID:27304274
Density-functional formalism: V xc, discontinuities, and the local density approximation
NASA Astrophysics Data System (ADS)
Gunnarsson, O.; Jones, R. O.; Schönhammer, K.
We have demonstrated that the nodal structure of the wave functions can have a great effect on the accuracy of the LSD approximation, and we have identified classes of problems where the LSD results must be treated by caution. For states with the minimum number of nodal planes consistent with the orthogonality of the orbitals, the LSD approximation usually leads to a moderate overestimate of the exchange-correlation energy. For states with additional nodal planes the exchange-correlation energy is often greatly overestimated. In atoms, the depopulation of s-orbitals can lead to large errors, and similar effects may be expected in bonding situations where sp or sd hybridization reduces the s occupancy. More work in this area is essential.
Linear-scaling time-dependent density-functional theory in the linear response formalism.
Zuehlsdorff, T J; Hine, N D M; Spencer, J S; Harrison, N M; Riley, D J; Haynes, P D
2013-08-14
We present an implementation of time-dependent density-functional theory (TDDFT) in the linear response formalism enabling the calculation of low energy optical absorption spectra for large molecules and nanostructures. The method avoids any explicit reference to canonical representations of either occupied or virtual Kohn-Sham states and thus achieves linear-scaling computational effort with system size. In contrast to conventional localised orbital formulations, where a single set of localised functions is used to span the occupied and unoccupied state manifold, we make use of two sets of in situ optimised localised orbitals, one for the occupied and one for the unoccupied space. This double representation approach avoids known problems of spanning the space of unoccupied Kohn-Sham states with a minimal set of localised orbitals optimised for the occupied space, while the in situ optimisation procedure allows for efficient calculations with a minimal number of functions. The method is applied to a number of medium sized organic molecules and a good agreement with traditional TDDFT methods is observed. Furthermore, linear scaling of computational cost with system size is demonstrated on (10,0) carbon nanotubes of different lengths. PMID:23947840
NASA Astrophysics Data System (ADS)
Painter, G. S.; Averill, F. W.
1983-11-01
The principle of augmentation, used to introduce inner-atom core structure into slowly varying basis functions, is applied to Gaussian orbitals to define a new basis set for highly accurate total-energy calculations for atomic clusters within the density-functional formalism. Diffuse Gaussian-orbital tails are matched continuously and differentiably to inner-atom numeric radial functions at the atomic-sphere radius. Major advantages of Gaussian-orbital basis sets are acquired without the need for numerous Gaussians of large exponent for the core region. The numeric functions used inside the atom permit essentially exact solutions for that region. Procedures are described which recover use of the efficient integral algorithms for the Gaussian-orbital-tail matrix elements. The interactions over the structured inner-atom region are treated by efficient integrand smoothing and integration procedures for the sphere. The new augmented Gaussian basis removes the primary limitations on the use of Gaussian orbitals for heavy atoms. As an illustration the method is applied to the copper dimer in an all-electron framework within the local-spin-density approximation (LSDA). The calculated binding energy, equilibrium separation, and first ionization potential of Cu2 are within 2% of experiment within the Xα model. Excitation energies are better described within more recent refined exchange-correlation functionals. These all-electron results show the LSDA model predicts a slightly contracted bond length for Cu2, consistent with bulk LSDA calculations for the 3d transition-metal series.
NASA Astrophysics Data System (ADS)
Xia, Junchao; Carter, Emily A.
2016-03-01
We propose a simple density decomposition formalism within orbital-free (OF) density functional theory (DFT) based on the Wang-Govind-Carter-decomposition (WGCD) kinetic energy density functional (KEDF). The resulting simple-WGCD (sWGCD) KEDF provides efficient density optimization, full cell relaxation, reasonable bulk properties for various materials compared to both the original OFDFT-WGCD and the Kohn-Sham (KS) DFT values, and has various numerical benefits including more stable convergence and lower computational cost (twice as fast as the WGCD KEDF). We also study amorphous (a-) Li-Si alloys with KSDFT and OFDFT using the Huang-Carter (HC), WGCD, and sWGCD KEDFs. The a-Li-Si alloy samples are prepared with the anneal-and-quench method using NVT molecular dynamics simulations. We report structural properties, equilibrium volumes, bulk moduli, and alloy formation energies for each a-alloy. The HC, WGCD, and sWGCD KEDFs within OFDFT all predict accurate equilibrium volumes compared against KSDFT benchmarks. The HC KEDF bulk moduli agree with KSDFT benchmarks whereas the WGCD/sWGCD KEDFs generally overestimate the bulk moduli, especially for alloys with low Li concentrations. All three KEDFs show limited ability to predict alloy formation energies, which indicates the lack of transferability of these KEDFs among such systems and motivates future developments in OFDFT and KEDF formalisms.
NASA Astrophysics Data System (ADS)
Liu, Jie; Liang, WanZhen
2011-11-01
The paper presents the formalism, implementation, and performance of the analytical approach for the excited-state Hessian in the time-dependent density functional theory (TDDFT) that extends our previous work [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011)] on the analytical Hessian in TDDFT within Tamm-Dancoff approximation (TDA) to full TDDFT. In contrast to TDA-TDDFT, an appreciable advantage of full TDDFT is that it maintains the oscillator strength sum rule, and therefore yields more precise results for the oscillator strength and other related physical quantities. For the excited-state harmonic vibrational frequency calculation, however, full TDDFT does not seem to be advantageous since the numerical tests demonstrate that the accuracy of TDDFT with and without TDA are comparable to each other. As a common practice, the computed harmonic vibrational frequencies are scaled by a suitable scale factor to yield good agreement with the experimental fundamental frequencies. Here we apply both the optimized ground-state and excited-state scale factors to scale the calculated excited-state harmonic frequencies and find that the scaling decreases the root-mean-square errors. The optimized scale factors derived from the excited-state calculations are slightly smaller than those from the ground-state calculations.
Send, Robert; Furche, Filipp
2010-01-28
First-order nonadiabatic coupling matrix elements (NACMEs) are key for phenomena such as nonradiative transitions and excited-state decay, yet a consistent and practical first principles treatment has been elusive for molecules with more than a few heavy atoms. Here we present theory, implementation using Gaussian basis sets, and benchmarks of first-order NACMEs between ground and excited states in the framework of time-dependent hybrid density functional theory (TDDFT). A time-dependent response approach to NACMEs which avoids explicit computation of excited-state wave functions is outlined. In contrast to previous approaches, the present treatment produces exact analytical derivative couplings between time-dependent Kohn-Sham (TDKS) determinants in a finite atom-centered basis set. As in analytical gradient theory, derivative molecular orbital coefficients can be eliminated, making the computational cost independent of the number of nuclear degrees of freedom. Our expression reduces to the exact Chernyak-Mukamel formula for first-order NACMEs in the complete basis-set limit, but greatly improves basis-set convergence in finite atom-centered basis sets due to additional Pulay type terms. The Chernyak-Mukamel formula is shown to be equivalent to the Hellmann-Feynman contribution in analytical gradient theory. Our formalism may be implemented in TDDFT analytical excited-state gradient codes with minor modifications. Tests for systems with up to 147 atoms show that evaluation of first-order NACMEs causes total computation times to increase by an insignificant 10% on average. The resolution-of-the-identity approximation for the Coulomb energy (RI-J) reduces the computational cost by an order of magnitude for nonhybrid functionals, while errors are insignificant with standard auxiliary basis sets. We compare the computed NACMEs to full configuration interaction (FCI) in benchmark results for diatomic molecules; hybrid TDDFT and FCI are found to be in agreement for
Prociuk, Alexander; Van Kuiken, Ben; Dunietz, Barry D
2006-11-28
Electronic transmission through a metal-molecule-metal system is calculated by employing a Green's function formalism in the scattering based scheme. Self-energy models representing the bulk and the potential bias are used to describe electron transport through the molecular system. Different self-energies can be defined by varying the partition between device and bulk regions of the metal-molecule-metal model system. In addition, the self-energies are calculated with different representations of the bulk through its Green's function. In this work, the dependence of the calculated transmission on varying the self-energy subspaces is benchmarked. The calculated transmission is monitored with respect to the different choices defining the self-energy model. In this report, we focus on one-dimensional model systems with electronic structures calculated at the density functional level of theory. PMID:17144733
Qian, Zekan; Li, Rui; Hou, Shimin; Xue, Zengquan; Sanvito, Stefano
2007-11-21
An efficient self-consistent approach combining the nonequilibrium Green's function formalism with density functional theory is developed to calculate electron transport properties of molecular devices with quasi-one-dimensional (1D) electrodes. Two problems associated with the low dimensionality of the 1D electrodes, i.e., the nonequilibrium state and the uncertain boundary conditions for the electrostatic potential, are circumvented by introducing the reflectionless boundary conditions at the electrode-contact interfaces and the zero electric field boundary conditions at the electrode-molecule interfaces. Three prototypical systems, respectively, an ideal ballistic conductor, a high resistance tunnel junction, and a molecular device, are investigated to illustrate the accuracy and efficiency of our approach. PMID:18035901
Formalism and functionalism in linguistics.
Newmeyer, Frederick J
2010-05-01
Formalism and functionalism in linguistics are often taken to be diametrically opposed approaches. However, close examination of the relevant phenomena reveals that the two are complementary, rather than being irrevocably in opposition to each other. One can be a formal linguist and a functional linguist at the same time, without there being any contradiction. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. PMID:26271372
NASA Astrophysics Data System (ADS)
Klein, Roman
2016-06-01
Electron storage rings with appropriate design are primary source standards, the spectral radiant intensity of which can be calculated from measured parameters using the Schwinger equation. PTB uses the electron storage rings BESSY II and MLS for source-based radiometry in the spectral range from the near-infrared to the x-ray region. The uncertainty of the calculated radiant intensity depends on the uncertainty of the measured parameters used for the calculation. Up to now the procedure described in the guide to the expression of uncertainty in measurement (GUM), i.e. the law of propagation of uncertainty, assuming a linear measurement model, was used to determine the combined uncertainty of the calculated spectral intensity, and for the determination of the coverage interval as well. Now it has been tested with a Monte Carlo simulation, according to Supplement 1 to the GUM, whether this procedure is valid for the rather complicated calculation by means of the Schwinger formalism and for different probability distributions of the input parameters. It was found that for typical uncertainties of the input parameters both methods yield similar results.
NASA Astrophysics Data System (ADS)
Cruz, Salvador A.
An assessment of the use of statistical atomic models for the study of many-electron atom confinement is presented. The Thomas-Fermi-Dirac-[lambda]-Weizsäcker TFD[lambda]W functional formalism based on known properties of the orbital electron density is shown to be an appropriate tool for the description of the ground-state energy evolution of many-electron atoms spatially limited by closed and open boundaries. A brief review of the strategy followed in the TFD[lambda]W method for the study of atoms enclosed in hard and soft spherical cavities is presented along with more refined quantitative calculations as compared with previous results. Also, detailed quantitative results are shown-for the first time-in the case of confinement by a hard prolate spheroidal box for nuclear positions located at one of the foci and for an atom located at a distance D from a hard plane. A discussion is presented on the physical consequences of different confinement geometries and the adequacy of the TFD[lambda]W formalism to explore many-electron atom confinement by open and closed boundaries.
Multifractal formalism and anisotropic selfsimilar functions
NASA Astrophysics Data System (ADS)
Ben Slimane, Mourad
1998-09-01
In this paper we prove that the conjectures of Frisch and Parisi and Arneodo et al. (called the multifractal formalism for functions) may fail for some non-homogeneous selfsimilar functions on [open face R]2. In these cases, we compute the correct spectrum of singularities and we show how the multifractal formalism must be modified.
Rodríguez, Juan I; Ayers, Paul W; Götz, Andreas W; Castillo-Alvarado, F L
2009-07-14
A new approach for computing the atom-in-molecule [quantum theory of atoms in molecule (QTAIM)] energies in Kohn-Sham density-functional theory is presented and tested by computing QTAIM energies for a set of representative molecules. In the new approach, the contribution for the correlation-kinetic energy (T(c)) is computed using the density-functional theory virial relation. Based on our calculations, it is shown that the conventional approach where atomic energies are computed using only the noninteracting part of the kinetic energy might be in error by hundreds of kJ/mol. PMID:19603962
Zobač, Vladimír; Lewis, James P; Abad, Enrique; Mendieta-Moreno, Jesús I; Hapala, Prokop; Jelínek, Pavel; Ortega, José
2015-05-01
The computational simulation of photo-induced processes in large molecular systems is a very challenging problem. Firstly, to properly simulate photo-induced reactions the potential energy surfaces corresponding to excited states must be appropriately accessed; secondly, understanding the mechanisms of these processes requires the exploration of complex configurational spaces and the localization of conical intersections; finally, photo-induced reactions are probability events, that require the simulation of hundreds of trajectories to obtain the statistical information for the analysis of the reaction profiles. Here, we present a detailed description of our implementation of a molecular dynamics with electronic transitions algorithm within the local-orbital density functional theory code FIREBALL, suitable for the computational study of these problems. As an example of the application of this approach, we also report results on the [2 + 2] cycloaddition of ethylene with maleic anhydride and on the [2 + 2] photo-induced polymerization reaction of two C60 molecules. We identify different deactivation channels of the initial electron excitation, depending on the time of the electronic transition from LUMO to HOMO, and the character of the HOMO after the transition. PMID:25791682
NASA Astrophysics Data System (ADS)
Zobač, Vladimír; Lewis, James P.; Abad, Enrique; Mendieta-Moreno, Jesús I.; Hapala, Prokop; Jelínek, Pavel; Ortega, José
2015-05-01
The computational simulation of photo-induced processes in large molecular systems is a very challenging problem. Firstly, to properly simulate photo-induced reactions the potential energy surfaces corresponding to excited states must be appropriately accessed; secondly, understanding the mechanisms of these processes requires the exploration of complex configurational spaces and the localization of conical intersections; finally, photo-induced reactions are probability events, that require the simulation of hundreds of trajectories to obtain the statistical information for the analysis of the reaction profiles. Here, we present a detailed description of our implementation of a molecular dynamics with electronic transitions algorithm within the local-orbital density functional theory code FIREBALL, suitable for the computational study of these problems. As an example of the application of this approach, we also report results on the [2 + 2] cycloaddition of ethylene with maleic anhydride and on the [2 + 2] photo-induced polymerization reaction of two C60 molecules. We identify different deactivation channels of the initial electron excitation, depending on the time of the electronic transition from LUMO to HOMO, and the character of the HOMO after the transition.
Floquet Green function formalism for harmonically driven Hamiltonians
NASA Astrophysics Data System (ADS)
Martinez, D. F.
2003-09-01
A method is proposed for the calculation of the Floquet-Green function of a general Hamiltonian with harmonic time dependence. We use matrix continued fractions to derive an expression for the 'dynamical effective potential' that can be used to calculate the Floquet-Green function of the system. We demonstrate the formalism for the simple case of a space-periodic (in the tight-binding approximation) Hamiltonian with a defect whose on-site energy changes harmonically with time. We study the local density of states for this system and the behaviour of the localized states as a function of the different parameters that characterize the system.
The Comparative Functionality of Formal and Non-Formal Education for Women: Final Report.
ERIC Educational Resources Information Center
Derryck, Vivian Lowery
This final report describes a five-phase study to ascertain whether formal or non-formal education has the greater functionality to accelerate women's integration into development activities. Part 1 (two chapters), introduction and background, defines the problem, sets parameters of the study, and provides definitions of education terms. Part 2…
Modelling charge transfer reactions with the frozen density embedding formalism
Pavanello, Michele; Neugebauer, Johannes
2011-12-21
The frozen density embedding (FDE) subsystem formulation of density-functional theory is a useful tool for studying charge transfer reactions. In this work charge-localized, diabatic states are generated directly with FDE and used to calculate electronic couplings of hole transfer reactions in two {pi}-stacked nucleobase dimers of B-DNA: 5{sup '}-GG-3{sup '} and 5{sup '}-GT-3{sup '}. The calculations rely on two assumptions: the two-state model, and a small differential overlap between donor and acceptor subsystem densities. The resulting electronic couplings agree well with benchmark values for those exchange-correlation functionals that contain a high percentage of exact exchange. Instead, when semilocal GGA functionals are used the electronic couplings are grossly overestimated.
NASA Astrophysics Data System (ADS)
Zeng, Qiao; Liu, Jie; Liang, WanZhen
2014-05-01
This work extends our previous works [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011); J. Liu and W. Z. Liang, J. Chem. Phys. 135, 184111 (2011)] on analytical excited-state energy Hessian within the framework of time-dependent density functional theory (TDDFT) to couple with molecular mechanics (MM). The formalism, implementation, and applications of analytical first and second energy derivatives of TDDFT/MM excited state with respect to the nuclear and electric perturbations are presented. Their performances are demonstrated by the calculations of adiabatic excitation energies, and excited-state geometries, harmonic vibrational frequencies, and infrared intensities for a number of benchmark systems. The consistent results with the full quantum mechanical method and other hybrid theoretical methods indicate the reliability of the current numerical implementation of developed algorithms. The computational accuracy and efficiency of the current analytical approach are also checked and the computational efficient strategies are suggested to speed up the calculations of complex systems with many MM degrees of freedom. Finally, we apply the current analytical approach in TDDFT/MM to a realistic system, a red fluorescent protein chromophore together with part of its nearby protein matrix. The calculated results indicate that the rearrangement of the hydrogen bond interactions between the chromophore and the protein matrix is responsible for the large Stokes shift.
Zeng, Qiao; Liang, WanZhen; Liu, Jie
2014-05-14
This work extends our previous works [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011); J. Liu and W. Z. Liang, J. Chem. Phys. 135, 184111 (2011)] on analytical excited-state energy Hessian within the framework of time-dependent density functional theory (TDDFT) to couple with molecular mechanics (MM). The formalism, implementation, and applications of analytical first and second energy derivatives of TDDFT/MM excited state with respect to the nuclear and electric perturbations are presented. Their performances are demonstrated by the calculations of adiabatic excitation energies, and excited-state geometries, harmonic vibrational frequencies, and infrared intensities for a number of benchmark systems. The consistent results with the full quantum mechanical method and other hybrid theoretical methods indicate the reliability of the current numerical implementation of developed algorithms. The computational accuracy and efficiency of the current analytical approach are also checked and the computational efficient strategies are suggested to speed up the calculations of complex systems with many MM degrees of freedom. Finally, we apply the current analytical approach in TDDFT/MM to a realistic system, a red fluorescent protein chromophore together with part of its nearby protein matrix. The calculated results indicate that the rearrangement of the hydrogen bond interactions between the chromophore and the protein matrix is responsible for the large Stokes shift.
Zeng, Qiao; Liu, Jie; Liang, WanZhen
2014-05-14
This work extends our previous works [J. Liu and W. Z. Liang, J. Chem. Phys. 135, 014113 (2011); J. Liu and W. Z. Liang, J. Chem. Phys. 135, 184111 (2011)] on analytical excited-state energy Hessian within the framework of time-dependent density functional theory (TDDFT) to couple with molecular mechanics (MM). The formalism, implementation, and applications of analytical first and second energy derivatives of TDDFT/MM excited state with respect to the nuclear and electric perturbations are presented. Their performances are demonstrated by the calculations of adiabatic excitation energies, and excited-state geometries, harmonic vibrational frequencies, and infrared intensities for a number of benchmark systems. The consistent results with the full quantum mechanical method and other hybrid theoretical methods indicate the reliability of the current numerical implementation of developed algorithms. The computational accuracy and efficiency of the current analytical approach are also checked and the computational efficient strategies are suggested to speed up the calculations of complex systems with many MM degrees of freedom. Finally, we apply the current analytical approach in TDDFT/MM to a realistic system, a red fluorescent protein chromophore together with part of its nearby protein matrix. The calculated results indicate that the rearrangement of the hydrogen bond interactions between the chromophore and the protein matrix is responsible for the large Stokes shift. PMID:24832314
Partition density functional theory
NASA Astrophysics Data System (ADS)
Nafziger, Jonathan
Partition density functional theory (PDFT) is a method for dividing a molecular electronic structure calculation into fragment calculations. The molecular density and energy corresponding to Kohn Sham density-functional theory (KS-DFT) may be exactly recovered from these fragments. Each fragment acts as an isolated system except for the influence of a global one-body 'partition' potential which deforms the fragment densities. In this work, the developments of PDFT are put into the context of other fragment-based density functional methods. We developed three numerical implementations of PDFT: One within the NWChem computational chemistry package using basis sets, and the other two developed from scratch using real-space grids. It is shown that all three of these programs can exactly reproduce a KS-DFT calculation via fragment calculations. The first of our in-house codes handles non-interacting electrons in arbitrary one-dimensional potentials with any number of fragments. This code is used to explore how the exact partition potential changes for different partitionings of the same system and also to study features which determine which systems yield non-integer PDFT occupations and which systems are locked into integer PDFT occupations. The second in-house code, CADMium, performs real-space calculations of diatomic molecules. Features of the exact partition potential are studied for a variety of cases and an analytical formula determining singularities in the partition potential is derived. We introduce an approximation for the non-additive kinetic energy and show how this quantity can be computed exactly. Finally a PDFT functional is developed to address the issues of static correlation and delocalization errors in approximations within DFT. The functional is applied to the dissociation of H2 + and H2.
Density functionals from deep learning
NASA Astrophysics Data System (ADS)
McMahon, Jeffrey
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional (DF) are necessary. Machine learning has recently been proposed as a novel approach to discover such a DF (or components of it). Conventional machine learning algorithms, however, are limited in their ability to process data in their raw form, leading to invariance and/or sensitivity issues. In this presentation, an alternative approach based on deep learning will be demonstrated. Deep learning allows computational models that are capable of discovering intricate structure in large and/or high-dimensional data sets with multiple levels of abstraction, and do not suffer from the aforementioned issues. Results from the application of this approach to the prediction of the kinetic-energy DF of noninteracting electrons will be presented. Using theoretical results from computer science, a connection between the underlying model and the theorems of Hohenberg and Kohn will also be suggested.
A logarithmic correction in the entropy functional formalism
NASA Astrophysics Data System (ADS)
Hammad, Fayçal; Faizal, Mir
2016-04-01
The entropy functional formalism allows one to recover general relativity, modified gravity theories, as well as the Bekenstein-Hawking entropy formula. In most approaches to quantum gravity, the Bekenstein-Hawking’s entropy formula acquires a logarithmic correction term. As such terms occur almost universally in most approaches to quantum gravity, we analyze the effect of such terms on the entropy functional formalism. We demonstrate that the leading correction to the micro-canonical entropy in the entropy functional formalism can be used to recover modified theories of gravity already obtained with an uncorrected micro-canonical entropy. Furthermore, since the entropy functional formalism reproduces modified gravity, the rise of gravity-dependent logarithmic corrections turns out to be one way to impose constraints on these theories of modified gravity. The constraints found here for the simple case of an ℱ(R)-gravity are the same as those obtained in the literature from cosmological considerations.
Inequalities for formal power series and entire functions
NASA Astrophysics Data System (ADS)
Grinshpan, Arcadii Z.
2008-02-01
We present several integral and exponential inequalities for formal power series and for both arbitrary entire functions of exponential type and generalized Borel transforms. They are obtained through certain limit procedures which involve the multiparameter binomial inequalities, integral inequalities for continuous functions, and weighted norm inequalities for analytic functions. Some applications to the confluent hypergeometric functions, Bessel functions, Laguerre polynomials, and trigonometric functions are discussed. Also some generalizations are given.
An envelope function formalism for lattice-matched heterostructures
NASA Astrophysics Data System (ADS)
Van de Put, Maarten L.; Vandenberghe, William G.; Magnus, Wim; Sorée, Bart
2015-08-01
The envelope function method traditionally employs a single basis set which, in practice, relates to a single material because the k · p matrix elements are generally only known in a particular basis. In this work, we defined a basis function transformation to alleviate this restriction. The transformation is completely described by the known inter-band momentum matrix elements. The resulting envelope function equation can solve the electronic structure in lattice matched heterostructures without resorting to boundary conditions at the interface between materials, while all unit-cell averaged observables can be calculated as with the standard envelope function formalism. In the case of two coupled bands, this heterostructure formalism is equivalent to the standard formalism while taking position dependent matrix elements.
Density-dependent covariant energy density functionals
Lalazissis, G. A.
2012-10-20
Relativistic nuclear energy density functionals are applied to the description of a variety of nuclear structure phenomena at and away fromstability line. Isoscalar monopole, isovector dipole and isoscalar quadrupole giant resonances are calculated using fully self-consistent relativistic quasiparticle randomphase approximation, based on the relativistic Hartree-Bogoliubovmodel. The impact of pairing correlations on the fission barriers in heavy and superheavy nuclei is examined. The role of pion in constructing desnity functionals is also investigated.
Combining Formal and Functional Approaches to Topic Structure
ERIC Educational Resources Information Center
Zellers, Margaret; Post, Brechtje
2012-01-01
Fragmentation between formal and functional approaches to prosodic variation is an ongoing problem in linguistic research. In particular, the frameworks of the Phonetics of Talk-in-Interaction (PTI) and Empirical Phonology (EP) take very different theoretical and methodological approaches to this kind of variation. We argue that it is fruitful to…
Formalization Studies in Functional Size Measurement: How Do They Help?
NASA Astrophysics Data System (ADS)
Ozkan, Baris; Demirors, Onur
Functional size has been favored as a software characteristic that can be measured early and independent of language, tools, techniques and technology; hence has many uses in software project management. It has been about three decades since Albrecht introduced the concept of functional size. However, Functional Size Measurement (FSM) has not been a common practice in the software community. The problems with FSM method structures and practices have been discussed to be the major factors to explain this situation. In this paper, we make a review of formalization proposals to the problems in Functional Size Measurement (FSM). We analyze the works included in the papers and we explore the extent of their contributions.
Teaching Density Functional Theory Through Experiential Learning
NASA Astrophysics Data System (ADS)
Narasimhan, Shobhana
2015-09-01
Today, quantum mechanical density functional theory is often the method of choice for performing accurate calculations on atomic, molecular and condensed matter systems. Here, I share some of my experiences in teaching the necessary basics of solid state physics, as well as the theory and practice of density functional theory, in a number of workshops held in developing countries over the past two decades. I discuss the advantages of supplementing the usual mathematically formal teaching methods, characteristic of graduate courses, with the use of visual imagery and analogies. I also describe a successful experiment we carried out, which resulted in a joint publication co-authored by 67 lecturers and students participating in a summer school.
Phenomenological Relativistic Energy Density Functionals
Lalazissis, G. A.; Kartzikos, S.; Niksic, T.; Paar, N.; Vretenar, D.; Ring, P.
2009-08-26
The framework of relativistic nuclear energy density functionals is applied to the description of a variety of nuclear structure phenomena, not only in spherical and deformed nuclei along the valley of beta-stability, but also in exotic systems with extreme isospin values and close to the particle drip-lines. Dynamical aspects of exotic nuclear structure is explored using the fully consistent quasiparticle random-phase approximation based on the relativistic Hartree-Bogoliubov model. Recent applications of energy density functionals with explicit density dependence of the meson-nucleon couplings are presented.
Density Functionals of Chemical Bonding
Putz, Mihai V.
2008-01-01
The behavior of electrons in general many-electronic systems throughout the density functionals of energy is reviewed. The basic physico-chemical concepts of density functional theory are employed to highlight the energy role in chemical structure while its extended influence in electronic localization function helps in chemical bonding understanding. In this context the energy functionals accompanied by electronic localization functions may provide a comprehensive description of the global-local levels electronic structures in general and of chemical bonds in special. Becke-Edgecombe and author’s Markovian electronic localization functions are discussed at atomic, molecular and solid state levels. Then, the analytical survey of the main workable kinetic, exchange, and correlation density functionals within local and gradient density approximations is undertaken. The hierarchy of various energy functionals is formulated by employing both the parabolic and statistical correlation degree of them with the electronegativity and chemical hardness indices by means of quantitative structure-property relationship (QSPR) analysis for basic atomic and molecular systems. PMID:19325846
Phonons in nonlocal van der Waals density functional theory
NASA Astrophysics Data System (ADS)
Sabatini, Riccardo; Küçükbenli, Emine; Pham, Cong Huy; de Gironcoli, Stefano
2016-06-01
We extend the formulation of density functional perturbation theory to treat nonlocal density functionals, accounting for van der Waals interactions, in a rigorous and efficient way. We provide a general formalism, suitable for any functional in this family, and give specific equations for the most widely used ones. We then study the lattice dynamics of graphite, comparing several nonlocal functionals and the local density approximation, showing that our recent revision of the VV10 functional [R. Sabatini et al., Phys. Rev. B 87, 041108(R) (2013), 10.1103/PhysRevB.87.041108] gives the best comparison with experiments.
Gutzwiller density functional theory for correlated electron systems
Ho, K. M.; Schmalian, J.; Wang, C. Z.
2008-02-04
We develop a density functional theory (DFT) and formalism for correlated electron systems by taking as reference an interacting electron system that has a ground state wave function which exactly obeys the Gutzwiller approximation for all one-particle operators. The solution of the many-electron problem is mapped onto the self-consistent solution of a set of single-particle Schroedinger equations, analogously to standard DFT-local density approximation calculations.
Semiclassical origins of density functionals
NASA Astrophysics Data System (ADS)
Burke, Kieron
By careful numerical analysis of non-relativistic atomic correlation energies, we show that (a) the local density approximation becomes relatively exact for the correlation energy as the atomic number approaches infinity, (b) we find the leading correction, which is about 38.5 milliHartrees per atom, (c) show how this correction dominates for larger atoms and (d) how to construct a generalized gradient approximation that respects this limit (See KB, A. Cancio, T. Gould, S. Pittalis, arXiv:1409.4834). The relevance to density functional calculations will also be explained. Support provided by NSF CHE-1464795.
NASA Astrophysics Data System (ADS)
Belluzzi, L.; Landi Degl'Innocenti, E.; Trujillo Bueno, J.
2013-04-01
Within the framework of the density matrix theory for the generation and transfer of polarized radiation, velocity density matrix correlations represent an important physical aspect that, however, is often neglected in practical applications when adopting the simplifying approximation of complete redistribution on velocity. In this paper, we present an application of the non-LTE problem for polarized radiation taking such correlations into account through the velocity-space density matrix formalism. We consider a two-level atom with infinitely sharp upper and lower levels, and we derive the corresponding statistical equilibrium equations, neglecting the contribution of velocity-changing collisions. Coupling such equations with the radiative transfer equations for polarized radiation, we derive a set of coupled equations for the velocity-dependent source function. This set of equations is then particularized to the case of a plane-parallel atmosphere. The equations presented in this paper provide a complete and solid description of the physics of pure Doppler redistribution, a phenomenon generally described within the framework of the redistribution matrix formalism. The redistribution matrix corresponding to this problem (generally referred to as RI) is derived starting from the statistical equilibrium equations for the velocity-space density matrix and from the radiative transfer equations for polarized radiation, thus showing the equivalence of the two approaches.
The stochastic tetrad magneto-hydrodynamics via functional formalism
NASA Astrophysics Data System (ADS)
Materassi, Massimo; Consolini, Giuseppe
2015-12-01
> In this work we discuss an application of the Tetrad Dynamics approach, a stochastic dynamical theory already introduced in hydrodynamic turbulence, to incompressible magneto-hydrodynamics. This theoretical framework is capable of taking into account some crucial aspects of turbulent plasmas, namely, (i) its material nature, which is stressed through the adoption of Lagrangian variables, (ii) its probabilistic dynamics, which is fundamental to understand the intermittency and highly irregular nature of turbulence, and (iii) the multi-scale character of interactions, which is approached by promoting the space size of parcels to the role of a dynamical variable. In particular, here, we construct the probabilistic equations of motion for quantities describing the evolution of a turbulent plasma (a matrix describing the parcel's shape, the plasma velocity and magnetic field coarse-grained gradient tensors, and ), resorting the functional formalism of classical statistical dynamics. Through the introduction of a stochastic action and using a path integral approach, the statistical properties of can be derived from those of noises appearing in their equations of motion, both at equilibrium and out of equilibrium.
Formal functional test designs with a test representation language
NASA Technical Reports Server (NTRS)
Hops, J. M.
1993-01-01
The application of the category-partition method to the test design phase of hardware, software, or system test development is discussed. The method provides a formal framework for reducing the total number of possible test cases to a minimum logical subset for effective testing. An automatic tool and a formal language were developed to implement the method and produce the specification of test cases.
Local spin analyses using density functional theory
NASA Astrophysics Data System (ADS)
Abate, Bayileyegn; Peralta, Juan
Local spin analysis is a valuable technique in computational investigations magnetic interactions on mono- and polynuclear transition metal complexes, which play vital roles in catalysis, molecular magnetism, artificial photosynthesis, and several other commercially important materials. The relative size and complex electronic structure of transition metal complexes often prohibits the use of multi-determinant approaches, and hence, practical calculations are often limited to single-determinant methods. Density functional theory (DFT) has become one of the most successful and widely used computational tools for the electronic structure study of complex chemical systems; transition metal complexes in particular. Within the DFT formalism, a more flexible and complete theoretical modeling of transition metal complexes can be achieved by considering noncollinear spins, in which the spin density is 'allowed to' adopt noncollinear structures in stead of being constrained to align parallel/antiparallel to a universal axis of magnetization. In this meeting, I will present local spin analyses results obtained using different DFT functionals. Local projection operators are used to decompose the expectation value
Density functional theory: Foundations reviewed
NASA Astrophysics Data System (ADS)
Kryachko, Eugene S.; Ludeña, Eduardo V.
2014-11-01
Guided by the above motto (quotation), we review a broad range of issues lying at the foundations of Density Functional Theory, DFT, a theory which is currently omnipresent in our everyday computational study of atoms and molecules, solids and nano-materials, and which lies at the heart of modern many-body computational technologies. The key goal is to demonstrate that there are definitely the ways to improve DFT. We start by considering DFT in the larger context provided by reduced density matrix theory (RDMT) and natural orbital functional theory (NOFT), and examine the implications that N-representability conditions on the second-order reduced density matrix (2-RDM) have not only on RDMT and NOFT but, also, by extension, on the functionals of DFT. This examination is timely in view of the fact that necessary and sufficient N-representability conditions on the 2-RDM have recently been attained. In the second place, we review some problems appearing in the original formulation of the first Hohenberg-Kohn theorem which is still a subject of some controversy. In this vein we recall Lieb's comment on this proof and the extension to this proof given by Pino et al. (2009), and in this context examine the conditions that must be met in order that the one-to-one correspondence between ground-state densities and external potentials remains valid for finite subspaces (namely, the subspaces where all Kohn-Sham solutions are obtained in practical applications). We also consider the issue of whether the Kohn-Sham equations can be derived from basic principles or whether they are postulated. We examine this problem in relation to ab initio DFT. The possibility of postulating arbitrary Kohn-Sham-type equations, where the effective potential is by definition some arbitrary mixture of local and non-local terms, is discussed. We also deal with the issue of whether there exists a universal functional, or whether one should advocate instead the construction of problem
NASA Astrophysics Data System (ADS)
Pribram-Jones, Aurora
Warm dense matter (WDM) is a high energy phase between solids and plasmas, with characteristics of both. It is present in the centers of giant planets, within the earth's core, and on the path to ignition of inertial confinement fusion. The high temperatures and pressures of warm dense matter lead to complications in its simulation, as both classical and quantum effects must be included. One of the most successful simulation methods is density functional theory-molecular dynamics (DFT-MD). Despite great success in a diverse array of applications, DFT-MD remains computationally expensive and it neglects the explicit temperature dependence of electron-electron interactions known to exist within exact DFT. Finite-temperature density functional theory (FT DFT) is an extension of the wildly successful ground-state DFT formalism via thermal ensembles, broadening its quantum mechanical treatment of electrons to include systems at non-zero temperatures. Exact mathematical conditions have been used to predict the behavior of approximations in limiting conditions and to connect FT DFT to the ground-state theory. An introduction to FT DFT is given within the context of ensemble DFT and the larger field of DFT is discussed for context. Ensemble DFT is used to describe ensembles of ground-state and excited systems. Exact conditions in ensemble DFT and the performance of approximations depend on ensemble weights. Using an inversion method, exact Kohn-Sham ensemble potentials are found and compared to approximations. The symmetry eigenstate Hartree-exchange approximation is in good agreement with exact calculations because of its inclusion of an ensemble derivative discontinuity. Since ensemble weights in FT DFT are temperature-dependent Fermi weights, this insight may help develop approximations well-suited to both ground-state and FT DFT. A novel, highly efficient approach to free energy calculations, finite-temperature potential functional theory, is derived, which has the
Trovato, M.; Reggiani, L.
2011-12-15
By introducing a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is asserted as fundamental principle of quantum statistical mechanics. Accordingly, we develop a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theoretical formalism is formulated in both thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of ({h_bar}/2{pi}){sup 2}. In particular, by using an arbitrary number of moments, we prove that (1) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives, both of the numerical density n and of the effective temperature T; (2) the results available from the literature in the framework of both a quantum Boltzmann gas and a degenerate quantum Fermi gas are recovered as a particular case; (3) the statistics for the quantum Fermi and Bose gases at different levels of degeneracy are explicitly incorporated; (4) a set of relevant applications admitting exact analytical equations are explicitly given and discussed; (5) the quantum maximum entropy principle keeps full validity in the classical limit, when ({h_bar}/2{pi}){yields}0.
]: a density functional theory investigation
NASA Astrophysics Data System (ADS)
Ulian, Gianfranco; Tosoni, Sergio; Valdrè, Giovanni
2014-09-01
In this work, we modelled the structure, the compressional behaviour and the physical properties of talc over a wide range of pressure using a quantum mechanical approach based on periodic boundary conditions. We adopted the density functional theory using the B3LYP-D* functional, which includes a correction for the dispersive forces and all-electron Gaussian-type orbitals basis sets. An atomic level description of the athermal pressure-induced structural modification of talc is provided. From the compression results, we obtained the athermal ( T = 0 K) bulk modulus ( K T0), its first derivative ( K') and the athermal volume at zero pressure ( V 0) by a third-order Birch-Murnaghan equation with parameters K T0 = 56.25 GPa, K' = 5.66 and V 0 = 450.34 Å3. The mechanical behaviour is highly anisotropic, as observed by the axial compressibility. The presented data are in very good agreement with recent experimental results obtained by single-crystal neutron and X-ray diffraction experiments.
Steady-State Density Functional Theory for Finite Bias Conductances.
Stefanucci, G; Kurth, S
2015-12-01
In the framework of density functional theory, a formalism to describe electronic transport in the steady state is proposed which uses the density on the junction and the steady current as basic variables. We prove that, in a finite window around zero bias, there is a one-to-one map between the basic variables and both local potential on as well as bias across the junction. The resulting Kohn-Sham system features two exchange-correlation (xc) potentials, a local xc potential, and an xc contribution to the bias. For weakly coupled junctions the xc potentials exhibit steps in the density-current plane which are shown to be crucial to describe the Coulomb blockade diamonds. At small currents these steps emerge as the equilibrium xc discontinuity bifurcates. The formalism is applied to a model benzene junction, finding perfect agreement with the orthodox theory of Coulomb blockade. PMID:26571349
Density-functional theory of superconductivity
NASA Astrophysics Data System (ADS)
Gross, E. K. U.
2008-03-01
A prominent challenge of modern condensed-matter theory is to predict reliably material-specific properties of superconductors, such as the critical temperature. The traditional model of Bardeen, Cooper and Schrieffer (BCS) properly describes the universal features that all conventional superconductors have in common, but it is not able to make accurate predictions of material-specific properties. To tackle this problem, a density-functional formalism has been developed [1] which describes superconductors in thermal equilibrium in terms of three quantities: the ordinary density, the superconducting order parameter, and the nuclear N-body density. These three ``densities'' are determined self-consistently through a set of Kohn-Sham equations. Approximations of the universal exchange-correlation functional are derived on the basis of many-body perturbation theory. In this way, a true ab-initio description is achieved which does not contain any adjustable parameters such as the μ* of Eliashberg theory. Numerical results for the critical temperature, the isotope effect, the gap function and the jump of the specific heat will be presented for simple metals, for MgB2 [2] and CaBeSi, and for calcium intercalated graphite (CaC6) [3]. Furthermore, results for Li, Al, K, and H under pressure will be discussed. The calculations explain why Li and Al behave very differently, leading to a strong enhancement of superconductivity for Li and to a clear suppression for Al with increasing pressure [4]. For K we predict a behavior similar to Li, i.e. a strong increase of Tc with increasing pressure. Finally, hydrogen is found to be a three-gap superconductor whose critical temperature increases with increasing pressure until about 100K (at 500 GPa). [1] M. Lüders, M.A.L. Marques, N.N. Lathiotakis, A. Floris,G. Profeta, L. Fast, A.Continenza, S. Massidda, E.K.U. Gross, PRB 72, 024545 (2005). [2] A. Floris, G. Profeta, N.N. Lathiotakis, M. Lüders, M.A.L. Marques, C. Franchini, E
Density functional theory for polymeric systems in 2D
NASA Astrophysics Data System (ADS)
Słyk, Edyta; Roth, Roland; Bryk, Paweł
2016-06-01
We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim’s first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys. 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT.
Density functional theory for polymeric systems in 2D.
Słyk, Edyta; Roth, Roland; Bryk, Paweł
2016-06-22
We propose density functional theory for polymeric fluids in two dimensions. The approach is based on Wertheim's first order thermodynamic perturbation theory (TPT) and closely follows density functional theory for polymers proposed by Yu and Wu (2002 J. Chem. Phys. 117 2368). As a simple application we evaluate the density profiles of tangent hard-disk polymers at hard walls. The theoretical predictions are compared against the results of the Monte Carlo simulations. We find that for short chain lengths the theoretical density profiles are in an excellent agreement with the Monte Carlo data. The agreement is less satisfactory for longer chains. The performance of the theory can be improved by recasting the approach using the self-consistent field theory formalism. When the self-avoiding chain statistics is used, the theory yields a marked improvement in the low density limit. Further improvements for long chains could be reached by going beyond the first order of TPT. PMID:27115343
Gonis, A.; Zhang, X. G.; Stocks, G. M.; Nicholson, D. M.
2015-10-23
Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide a complete solution of the v-representability problem by establishing a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of the density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism.
Gonis, A.; Zhang, X. G.; Stocks, G. M.; Nicholson, D. M.
2015-10-23
Density functional theory for the case of general, N-representable densities is reformulated in terms of density functional derivatives of expectation values of operators evaluated with wave functions leading to a density, making no reference to the concept of potential. The developments provide a complete solution of the v-representability problem by establishing a mathematical procedure that determines whether a density is v-representable and in the case of an affirmative answer determines the potential (within an additive constant) as a derivative with respect to the density of a constrained search functional. It also establishes the existence of an energy functional of themore » density that, for v-representable densities, assumes its minimum value at the density describing the ground state of an interacting many-particle system. The theorems of Hohenberg and Kohn emerge as special cases of the formalism.« less
Gedanken densities and exact constraints in density functional theory
Perdew, John P.; Ruzsinszky, Adrienn; Sun, Jianwei; Burke, Kieron
2014-05-14
Approximations to the exact density functional for the exchange-correlation energy of a many-electron ground state can be constructed by satisfying constraints that are universal, i.e., valid for all electron densities. Gedanken densities are designed for the purpose of this construction, but need not be realistic. The uniform electron gas is an old gedanken density. Here, we propose a spherical two-electron gedanken density in which the dimensionless density gradient can be an arbitrary positive constant wherever the density is non-zero. The Lieb-Oxford lower bound on the exchange energy can be satisfied within a generalized gradient approximation (GGA) by bounding its enhancement factor or simplest GGA exchange-energy density. This enhancement-factor bound is well known to be sufficient, but our gedanken density shows that it is also necessary. The conventional exact exchange-energy density satisfies no such local bound, but energy densities are not unique, and the simplest GGA exchange-energy density is not an approximation to it. We further derive a strongly and optimally tightened bound on the exchange enhancement factor of a two-electron density, which is satisfied by the local density approximation but is violated by all published GGA's or meta-GGA’s. Finally, some consequences of the non-uniform density-scaling behavior for the asymptotics of the exchange enhancement factor of a GGA or meta-GGA are given.
Green's-function formalism for waveguide QED applications
NASA Astrophysics Data System (ADS)
Schneider, Michael P.; Sproll, Tobias; Stawiarski, Christina; Schmitteckert, Peter; Busch, Kurt
2016-01-01
We present a quantum-field-theoretical framework based on path integrals and Feynman diagrams for the investigation of the quantum-optical properties of one-dimensional waveguiding structures with embedded quantum impurities. In particular, we obtain the Green's functions for a waveguide with an embedded two-level system in the single- and two-excitation sector for arbitrary dispersion relations both in the time and the frequency domains. In the single-excitation sector, we show how to sum the diagrammatic perturbation series to all orders and thus obtain explicit expressions for physical quantities such as the spectral density and the scattering matrix. In the two-excitation sector, we show that strictly linear dispersion relations exhibit the special property that the corresponding diagrammatic perturbation series terminates after two terms, again allowing for closed-form expressions for physical quantities. In the case of general dispersion relations, notably those exhibiting a band edge or waveguide cutoff frequencies, the perturbation series cannot be summed explicitly. Instead, we derive a self-consistent T -matrix equation that reduces the computational effort to that of a single-excitation computation. This analysis allows us to identify a Fano resonance between the occupied quantum impurity and a free photon in the waveguide as a unique signature of the few-photon nonlinearity inherent in such systems. In addition, our diagrammatic approach allows for the classification of different physical processes such as the creation of photon-photon correlations and interaction-induced radiation trapping, the latter being absent for strictly linear dispersion relations. Our framework can serve as the basis for further studies that involve more complex scenarios such as several and many-level quantum impurities, networks of coupled waveguides, disordered systems, and nonequilibrium effects.
Unexpected properties of a density functional
Karwowski, J.; Stanke, M.
2005-02-01
An observation on a pathological behavior of an exact density functional derived from either relativistic (Dirac) or nonrelativistic (Levy-Leblond) quantum-mechanical equation is reported. As expected, in the case of a one-electron atom the variational minimum of this functional is equal to the exact ground-state energy. However, apart from the correct density, this minimum is reached also by an infinite set of densities which do not correspond to the exact wave function. This paradoxical property of the functional is related to the multicomponent structure of both Dirac and Levy-Leblond wave functions. In particular, imposing the correct boundary conditions upon the trial densities removes only a part of the fake solutions. The results of this study demonstrate that in density-functional theories derived from models based on multicomponent wave functions, one should not expect any simple relation between the accuracy of the energy and the correctness of the corresponding density.
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.
2014-11-04
Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number L_{max} = (l,m)_{max}, while scattering matrices, which determine spectral properties, are truncated at L_{tr} = (l,m)_{tr} where phase shifts δl>l_{tr} are negligible. Historically, L_{max} is set equal to L_{tr}, which is correct for large enough L_{max} but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for L_{max} > L_{tr} with δl>l_{tr} set to zero [Zhang and Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R^{3} process with rank N(l_{tr} + 1)^{2}] and includes higher-L contributions via linear algebra [R^{2} process with rank N(l_{max} +1)^{2}]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L1_{0} CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus L_{max} for a given L_{tr}.
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.
2014-11-04
Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number Lmax = (l,m)max, while scattering matrices, which determine spectral properties, are truncated at Ltr = (l,m)tr where phase shifts δl>ltr are negligible. Historically, Lmax is set equal to Ltr, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax > Ltr with δl>ltr set to zero [Zhang andmore » Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R3 process with rank N(ltr + 1)2] and includes higher-L contributions via linear algebra [R2 process with rank N(lmax +1)2]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L10 CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Ltr.« less
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
NASA Astrophysics Data System (ADS)
Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.
2014-11-01
The Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient site-centered, electronic-structure technique for addressing an assembly of N scatterers. Wave functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number Lmax=(l,mmax), while scattering matrices, which determine spectral properties, are truncated at Lt r=(l,mt r) where phase shifts δl >ltr are negligible. Historically, Lmax is set equal to Lt r, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax>Lt r with δl >ltr set to zero [X.-G. Zhang and W. H. Butler, Phys. Rev. B 46, 7433 (1992), 10.1103/PhysRevB.46.7433]. We present a numerically efficient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R3 process with rank N (ltr+1 ) 2 ] and includes higher-L contributions via linear algebra [R2 process with rank N (lmax+1) 2 ]. The augmented-KKR approach yields properly normalized wave functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe, and L 1 0 CoPt and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Lt r.
Comments on the locality in density-functional theory
Lindgren, Ingvar; Salomonson, Sten
2003-05-01
The 'locality hypothesis' in density-functional theory (DFT), implying that the functional derivative is equivalent to a multiplicative local function, forms the basis of models of Kohn-Sham type. This has been generally accepted by the community since the advent of the model, and has later been formally proved for a large class of functionals. The hypothesis has recently been questioned by Nesbet [Phys. Rev. A 58, R12 (1998) and Phys. Rev. A 65, 010502 (2001)], who claims that it fails for the kinetic-energy functional for a system with more than two noninteracting electrons with a nondegenerate ground state. This conclusion has been questioned by Gal [Phys. Rev. A 62, 044501 (2000)] and by Holas and March [Phys. Rev. A 64, 016501 (2001)]. We claim that the arguments of Nesbet are incorrect, since the orbital functional used for the kinetic energy is not a unique functional of the total density in the domain of unnormalized orbitals. We have demonstrated that with a proper definition of the kinetic energy, which is a unique density functional also in the unnormalized region, the derivative can be represented by a single local multiplicative function for all v-representable densities. Therefore, we consider the controversy connected with the issue raised by Nesbet as resolved. We believe that the proof of the differentiability given here can be extended to larger groups of DFT functionals, and works along these lines are in progress.
Free Electron Laser Theory Using Two Times Green Function Formalism
NASA Astrophysics Data System (ADS)
Takahashi, Hiroshi
2002-04-01
In this paper, we present a quatum theory for free electron laser obtained by firstly using the Two time's Green Function method developed by Matsubara for solid physics theory. The dispersion relation for the laser photon obtained is limited to the case of low intensity of the laser due to the decoupling the correlation function in low order. For the analysis of the self-amplified emission (SASE), the high intensity laser radiation which strongly affect the trajectory of the free electron is involved, the use of the classical approximation for laser can formulate the laser radiation with multiple frequency. To get the quantum effects in the high intensity laser, use of the perturbation theory, and the expansion methods of state function using the coherent, squeeze and super-radiant states have discussed.
A Safari Through Density Functional Theory
NASA Astrophysics Data System (ADS)
Dreizler, Reiner M.; Lüdde, Cora S.
Density functional theory is widely used to treat quantum many body problems in many areas of physics and related fields. A brief survey of this method covering foundations, functionals and applications is presented here.
Magnetic fields and density functional theory
Salsbury Jr., Freddie
1999-02-01
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
Density functional theory for carbon dioxide crystal
Chang, Yiwen; Mi, Jianguo Zhong, Chongli
2014-05-28
We present a density functional approach to describe the solid−liquid phase transition, interfacial and crystal structure, and properties of polyatomic CO{sub 2}. Unlike previous phase field crystal model or density functional theory, which are derived from the second order direct correlation function, the present density functional approach is based on the fundamental measure theory for hard-sphere repulsion in solid. More importantly, the contributions of enthalpic interactions due to the dispersive attractions and of entropic interactions arising from the molecular architecture are integrated in the density functional model. Using the theoretical model, the predicted liquid and solid densities of CO{sub 2} at equilibrium triple point are in good agreement with the experimental values. Based on the structure of crystal-liquid interfaces in different planes, the corresponding interfacial tensions are predicted. Their respective accuracies need to be tested.
NASA Astrophysics Data System (ADS)
Ritboon, Atirach; Daengngam, Chalongrat; Pengpan, Teparksorn
2016-08-01
Biakynicki-Birula introduced a photon wave function similar to the matter wave function that satisfies the Schrödinger equation. Its second quantization form can be applied to investigate nonlinear optics at nearly full quantum level. In this paper, we applied the photon wave function formalism to analyze both linear optical processes in the well-known Mach-Zehnder interferometer and nonlinear optical processes for sum-frequency generation in dispersive and lossless medium. Results by photon wave function formalism agree with the well-established Maxwell treatments and existing experimental verifications.
Accurate density functional thermochemistry for larger molecules.
Raghavachari, K.; Stefanov, B. B.; Curtiss, L. A.; Lucent Tech.
1997-06-20
Density functional methods are combined with isodesmic bond separation reaction energies to yield accurate thermochemistry for larger molecules. Seven different density functionals are assessed for the evaluation of heats of formation, Delta H 0 (298 K), for a test set of 40 molecules composed of H, C, O and N. The use of bond separation energies results in a dramatic improvement in the accuracy of all the density functionals. The B3-LYP functional has the smallest mean absolute deviation from experiment (1.5 kcal mol/f).
Locality of correlation in density functional theory
NASA Astrophysics Data System (ADS)
Burke, Kieron; Cancio, Antonio; Gould, Tim; Pittalis, Stefano
2016-08-01
The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that EC → -AC ZlnZ + BCZ as Z → ∞, where Z is the atomic number, AC is known, and we estimate BC to be about 37 mhartree. The local density approximation yields AC exactly, but a very incorrect value for BC, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with BC a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.
Locality of correlation in density functional theory.
Burke, Kieron; Cancio, Antonio; Gould, Tim; Pittalis, Stefano
2016-08-01
The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that EC → -AC ZlnZ + BCZ as Z → ∞, where Z is the atomic number, AC is known, and we estimate BC to be about 37 mhartree. The local density approximation yields AC exactly, but a very incorrect value for BC, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with BC a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed. PMID:27497544
Computational complexity of time-dependent density functional theory
NASA Astrophysics Data System (ADS)
Whitfield, J. D.; Yung, M.-H.; Tempel, D. G.; Boixo, S.; Aspuru-Guzik, A.
2014-08-01
Time-dependent density functional theory (TDDFT) is rapidly emerging as a premier method for solving dynamical many-body problems in physics and chemistry. The mathematical foundations of TDDFT are established through the formal existence of a fictitious non-interacting system (known as the Kohn-Sham system), which can reproduce the one-electron reduced probability density of the actual system. We build upon these works and show that on the interior of the domain of existence, the Kohn-Sham system can be efficiently obtained given the time-dependent density. We introduce a V-representability parameter which diverges at the boundary of the existence domain and serves to quantify the numerical difficulty of constructing the Kohn-Sham potential. For bounded values of V-representability, we present a polynomial time quantum algorithm to generate the time-dependent Kohn-Sham potential with controllable error bounds.
Density functional theory: Its origins, rise to prominence, and future
NASA Astrophysics Data System (ADS)
Jones, R. O.
2015-07-01
In little more than 20 years, the number of applications of the density functional (DF) formalism in chemistry and materials science has grown in an astonishing fashion. The number of publications alone shows that DF calculations make up a huge success story, and many younger colleagues are surprised to learn that the widespread application of density functional methods, particularly in chemistry, began only after 1990. This is indeed unexpected, because the origins are usually traced to the papers of Hohenberg, Kohn, and Sham more than a quarter of a century earlier. The DF formalism, its applications, and prospects were reviewed for this journal in 1989. About the same time, the combination of DF calculations with molecular dynamics promised to provide an efficient way to study structures and reactions in molecules and extended systems. This paper reviews the development of density-related methods back to the early years of quantum mechanics and follows the breakthrough in their application after 1990. The two examples from biochemistry and materials science are among the many current applications that were simply far beyond expectations in 1990. The reasons why—50 years after its modern formulation and after two decades of rapid expansion—some of the most cited practitioners in the field are concerned about its future are discussed.
DENSITY-FUNCTIONAL STUDY OF Zr-BASED ACTINIDE ALLOYS
Landa, A; Soderlind, P; Turchi, P; Vitos, L; Ruban, A
2008-06-26
Density-functional formalism is applied to study the phase equilibria in the U-Zr system. The obtained ground-state properties of the {gamma} (bcc) and {delta} (C32) phases are in good agreement with experimental data. The decomposition curve for the {gamma}-based U-Zr solutions is calculated. We argue that stabilization of the {delta}-UZr{sub 2} phase relative to the {alpha}-Zr (hcp) structure is due to an increase of the Zr d-band occupancy that occurs when U is alloyed with Zr.
Semilocal density functional theory with correct surface asymptotics
NASA Astrophysics Data System (ADS)
Constantin, Lucian A.; Fabiano, Eduardo; Pitarke, J. M.; Della Sala, Fabio
2016-03-01
Semilocal density functional theory is the most used computational method for electronic structure calculations in theoretical solid-state physics and quantum chemistry of large systems, providing good accuracy with a very attractive computational cost. Nevertheless, because of the nonlocality of the exchange-correlation hole outside a metal surface, it was always considered inappropriate to describe the correct surface asymptotics. Here, we derive, within the semilocal density functional theory formalism, an exact condition for the imagelike surface asymptotics of both the exchange-correlation energy per particle and potential. We show that this condition can be easily incorporated into a practical computational tool, at the simple meta-generalized-gradient approximation level of theory. Using this tool, we also show that the Airy-gas model exhibits asymptotic properties that are closely related to those at metal surfaces. This result highlights the relevance of the linear effective potential model to the metal surface asymptotics.
Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism.
Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G
2015-04-01
We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation. PMID:25974436
Langevin dynamics for vector variables driven by multiplicative white noise: A functional formalism
NASA Astrophysics Data System (ADS)
Moreno, Miguel Vera; Arenas, Zochil González; Barci, Daniel G.
2015-04-01
We discuss general multidimensional stochastic processes driven by a system of Langevin equations with multiplicative white noise. In particular, we address the problem of how time reversal diffusion processes are affected by the variety of conventions available to deal with stochastic integrals. We present a functional formalism to build up the generating functional of correlation functions without any type of discretization of the Langevin equations at any intermediate step. The generating functional is characterized by a functional integration over two sets of commuting variables, as well as Grassmann variables. In this representation, time reversal transformation became a linear transformation in the extended variables, simplifying in this way the complexity introduced by the mixture of prescriptions and the associated calculus rules. The stochastic calculus is codified in our formalism in the structure of the Grassmann algebra. We study some examples such as higher order derivative Langevin equations and the functional representation of the micromagnetic stochastic Landau-Lifshitz-Gilbert equation.
NASA Astrophysics Data System (ADS)
He, Yuan-Yao; Wu, Han-Qing; Meng, Zi Yang; Lu, Zhong-Yi
2016-05-01
Topological phase transitions in free fermion systems can be characterized by the closing of single-particle gap and the change in topological invariants. However, in the presence of electronic interactions, topological phase transitions can be more complicated. In paper I of this series [Phys. Rev. B 93, 195163 (2016), 10.1103/PhysRevB.93.195163], we have proposed an efficient scheme to evaluate the topological invariants based on the single-particle Green's function formalism. Here, in paper II, we demonstrate several interaction-driven topological phase transitions (TPTs) in two-dimensional (2D) interacting topological insulators (TIs) via large-scale quantum Monte Carlo (QMC) simulations, based on the scheme of evaluating topological invariants presented in paper I. Across these transitions, the defining symmetries of the TIs have been neither explicitly nor spontaneously broken. In the first two models, the topological invariants calculated from the Green's function formalism succeed in characterizing the topologically distinct phases and identifying interaction-driven TPTs. However, in the other two models, we find that the single-particle gap does not close and the topological invariants constructed from the single-particle Green's function acquire no change across the TPTs. Unexpected breakdown of the Green's function formalism in constructing the topological invariants is thus discovered. We thence classify the topological phase transitions in interacting TIs into two categories in practical computation: Those that have noninteracting correspondence can be characterized successfully by the topological invariants constructed from the Green's functions, while for the others that do not have noninteracting correspondence, the Green's function formalism experiences a breakdown, but more interesting and exciting phenomena, such as emergent collective critical modes at the transition, arise. Discussion on the success and breakdown of topological invariants
Particle conservation in dynamical density functional theory
NASA Astrophysics Data System (ADS)
de las Heras, Daniel; Brader, Joseph M.; Fortini, Andrea; Schmidt, Matthias
2016-06-01
We present the exact adiabatic theory for the dynamics of the inhomogeneous density distribution of a classical fluid. Erroneous particle number fluctuations of dynamical density functional theory are absent, both for canonical and grand canonical initial conditions. We obtain the canonical free energy functional, which yields the adiabatic interparticle forces of overdamped Brownian motion. Using an exact and one of the most advanced approximate hard core free energy functionals, we obtain excellent agreement with simulations. The theory applies to finite systems in and out of equilibrium.
Particle conservation in dynamical density functional theory.
de Las Heras, Daniel; Brader, Joseph M; Fortini, Andrea; Schmidt, Matthias
2016-06-22
We present the exact adiabatic theory for the dynamics of the inhomogeneous density distribution of a classical fluid. Erroneous particle number fluctuations of dynamical density functional theory are absent, both for canonical and grand canonical initial conditions. We obtain the canonical free energy functional, which yields the adiabatic interparticle forces of overdamped Brownian motion. Using an exact and one of the most advanced approximate hard core free energy functionals, we obtain excellent agreement with simulations. The theory applies to finite systems in and out of equilibrium. PMID:27115673
Petrenko, Taras; Kossmann, Simone; Neese, Frank
2011-02-01
In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The
NASA Astrophysics Data System (ADS)
Petrenko, Taras; Kossmann, Simone; Neese, Frank
2011-02-01
In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ˜26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ˜27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ˜24 on 30 processors. The
Nonlocal kinetic-energy-density functionals
Garcia-Gonzalez, P.; Alvarellos, J.E.; Chacon, E. |
1996-04-01
In this paper we present nonlocal kinetic-energy functionals {ital T}[{ital n}] within the average density approximation (ADA) framework, which do not require any extra input when applied to any electron system and recover the exact kinetic energy and the linear response function of a homogeneous system. In contrast with previous ADA functionals, these present good behavior of the long-range tail of the exact weight function. The averaging procedure for the kinetic functional (averaging the Fermi momentum of the electron gas, instead of averaging the electron density) leads to a functional without numerical difficulties in the calculation of extended systems, and it gives excellent results when applied to atoms and jellium surfaces. {copyright} {ital 1996 The American Physical Society.}
Density Functional Calculations for Atoms, Molecules and Clusters
NASA Astrophysics Data System (ADS)
Gunnarsson, O.; Jones, R. O.
1980-01-01
The density functional formalism provides a framework for including exchange and correlation effects in the calculation of ground state properties of many-electron systems. The reduction of the problem to the solution of single-particle equations leads to important numerical advantages over other ab initio methods of incorporating correlation effects. The essential features of the scheme are outlined and results obtained for atomic and molecular systems are surveyed. The local spin density (LSD) approximation gives generally good results for systems where the bonding involves s and p electrons, but results are less satisfactory for d-bonded systems. Non-local modifications to the LSD approximation have been tested on atomic systems yielding much improved total energies.
Relativistic density functional theory for finite nuclei and neutron stars
NASA Astrophysics Data System (ADS)
Piekarewicz, Jorge
In 1939 Oppenheimer and Volkoff demonstrated using Einstein's theory of general relativity that a neutron star supported exclusively by neutron degeneracy pressure will collapse into a black hole if its mass exceeds seven tenths of a solar mass. Seventy five years after such a pioneering prediction the existence of neutron stars with masses as large as two solar masses has been firmly established. This fact alone highlights the critical role that nuclear interactions play in explaining the structure of neutron stars. Indeed, a neutron star is a gold mine for the study of nuclear phenomena that span an enormous range of densities and neutron-proton asymmetries. Physical phenomena over such diverse scales are best described by a formalism based on Relativistic Density Functional Theory. In this contribution I focus on the synergy between theory, experiment, and observation that is needed to elucidate the myriad of exotic states of matter that are believed to exist in a neutron star.
Nuclear chiral and magnetic rotation in covariant density functional theory
NASA Astrophysics Data System (ADS)
Meng, Jie; Zhao, Pengwei
2016-05-01
Excitations of chiral rotation observed in triaxial nuclei and magnetic and/or antimagnetic rotations (AMR) seen in near-spherical nuclei have attracted a lot of attention. Unlike conventional rotation in well-deformed or superdeformed nuclei, here the rotational axis is not necessary coinciding with any principal axis of the nuclear density distribution. Thus, tilted axis cranking (TAC) is mandatory to describe these excitations self-consistently in the framework of covariant density functional theory (CDFT). We will briefly introduce the formalism of TAC–CDFT and its application for magnetic and AMR phenomena. Configuration-fixed CDFT and its predictions for nuclear chiral configurations and for favorable triaxial deformation parameters are also presented, and the discoveries of the multiple chiral doublets in 133Ce and 103Rh are discussed.
Filter function formalism beyond pure dephasing and non-Markovian noise in singlet-triplet qubits
NASA Astrophysics Data System (ADS)
Barnes, Edwin; Rudner, Mark S.; Martins, Frederico; Malinowski, Filip K.; Marcus, Charles M.; Kuemmeth, Ferdinand
2016-03-01
The filter function formalism quantitatively describes the dephasing of a qubit by a bath that causes Gaussian fluctuations in the qubit energies with an arbitrary noise power spectrum. Here, we extend this formalism to account for more general types of noise that couple to the qubit through terms that do not commute with the qubit's bare Hamiltonian. Our approach applies to any power spectrum that generates slow noise fluctuations in the qubit's evolution. We demonstrate our formalism in the case of singlet-triplet qubits subject to both quasistatic nuclear noise and 1 /ωα charge noise and find good agreement with recent experimental findings. This comparison shows the efficacy of our approach in describing real systems and additionally highlights the challenges with distinguishing different types of noise in free induction decay experiments.
Density Functionals with Broad Applicability in Chemistry
Zhao, Yan; Truhlar, Donald G.
2008-02-01
The research described in this product was performed in part in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. Although density functional theory is widely used in the computational chemistry community, the most popular density functional, B3LYP, has some serious shortcomings: (i) it is better for main-group chemistry than for transition metals; (ii) it systematically underestimates reaction barrier heights; (iii) it is inaccurate for interactions dominated by mediumrange correlation energy, such as van der Waals attraction, aromatic-aromatic stacking, and alkane isomerization energies. We have developed a variety of databases for testing and designing new density functionals. We used these data to design new density functionals, called M06-class (and, earlier, M05-class) functionals, for which we enforced some fundamental exact constraints such as the uniform-electron-gas limit and the absence of self-correlation energy. Our M06-class functionals depend on spin-up and spin-down electron densities (i.e., spin densities), spin density gradients, spin kinetic energy densities, and, for nonlocal (also called hybrid) functionals, Hartree-Fock exchange. We have developed four new functionals that overcome the above-mentioned difficulties: (a) M06, a hybrid meta functional, is a functional with good accuracy “across-theboard” for transition metals, main group thermochemistry, medium-range correlation energy, and barrier heights; (b) M06- 2X, another hybrid meta functional, is not good for transition metals but has excellent performance for main group chemistry, predicts accurate valence and Rydberg electronic excitation energies, and is an excellent functional for aromatic-aromatic stacking interactions; (c) M06-L is not as accurate as M06 for barrier heights but is the most accurate
Periodic subsystem density-functional theory
Genova, Alessandro; Pavanello, Michele; Ceresoli, Davide
2014-11-07
By partitioning the electron density into subsystem contributions, the Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) has recently emerged as a powerful tool for reducing the computational scaling of Kohn–Sham DFT. To date, however, FDE has been employed to molecular systems only. Periodic systems, such as metals, semiconductors, and other crystalline solids have been outside the applicability of FDE, mostly because of the lack of a periodic FDE implementation. To fill this gap, in this work we aim at extending FDE to treat subsystems of molecular and periodic character. This goal is achieved by a dual approach. On one side, the development of a theoretical framework for periodic subsystem DFT. On the other, the realization of the method into a parallel computer code. We find that periodic FDE is capable of reproducing total electron densities and (to a lesser extent) also interaction energies of molecular systems weakly interacting with metallic surfaces. In the pilot calculations considered, we find that FDE fails in those cases where there is appreciable density overlap between the subsystems. Conversely, we find FDE to be in semiquantitative agreement with Kohn–Sham DFT when the inter-subsystem density overlap is low. We also conclude that to make FDE a suitable method for describing molecular adsorption at surfaces, kinetic energy density functionals that go beyond the GGA level must be employed.
Energy density matrix formalism for interacting quantum systems: a quantum Monte Carlo study
Krogel, Jaron T; Kim, Jeongnim; Reboredo, Fernando A
2014-01-01
We develop an energy density matrix that parallels the one-body reduced density matrix (1RDM) for many-body quantum systems. Just as the density matrix gives access to the number density and occupation numbers, the energy density matrix yields the energy density and orbital occupation energies. The eigenvectors of the matrix provide a natural orbital partitioning of the energy density while the eigenvalues comprise a single particle energy spectrum obeying a total energy sum rule. For mean-field systems the energy density matrix recovers the exact spectrum. When correlation becomes important, the occupation energies resemble quasiparticle energies in some respects. We explore the occupation energy spectrum for the finite 3D homogeneous electron gas in the metallic regime and an isolated oxygen atom with ground state quantum Monte Carlo techniques imple- mented in the QMCPACK simulation code. The occupation energy spectrum for the homogeneous electron gas can be described by an effective mass below the Fermi level. Above the Fermi level evanescent behavior in the occupation energies is observed in similar fashion to the occupation numbers of the 1RDM. A direct comparison with total energy differences demonstrates a quantita- tive connection between the occupation energies and electron addition and removal energies for the electron gas. For the oxygen atom, the association between the ground state occupation energies and particle addition and removal energies becomes only qualitative. The energy density matrix provides a new avenue for describing energetics with quantum Monte Carlo methods which have traditionally been limited to total energies.
Connection formulas for thermal density functional theory
NASA Astrophysics Data System (ADS)
Pribram-Jones, A.; Burke, K.
2016-05-01
The adiabatic connection formula of ground-state density functional theory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and is widely used to understand and improve approximations. The corresponding formula for thermal density functional theory is cast as an integral over temperatures instead, ranging upward from the system's physical temperature. We also show how to relate different correlation components to each other, either in terms of temperature or coupling-constant integrations. We illustrate our results on the uniform electron gas.
Koopmans' condition for density-functional theory
Dabo, Ismaila; Ferretti, Andrea; Poilvert, Nicolas; Marzari, Nicola; Li, Yanli; Cococcioni, Matteo
2010-09-15
In approximate Kohn-Sham density-functional theory, self-interaction manifests itself as the dependence of the energy of an orbital on its fractional occupation. This unphysical behavior translates into qualitative and quantitative errors that pervade many fundamental aspects of density-functional predictions. Here, we first examine self-interaction in terms of the discrepancy between total and partial electron removal energies, and then highlight the importance of imposing the generalized Koopmans' condition - that identifies orbital energies as opposite total electron removal energies - to resolve this discrepancy. In the process, we derive a correction to approximate functionals that, in the frozen-orbital approximation, eliminates the unphysical occupation dependence of orbital energies up to the third order in the single-particle densities. This non-Koopmans correction brings physical meaning to single-particle energies; when applied to common local or semilocal density functionals it provides results that are in excellent agreement with experimental data - with an accuracy comparable to that of GW many-body perturbation theory - while providing an explicit total energy functional that preserves or improves on the description of established structural properties.
NASA Astrophysics Data System (ADS)
Karimi, F.; Davoody, A. H.; Knezevic, I.
2016-05-01
We introduce a method for calculating the dielectric function of nanostructures with an arbitrary band dispersion and Bloch wave functions. The linear response of a dissipative electronic system to an external electromagnetic field is calculated by a self-consistent-field approach within a Markovian master-equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations. The SCF-MMEF accurately accounts for several concurrent scattering mechanisms. The method captures interband electron-hole-pair generation, as well as the interband and intraband electron scattering with phonons and impurities. We employ the SCF-MMEF to calculate the dielectric function, complex conductivity, and loss function for supported graphene. From the loss-function maximum, we obtain plasmon dispersion and propagation length for different substrate types [nonpolar diamondlike carbon (DLC) and polar SiO2 and hBN], impurity densities, carrier densities, and temperatures. Plasmons on the two polar substrates are suppressed below the highest surface phonon energy, while the spectrum is broad on the nonpolar DLC. Plasmon propagation lengths are comparable on polar and nonpolar substrates and are on the order of tens of nanometers, considerably shorter than previously reported. They improve with fewer impurities, at lower temperatures, and at higher carrier densities.
Putz, Mihai V.
2009-01-01
The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems. PMID:20087467
Precise effective masses from density functional perturbation theory
NASA Astrophysics Data System (ADS)
Laflamme Janssen, J.; Gillet, Y.; Poncé, S.; Martin, A.; Torrent, M.; Gonze, X.
2016-05-01
The knowledge of effective masses is a key ingredient to analyze numerous properties of semiconductors, like carrier mobilities, (magneto)transport properties, or band extrema characteristics yielding carrier densities and density of states. Currently, these masses are usually calculated using finite-difference estimation of density functional theory (DFT) electronic band curvatures. However, finite differences require an additional convergence study and are prone to numerical noise. Moreover, the concept of effective mass breaks down at degenerate band extrema. We assess the former limitation by developing a method that allows to obtain the Hessian of DFT bands directly, using density functional perturbation theory. Then, we solve the latter issue by adapting the concept of "transport equivalent effective mass" to the k .p ̂ framework. The numerical noise inherent to finite-difference methods is thus eliminated, along with the associated convergence study. The resulting method is therefore more general, more robust, and simpler to use, which makes it especially appropriate for high-throughput computing. After validating the developed techniques, we apply them to the study of silicon, graphane, and arsenic. The formalism is implemented into the abinit software and supports the norm-conserving pseudopotential approach, the projector augmented-wave method, and the inclusion of spin-orbit coupling. The derived expressions also apply to the ultrasoft pseudopotential method.
Generalized local-spin-density-functional theory
NASA Astrophysics Data System (ADS)
Guo, Yufei; Whitehead, M. A.
1991-01-01
An alternative density-functional theory, the generalized local-spin-density-functional (G-LSD) theory, is proposed based on the boundary conditions and sum rule of the Fermi-correlation factor in the Hartree-Fock (HF) limit. It avoids the physical restrictions to the boundary conditions and the sum rule used in the generalized exchange local-spin-density-functional (GX-LSD) theory completely, the homogeneous electron-density approximation in the Hartree-Fock-Slater (HFS) theory and in the Gáspár-Kohn-Sham (GKS) theory partly, and the time-consuming step to search for the optimal exchange parameter for each atom or ion in the Xα and Ξa theories. The alternative G-LSD theory generates the GX-LSD, HFS, GKS, Xα, and Ξa theories, when additional approximations or certain Fermi-hole shapes or high electron-density limit in a system are used. Theoretically, the G-LSD theory is more rigorous than the GX-LSD, HFS, GKS, and Ξa theories. Numerically, the statistical total energies for atoms in the G-LSD theory are in excellent agreement with the HF results, when the Gopinathan, Whitehead, and Bogdanovic [Phys. Rev. A 14, 1 (1976)] Fermi-hole parameters are used.
Density-functional expansion methods: Grand challenges
Giese, Timothy J.; York, Darrin M.
2016-01-01
We discuss the source of errors in semiempirical density functional expansion (VE) methods. In particular, we show that VE methods are capable of well-reproducing their standard Kohn-Sham density functional method counterparts, but suffer from large errors upon using one or more of these approximations: the limited size of the atomic orbital basis, the Slater monopole auxiliary basis description of the response density, and the one- and two-body treatment of the core-Hamiltonian matrix elements. In the process of discussing these approximations and highlighting their symptoms, we introduce a new model that supplements the second-order density-functional tight-binding model with a self-consistent charge-dependent chemical potential equalization correction; we review our recently reported method for generalizing the auxiliary basis description of the atomic orbital response density; and we decompose the first-order potential into a summation of additive atomic components and many-body corrections, and from this examination, we provide new insights and preliminary results that motivate and inspire new approximate treatments of the core-Hamiltonian. PMID:27293378
Density functional theory for protein transfer free energy.
Mills, Eric A; Plotkin, Steven S
2013-10-24
We cast the problem of protein transfer free energy within the formalism of density functional theory (DFT), treating the protein as a source of external potential that acts upon the solvent. Solvent excluded volume, solvent-accessible surface area, and temperature dependence of the transfer free energy all emerge naturally within this formalism, and may be compared with simplified "back of the envelope" models, which are also developed here. Depletion contributions to osmolyte induced stability range from 5 to 10 kBT for typical protein lengths. The general DFT transfer theory developed here may be simplified to reproduce a Langmuir isotherm condensation mechanism on the protein surface in the limits of short-ranged interactions, and dilute solute. Extending the equation of state to higher solute densities results in non-monotonic behavior of the free energy driving protein or polymer collapse. Effective interaction potentials between protein backbone or side chains and TMAO are obtained, assuming a simple backbone/side chain two-bead model for the protein with an effective 6-12 potential with the osmolyte. The transfer free energy δg shows significant entropy: d(δg)/dT ≈ 20 kB for a 100-residue protein. The application of DFT to effective solvent forces for use in implicit-solvent molecular dynamics is also developed. The simplest DFT expressions for implicit-solvent forces contain both depletion interactions and an "impeded-solvation" repulsive force at larger distances. PMID:23944753
Communication: Embedded fragment stochastic density functional theory
Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2014-07-28
We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the scaling and the simplicity of the stochastic DFT but cures the slow convergence that occurs when weakly coupled subsystems are treated. It overcomes the spurious charge fluctuations that impair the applications of the original stochastic DFT approach. We demonstrate the new approach on a fullerene dimer and on clusters of water molecules and show that the density of states and the total energy can be accurately described with a relatively small number of stochastic orbitals.
Density functional theory studies of etoricoxib
NASA Astrophysics Data System (ADS)
Sachdeva, Ritika; Kaur, Prabhjot; Singh, V. P.; Saini, G. S. S.
2016-05-01
Etoricoxib is a COX-2 selective inhibitor drug with molecular formula C18H15ClN2O2S. It is primarily used for the treatment of arthritis(rheumatoid, psoriatic, osteoarthritis), ankylosing spondylitis, gout and chronic low back pain. Theoretical studies of the molecule including geometry optimization and vibrational frequency calculations were carried out with the help of density functional theory calculations using 6-311++ g (d, p) basis set and B3LYP functional.
Nuclear moments in covariant density functional theory
NASA Astrophysics Data System (ADS)
Meng, J.; Zhao, P. W.; Zhang, S. Q.; Hu, J. N.; Li, J.
2014-05-01
Recent progresses on microscopic and self-consistent description of the nuclear moments in covariant density functional theory based on a point-coupling interaction are briefly reviewed. In particular, the electric quadrupole moments of Cd isotopes and the magnetic moments of Pb isotopes are discussed.
A Wigner Monte Carlo approach to density functional theory
NASA Astrophysics Data System (ADS)
Sellier, J. M.; Dimov, I.
2014-08-01
In order to simulate quantum N-body systems, stationary and time-dependent density functional theories rely on the capacity of calculating the single-electron wave-functions of a system from which one obtains the total electron density (Kohn-Sham systems). In this paper, we introduce the use of the Wigner Monte Carlo method in ab-initio calculations. This approach allows time-dependent simulations of chemical systems in the presence of reflective and absorbing boundary conditions. It also enables an intuitive comprehension of chemical systems in terms of the Wigner formalism based on the concept of phase-space. Finally, being based on a Monte Carlo method, it scales very well on parallel machines paving the way towards the time-dependent simulation of very complex molecules. A validation is performed by studying the electron distribution of three different systems, a Lithium atom, a Boron atom and a hydrogenic molecule. For the sake of simplicity, we start from initial conditions not too far from equilibrium and show that the systems reach a stationary regime, as expected (despite no restriction is imposed in the choice of the initial conditions). We also show a good agreement with the standard density functional theory for the hydrogenic molecule. These results demonstrate that the combination of the Wigner Monte Carlo method and Kohn-Sham systems provides a reliable computational tool which could, eventually, be applied to more sophisticated problems.
Probability density function learning by unsupervised neurons.
Fiori, S
2001-10-01
In a recent work, we introduced the concept of pseudo-polynomial adaptive activation function neuron (FAN) and presented an unsupervised information-theoretic learning theory for such structure. The learning model is based on entropy optimization and provides a way of learning probability distributions from incomplete data. The aim of the present paper is to illustrate some theoretical features of the FAN neuron, to extend its learning theory to asymmetrical density function approximation, and to provide an analytical and numerical comparison with other known density function estimation methods, with special emphasis to the universal approximation ability. The paper also provides a survey of PDF learning from incomplete data, as well as results of several experiments performed on real-world problems and signals. PMID:11709808
Differentiability of Lieb functional in electronic density functional theory
NASA Astrophysics Data System (ADS)
Lammert, Paul E.
A solid understanding of the Lieb functional FL is important because of its centrality in the foundations of electronic density functional theory. A basic question is whether directional derivatives of FL at an ensemble-V-representable density are given by (minus) the potential. A widely accepted purported proof that FL is Gâteaux differentiable at EV-representable densities would say, ?yes.? But that proof is fallacious, as shown here. FL is not Gâteaux differentiable in the normal sense, nor is it continuous. By means of a constructive approach, however, we are able to show that the derivative of FL at an EV-representable density ?0 in the direction of ?1 is given by the potential if ?0 and ?1 are everywhere strictly greater than zero, and they and the ground state wave function have square integrable derivatives through second order.
Pereira, E.; Procacci, A.
1997-03-01
Searching for a general and technically simple multiscale formalism to treat interacting fermions, we develop a (Wilson{endash}Kadanoff) block renormalization group mechanism, which, due to the property of {open_quotes}orthogonality between scales,{close_quotes} establishes a trivial link between the correlation functions and the effective potential flow, leading to simple expressions for the generating and correlation functions. Everything is based on the existence of {open_quotes}special configurations{close_quotes} (lattice wavelets) for multiscale problems: using a simple linear change of variables relating the initial fields to these configurations, we establish the formalism. The algebraic formulas show a perfect parallel with those obtained for bosonic problems, considered in previous works. {copyright} 1997 Academic Press, Inc.
Density gradient expansion of correlation functions
NASA Astrophysics Data System (ADS)
van Leeuwen, Robert
2013-04-01
We present a general scheme based on nonlinear response theory to calculate the expansion of correlation functions such as the pair-correlation function or the exchange-correlation hole of an inhomogeneous many-particle system in terms of density derivatives of arbitrary order. We further derive a consistency condition that is necessary for the existence of the gradient expansion. This condition is used to carry out an infinite summation of terms involving response functions up to infinite order from which it follows that the coefficient functions of the gradient expansion can be expressed in terms of the local density profile rather than the background density around which the expansion is carried out. We apply the method to the calculation of the gradient expansion of the one-particle density matrix to second order in the density gradients and recover in an alternative manner the result of Gross and Dreizler [Gross and Dreizler, Z. Phys. AZPAADB0340-219310.1007/BF01413038 302, 103 (1981)], which was derived using the Kirzhnits method. The nonlinear response method is more general and avoids the turning point problem of the Kirzhnits expansion. We further give a description of the exchange hole in momentum space and confirm the wave vector analysis of Langreth and Perdew [Langreth and Perdew, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.21.5469 21, 5469 (1980)] for this case. This is used to derive that the second-order gradient expansion of the system averaged exchange hole satisfies the hole sum rule and to calculate the gradient coefficient of the exchange energy without the need to regularize divergent integrals.
β-function formalism for inflationary models with a non minimal coupling with gravity
NASA Astrophysics Data System (ADS)
Pieroni, M.
2016-02-01
We discuss the introduction of a non minimal coupling between the inflaton and gravity in terms of our recently proposed β-function formalism for inflation. Via a field redefinition we reduce to the case of minimally coupled theories. The universal attractor at strong coupling has a simple explanation in terms of the new field. Generalizations are discussed and the possibility of evading the universal attractor is shown.
Density-Functional Theory of Thermal Transport
NASA Astrophysics Data System (ADS)
Eich, F. G.; Principi, A.; di Ventra, M.; Vignale, G.
2014-03-01
We have recently introduced a non-equilibrium density-functional theory of local temperature and associated energy density that is suitable for the study of thermoelectric phenomena from first principles. This theory rests on a local temperature field coupled to the energy-density operator. Here we apply the theory to a simple two-terminal setup, in which the terminals are held at different temperatures. We show that our treatment becomes equivalent to the standard Landauer-Büttiker formulation of thermal transport in the non-interacting limit. We gratefully acknowledge support from DOE under Grant No. DE-FG02-05ER46203 (FGE, AP, GV) and DE-FG02-05ER46204 (MD).
Jankowski, K; Nowakowski, K; Grabowski, I; Wasilewski, J
2009-04-28
The problem of linking the dynamic electron correlation effects defined in traditional ab initio methods [or wave function theories (WFTs)] with the structure of the individual density functional theory (DFT) exchange and correlation functionals has been analyzed for the Ne atom, for which nondynamic correlation effects play a negligible role. A density-based approach directly hinged on difference radial-density (DRD) distributions defined with respect the Hartree-Fock radial density has been employed for analyzing the impact of dynamic correlation effects on the density. Attention has been paid to the elimination of basis-set incompleteness errors. The DRD distributions calculated by several ab initio methods have been compared to their DFT counterparts generated for representatives of several generations of broadly used exchange-correlation functionals and for the recently developed orbital-dependent OEP2 exchange-correlation functional [Bartlett et al., J. Chem. Phys. 122, 034104 (2005)]. For the local, generalized-gradient, and hybrid functionals it has been found that the dynamic correlation effects are to a large extend accounted for by densities resulting from exchange-only calculations. Additional calculations with self-interaction corrected exchange potentials indicate that this finding cannot be explained as an artifact caused by the self-interaction error. It has been demonstrated that the VWN5 and LYP correlation functionals do not represent any substantial dynamical correlation effects on the electron density, whereas these effects are well represented by the orbital-dependent OEP2 correlation functional. Critical comparison of the present results with their counterparts reported in literature has been made. Some attention has been paid to demonstrating the differences between the energy- and density-based perspectives. They indicate the usefulness of density-based criteria for developing new exchange-correlation functionals. PMID:19405556
NASA Astrophysics Data System (ADS)
Jankowski, K.; Nowakowski, K.; Grabowski, I.; Wasilewski, J.
2009-04-01
The problem of linking the dynamic electron correlation effects defined in traditional ab initio methods [or wave function theories (WFTs)] with the structure of the individual density functional theory (DFT) exchange and correlation functionals has been analyzed for the Ne atom, for which nondynamic correlation effects play a negligible role. A density-based approach directly hinged on difference radial-density (DRD) distributions defined with respect the Hartree-Fock radial density has been employed for analyzing the impact of dynamic correlation effects on the density. Attention has been paid to the elimination of basis-set incompleteness errors. The DRD distributions calculated by several ab initio methods have been compared to their DFT counterparts generated for representatives of several generations of broadly used exchange-correlation functionals and for the recently developed orbital-dependent OEP2 exchange-correlation functional [Bartlett et al., J. Chem. Phys. 122, 034104 (2005)]. For the local, generalized-gradient, and hybrid functionals it has been found that the dynamic correlation effects are to a large extend accounted for by densities resulting from exchange-only calculations. Additional calculations with self-interaction corrected exchange potentials indicate that this finding cannot be explained as an artifact caused by the self-interaction error. It has been demonstrated that the VWN5 and LYP correlation functionals do not represent any substantial dynamical correlation effects on the electron density, whereas these effects are well represented by the orbital-dependent OEP2 correlation functional. Critical comparison of the present results with their counterparts reported in literature has been made. Some attention has been paid to demonstrating the differences between the energy- and density-based perspectives. They indicate the usefulness of density-based criteria for developing new exchange-correlation functionals.
LETTER TO THE EDITOR: Mean-field dynamical density functional theory
NASA Astrophysics Data System (ADS)
Dzubiella, J.; Likos, C. N.
2003-02-01
We examine the out-of-equilibrium dynamical evolution of density profiles of ultrasoft particles under time-varying external confining potentials in three spatial dimensions. The theoretical formalism employed is the dynamical density functional theory (DDFT) of Marini, Bettolo, Marconi and Tarazona (1999 J. Chem. Phys. 110 8032), supplied by an equilibrium excess free energy functional that is essentially exact. We complement our theoretical analysis by carrying out extensive Brownian dynamics simulations. We find excellent agreement between theory and simulations for the whole time evolution of density profiles, demonstrating thereby the validity of the DDFT when an accurate equilibrium free energy functional is employed.
Dane, Markus; Gonis, Antonios
2016-07-05
Based on a computational procedure for determining the functional derivative with respect to the density of any antisymmetric N-particle wave function for a non-interacting system that leads to the density, we devise a test as to whether or not a wave function known to lead to a given density corresponds to a solution of a Schrödinger equation for some potential. We examine explicitly the case of non-interacting systems described by Slater determinants. Here, numerical examples for the cases of a one-dimensional square-well potential with infinite walls and the harmonic oscillator potential illustrate the formalism.
Density functional calculations on model tyrosyl radicals.
Himo, F; Gräslund, A; Eriksson, L A
1997-01-01
A gradient-corrected density functional theory approach (PWP86) has been applied, together with large basis sets (IGLO-III), to investigate the structure and hyperfine properties of model tyrosyl free radicals. In nature, these radicals are observed in, e.g., the charge transfer pathways in photosystem II (PSII) and in ribonucleotide reductases (RNRs). By comparing spin density distributions and proton hyperfine couplings with experimental data, it is confirmed that the tyrosyl radicals present in the proteins are neutral. It is shown that hydrogen bonding to the phenoxyl oxygen atom, when present, causes a reduction in spin density on O and a corresponding increase on C4. Calculated proton hyperfine coupling constants for the beta-protons show that the alpha-carbon is rotated 75-80 degrees out of the plane of the ring in PSII and Salmonella typhimurium RNR, but only 20-30 degrees in, e.g., Escherichia coli, mouse, herpes simplex, and bacteriophage T4-induced RNRs. Furthermore, based on the present calculations, we have revised the empirical parameters used in the experimental determination of the oxygen spin density in the tyrosyl radical in E. coli RNR and of the ring carbon spin densities, from measured hyperfine coupling constants. Images FIGURE 1 FIGURE 5 PMID:9083661
Orbital-optimized density cumulant functional theory
Sokolov, Alexander Yu. Schaefer, Henry F.
2013-11-28
In density cumulant functional theory (DCFT) the electronic energy is evaluated from the one-particle density matrix and two-particle density cumulant, circumventing the computation of the wavefunction. To achieve this, the one-particle density matrix is decomposed exactly into the mean-field (idempotent) and correlation components. While the latter can be entirely derived from the density cumulant, the former must be obtained by choosing a specific set of orbitals. In the original DCFT formulation [W. Kutzelnigg, J. Chem. Phys. 125, 171101 (2006)] the orbitals were determined by diagonalizing the effective Fock operator, which introduces partial orbital relaxation. Here we present a new orbital-optimized formulation of DCFT where the energy is variationally minimized with respect to orbital rotations. This introduces important energy contributions and significantly improves the description of the dynamic correlation. In addition, it greatly simplifies the computation of analytic gradients, for which expressions are also presented. We offer a perturbative analysis of the new orbital stationarity conditions and benchmark their performance for a variety of chemical systems.
Density Functional Theory Models for Radiation Damage
NASA Astrophysics Data System (ADS)
Dudarev, S. L.
2013-07-01
Density functional theory models developed over the past decade provide unique information about the structure of nanoscale defects produced by irradiation and about the nature of short-range interaction between radiation defects, clustering of defects, and their migration pathways. These ab initio models, involving no experimental input parameters, appear to be as quantitatively accurate and informative as the most advanced experimental techniques developed for the observation of radiation damage phenomena. Density functional theory models have effectively created a new paradigm for the scientific investigation and assessment of radiation damage effects, offering new insight into the origin of temperature- and dose-dependent response of materials to irradiation, a problem of pivotal significance for applications.
The problem of the universal density functional and the density matrix functional theory
Bobrov, V. B. Trigger, S. A.
2013-04-15
The analysis in this paper shows that the Hohenberg-Kohn theorem is the constellation of two statements: (i) the mathematically rigorous Hohenberg-Kohn lemma, which demonstrates that the same ground-state density cannot correspond to two different potentials of an external field, and (ii) the hypothesis of the existence of the universal density functional. Based on the obtained explicit expression for the nonrel-ativistic particle energy in a local external field, we prove that the energy of the system of more than two non-interacting electrons cannot be a functional of the inhomogeneous density. This result is generalized to the system of interacting electrons. It means that the Hohenberg-Kohn lemma cannot provide justification of the universal density functional for fermions. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect. In the framework of the density matrix functional theory, the hypothesis of the existence of the universal density matrix functional corresponds to the cases of noninteracting particles and to interaction in the Hartree-Fock approximation.
Pairing Nambu-Goldstone Modes within Nuclear Density Functional Theory.
Hinohara, Nobuo; Nazarewicz, Witold
2016-04-15
We show that the Nambu-Goldstone formalism of the broken gauge symmetry in the presence of the T=1 pairing condensate offers a quantitative description of the binding-energy differences of open-shell superfluid nuclei. We conclude that the pairing-rotational moments of inertia are excellent pairing indicators, which are free from ambiguities attributed to odd-mass systems. We offer a new, unified interpretation of the binding-energy differences traditionally viewed in the shell model picture as signatures of the valence nucleon properties. We present the first systematic analysis of the off-diagonal pairing-rotational moments of inertia and demonstrate the mixing of the neutron and proton pairing-rotational modes in the ground states of even-even nuclei. Finally, we discuss the importance of mass measurements of neutron-rich nuclei for constraining the pairing energy density functional. PMID:27127964
β -decay study within multireference density functional theory and beyond
NASA Astrophysics Data System (ADS)
Konieczka, M.; Bączyk, P.; Satuła, W.
2016-04-01
A pioneering study of Gamow-Teller (GT) and Fermi matrix elements (MEs) using no-core-configuration-interaction formalism rooted in multireference density functional theory is presented. After a successful test performed for 6He→6Liβ decay, the model is applied to compute MEs in the s d - and p f -shell T =1 /2 mirror nuclei. The calculated GT MEs and the isospin-symmetry-breaking corrections to the Fermi branch are found to be in very good agreement with shell-model predictions in spite of fundamental differences between these models concerning model space, treatment of correlations, or inclusion of a core. This result indirectly supports the two-body-current-based scenarios behind the quenching of the axial-vector coupling constant.
Reproducibility in density functional theory calculations of solids.
Lejaeghere, Kurt; Bihlmayer, Gustav; Björkman, Torbjörn; Blaha, Peter; Blügel, Stefan; Blum, Volker; Caliste, Damien; Castelli, Ivano E; Clark, Stewart J; Dal Corso, Andrea; de Gironcoli, Stefano; Deutsch, Thierry; Dewhurst, John Kay; Di Marco, Igor; Draxl, Claudia; Dułak, Marcin; Eriksson, Olle; Flores-Livas, José A; Garrity, Kevin F; Genovese, Luigi; Giannozzi, Paolo; Giantomassi, Matteo; Goedecker, Stefan; Gonze, Xavier; Grånäs, Oscar; Gross, E K U; Gulans, Andris; Gygi, François; Hamann, D R; Hasnip, Phil J; Holzwarth, N A W; Iuşan, Diana; Jochym, Dominik B; Jollet, François; Jones, Daniel; Kresse, Georg; Koepernik, Klaus; Küçükbenli, Emine; Kvashnin, Yaroslav O; Locht, Inka L M; Lubeck, Sven; Marsman, Martijn; Marzari, Nicola; Nitzsche, Ulrike; Nordström, Lars; Ozaki, Taisuke; Paulatto, Lorenzo; Pickard, Chris J; Poelmans, Ward; Probert, Matt I J; Refson, Keith; Richter, Manuel; Rignanese, Gian-Marco; Saha, Santanu; Scheffler, Matthias; Schlipf, Martin; Schwarz, Karlheinz; Sharma, Sangeeta; Tavazza, Francesca; Thunström, Patrik; Tkatchenko, Alexandre; Torrent, Marc; Vanderbilt, David; van Setten, Michiel J; Van Speybroeck, Veronique; Wills, John M; Yates, Jonathan R; Zhang, Guo-Xu; Cottenier, Stefaan
2016-03-25
The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements. PMID:27013736
Pairing Nambu-Goldstone Modes within Nuclear Density Functional Theory
NASA Astrophysics Data System (ADS)
Hinohara, Nobuo; Nazarewicz, Witold
2016-04-01
We show that the Nambu-Goldstone formalism of the broken gauge symmetry in the presence of the T =1 pairing condensate offers a quantitative description of the binding-energy differences of open-shell superfluid nuclei. We conclude that the pairing-rotational moments of inertia are excellent pairing indicators, which are free from ambiguities attributed to odd-mass systems. We offer a new, unified interpretation of the binding-energy differences traditionally viewed in the shell model picture as signatures of the valence nucleon properties. We present the first systematic analysis of the off-diagonal pairing-rotational moments of inertia and demonstrate the mixing of the neutron and proton pairing-rotational modes in the ground states of even-even nuclei. Finally, we discuss the importance of mass measurements of neutron-rich nuclei for constraining the pairing energy density functional.
NASA Astrophysics Data System (ADS)
Gelis, François; Tanji, Naoto
2016-02-01
We revisit the problem of quark production in high energy heavy ion collisions, at leading order in α s in the color glass condensate framework. In this first paper, we setup the formalism and express the quark spectrum in terms of a basis of solutions of the Dirac equation (the mode functions). We determine analytically their initial value in the Fock-Schwinger gauge on a proper time surface Q s τ 0 ≪ 1, in a basis that makes manifest the boost invariance properties of this problem. We also describe a statistical algorithm to perform the sampling of the mode functions.
The correlation function for density perturbations in an expanding universe. II - Nonlinear theory
NASA Technical Reports Server (NTRS)
Mcclelland, J.; Silk, J.
1977-01-01
A formalism is developed to find the two-point and higher-order correlation functions for a given distribution of sizes and shapes of perturbations which are randomly placed in three-dimensional space. The perturbations are described by two parameters such as central density and size, and the two-point correlation function is explicitly related to the luminosity function of groups and clusters of galaxies
Properties of the cosmological density distribution function
NASA Astrophysics Data System (ADS)
Bernardeau, Francis; Kofman, Lev
1995-04-01
The properties of the probability distribution function (PDF) of the cosmological continuous density field are studied. We focus our analysis on the quasi-linear regime where various calculations, based on dynamically motivated methods, have been presented: either by using the Zel'dovich approximation (ZA) or by using the perturbation theory to evaluate the behavior of the moments of the distribution function. We show how these two approaches are related to each other and that they can be used in a complementary way. For that respect, the one-dimensional dynamics, where the ZA is exact solution, has first been used as a testing ground. In particular, we show that, when the density PDF obtained with the ZA is regularized, its various moments exhibit the behavior expected by the perturbation theory applied to the ZA. We show that ZA approach can be used for arbitrary initial conditions (not only Gaussian) and that the nonlinear evolution of the moments can be obtained. The perturbation theory can be used for the exact dynamics. We take into account the final filtering of the density field both for ZA and perturbation theory. Applying these techniques, we got the generating function of the moments for the one-dimensional dynamics, the three-dimensional ZA, with and without smoothing effects. We also suggest methods to build PDFs. One is based on the Laplace inverse transform of the moment generating function. The other, the Edgeworth expansion, is obtained when the previous generating function is truncated at a given order and allows evaluation of the PDF out of limited number of moments. It provides insight on the relationship between the moments and the shape of the density PDF. In particular, it provides an alternative method to evaluate the skewness and kurtosis by measuring the PDF around its maximum. Eventually, results obtained from a numerical simulation with cold dark matter initial conditions have been used to validate the accuracy of the considered
Tabacchi, G; Hutter, J; Mundy, C
2005-04-07
A combined linear response--frozen electron density model has been implemented in a molecular dynamics scheme derived from an extended Lagrangian formalism. This approach is based on a partition of the electronic charge distribution into a frozen region described by Kim-Gordon theory, and a response contribution determined by the instaneous ionic configuration of the system. The method is free from empirical pair-potentials and the parameterization protocol involves only calculations on properly chosen subsystems. They apply this method to a series of alkali halides in different physical phases and are able to reproduce experimental structural and thermodynamic properties with an accuracy comparable to Kohn-Sham density functional calculations.
Density-functional calculations of the surface tension of liquid Al and Na
NASA Technical Reports Server (NTRS)
Stroud, D.; Grimson, M. J.
1984-01-01
Calculations of the surface tensions of liquid Al and Na are described using the full ionic density functional formalism of Wood and Stroud (1983). Surface tensions are in good agreement with experiment in both cases, with results substantially better for Al than those found previously in the gradient approximation. Preliminary minimization with respect to surface profile leads to an oscillatory profile superimposed on a nearly steplike ionic density disribution; the oscillations have a wavellength of about a hardsphere diameter.
Pseudospectral time-dependent density functional theory
NASA Astrophysics Data System (ADS)
Ko, Chaehyuk; Malick, David K.; Braden, Dale A.; Friesner, Richard A.; Martínez, Todd J.
2008-03-01
Time-dependent density functional theory (TDDFT) is implemented within the Tamm-Dancoff approximation (TDA) using a pseudospectral approach to evaluate two-electron repulsion integrals. The pseudospectral approximation uses a split representation with both spectral basis functions and a physical space grid to achieve a reduction in the scaling behavior of electronic structure methods. We demonstrate here that exceptionally sparse grids may be used in the excitation energy calculation, following earlier work employing the pseudospectral approximation for determining correlation energies in wavefunction-based methods with similar conclusions. The pseudospectral TDA-TDDFT method is shown to be up to ten times faster than a conventional algorithm for hybrid functionals without sacrificing chemical accuracy.
Optimization of constrained density functional theory
NASA Astrophysics Data System (ADS)
O'Regan, David D.; Teobaldi, Gilberto
2016-07-01
Constrained density functional theory (cDFT) is a versatile electronic structure method that enables ground-state calculations to be performed subject to physical constraints. It thereby broadens their applicability and utility. Automated Lagrange multiplier optimization is necessary for multiple constraints to be applied efficiently in cDFT, for it to be used in tandem with geometry optimization, or with molecular dynamics. In order to facilitate this, we comprehensively develop the connection between cDFT energy derivatives and response functions, providing a rigorous assessment of the uniqueness and character of cDFT stationary points while accounting for electronic interactions and screening. In particular, we provide a nonperturbative proof that stable stationary points of linear density constraints occur only at energy maxima with respect to their Lagrange multipliers. We show that multiple solutions, hysteresis, and energy discontinuities may occur in cDFT. Expressions are derived, in terms of convenient by-products of cDFT optimization, for quantities such as the dielectric function and a condition number quantifying ill definition in multiple constraint cDFT.
Recent progress in density functional theory
NASA Astrophysics Data System (ADS)
Truhlar, Donald
2014-03-01
Ongoing work involves several areas of density functional theory: new methods for computing electronic excitation energies, including a new way to remove spin contamination in the spin-flip Tamm-Dancoff approximation and a configuration-interaction-corrected Tamm-Dancoff Approximation for treating conical intersections; new ways to treat open-shell states, including a reinterpreted broken-symmetry method and multi-configuration Kohn-Sham theory; a new exchange-correlation functional; new tests of density functional theory against databases for electronic transition energies and molecules and solids containing metal atoms; and applications. A selection of results will be presented. I am grateful to the following collaborators for contributions to the ongoing work: Boris Averkiev, Rebecca Carlson, Laura Fernandez, Laura Gagliardi, Chad Hoyer, Francesc Illas, Miho Isegawa, Shaohong Li, Giovanni Li Manni, Sijie Luo, Dongxia Ma, Remi Maurice, Rubén Means-Pañeda, Roberto Peverati, Nora Planas, Prasenjit Seal, Pragya Verma, Bo Wang, Xuefei Xu, Ke R. Yang, Haoyu Yu, Wenjing Zhang, and Jingjing Zheng. Supported in part by the AFOSR and U.S. DOE.
Modulation Based on Probability Density Functions
NASA Technical Reports Server (NTRS)
Williams, Glenn L.
2009-01-01
A proposed method of modulating a sinusoidal carrier signal to convey digital information involves the use of histograms representing probability density functions (PDFs) that characterize samples of the signal waveform. The method is based partly on the observation that when a waveform is sampled (whether by analog or digital means) over a time interval at least as long as one half cycle of the waveform, the samples can be sorted by frequency of occurrence, thereby constructing a histogram representing a PDF of the waveform during that time interval.
Assessment of the ΔSCF density functional theory approach for electronic excitations in organic dyes
Kowalczyk, T.; Yost, S. R.; Van Voorhis, T.
2010-01-01
This paper assesses the accuracy of the ΔSCF method for computing low-lying HOMO→LUMO transitions in organic dye molecules. For a test set of vertical excitation energies of 16 chromophores, surprisingly similar accuracy is observed for time-dependent density functional theory and for ΔSCF density functional theory. In light of this performance, we reconsider the ad hoc ΔSCF prescription and demonstrate that it formally obtains the exact stationary density within the adiabatic approximation, partially justifying its use. The relative merits and future prospects of ΔSCF for simulating individual excited states are discussed.
Adiabatic corrections to density functional theory energies and wave functions.
Mohallem, José R; Coura, Thiago de O; Diniz, Leonardo G; de Castro, Gustavo; Assafrão, Denise; Heine, Thomas
2008-09-25
The adiabatic finite-nuclear-mass-correction (FNMC) to the electronic energies and wave functions of atoms and molecules is formulated for density-functional theory and implemented in the deMon code. The approach is tested for a series of local and gradient corrected density functionals, using MP2 results and diagonal-Born-Oppenheimer corrections from the literature for comparison. In the evaluation of absolute energy corrections of nonorganic molecules the LDA PZ81 functional works surprisingly better than the others. For organic molecules the GGA BLYP functional has the best performance. FNMC with GGA functionals, mainly BLYP, show a good performance in the evaluation of relative corrections, except for nonorganic molecules containing H atoms. The PW86 functional stands out with the best evaluation of the barrier of linearity of H2O and the isotopic dipole moment of HDO. In general, DFT functionals display an accuracy superior than the common belief and because the corrections are based on a change of the electronic kinetic energy they are here ranked in a new appropriate way. The approach is applied to obtain the adiabatic correction for full atomization of alcanes C(n)H(2n+2), n = 4-10. The barrier of 1 mHartree is approached for adiabatic corrections, justifying its insertion into DFT. PMID:18537228
Unified Description of Electron-Nucleus Scattering within the Spectral Function Formalism
NASA Astrophysics Data System (ADS)
Rocco, Noemi; Lovato, Alessandro; Benhar, Omar
2016-05-01
The formalism based on factorization and nuclear spectral functions has been generalized to treat transition matrix elements involving two-nucleon currents, whose contribution to the nuclear electromagnetic response in the transverse channel is known to be significant. We report the results of calculations of the inclusive electron-carbon cross section, showing that the inclusion of processes involving two-nucleon currents appreciably improves the agreement between theory and data in the dip region, between the quasielastic and Δ -production peaks. The relation to approaches based on the independent particle of the nucleus and the implications for the analysis of flux-integrated neutrino-nucleus cross sections are discussed.
Time-Dependent Electronic Populations in Fragment-Based Time-Dependent Density Functional Theory.
Mosquera, Martín A; Wasserman, Adam
2015-08-11
Conceiving a molecule as being composed of smaller molecular fragments, or subunits, is one of the pillars of the chemical and physical sciences and leads to productive methods in quantum chemistry. Using a fragmentation scheme, efficient algorithms can be proposed to address problems in the description of chemical bond formation and breaking. We present a formally exact time-dependent density functional theory for the electronic dynamics of molecular fragments with a variable number of electrons. This new formalism is an extension of previous work [Phys. Rev. Lett. 111, 023001 (2013)]. We also introduce a stable density-inversion method that is applicable to time-dependent and ground-state density functional theories and their extensions, including those discussed in this work. PMID:26574438
Nishimoto, Yoshio
2015-09-07
We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of the third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well.
Nishimoto, Yoshio
2015-09-01
We develop a formalism for the calculation of excitation energies and excited state gradients for the self-consistent-charge density-functional tight-binding method with the third-order contributions of a Taylor series of the density functional theory energy with respect to the fluctuation of electron density (time-dependent density-functional tight-binding (TD-DFTB3)). The formulation of the excitation energy is based on the existing time-dependent density functional theory and the older TD-DFTB2 formulae. The analytical gradient is computed by solving Z-vector equations, and it requires one to calculate the third-order derivative of the total energy with respect to density matrix elements due to the inclusion of the third-order contributions. The comparison of adiabatic excitation energies for selected small and medium-size molecules using the TD-DFTB2 and TD-DFTB3 methods shows that the inclusion of the third-order contributions does not affect excitation energies significantly. A different set of parameters, which are optimized for DFTB3, slightly improves the prediction of adiabatic excitation energies statistically. The application of TD-DFTB for the prediction of absorption and fluorescence energies of cresyl violet demonstrates that TD-DFTB3 reproduced the experimental fluorescence energy quite well. PMID:26342360
Chemistry by Way of Density Functional Theory
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Ricca, Alessandra; Partridge, Harry; Langohff, Stephen R.; Arnold, James O. (Technical Monitor)
1996-01-01
In this work we demonstrate that density functional theory (DFT) methods make an important contribution to understanding chemical systems and are an important additional method for the computational chemist. We report calibration calculations obtained with different functionals for the 55 G2 molecules to justify our selection of the B3LYP functional. We show that accurate geometries and vibrational frequencies obtained at the B3LYP level can be combined with traditional methods to simplify the calculation of accurate heats of formation. We illustrate the application of the B3LYP approach to a variety of chemical problems from the vibrational frequencies of polycyclic aromatic hydrocarbons to transition metal systems. We show that the B3LYP method typically performs better than the MP2 method at a significantly lower computational cost. Thus the B3LYP method allows us to extend our studies to much larger systems while maintaining a high degree of accuracy. We show that for transition metal systems, the B3LYP bond energies are typically of sufficient accuracy that they can be used to explain experimental trends and even differentiate between different experimental values. We show that for boron clusters the B3LYP energetics are not as good as for many of the other systems presented, but even in this case the B3LYP approach is able to help understand the experimental trends.
Density functional studies of representative pericyclic reactions
NASA Astrophysics Data System (ADS)
Carpenter, John E.; Sosa, Carlos P.
1994-07-01
Density functional theory (DFT) has traditionally been shunned by computational chemists, but has long seen widespread use in the physics community. Recently, however, DFT has been adopted by the ab initio quantum chemistry community and much activity has been devoted to refining the methodology and exploring the range of its applicability. We investigate the use of DFT (both local (LDF) and non-local (NLDF) spin density approximations) to calculate transition and equilibrium structures for three representative pericyclic reactions: the electrocyclic ring opening reaction of cyclobutene, the [1,5] sigmatropic hydrogen shift reaction in (Z)-1,3-pentadiene, and the Diels-Alder cycloaddition reaction between ethylene and butadiene. LDF theory tends to overemphasize the stability of the ringed structures in each of these reactions. For example, LDF predicts a very low (6 kcal mol -1) barrier to reaction for the Deils-Alder reaction. NLDF theory substantially improves the calculated reaction barrier (20 kcal mol -1), but it is still low with respect to experiment.
Semiconductor Thermochemistry in Density Functional Calculations
Lany, S.
2008-01-01
The local-density and generalized gradient approximations (LDA and GGA) to density functional theory (DFT) exhibit incomplete error cancellation when energy differences are taken between chemically dissimilar systems. This energy inconsistency is manifested, e.g., in the tendency to underestimate the heat (enthalpy) of formation of semiconducting and insulating compounds in LDA and, even more so, in GGA. Considering a set of 61 compounds that can be formed from 14 elements (cations: Cu, Mg, Ca, Zn, Cd, Al, Ga, and In; anions: N, P, As, O, S, and Se), optimized elemental reference energies are determined by least-squares error minimization of an overdetermined set of linear equations. These elemental energies are 'optimally consistent' with the DFT energies of the semiconductor compounds and imply corrections of up to 1 eV compared to the respective LDA or GGA energies. While these 'corrections' are not to be understood to yield the correct absolute total energies of the elements, they are proposed to give appropriate bounds for the chemical potentials for thermodynamic processes in semiconductors and insulators, such as, e.g., defect formation, surface reconstruction, or catalytic processes. The present model allows to evaluate thermodynamic processes using DFT energy differences taken only between systems that are expected to show good error cancellation.
Carrier Modulation Via Waveform Probability Density Function
NASA Technical Reports Server (NTRS)
Williams, Glenn L.
2004-01-01
Beyond the classic modes of carrier modulation by varying amplitude (AM), phase (PM), or frequency (FM), we extend the modulation domain of an analog carrier signal to include a class of general modulations which are distinguished by their probability density function histogram. Separate waveform states are easily created by varying the pdf of the transmitted waveform. Individual waveform states are assignable as proxies for digital ONEs or ZEROs. At the receiver, these states are easily detected by accumulating sampled waveform statistics and performing periodic pattern matching, correlation, or statistical filtering. No fundamental natural laws are broken in the detection process. We show how a typical modulation scheme would work in the digital domain and suggest how to build an analog version. We propose that clever variations of the modulating waveform (and thus the histogram) can provide simple steganographic encoding.
Carrier Modulation Via Waveform Probability Density Function
NASA Technical Reports Server (NTRS)
Williams, Glenn L.
2006-01-01
Beyond the classic modes of carrier modulation by varying amplitude (AM), phase (PM), or frequency (FM), we extend the modulation domain of an analog carrier signal to include a class of general modulations which are distinguished by their probability density function histogram. Separate waveform states are easily created by varying the pdf of the transmitted waveform. Individual waveform states are assignable as proxies for digital one's or zero's. At the receiver, these states are easily detected by accumulating sampled waveform statistics and performing periodic pattern matching, correlation, or statistical filtering. No fundamental physical laws are broken in the detection process. We show how a typical modulation scheme would work in the digital domain and suggest how to build an analog version. We propose that clever variations of the modulating waveform (and thus the histogram) can provide simple steganographic encoding.
Phases of Polonium via Density Functional Theory
NASA Astrophysics Data System (ADS)
Verstraete, Matthieu J.
2010-01-01
The thermodynamical properties of the main phases of metallic polonium are examined using density functional theory. The exceptional nature of the solid-solid phase transition of α to β Po is underlined: it induces a lowering in symmetry, from cubic to rhombohedral, with increasing temperature. This is explained as the result of a delicate balance between bonding and entropic effects. Overall agreement with existing experimental data is good by state-of-the-art standards. The phonons of Po present Kohn anomalies, and it is shown that the effect of spin-orbit interactions is the inverse of that in normal metals: due to the nonspherical nature of the Fermi Surface, spin-orbit effects reduce nesting and harden most phonon frequencies.
Effective potential in density matrix functional theory.
Nagy, A; Amovilli, C
2004-10-01
In the previous paper it was shown that in the ground state the diagonal of the spin independent second-order density matrix n can be determined by solving a single auxiliary equation of a two-particle problem. Thus the problem of an arbitrary system with even electrons can be reduced to a two-particle problem. The effective potential of the two-particle equation contains a term v(p) of completely kinetic origin. Virial theorem and hierarchy of equations are derived for v(p) and simple approximations are proposed. A relationship between the effective potential u(p) of the shape function equation and the potential v(p) is established. PMID:15473719
Nonlocal density-functional description constructed from a correlated many-body wave function
NASA Astrophysics Data System (ADS)
Umezawa, Naoto; Tsuneyuki, Shinji
2004-03-01
We suggest a new approach to the nonlocal density-functional theory. In our method, the nonlocal correlation functional is derived from a correlated many-body wave function using the transcorrelated similarity transformation [1,2]. Our formalism is rigorous in principle if the v-representable density is assumed. In practice, Jastrow-Slater-type wave function is adopted and the correlation functional consists of many-body interactions originated from the Jastrow factor. Instead of struggling with these higher order interactions, we retain only 2-body interactions multiplying an adjusting parameter so that it can reproduce the exact correlation energy for the homogeneous electron gas. Therefore, the computational cost is comparable to the exact exchange method. Moreover, parameters in the Jastrow factor are determined by the two conditions: the cusp conditions and the random-phase approximation without empirical fitting. We found that our correlation functional gives fairly good results for small atoms and ions (He, Li^+, Be^2+, Li, and Be). [1]S. F. Boys and N. C. Handy, Proc. Roy. Soc. A, 309, 209; 310, 43; 310, 63; 311, 309. [2] N. Umezawa and S. Tsuneyuki, J. Chem. Phys. 119, 10015 (2003).
NASA Astrophysics Data System (ADS)
Rajagopal, A. K.; Mochena, Mogus
2000-12-01
The group-theory framework developed by Fukutome for a systematic analysis of the various broken-symmetry types of Hartree-Fock solution exhibiting spin structures is here extended to the general many-body context using spinor Green function formalism for describing magnetic systems. Consequences of this theory are discussed for examining the magnetism of itinerant electrons in nanometric systems of current interest as well as bulk systems where a vector spin-density form is required, by specializing our work to spin-density-functional formalism. We also formulate the linear-response theory for such a system and compare and contrast our results with the recent results obtained for localized electron systems. The various phenomenological treatments of itinerant magnetic systems are here unified in this group-theoretical description. We apply this theory to the one-band Hubbard model to illustrate the usefulness of this approach.
Hot-electron relaxation in metals within the Götze-Wölfle memory function formalism
NASA Astrophysics Data System (ADS)
Das, Nabyendu; Singh, Navinder
2016-04-01
We consider nonequilibrium relaxation of electrons due to their coupling with phonons in a simple metal. In our model, electrons are living at a higher temperature than that of the phonon bath, mimicking a nonequilibrium steady-state situation. We study the relaxation of such hot electrons proposing a suitable generalization of the memory function formalism formulated by Götze and Wölfle (GW) [W. Götze and P. Wölfle, Phys. Rev. B 6, 1226 (1972)]. We derive analytical expressions for both the DC or zero frequency scattering rates and the optical scattering rates in various temperature and frequency regimes. Limiting cases are in accord with the previous studies. An interesting feature that the DC scattering rate at high temperatures and optical scattering rate at high frequencies are independent of the temperature difference between the electrons and the phonons is found in this study. The present formalism forms a basis which can also be extended to study hot-electron relaxation in variety of complex materials.
Improving Density Functionals with Quantum Harmonic Oscillators
NASA Astrophysics Data System (ADS)
Tkatchenko, Alexandre
2013-03-01
Density functional theory (DFT) is the most widely used and successful approach for electronic structure calculations. However, one of the pressing challenges for DFT is developing efficient functionals that can accurately capture the omnipresent long-range electron correlations, which determine the structure and stability of many molecules and materials. Here we show that, under certain conditions, the problem of computing the long-range correlation energy of interacting electrons can be mapped to a system of coupled quantum harmonic oscillators (QHOs). The proposed model allows us to synergistically combine concepts from DFT, quantum chemistry, and the widely discussed random-phase approximation for the correlation energy. In the dipole limit, the interaction energy for a system of coupled QHOs can be calculated exactly, thereby leading to an efficient and accurate model for the many-body dispersion energy of complex molecules and materials. The studied examples include intermolecular binding energies, the conformational hierarchy of DNA structures, the geometry and stability of molecular crystals, and supramolecular host-guest complexes (A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012); R. A. DiStasio Jr., A. von Lilienfeld, A. Tkatchenko, PNAS 109, 14791 (2012); A. Tkatchenko, D. Alfe, K. S. Kim, J. Chem. Theory and Comp. (2012), doi: 10.1021/ct300711r; A. Tkatchenko, A. Ambrosetti, R. A. DiStasio Jr., arXiv:1210.8343v1).
Building a Universal Nuclear Energy Density Functional
Carlson, Joe A.; Furnstahl, Dick; Horoi, Mihai; Lust, Rusty; Nazaewicc, Witek; Ng, Esmond; Thompson, Ian; Vary, James
2012-12-30
During the period of Dec. 1 2006 – Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: First, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; Second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; Third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory.
A density functional for sparse matter
NASA Astrophysics Data System (ADS)
Langreth, D. C.; Lundqvist, B. I.; Chakarova-Käck, S. D.; Cooper, V. R.; Dion, M.; Hyldgaard, P.; Kelkkanen, A.; Kleis, J.; Kong, Lingzhu; Li, Shen; Moses, P. G.; Murray, E.; Puzder, A.; Rydberg, H.; Schröder, E.; Thonhauser, T.
2009-02-01
Sparse matter is abundant and has both strong local bonds and weak nonbonding forces, in particular nonlocal van der Waals (vdW) forces between atoms separated by empty space. It encompasses a broad spectrum of systems, like soft matter, adsorption systems and biostructures. Density-functional theory (DFT), long since proven successful for dense matter, seems now to have come to a point, where useful extensions to sparse matter are available. In particular, a functional form, vdW-DF (Dion et al 2004 Phys. Rev. Lett. 92 246401; Thonhauser et al 2007 Phys. Rev. B 76 125112), has been proposed for the nonlocal correlations between electrons and applied to various relevant molecules and materials, including to those layered systems like graphite, boron nitride and molybdenum sulfide, to dimers of benzene, polycyclic aromatic hydrocarbons (PAHs), doped benzene, cytosine and DNA base pairs, to nonbonding forces in molecules, to adsorbed molecules, like benzene, naphthalene, phenol and adenine on graphite, alumina and metals, to polymer and carbon nanotube (CNT) crystals, and hydrogen storage in graphite and metal-organic frameworks (MOFs), and to the structure of DNA and of DNA with intercalators. Comparison with results from wavefunction calculations for the smaller systems and with experimental data for the extended ones show the vdW-DF path to be promising. This could have great ramifications.
Semiclassical origins of density functional theory
NASA Astrophysics Data System (ADS)
Burke, Kieron
2009-03-01
Until the seminal work of Hohenberg, Kohn, and Sham of the mid 60's, most density functional theory (DFT) was derived from semiclassical approximations. This non-empirical approach shows an intrinsic difference between solids (for which DFT was originally developed) and molecules, and explains many of its more mysterious manifestations. For example, the success of DFT for molecules has nothing to do with the uniform gas. Results include [1] a derivation of the empirical parameter in the B88 exchange functional, [2] PBEsol, a new GGA that restores the exchange gradient expansion and improves lattice constants in solids, [3] a novel approach to ``orbital-free'' DFT that, in preliminary tests, is 40 times more accurate than its DFT counterpart. The talk is aimed at a general theoretical audience. Detailed technical knowledge of DFT is neither needed, nor desirable. [4pt] [1] J.P. Perdew, L.A. Constantin, E. Sagvolden, and KB, Phys. Rev. Lett. 97, 223002 (2006). [0pt] [2] J.P. Perdew, A. Ruzsinszky, G.I. Csonka, O.A. Vydrov, G.E. Scuseria, L.A. Constantin, X. Zhou, and KB, Phys. Rev. Lett. 100, 136406 (2008). [0pt] [3] Peter Elliott, Donghyung Lee, Attila Cangi, KB, Phys. Rev. Lett. 100, 256406 (2008).
Rationale for switching to nonlocal functionals in density functional theory
NASA Astrophysics Data System (ADS)
Lazić, P.; Atodiresei, N.; Caciuc, V.; Brako, R.; Gumhalter, B.; Blügel, S.
2012-10-01
Density functional theory (DFT) has been steadily improving over the past few decades, becoming the standard tool for electronic structure calculations. The early local functionals (LDA) were eventually replaced by more accurate semilocal functionals (GGA) which are in use today. A major persisting drawback is the lack of the nonlocal correlation which is at the core of dispersive (van der Waals) forces, so that a large and important class of systems remains outside the scope of DFT. The vdW-DF correlation functional of Langreth and Lundqvist, published in 2004, was the first nonlocal functional which could be easily implemented. Beyond expectations, the nonlocal functional has brought significant improvement to systems that were believed not to be sensitive to nonlocal correlations. In this paper, we use the example of graphene nanodomes growing on the Ir(111) surface, where with an increase of the size of the graphene islands the character of the bonding changes from strong chemisorption towards almost pure physisorption. We demonstrate how the seamless character of the vdW-DF functionals makes it possible to treat all regimes self-consistently, proving to be a systematic and consistent improvement of DFT regardless of the nature of bonding. We also discuss the typical surface science example of CO adsorption on (111) surfaces of metals, which shows that the nonlocal correlation may also be crucial for strongly chemisorbed systems. We briefly discuss open questions, in particular the choice of the most appropriate exchange part of the functional. As the vdW-DF begins to appear implemented self-consistently in a number of popular DFT codes, with numerical costs close to the GGA calculations, we draw the attention of the DFT community to the advantages and benefits of the adoption of this new class of functionals.
Density Functional Theory study of the equilibrium density of water at normal conditions
NASA Astrophysics Data System (ADS)
Wang, Jue; Roman-Perez, Guillermo; Soler, Jose M.; Artacho, Emilio; Fernandez-Serra, Marivi
2010-03-01
Ab initio molecular dynamics of liquid water with the use of density functional theory (DFT) currently underperform experimental equilibrium density 1g/cm^3 under room temperature. At constant density, not much is known about the equilibrium density of commonly used GGA functionals in liquid water simulations. We present a DFT-based AIMD study of liquid water at different densities and analyze the structure and diffusivity of water with different exchange and correlation functionals. We show that all current GGA functionals fail to reproduce experimental density, however, the explicit description of long range correlations through a Van der Walls density functional (DRSLL)footnotetextM. Dion, H. Rydberg, E. Schr"oder, D. C. Langreth, and B. I. Lundqvist, Phys. Rev. Lett. 92, 246401 (2004) can potentially transform our current understanding of the structure of liquid water. Our results shows that this new functional improves density, with only 2% error to experiment. But it underperforms GGA functionals in terms of structure.
Pederson, Mark R
2015-02-14
A recent modification of the Perdew-Zunger self-interaction-correction to the density-functional formalism has provided a framework for explicitly restoring unitary invariance to the expression for the total energy. The formalism depends upon construction of Löwdin orthonormalized Fermi-orbitals which parametrically depend on variational quasi-classical electronic positions. Derivatives of these quasi-classical electronic positions, required for efficient minimization of the self-interaction corrected energy, are derived and tested, here, on atoms. Total energies and ionization energies in closed-shell singlet atoms, where correlation is less important, using the Perdew-Wang 1992 Local Density Approximation (PW92) functional, are in good agreement with experiment and non-relativistic quantum-Monte-Carlo results albeit slightly too low. PMID:25681892
Flexoelectricity from density-functional perturbation theory
NASA Astrophysics Data System (ADS)
Stengel, Massimiliano
2013-11-01
We derive the complete flexoelectric tensor, including electronic and lattice-mediated effects, of an arbitrary insulator in terms of the microscopic linear response of the crystal to atomic displacements. The basic ingredient, which can be readily calculated from first principles in the framework of density-functional perturbation theory, is the quantum-mechanical probability current response to a long-wavelength acoustic phonon. Its second-order Taylor expansion in the wave vector q around the Γ (q=0) point in the Brillouin zone naturally yields the flexoelectric tensor. At order one in q we recover Martin's theory of piezoelectricity [Martin, Phys. Rev. B 5, 1607 (1972)], thus providing an alternative derivation thereof. To put our derivations on firm theoretical grounds, we perform a thorough analysis of the nonanalytic behavior of the dynamical matrix and other response functions in a vicinity of Γ. Based on this analysis, we find that there is an ambiguity in the specification of the “zero macroscopic field” condition in the flexoelectric case; such arbitrariness can be related to an analytic band-structure term, in close analogy to the theory of deformation potentials. As a by-product, we derive a rigorous generalization of the Cochran-Cowley formula [Cochran and Cowley, J. Phys. Chem. Solids 23, 447 (1962)] to higher orders in q. This can be of great utility in building reliable atomistic models of electromechanical phenomena, as well as for improving the accuracy of the calculation of phonon dispersion curves. Finally, we discuss the physical interpretation of the various contributions to the flexoelectric response, either in the static or dynamic regime, and we relate our findings to earlier theoretical works on the subject.
Bone mineral density, adiposity, and cognitive functions
Sohrabi, Hamid R.; Bates, Kristyn A.; Weinborn, Michael; Bucks, Romola S.; Rainey-Smith, Stephanie R.; Rodrigues, Mark A.; Bird, Sabine M.; Brown, Belinda M.; Beilby, John; Howard, Matthew; Criddle, Arthur; Wraith, Megan; Taddei, Kevin; Martins, Georgia; Paton, Athena; Shah, Tejal; Dhaliwal, Satvinder S.; Mehta, Pankaj D.; Foster, Jonathan K.; Martins, Ian J.; Lautenschlager, Nicola T.; Mastaglia, Francis; Laws, Simon M.; Martins, Ralph N.
2015-01-01
Cognitive decline and dementia due to Alzheimer's disease (AD) have been associated with genetic, lifestyle, and environmental factors. A number of potentially modifiable risk factors should be taken into account when preventive or ameliorative interventions targeting dementia and its preclinical stages are investigated. Bone mineral density (BMD) and body composition are two such potentially modifiable risk factors, and their association with cognitive decline was investigated in this study. 164 participants, aged 34–87 years old (62.78 ± 9.27), were recruited for this longitudinal study and underwent cognitive and clinical examinations at baseline and after 3 years. Blood samples were collected for apolipoprotein E (APOE) genotyping and dual energy x-ray absorptiometry (DXA) was conducted at the same day as cognitive assessment. Using hierarchical regression analysis, we found that BMD and lean body mass, as measured using DXA were significant predictors of episodic memory. Age, gender, APOE status, and premorbid IQ were controlled for. Specifically, the List A learning from California Verbal Learning Test was significantly associated with BMD and lean mass both at baseline and at follow up assessment. Our findings indicate that there is a significant association between BMD and lean body mass and episodic verbal learning. While the involvement of modifiable lifestyle factors in human cognitive function has been examined in different studies, there is a need for further research to understand the potential underlying mechanisms. PMID:25741279
Bone mineral density, adiposity, and cognitive functions.
Sohrabi, Hamid R; Bates, Kristyn A; Weinborn, Michael; Bucks, Romola S; Rainey-Smith, Stephanie R; Rodrigues, Mark A; Bird, Sabine M; Brown, Belinda M; Beilby, John; Howard, Matthew; Criddle, Arthur; Wraith, Megan; Taddei, Kevin; Martins, Georgia; Paton, Athena; Shah, Tejal; Dhaliwal, Satvinder S; Mehta, Pankaj D; Foster, Jonathan K; Martins, Ian J; Lautenschlager, Nicola T; Mastaglia, Francis; Laws, Simon M; Martins, Ralph N
2015-01-01
Cognitive decline and dementia due to Alzheimer's disease (AD) have been associated with genetic, lifestyle, and environmental factors. A number of potentially modifiable risk factors should be taken into account when preventive or ameliorative interventions targeting dementia and its preclinical stages are investigated. Bone mineral density (BMD) and body composition are two such potentially modifiable risk factors, and their association with cognitive decline was investigated in this study. 164 participants, aged 34-87 years old (62.78 ± 9.27), were recruited for this longitudinal study and underwent cognitive and clinical examinations at baseline and after 3 years. Blood samples were collected for apolipoprotein E (APOE) genotyping and dual energy x-ray absorptiometry (DXA) was conducted at the same day as cognitive assessment. Using hierarchical regression analysis, we found that BMD and lean body mass, as measured using DXA were significant predictors of episodic memory. Age, gender, APOE status, and premorbid IQ were controlled for. Specifically, the List A learning from California Verbal Learning Test was significantly associated with BMD and lean mass both at baseline and at follow up assessment. Our findings indicate that there is a significant association between BMD and lean body mass and episodic verbal learning. While the involvement of modifiable lifestyle factors in human cognitive function has been examined in different studies, there is a need for further research to understand the potential underlying mechanisms. PMID:25741279
Density functional theory in the solid state
Hasnip, Philip J.; Refson, Keith; Probert, Matt I. J.; Yates, Jonathan R.; Clark, Stewart J.; Pickard, Chris J.
2014-01-01
Density functional theory (DFT) has been used in many fields of the physical sciences, but none so successfully as in the solid state. From its origins in condensed matter physics, it has expanded into materials science, high-pressure physics and mineralogy, solid-state chemistry and more, powering entire computational subdisciplines. Modern DFT simulation codes can calculate a vast range of structural, chemical, optical, spectroscopic, elastic, vibrational and thermodynamic phenomena. The ability to predict structure–property relationships has revolutionized experimental fields, such as vibrational and solid-state NMR spectroscopy, where it is the primary method to analyse and interpret experimental spectra. In semiconductor physics, great progress has been made in the electronic structure of bulk and defect states despite the severe challenges presented by the description of excited states. Studies are no longer restricted to known crystallographic structures. DFT is increasingly used as an exploratory tool for materials discovery and computational experiments, culminating in ex nihilo crystal structure prediction, which addresses the long-standing difficult problem of how to predict crystal structure polymorphs from nothing but a specified chemical composition. We present an overview of the capabilities of solid-state DFT simulations in all of these topics, illustrated with recent examples using the CASTEP computer program. PMID:24516184
Photostriction in Ferroelectrics from Density Functional Theory
NASA Astrophysics Data System (ADS)
Paillard, Charles; Xu, Bin; Dkhil, Brahim; Geneste, Grégory; Bellaiche, L.
2016-06-01
An ab initio procedure allowing the computation of the deformation of ferroelectric-based materials under light is presented. This numerical scheme consists in structurally relaxing the system under the constraint of a fixed ne concentration of electrons photoexcited into a specific conduction band edge state from a chosen valence band state, via the use of a constrained density functional theory method. The resulting change in lattice constant along a selected crystallographic direction is then calculated for a reasonable estimate of ne. This method is applied to bulk multiferroic BiFeO3 and predicts a photostriction effect of the same order of magnitude than the ones recently observed. A strong dependence of photostrictive response on both the reached conduction state and the crystallographic direction (along which this effect is determined) is also revealed. Furthermore, analysis of the results demonstrates that the photostriction mechanism mostly originates from the screening of the spontaneous polarization by the photoexcited electrons in combination with the inverse piezoelectric effect.
Dynamical density functional theory for microswimmers
NASA Astrophysics Data System (ADS)
Menzel, Andreas M.; Saha, Arnab; Hoell, Christian; Löwen, Hartmut
2016-01-01
Dynamical density functional theory (DDFT) has been successfully derived and applied to describe on one hand passive colloidal suspensions, including hydrodynamic interactions between individual particles. On the other hand, active "dry" crowds of self-propelled particles have been characterized using DDFT. Here, we go one essential step further and combine these two approaches. We establish a DDFT for active microswimmer suspensions. For this purpose, simple minimal model microswimmers are introduced. These microswimmers self-propel by setting the surrounding fluid into motion. They hydrodynamically interact with each other through their actively self-induced fluid flows and via the common "passive" hydrodynamic interactions. An effective soft steric repulsion is also taken into account. We derive the DDFT starting from common statistical approaches. Our DDFT is then tested and applied by characterizing a suspension of microswimmers, the motion of which is restricted to a plane within a three-dimensional bulk fluid. Moreover, the swimmers are confined by a radially symmetric trapping potential. In certain parameter ranges, we find rotational symmetry breaking in combination with the formation of a "hydrodynamic pumping state," which has previously been observed in the literature as a result of particle-based simulations. An additional instability of this pumping state is revealed.
Photostriction in Ferroelectrics from Density Functional Theory.
Paillard, Charles; Xu, Bin; Dkhil, Brahim; Geneste, Grégory; Bellaiche, L
2016-06-17
An ab initio procedure allowing the computation of the deformation of ferroelectric-based materials under light is presented. This numerical scheme consists in structurally relaxing the system under the constraint of a fixed n_{e} concentration of electrons photoexcited into a specific conduction band edge state from a chosen valence band state, via the use of a constrained density functional theory method. The resulting change in lattice constant along a selected crystallographic direction is then calculated for a reasonable estimate of n_{e}. This method is applied to bulk multiferroic BiFeO_{3} and predicts a photostriction effect of the same order of magnitude than the ones recently observed. A strong dependence of photostrictive response on both the reached conduction state and the crystallographic direction (along which this effect is determined) is also revealed. Furthermore, analysis of the results demonstrates that the photostriction mechanism mostly originates from the screening of the spontaneous polarization by the photoexcited electrons in combination with the inverse piezoelectric effect. PMID:27367406
Reflection asymmetric shapes in covariant density functional theory
NASA Astrophysics Data System (ADS)
Afanasjev, A. V.; Agbemava, S.; Ring, P.
2014-03-01
Reflection asymmetric (octupole deformed) shapes play an important role in some areas of nuclear chart. For example, the outer fission barriers in actinides and superheavy nuclei are strongly affected by such shapes. The recent progress in the study of such shapes and octupole softness at ground states of lanthanides (A ~ 145) and actinides (A ~ 224) as well as at outer fission barriers of actinides and superheavy nuclei within the covariant density functional theory will be reviewed. New results obtained within the relativistic Hartree-Bogoliubov framework with separable limit of finite range Gogny D1S pairing in the pairing channel will be discussed. The experimental data will be systematically compared with model calculations. The work on the extension of the relativistic Hartree-Bogoliubov formalism to the description of odd, odd-odd and rotating nuclei with reflections asymmetric shapes is currently in progress. New results obtained with these extensions will be reported. This work has been supported by the U.S. Department of Energy under the grant DE-FG02-07ER41459 and by the DFG cluster of excellence ``Origin and Structure of the Universe '' (www.universe-cluster.de).
Predicting stability constants for uranyl complexes using density functional theory.
Vukovic, Sinisa; Hay, Benjamin P; Bryantsev, Vyacheslav S
2015-04-20
The ability to predict the equilibrium constants for the formation of 1:1 uranyl/ligand complexes (log K1 values) provides the essential foundation for the rational design of ligands with enhanced uranyl affinity and selectivity. We use density functional theory (B3LYP) and the integral equation formalism polarizable continuum model (IEF-PCM) to compute aqueous stability constants for UO2(2+) complexes with 18 donor ligands. Theoretical calculations permit reasonably good estimates of relative binding strengths, while the absolute log K1 values are significantly overestimated. Accurate predictions of the absolute log K1 values (root-mean-square deviation from experiment <1.0 for log K1 values ranging from 0 to 16.8) can be obtained by fitting the experimental data for two groups of mono- and divalent negative oxygen donor ligands. The utility of correlations is demonstrated for amidoxime and imide dioxime ligands, providing a useful means of screening for new ligands with strong chelating capability to uranyl. PMID:25835578
DENSITY-FUNCTIONAL STUDY OF THE U-ZR SYSTEM
Landa, A; Soderlind, P; Turchi, P
2008-06-25
Density-functional formalism is applied to study the phase equilibria in the U-Zr system. The obtained ground-state properties of the {gamma} (bcc) and {delta} (C32) phases are in good agreement with experimental data. The decomposition curve for the {gamma}-based U-Zr solutions is calculated. Our calculations confirm that experimentally observed 'partial' ordering of the alloy components in the {delta}-UZr{sub 2} (AlB{sub 2}) phase, in which Zr atoms occupy the 'Al' position and the two 'B' sites are randomly shared by the U and Zr atoms, is the most energetically favorable within the C32 structure. We argue that stabilization of the {delta}-UZr{sub 2} phase relative to the {alpha}-Zr (hcp) structure is due to an increase of the Zr d-band occupancy that occurs when U is alloyed with Zr. A comparison with stabilization of the {omega}-phase (also C32) in Zr under compression is made.
Two-component hybrid time-dependent density functional theory within the Tamm-Dancoff approximation.
Kühn, Michael; Weigend, Florian
2015-01-21
We report the implementation of a two-component variant of time-dependent density functional theory (TDDFT) for hybrid functionals that accounts for spin-orbit effects within the Tamm-Dancoff approximation (TDA) for closed-shell systems. The influence of the admixture of Hartree-Fock exchange on excitation energies is investigated for several atoms and diatomic molecules by comparison to numbers for pure density functionals obtained previously [M. Kühn and F. Weigend, J. Chem. Theory Comput. 9, 5341 (2013)]. It is further related to changes upon switching to the local density approximation or using the full TDDFT formalism instead of TDA. Efficiency is demonstrated for a comparably large system, Ir(ppy)3 (61 atoms, 1501 basis functions, lowest 10 excited states), which is a prototype molecule for organic light-emitting diodes, due to its "spin-forbidden" triplet-singlet transition. PMID:25612698
Two-component hybrid time-dependent density functional theory within the Tamm-Dancoff approximation
Kühn, Michael; Weigend, Florian
2015-01-21
We report the implementation of a two-component variant of time-dependent density functional theory (TDDFT) for hybrid functionals that accounts for spin-orbit effects within the Tamm-Dancoff approximation (TDA) for closed-shell systems. The influence of the admixture of Hartree-Fock exchange on excitation energies is investigated for several atoms and diatomic molecules by comparison to numbers for pure density functionals obtained previously [M. Kühn and F. Weigend, J. Chem. Theory Comput. 9, 5341 (2013)]. It is further related to changes upon switching to the local density approximation or using the full TDDFT formalism instead of TDA. Efficiency is demonstrated for a comparably large system, Ir(ppy){sub 3} (61 atoms, 1501 basis functions, lowest 10 excited states), which is a prototype molecule for organic light-emitting diodes, due to its “spin-forbidden” triplet-singlet transition.
Two-component hybrid time-dependent density functional theory within the Tamm-Dancoff approximation
NASA Astrophysics Data System (ADS)
Kühn, Michael; Weigend, Florian
2015-01-01
We report the implementation of a two-component variant of time-dependent density functional theory (TDDFT) for hybrid functionals that accounts for spin-orbit effects within the Tamm-Dancoff approximation (TDA) for closed-shell systems. The influence of the admixture of Hartree-Fock exchange on excitation energies is investigated for several atoms and diatomic molecules by comparison to numbers for pure density functionals obtained previously [M. Kühn and F. Weigend, J. Chem. Theory Comput. 9, 5341 (2013)]. It is further related to changes upon switching to the local density approximation or using the full TDDFT formalism instead of TDA. Efficiency is demonstrated for a comparably large system, Ir(ppy)3 (61 atoms, 1501 basis functions, lowest 10 excited states), which is a prototype molecule for organic light-emitting diodes, due to its "spin-forbidden" triplet-singlet transition.
FDE-vdW: A van der Waals inclusive subsystem density-functional theory
Kevorkyants, Ruslan; Pavanello, Michele; Eshuis, Henk
2014-07-28
We present a formally exact van der Waals inclusive electronic structure theory, called FDE-vdW, based on the Frozen Density Embedding formulation of subsystem Density-Functional Theory. In subsystem DFT, the energy functional is composed of subsystem additive and non-additive terms. We show that an appropriate definition of the long-range correlation energy is given by the value of the non-additive correlation functional. This functional is evaluated using the fluctuation–dissipation theorem aided by a formally exact decomposition of the response functions into subsystem contributions. FDE-vdW is derived in detail and several approximate schemes are proposed, which lead to practical implementations of the method. We show that FDE-vdW is Casimir-Polder consistent, i.e., it reduces to the generalized Casimir-Polder formula for asymptotic inter-subsystems separations. Pilot calculations of binding energies of 13 weakly bound complexes singled out from the S22 set show a dramatic improvement upon semilocal subsystem DFT, provided that an appropriate exchange functional is employed. The convergence of FDE-vdW with basis set size is discussed, as well as its dependence on the choice of associated density functional approximant.
A half century of density functional theory
Zangwill, Andrew
2015-07-15
Today’s most popular method for calculating the electronic structure of atoms, molecules, liquids, solids, and plasmas began as a bold hypothesis: The electron density distribution completely characterizes the ground state of a many-electron system.
A density functional theory for colloids with two multiple bonding associating sites.
Haghmoradi, Amin; Wang, Le; Chapman, Walter G
2016-06-22
Wertheim's multi-density formalism is extended for patchy colloidal fluids with two multiple bonding patches. The theory is developed as a density functional theory to predict the properties of an associating inhomogeneous fluid. The equation of state developed for this fluid depends on the size of the patch, and includes formation of cyclic, branched and linear clusters of associated species. The theory predicts the density profile and the fractions of colloids in different bonding states versus the distance from one wall as a function of bulk density and temperature. The predictions from our theory are compared with previous results for a confined fluid with four single bonding association sites. Also, comparison between the present theory and Monte Carlo simulation indicates a good agreement. PMID:27115237
A density functional theory for colloids with two multiple bonding associating sites
NASA Astrophysics Data System (ADS)
Haghmoradi, Amin; Wang, Le; Chapman, Walter G.
2016-06-01
Wertheim’s multi-density formalism is extended for patchy colloidal fluids with two multiple bonding patches. The theory is developed as a density functional theory to predict the properties of an associating inhomogeneous fluid. The equation of state developed for this fluid depends on the size of the patch, and includes formation of cyclic, branched and linear clusters of associated species. The theory predicts the density profile and the fractions of colloids in different bonding states versus the distance from one wall as a function of bulk density and temperature. The predictions from our theory are compared with previous results for a confined fluid with four single bonding association sites. Also, comparison between the present theory and Monte Carlo simulation indicates a good agreement.
Ions in solution: Density corrected density functional theory (DC-DFT)
Kim, Min-Cheol; Sim, Eunji; Burke, Kieron
2014-05-14
Standard density functional approximations often give questionable results for odd-electron radical complexes, with the error typically attributed to self-interaction. In density corrected density functional theory (DC-DFT), certain classes of density functional theory calculations are significantly improved by using densities more accurate than the self-consistent densities. We discuss how to identify such cases, and how DC-DFT applies more generally. To illustrate, we calculate potential energy surfaces of HO·Cl{sup −} and HO·H{sub 2}O complexes using various common approximate functionals, with and without this density correction. Commonly used approximations yield wrongly shaped surfaces and/or incorrect minima when calculated self consistently, while yielding almost identical shapes and minima when density corrected. This improvement is retained even in the presence of implicit solvent.
TRL - A FORMAL TEST REPRESENTATION LANGUAGE AND TOOL FOR FUNCTIONAL TEST DESIGNS
NASA Technical Reports Server (NTRS)
Hops, J. M.
1994-01-01
A Formal Test Representation Language and Tool for Functional Test Designs (TRL) is an automatic tool and a formal language that is used to implement the Category-Partition Method and produce the specification of test cases in the testing phase of software development. The Category-Partition Method is particularly useful in defining the inputs, outputs and purpose of the test design phase and combines the benefits of choosing normal cases with error exposing properties. Traceability can be maintained quite easily by creating a test design for each objective in the test plan. The effort to transform the test cases into procedures is simplified by using an automatic tool to create the cases based on the test design. The method allows the rapid elimination of undesired test cases from consideration, and easy review of test designs by peer groups. The first step in the category-partition method is functional decomposition, in which the specification and/or requirements are decomposed into functional units that can be tested independently. A secondary purpose of this step is to identify the parameters that affect the behavior of the system for each functional unit. The second step, category analysis, carries the work done in the previous step further by determining the properties or sub-properties of the parameters that would make the system behave in different ways. The designer should analyze the requirements to determine the features or categories of each parameter and how the system may behave if the category were to vary its value. If the parameter undergoing refinement is a data-item, then categories of this data-item may be any of its attributes, such as type, size, value, units, frequency of change, or source. After all the categories for the parameters of the functional unit have been determined, the next step is to partition each category's range space into mutually exclusive values that the category can assume. In choosing partition values, all possible kinds
a Renormalization Group Calculation of the Velocity - and Density-Density Correlation Functions.
NASA Astrophysics Data System (ADS)
Cowan, Mark Timothy
The velocity-velocity correlation function of a free field theory is obtained. The renormalization group, along with a 4-varepsilon expansion, is then used to find the leading order behavior of the velocity-velocity correlation function for an interacting field theory in the high temperature phase near the critical point. The details of the calculation of the density-density correlation function for Hedgehogs, in the context of a free field theory, is presented next. Finally the renormalization group, along with a 4-varepsilon expansion, is used to find the leading order behavior of the density-density correlation function for Hedgehogs in an interacting field theory near the critical point.
ERIC Educational Resources Information Center
Purse, Katie; Gardner, Hilary
2013-01-01
This study aimed to consider collaborative practice in contributing to joint assessment and producing appropriate referral of children to speech and language therapy (SLT). Results of formal testing of selected comprehension skills are compared with functional/classroom performance as rated by class teachers. Thirty children aged 6.5-8.4 years,…
Fermionic density functional at a Feshbach resonance
Seidl, Michael; Bhaduri, Rajat K.
2007-05-15
We consider a dilute gas of neutral unpolarized fermionic atoms at zero temperature. The atoms interact via a short-range (tunable) attractive interaction. We demonstrate analytically a curious property of the gas at unitarity. Namely, the correlation energy of the gas, evaluated by second-order perturbation theory, has the same density dependence as the first-order exchange energy, and the two almost exactly cancel each other at a Feshbach resonance irrespective of the shape of the potential, provided ({mu}r{sub s})>>1. Here ({mu}){sup -1} is the range of the two-body potential, and r{sub s} is defined through the number density, n=3/(4{pi}r{sub s}{sup 3}). The implications of this result for universality are discussed.
Density functional theory for Yukawa fluids
NASA Astrophysics Data System (ADS)
Hatlo, Marius M.; Banerjee, Priyanka; Forsman, Jan; Lue, Leo
2012-08-01
We develop an approximate field theory for particles interacting with a generalized Yukawa potential. This theory improves and extends a previous splitting field theory, originally developed for counterions around a fixed charge distribution. The resulting theory bridges between the second virial approximation, which is accurate at low particle densities, and the mean-field approximation, accurate at high densities. We apply this theory to charged, screened ions in bulk solution, modeled to interact with a Yukawa potential; the theory is able to accurately reproduce the thermodynamic properties of the system over a broad range of conditions. The theory is also applied to "dressed counterions," interacting with a screened electrostatic potential, contained between charged plates. It is found to work well from the weak coupling to the strong coupling limits. The theory is able to reproduce the counterion profiles and force curves for closed and open systems obtained from Monte Carlo simulations.
Molecular dynamics simulation of liquid water: Hybrid density functionals
Todorova, T; Seitsonen, A; Hutter, J; Kuo, W; Mundy, C
2005-09-12
The structure, dynamical and electronic properties of liquid water utilizing different hybrid density functionals were tested within the plane wave framework of first principles molecular dynamics simulations. The computational approach, which employs modified functionals with short-ranged Hartree-Fock exchange, was first tested in calculations of the structural and bonding properties of the water dimer and cyclic water trimer. Liquid water simulations were performed at the state point of 350 K at the experimental density. Simulations included three different hybrid functionals, a meta functional, four gradient corrected functionals, the local density and Hartree-Fock approximation. It is found that hybrid functionals are superior in reproducing the experimental structure and dynamical properties as measured by the radial distribution function and self diffusion constant when compared to the pure density functionals. The local density and Hartree-Fock approximations show strongly over- and under-structured liquids, respectively. Hydrogen bond analysis shows that the hybrid functionals give slightly smaller averaged numbers of hydrogen bonds and similar hydrogen bond populations as pure density functionals. The average molecular dipole moments in the liquid from the three hybrid functionals are lower than from the corresponding pure density functionals.
Density functional theory based simulations of silicon nanowire field effect transistors
NASA Astrophysics Data System (ADS)
Shin, Mincheol; Jeong, Woo Jin; Lee, Jaehyun
2016-04-01
First-principles density functional theory (DFT) based, atomistic, self-consistent device simulations are performed for realistically sized Si nanowire field effect transistors (NW FETs) having tens of thousands of atoms. Through mode space transformation, DFT Hamiltonian and overlap matrices are reduced in size from a few thousands to around one hundred. Ultra-efficient quantum-mechanical transport calculations in the non-equilibrium Green's function formalism in a non-orthogonal basis are therefore made possible. The n-type and p-type Si NW FETs are simulated and found to exhibit similar device performance in the nanoscale regime.
Maximally localized Wannier functions in antiferromagnetic MnO within the FLAPW formalism
NASA Astrophysics Data System (ADS)
Posternak, Michel; Baldereschi, Alfonso; Massidda, Sandro; Marzari, Nicola
2002-05-01
We have calculated the maximally localized Wannier functions of MnO in its antiferromagnetic (AFM) rhombohedral unit cell, which contains two formula units. Electron Bloch functions are obtained with the linearized-augmented-plane-wave method within both the local-spin density (LSD) and the LSD+U schemes. The thirteen uppermost occupied spin-up bands correspond in a pure ionic scheme to the five Mn 3d orbitals at the Mn1 (spin-up) site and the four O 2s/2p orbitals at each of the O1 and O2 sites. Maximal localization identifies uniquely four Wannier functions for each O, which are trigonally distorted sp3-like orbitals. They display a weak covalent bonding between O 2s/2p states and minority-spin d states of Mn2, which is absent in a fully ionic picture. This bonding is the fingerprint of the interaction responsible for the AFM ordering, and its strength depends on the one-electron scheme being used. The five Mn Wannier functions are centered on the Mn1 site, and are atomic orbitals modified by the crystal field. They are not uniquely defined by the criterion of maximal localization and we choose them as the linear combinations that diagonalize the r2 operator, so that they display the D3d symmetry of the Mn1 site.
Exact conditions on the temperature dependence of density functionals
NASA Astrophysics Data System (ADS)
Burke, K.; Smith, J. C.; Grabowski, P. E.; Pribram-Jones, A.
2016-05-01
Universal exact conditions guided the construction of most ground-state density functional approximations in use today. We derive the relation between the entropy and Mermin free energy density functionals for thermal density functional theory. Both the entropy and sum of kinetic and electron-electron repulsion functionals are shown to be monotonically increasing with temperature, while the Mermin functional is concave downwards. Analogous relations are found for both exchange and correlation. The importance of these conditions is illustrated in two extremes: the Hubbard dimer and the uniform gas.
The computational foundations of time dependent density functional theory
NASA Astrophysics Data System (ADS)
Whitfield, James
2014-03-01
The mathematical foundations of TDDFT are established through the formal existence of a fictitious non-interacting system (known as the Kohn-Sham system), which can reproduce the one-electron reduced probability density of the actual system. We build upon these works and show that on the interior of the domain of existence, the Kohn-Sham system can be efficiently obtained given the time-dependent density. Since a quantum computer can efficiently produce such time-dependent densities, we present a polynomial time quantum algorithm to generate the time-dependent Kohn-Sham potential with controllable error bounds. Further, we find that systems do not immediately become non-representable but rather become ill-representable as one approaches this boundary. A representability parameter is defined in our work which quantifies the distance to the boundary of representability and the computational difficulty of finding the Kohn-Sham system.
NASA Astrophysics Data System (ADS)
Nourali, Mahrouz; Ghahraman, Bijan; Pourreza-Bilondi, Mohsen; Davary, Kamran
2016-09-01
In the present study, DREAM(ZS), Differential Evolution Adaptive Metropolis combined with both formal and informal likelihood functions, is used to investigate uncertainty of parameters of the HEC-HMS model in Tamar watershed, Golestan province, Iran. In order to assess the uncertainty of 24 parameters used in HMS, three flood events were used to calibrate and one flood event was used to validate the posterior distributions. Moreover, performance of seven different likelihood functions (L1-L7) was assessed by means of DREAM(ZS)approach. Four likelihood functions, L1-L4, Nash-Sutcliffe (NS) efficiency, Normalized absolute error (NAE), Index of agreement (IOA), and Chiew-McMahon efficiency (CM), is considered as informal, whereas remaining (L5-L7) is represented in formal category. L5 focuses on the relationship between the traditional least squares fitting and the Bayesian inference, and L6, is a hetereoscedastic maximum likelihood error (HMLE) estimator. Finally, in likelihood function L7, serial dependence of residual errors is accounted using a first-order autoregressive (AR) model of the residuals. According to the results, sensitivities of the parameters strongly depend on the likelihood function, and vary for different likelihood functions. Most of the parameters were better defined by formal likelihood functions L5 and L7 and showed a high sensitivity to model performance. Posterior cumulative distributions corresponding to the informal likelihood functions L1, L2, L3, L4 and the formal likelihood function L6 are approximately the same for most of the sub-basins, and these likelihood functions depict almost a similar effect on sensitivity of parameters. 95% total prediction uncertainty bounds bracketed most of the observed data. Considering all the statistical indicators and criteria of uncertainty assessment, including RMSE, KGE, NS, P-factor and R-factor, results showed that DREAM(ZS) algorithm performed better under formal likelihood functions L5 and L7
Density-potential mapping in time-dependent density-functional theory
Maitra, N. T.; Todorov, T. N.; Woodward, C.; Burke, K.
2010-04-15
The key questions of uniqueness and existence in time-dependent density-functional theory are usually formulated only for potentials and densities that are analytic in time. Simple examples, standard in quantum mechanics, lead, however, to nonanalyticities. We reformulate these questions in terms of a nonlinear Schroedinger equation with a potential that depends nonlocally on the wave function.
NASA Astrophysics Data System (ADS)
Mintmire, J. W.; White, C. T.
1987-03-01
We report the results of a computational study of the dimerization of the all-trans-polyacetylene chain within the local-density-func- tional formalism employing the Gáspár-Kohn-Sham exchange-correlation potential. Our calculated bond alternation at equilibrium is less than experimentally implied by roughly a factor of 3. Evidence is presented that suggests that this underestimation of dimerization is closely connected with the much discussed band-gap problem in local-density-functional theory.
Spin constraints on nuclear energy density functionals
NASA Astrophysics Data System (ADS)
Robledo, L. M.; Bernard, R. N.; Bertsch, G. F.
2014-02-01
The Gallagher-Moszkowski rule in the spectroscopy of odd-odd nuclei imposes a new spin constraint on the energy functionals for self-consistent mean field theory. The commonly used parametrization of the effective three-body interaction in the Gogny and Skyrme families of energy functionals is ill suited to satisfy the spin constraint. In particular, the Gogny parametrization of the three-body interaction has the spin dependence opposite to that required by the observed spectra. The two-body part has a correct sign, but in combination the rule is violated as often as not. We conclude that a new functional form is needed for the effective three-body interaction that can take into better account the different spin-isospin channels of the interaction.
Introduction to Classical Density Functional Theory by a Computational Experiment
ERIC Educational Resources Information Center
Jeanmairet, Guillaume; Levy, Nicolas; Levesque, Maximilien; Borgis, Daniel
2014-01-01
We propose an in silico experiment to introduce the classical density functional theory (cDFT). Density functional theories, whether quantum or classical, rely on abstract concepts that are nonintuitive; however, they are at the heart of powerful tools and active fields of research in both physics and chemistry. They led to the 1998 Nobel Prize in…
Nuclear collective excitations: A relativistic density functional approach
NASA Astrophysics Data System (ADS)
Piekarewicz, J.
2015-08-01
Density functional theory provides the most promising, and likely unique, microscopic framework to describe nuclear systems ranging from finite nuclei to neutron stars. Properly optimized energy density functionals define a new paradigm in nuclear theory where predictive capability is possible and uncertainty quantification is demanded. Moreover, density functional theory offers a consistent approach to the linear response of the nuclear ground state. In this paper, we review the fundamental role played by nuclear collective modes in uncovering novel excitations and in guiding the optimization of the density functional. Indeed, without collective excitations the determination of the density functional remains incomplete. Without collective excitations, the equation of state of neutron-rich matter continues to be poorly constrained. We conclude with a discussion of some of the remaining challenges in this field and propose a path forward to address these challenges.
NASA Astrophysics Data System (ADS)
Bochevarov, Arteum D.; Friesner, Richard A.
2008-01-01
We investigate one of the fundamental observables, electronic charge density, as produced by a number of popular functionals of the density functional theory (DFT): SVWN5, B3LYP, B3LYP, OLYP, O3LYP, BP86, B3P86, O3P86, and PBE using restricted and unrestricted orbitals. Measuring and comparing the quality of the densities could tell us more about the physical soundness of the functional models. The study is performed on the small molecules He, H2, LiH, H4 in an extensive range of correlation-consistent basis sets. We compare DFT densities to those of full configuration interaction (FCI) under the assumption that the FCI density in the largest employed basis set is sufficiently close to the exact one. For LiH and H4, we also compare the DFT densities to those of CCSD. The SVWN5 functional consistently shows the worst performance. The OPTX exchange functional regularly beats the Becke exchange. Among the best performers are all the hybrid functionals, the novel O3P86 being the most accurate in most cases. The popular functional B3LYP was consistently outmatched by O3LYP, and produced, in fact, some of the poorest densities among the hybrids. CCSD was found to produce much more accurate densities than any DFT functional in the case of LiH in equilibrium geometry, but was sometimes outperformed by DFT in the case of slightly stretched H4, where CCSD theory itself starts to break down. Surprisingly, as one stretches the H2 molecule, BP86 and PBE improve the description of density although such behavior is not observed in other systems. We conclude by reasoning how functionals such as B3LYP, despite being quite average for density, could still be very successful in predicting thermodynamic properties.
Molecular density functional theory of water including density-polarization coupling.
Jeanmairet, Guillaume; Levy, Nicolas; Levesque, Maximilien; Borgis, Daniel
2016-06-22
We present a three-dimensional molecular density functional theory of water derived from first-principles that relies on the particle's density and multipolar polarization density and includes the density-polarization coupling. This brings two main benefits: (i) scalar density and vectorial multipolar polarization density fields are much more tractable and give more physical insight than the full position and orientation densities, and (ii) it includes the full density-polarization coupling of water, that is known to be non-vanishing but has never been taken into account. Furthermore, the theory requires only the partial charge distribution of a water molecule and three measurable bulk properties, namely the structure factor and the Fourier components of the longitudinal and transverse dielectric susceptibilities. PMID:27116250
The benchmark of gutzwiller density functional theory in hydrogen systems
Yao, Y.; Wang, Cai-Zhuang; Ho, Kai-Ming
2012-02-23
We propose an approximate form of the exchange-correlation energy functional for the Gutzwiller density functional theory. It satisfies certain physical constraints in both weak and strong electron correlation limits. We benchmark the Gutzwiller density functional approximation in the hydrogen systems, where the static correlation error is shown to be negligible. The good transferability is demonstrated by applications to the hydrogen molecule and some crystal structures.
The Benchmark of Gutzwiller Density Functional Theory in Hydrogen Systems
Yao, Yongxin; Wang, Cai-Zhuang; Ho, Kai-Ming
2011-01-13
We propose an approximate form of the exchange-correlation energy functional for the Gutzwiller density functional theory. It satisfies certain physical constraints in both weak and strong electron correlation limits. We benchmark the Gutzwiller density functional approximation in the hydrogen systems, where the static correlation error is shown to be negligible. The good transferability is demonstrated by applications to the hydrogen molecule and some crystal structures. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012
Generalized van der Waals density functional theory for nonuniform polymers
Patra, Chandra N.; Yethiraj, Arun
2000-01-15
A density functional theory is presented for the effect of attractions on the structure of polymers at surfaces. The theory treats the ideal gas functional exactly, and uses a weighted density approximation for the hard chain contribution to the excess free energy functional. The attractive interactions are treated using a van der Waals approximation. The theory is in good agreement with computer simulations for the density profiles at surfaces for a wide range of densities and temperatures, except for low polymer densities at low temperatures where it overestimates the depletion of chains from the surface. This deficiency is attributed to the neglect of liquid state correlations in the van der Waals term of the free energy functional. (c) 2000 American Institute of Physics.
Connection between Hybrid Functionals and Importance of the Local Density Approximation.
Mosquera, Martín A; Borca, Carlos H; Ratner, Mark A; Schatz, George C
2016-03-10
The exchange-correlation (XC) local density approximation (LDA) is the original density functional used to investigate the electronic structure of molecules and solids within the formulation of Kohn and Sham. The LDA is fundamental for the development of density-functional approximations. In this work we consider the generalized Kohn-Sham (GKS) theory of hybrid functionals. The GKS formalism is an extension of the Kohn-Sham theory for electronic ground states and leads to a vast set of alternative density functionals, which can be estimated by the LDA and related methods. Herein we study auxiliary electronic systems with parametrized interactions and derive (i) a set of exact equations relating the GKS XC energies in the parameter space and (ii) a formal relation between the parameters and the standard XC derivative discontinuity. In view of the new results and previously reported findings, we discuss why the inclusion of Fock exchange, and its long-range-corrected form (in the ground-state calculations and in linear-response Kohn-Sham equations), dominate over the generalized gradient corrections to enhance the quality of the fundamental gap and to enhance excitation-energy estimations. As an example, we show that the adiabatic CAM-LDA0 (a functional with 1/4 global and 1/2 long-range Hartree-Fock interaction, respectively, a range separation factor of 1/3, and pure LDA exchange and correlation) works for electronic excitations as well as the adiabatic CAM-B3LYP functional. PMID:26901359
Orthogonality of embedded wave functions for different states in frozen-density embedding theory.
Zech, Alexander; Aquilante, Francesco; Wesolowski, Tomasz A
2015-10-28
Other than lowest-energy stationary embedded wave functions obtained in Frozen-Density Embedding Theory (FDET) [T. A. Wesolowski, Phys. Rev. A 77, 012504 (2008)] can be associated with electronic excited states but they can be mutually non-orthogonal. Although this does not violate any physical principles--embedded wave functions are only auxiliary objects used to obtain stationary densities--working with orthogonal functions has many practical advantages. In the present work, we show numerically that excitation energies obtained using conventional FDET calculations (allowing for non-orthogonality) can be obtained using embedded wave functions which are strictly orthogonal. The used method preserves the mathematical structure of FDET and self-consistency between energy, embedded wave function, and the embedding potential (they are connected through the Euler-Lagrange equations). The orthogonality is built-in through the linearization in the embedded density of the relevant components of the total energy functional. Moreover, we show formally that the differences between the expectation values of the embedded Hamiltonian are equal to the excitation energies, which is the exact result within linearized FDET. Linearized FDET is shown to be a robust approximation for a large class of reference densities. PMID:26520497
Orthogonality of embedded wave functions for different states in frozen-density embedding theory
Zech, Alexander; Wesolowski, Tomasz A.; Aquilante, Francesco
2015-10-28
Other than lowest-energy stationary embedded wave functions obtained in Frozen-Density Embedding Theory (FDET) [T. A. Wesolowski, Phys. Rev. A 77, 012504 (2008)] can be associated with electronic excited states but they can be mutually non-orthogonal. Although this does not violate any physical principles — embedded wave functions are only auxiliary objects used to obtain stationary densities — working with orthogonal functions has many practical advantages. In the present work, we show numerically that excitation energies obtained using conventional FDET calculations (allowing for non-orthogonality) can be obtained using embedded wave functions which are strictly orthogonal. The used method preserves the mathematical structure of FDET and self-consistency between energy, embedded wave function, and the embedding potential (they are connected through the Euler-Lagrange equations). The orthogonality is built-in through the linearization in the embedded density of the relevant components of the total energy functional. Moreover, we show formally that the differences between the expectation values of the embedded Hamiltonian are equal to the excitation energies, which is the exact result within linearized FDET. Linearized FDET is shown to be a robust approximation for a large class of reference densities.
Exact maps in density functional theory for lattice models
NASA Astrophysics Data System (ADS)
Dimitrov, Tanja; Appel, Heiko; Fuks, Johanna I.; Rubio, Angel
2016-08-01
In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and graphically illustrate the complete exact density-to-wavefunction map that underly the Hohenberg–Kohn theorem in density functional theory. Having the explicit wavefunction-to-density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragments decreases and the correlation grows. We denominate this feature as intra-system steepening and discuss how it relates to the well-known inter-system derivative discontinuity. The inter-system derivative discontinuity is an exact concept for coupled subsystems with degenerate ground state. However, the coupling between subsystems as in charge transfer processes can lift the degeneracy. An important conclusion is that for such systems with a near-degenerate ground state, the corresponding cut along the particle number N of the exact density functionals is differentiable with a well-defined gradient near integer particle number.
Postfragmentation density function for bacterial aggregates in laminar flow
NASA Astrophysics Data System (ADS)
Byrne, Erin; Bortz, David M.; Dzul, Steve; Solomon, Michael; Younger, John
2011-04-01
The postfragmentation probability density of daughter flocs is one of the least well-understood aspects of modeling flocculation. We use three-dimensional positional data of Klebsiella pneumoniae bacterial flocs in suspension and the knowledge of hydrodynamic properties of a laminar flow field to construct a probability density function of floc volumes after a fragmentation event. We provide computational results which predict that the primary fragmentation mechanism for large flocs is erosion. The postfragmentation probability density function has a strong dependence on the size of the original floc and indicates that most fragmentation events result in clumps of one to three bacteria eroding from the original floc. We also provide numerical evidence that exhaustive fragmentation yields a limiting density inconsistent with the log-normal density predicted in the literature, most likely due to the heterogeneous nature of K. pneumoniae flocs. To support our conclusions, artificial flocs were generated and display similar postfragmentation density and exhaustive fragmentation.
Application of the green function formalism to nonlinear evolution of the low gain FEL oscillator
Shvets, G.; Wurtele, J.S.; Gardent, D.
1995-12-31
A matrix formalism for the optical pulse evolution in the frequency domain, is applied to the nonlinear regime of operation. The formalism was previously developed for studies of the linear evolution of the low-gain FEL oscillator with an arbitrary shape of the electron beam. By varying experimentally controllable parameters, such as cavity detunning and cavity losses, different regimes of operation of the FEL oscillator, such as a steady state saturation and limit cycle saturation, are studied numerically. It is demonstrated that the linear supermodes, numerically obtained from the matrix formalism, provide an appropriate framework for analyzing the periodic change in the output power in the limit cycle regime. The frequency of this oscillation is related to the frequencies of the lowest-order linear supermodes. The response of the output radiation to periodic variation of the electron energy is studied. It is found that the response is enhanced when the frequency of the energy variation corresponds to the difference of per-pass phase advances of the lowest linear supermodes. Finally, various nonlinear models are tested to capture the steady state saturation and limit cycle variation of the EM field in the oscillator cavity.
Integration, Continuity and a Connection with Probability Density Functions
ERIC Educational Resources Information Center
Samuels, M.
2006-01-01
This note considers functions of two variables which are continuous on a possibly unbounded closed region in [vertical bar]R[squared], and the functions of one variable obtained by integrating out the other variable over this region. The question of continuity of these functions is investigated, as are connections with joint density and marginal…
Testing for parity violation in nuclei using spin density matrices for nuclear density functionals
NASA Astrophysics Data System (ADS)
Barrett, B. R.; Giraud, B. G.
2015-06-01
The spin density matrix (SDM) used in atomic and molecular physics is revisited for nuclear physics, in the context of the radial density functional theory. The vector part of the SDM defines a ‘hedgehog’ situation, which exists only if nuclear states contain some amount of parity violation. A toy model is given as an illustrative example.
Fluctuation-dissipation theorem density-functional theory
NASA Astrophysics Data System (ADS)
Furche, Filipp; Van Voorhis, Troy
2005-04-01
Using the fluctuation-dissipation theorem (FDT) in the context of density-functional theory (DFT), one can derive an exact expression for the ground-state correlation energy in terms of the frequency-dependent density response function. When combined with time-dependent density-functional theory, a new class of density functionals results that use approximations to the exchange-correlation kernel fxc as input. This FDT-DFT scheme holds promise to solve two of the most distressing problems of conventional Kohn-Sham DFT: (i) It leads to correlation energy functionals compatible with exact exchange, and (ii) it naturally includes dispersion. The price is a moderately expensive O(N6) scaling of computational cost and a slower basis set convergence. These general features of FDT-DFT have all been recognized previously. In this paper, we present the first benchmark results for a set of molecules using FDT-DFT beyond the random-phase approximation (RPA)—that is, the first such results with fxc≠0. We show that kernels derived from the adiabatic local-density approximation and other semilocal functionals suffer from an "ultraviolet catastrophe," producing a pair density that diverges at small interparticle distance. Nevertheless, dispersion interactions can be treated accurately if hybrid functionals are employed, as is demonstrated for He2 and HeNe. We outline constraints that future approximations to fxc should satisfy and discuss the prospects of FDT-DFT.
Charge and spin fluctuations in the density functional theory
Gyoerffy, B.L.; Barbieri, A. . H.H. Wills Physics Lab.); Staunton, J.B. . Dept. of Physics); Shelton, W.A.; Stocks, G.M. )
1990-01-01
We introduce a conceptual framework which allow us to treat charge and spin fluctuations about the Local density Approximation (LDA) to the Density Functional Theory (DFT). We illustrate the approach by explicit study of the Disordered Local Moment (DLM) state in Fe above the Curie Temperature {Tc} and the Mott insulating state in MnO. 27 refs., 6 figs.
Density Functional Model for Nondynamic and Strong Correlation.
Kong, Jing; Proynov, Emil
2016-01-12
A single-term density functional model for the left-right nondynamic/strong electron correlation is presented based on single-determinant Kohn-Sham density functional theory. It is derived from modeling the adiabatic connection for kinetic correlation energy based on physical arguments, with the correlation potential energy based on the Becke'13 model ( Becke, A.D. J. Chem. Phys . 2013 , 138 , 074109 ). This functional satisfies some known scaling relationships for correlation functionals. The fractional spin error is further reduced substantially with a new density-functional correction. Preliminary tests with self-consistent-field implementation show that the model, with only three empirical parameters, recovers the majority of left-right nondynamic/strong correlation upon bond dissociation and performs reasonably well for atomization energies and singlet-triplet energy splittings. This study also demonstrates the feasibility of developing DFT functionals for nondynamic and strong correlation within the single-determinant KS scheme. PMID:26636190
Density and Spin Response Functions in Ultracold Fermionic Atom Gases
Mihaila, Bogdan; Blagoev, Krastan B.; Balatsky, Alexander V.; Smith, Darryl L.; Gaudio, Sergio; Littlewood, Peter B.
2005-08-26
We propose a new method of detecting the onset of superfluidity in a two-component ultracold fermionic gas of atoms governed by an attractive short-range interaction. By studying the two-body correlation functions we find that a measurement of the momentum distribution of the density and spin-response functions allows one to access separately the normal and anomalous densities. The change in sign at low momentum transfer of the normal-ordered part of the density response function signals the transition between a BEC and a BCS regime, characterized by small and large pairs, respectively. This change in sign of the density response function represents an unambiguous signature of the BEC-to-BCS crossover. Spin rotational symmetry breaking due to the magnetic field, if observed, can be used to validate the one-channel model.
Density Functional Approximation for Non-Hard Sphere Fluids Subjected to External Fields
NASA Astrophysics Data System (ADS)
Zhou, Shiqi
A theoretical way is proposed, by which any hard sphere density functional approximation (DFA) can be applied to non-hard sphere fluids for the calculation of density profile in the framework of density functional theory (DFT). Used as examples, the present formalism is combined respectively with two recently proposed hard sphere DFAs to predict the density profile of Lennard-Jones (LJ) fluid, hard core square well (SW) fluid and penetrable potenial fluid subjected to diverse external fields. Extensive comparison between theoretical predictions and corresponding simulation results shows that the present theoretical way, when combined with an accurate hard sphere DFA, can perform well for calculating the density profile of the non-uniform fluids of the above mentioned potentials. Concretely speaking, for LJ and hard core SW fluid, even a less accurate FEDFA is sufficient, while for extreme potential such as the penetrable potenial, a more accurate adjustable parameter free version of LTDFA is needed to combine with the present theoretical way to predict density profile satisfactorily. The advantage of the proposed theoretical way is that the resultant DFA is applicable to both subcritical and supercritical temperature cases, thereby overcoming the disadvantages of previous two categories of DFT approach.
Density Functional Theory with Dissipation: Transport through Single Molecules
Kieron Burke
2012-04-30
A huge amount of fundamental research was performed on this grant. Most of it focussed on fundamental issues of electronic structure calculations of transport through single molecules, using density functional theory. Achievements were: (1) First density functional theory with dissipation; (2) Pseudopotential plane wave calculations with master equation; (3) Weak bias limit; (4) Long-chain conductance; and (5) Self-interaction effects in tunneling.
Preface: Special Topic on Advances in Density Functional Theory
Yang, Weitao
2014-05-14
This Special Topic Issue on the Advances in Density Functional Theory, published as a celebration of the fifty years of density functional theory, contains a retrospective article, a perspective article, and a collection of original research articles that showcase recent theoretical advances in the field. It provides a timely discussion reflecting a cross section of our understanding, and the theoretical and computational developments, which have significant implications in broad areas of sciences and engineering.
Preface: Special topic on advances in density functional theory.
Yang, Weitao
2014-05-14
This Special Topic Issue on the Advances in Density Functional Theory, published as a celebration of the fifty years of density functional theory, contains a retrospective article, a perspective article, and a collection of original research articles that showcase recent theoretical advances in the field. It provides a timely discussion reflecting a cross section of our understanding, and the theoretical and computational developments, which have significant implications in broad areas of sciences and engineering. PMID:24832306
Reflection-Asymmetric Nuclear Deformations within the Density Functional Theory
Olsen, E; Erler, J; Nazarewicz, W.; Stoitsov, M
2012-01-01
Within the nuclear density functional theory (DFT) we study the effect of reflection- asymmetric shapes on ground-state binding energies and binding energy differences. To this end, we developed the new DFT solver axialhfb that uses an approximate second-order gradient to solve the Hartree-Fock-Bogoliubov equations of superconducting DFT with the quasi-local Skyrme energy density functionals. Illustrative calculations are carried out for even- even isotopes of radium and thorium.
Energy Densities in the Strong-Interaction Limit of Density Functional Theory.
Mirtschink, André; Seidl, Michael; Gori-Giorgi, Paola
2012-09-11
We discuss energy densities in the strong-interaction limit of density functional theory, deriving an exact expression within the definition (gauge) of the electrostatic potential of the exchange-correlation hole. Exact results for small atoms and small model quantum dots (Hooke's atoms) are compared with available approximations defined in the same gauge. The idea of a local interpolation along the adiabatic connection is discussed, comparing the energy densities of the Kohn-Sham, the physical, and the strong-interacting systems. We also use our results to analyze the local version of the Lieb-Oxford bound, widely used in the construction of approximate exchange-correlation functionals. PMID:26605721
Santiago, Régis Tadeu; Haiduke, Roberto Luiz Andrade
2015-10-30
This research provides a performance investigation of density functional theory and also proposes new functional parameterizations to deal with electric field gradient (EFG) calculations at nuclear positions. The entire procedure is conducted within the four-component formalism. First, we noticed that traditional hybrid and long-range corrected functionals are more efficient in the description of EFG variations for a set of elements (indium, antimony, iodine, lutetium, and hafnium) among linear molecules. Thus, we selected the PBE0, B3LYP, and CAM-B3LYP functionals and promoted a reoptimization of their parameters for a better description of these EFG changes. The PBE0q variant developed here showed an overall promising performance in a validation test conducted with potassium, iodine, copper, and gold. In general, the correlation coefficients found in linear regressions between experimental nuclear quadrupole coupling constants and calculated EFGs are improved while the systematic EFG errors also decrease as a result of this reparameterization. PMID:26284820
NASA Astrophysics Data System (ADS)
Ayalon, Michal; Watson, Anne; Lerman, Steve
2016-05-01
This study examines expressions of reasoning by some higher achieving 11 to 18 year-old English students responding to a survey consisting of function tasks developed in collaboration with their teachers. We report on 70 students, 10 from each of English years 7-13. Iterative and comparative analysis identified capabilities and difficulties of students and suggested conjectures concerning links between the affordances of the tasks, the curriculum, and students' responses. The paper focuses on five of the survey tasks and highlights connections between informal and formal expressions of reasoning about variables in learning. We introduce the notion of `schooled' expressions of reasoning, neither formal nor informal, to emphasise the role of the formatting tools introduced in school that shape future understanding and reasoning.
Franca, Vivian V.; D'Amico, Irene
2011-04-15
We derive an analytical density functional for the single-site entanglement of the one-dimensional homogeneous Hubbard model by means of an approximation to the linear entropy. We show that this very simple density functional reproduces quantitatively the exact results. We then use this functional as input for a local-density approximation to the single-site entanglement of inhomogeneous systems. We illustrate the power of this approach in a harmonically confined system, which could simulate recent experiments with ultracold atoms in optical lattices as well as in a superlattice and in an impurity system. The impressive quantitative agreement with numerical calculations--which includes reproducing subtle signatures of the particle density stages--shows that our density functional can provide entanglement calculations for actual experiments via density measurements. Next we use our functional to calculate the entanglement in disordered systems. We find that, in contrast with the expectation that disorder destroys the entanglement, there exist regimes for which the entanglement remains almost unaffected by the presence of disordered impurities.
Reactivity of Graphene Investigated by Density-Functional Theory
NASA Astrophysics Data System (ADS)
Soni, Himadri; Gebhardt, Julian; Görling, Andreas; Chair of Theoretical Chemistry Team
Using spin-polarized density-functional theory, we study the adsorption and reaction of hydrogen and fluorine with graphene. Graphene has a bipartite lattice with two different sublattices and hence, due to Lieb's theorem, the inequality between two sublattices should lead to a net magnetic moment upon adsorption of hydrogen or fluorine. Our calculations using density-functional theory with the generalized gradient approximation predict a magnetic moment of 1 µB for a single hydrogen adsorbed on graphene but not for a single fluorine atom adsorbed on graphene. Switching to hybrid density-functional theory with the HSE functional, we obtain a magnetic moment of 1 µB for of a single fluorine atom adsorption on graphene. This is in line with work of Kim et al., who also found in density-functional theory calculations with the HSE exchange-correlation functional spin-polarization for a fluorine adatom on graphene. Here, we present a systematic study of the reactivity and relevant adsorption mechanism for single-sided graphene, i.e., a graphene sheet which is accessible by an adsorbate from only one side with hydrogen and fluorine using hybrid density-functional theory. German Research Council (DFG) by the Collaborative Research Center 953.
Range Separation and Local Hybridization in Density Functional Theory†
Henderson, Thomas M.; Janesko, Benjamin G.; Scuseria, Gustavo E.
2016-01-01
Kohn–Sham density functional theory has become a standard method for modeling energetic, spectroscopic, and chemical reactivity properties of large molecules and solids. Density functional theory provides a rigorous theoretical framework for modeling the many-body exchange-correlation effects that dominate the computational cost of traditional wave function approaches. The advent of hybrid exchange-correlation functionals which incorporate a fraction of nonlocal exact exchange has solidified the prominence of density functional theory within computational chemistry. Hybrids provide accurate treatments of properties such as thermochemistry and molecular geometry. But they also exhibit some rather spectacular failures, and often contain multiple empirical parameters. This article reviews our work on developing novel exchange-correlation functionals that build upon the successes of global hybrids. We focus on more flexible functional forms, including local and range-separated hybrid functionals, constructed to obey known exact constraints and (ideally) to incorporate a minimum of empirical parametrization. The article places our work within the context of some other new approximate density functionals and discusses prospects for future work. PMID:19006280
Optimal-transport formulation of electronic density-functional theory
NASA Astrophysics Data System (ADS)
Buttazzo, Giuseppe; De Pascale, Luigi; Gori-Giorgi, Paola
2012-06-01
The most challenging scenario for Kohn-Sham density-functional theory, that is, when the electrons move relatively slowly trying to avoid each other as much as possible because of their repulsion (strong-interaction limit), is reformulated here as an optimal transport (or mass transportation theory) problem, a well-established field of mathematics and economics. In practice, we show that to solve the problem of finding the minimum possible internal repulsion energy for N electrons in a given density ρ(r) is equivalent to find the optimal way of transporting N-1 times the density ρ into itself, with the cost function given by the Coulomb repulsion. We use this link to set the strong-interaction limit of density-functional theory on firm ground and to discuss the potential practical aspects of this reformulation.
Optimization of an exchange-correlation density functional for water.
Fritz, Michelle; Fernández-Serra, Marivi; Soler, José M
2016-06-14
We describe a method, that we call data projection onto parameter space (DPPS), to optimize an energy functional of the electron density, so that it reproduces a dataset of experimental magnitudes. Our scheme, based on Bayes theorem, constrains the optimized functional not to depart unphysically from existing ab initio functionals. The resulting functional maximizes the probability of being the "correct" parameterization of a given functional form, in the sense of Bayes theory. The application of DPPS to water sheds new light on why density functional theory has performed rather poorly for liquid water, on what improvements are needed, and on the intrinsic limitations of the generalized gradient approximation to electron exchange and correlation. Finally, we present tests of our water-optimized functional, that we call vdW-DF-w, showing that it performs very well for a variety of condensed water systems. PMID:27305990
Optimization of an exchange-correlation density functional for water
NASA Astrophysics Data System (ADS)
Fritz, Michelle; Fernández-Serra, Marivi; Soler, José M.
2016-06-01
We describe a method, that we call data projection onto parameter space (DPPS), to optimize an energy functional of the electron density, so that it reproduces a dataset of experimental magnitudes. Our scheme, based on Bayes theorem, constrains the optimized functional not to depart unphysically from existing ab initio functionals. The resulting functional maximizes the probability of being the "correct" parameterization of a given functional form, in the sense of Bayes theory. The application of DPPS to water sheds new light on why density functional theory has performed rather poorly for liquid water, on what improvements are needed, and on the intrinsic limitations of the generalized gradient approximation to electron exchange and correlation. Finally, we present tests of our water-optimized functional, that we call vdW-DF-w, showing that it performs very well for a variety of condensed water systems.
Density functional for ternary non-additive hard sphere mixtures.
Schmidt, Matthias
2011-10-19
Based on fundamental measure theory, a Helmholtz free energy density functional for three-component mixtures of hard spheres with general, non-additive interaction distances is constructed. The functional constitutes a generalization of the previously given theory for binary non-additive mixtures. The diagrammatic structure of the spatial integrals in both functionals is of star-like (or tree-like) topology. The ternary diagrams possess a higher degree of complexity than the binary diagrams. Results for partial pair correlation functions, obtained via the Ornstein-Zernike route from the second functional derivatives of the excess free energy functional, agree well with Monte Carlo simulation data. PMID:21946780
Modal density function and number of propagating modes in ducts
NASA Technical Reports Server (NTRS)
Rice, E. J.
1976-01-01
Often raised questions in duct sound propagation studies involve the total number of propagating modes, the number of propagating radial modes for a particular spinning lobe number, and the number of modes possible between two given values of cutoff ratio or eigenvalue. These questions can be answered approximately by using the modal distribution function which is the integral of the modal density function for ducts in a manner similar to that previously published for architectural acoustics. The modal density functions are derived for rectangular and circular ducts with a uniform steady flow. Results from this continuous theory are compared to the actual (discrete) modal distributions.
Van der Waals density functional applied to adsorption systems
NASA Astrophysics Data System (ADS)
Hamada, Ikutaro
2013-03-01
The van der Waals density functional (vdW-DF) is a promising density functional to describe the van der Waals forces within density functional theory. However, despite the recent efforts, there is still room for further improvement, especially for describing molecular adsorption on metal surfaces. I will show that by choosing appropriate exchange and nonlocal correlation functionals, it is possible to calculate geometries and electronic structures for adsorption systems accurately within the framework of vdW-DF. Applicability of the present approach will be illustrated with its applications to graphene/metal, fullerene/metal, and water/graphene interfaces. This work is partly supported by a Grant-in-Aid for Scientific Research on Innovative Area (No. 23104501). AIMR was established by the World Premier International Research Center Initiative (WPI), MEXT, Japan.
Force Density Function Relationships in 2-D Granular Media
NASA Technical Reports Server (NTRS)
Youngquist, Robert C.; Metzger, Philip T.; Kilts, Kelly N.
2004-01-01
An integral transform relationship is developed to convert between two important probability density functions (distributions) used in the study of contact forces in granular physics. Developing this transform has now made it possible to compare and relate various theoretical approaches with one another and with the experimental data despite the fact that one may predict the Cartesian probability density and another the force magnitude probability density. Also, the transforms identify which functional forms are relevant to describe the probability density observed in nature, and so the modified Bessel function of the second kind has been identified as the relevant form for the Cartesian probability density corresponding to exponential forms in the force magnitude distribution. Furthermore, it is shown that this transform pair supplies a sufficient mathematical framework to describe the evolution of the force magnitude distribution under shearing. Apart from the choice of several coefficients, whose evolution of values must be explained in the physics, this framework successfully reproduces the features of the distribution that are taken to be an indicator of jamming and unjamming in a granular packing. Key words. Granular Physics, Probability Density Functions, Fourier Transforms
Improved association in a classical density functional theory for water.
Krebs, Eric J; Schulte, Jeff B; Roundy, David
2014-03-28
We present a modification to our recently published statistical associating fluid theory-based classical density functional theory for water. We have recently developed and tested a functional for the averaged radial distribution function at contact of the hard-sphere fluid that is dramatically more accurate at interfaces than earlier approximations. We now incorporate this improved functional into the association term of our free energy functional for water, improving its description of hydrogen bonding. We examine the effect of this improvement by studying two hard solutes (a hard hydrophobic rod and a hard sphere) and a Lennard-Jones approximation of a krypton atom solute. The improved functional leads to a moderate change in the density profile and a large decrease in the number of hydrogen bonds broken in the vicinity of the hard solutes. We find an improvement of the partial radial distribution for a krypton atom in water when compared with experiment. PMID:24697459
Improved association in a classical density functional theory for water
Krebs, Eric J.; Schulte, Jeff B.; Roundy, David
2014-03-28
We present a modification to our recently published statistical associating fluid theory-based classical density functional theory for water. We have recently developed and tested a functional for the averaged radial distribution function at contact of the hard-sphere fluid that is dramatically more accurate at interfaces than earlier approximations. We now incorporate this improved functional into the association term of our free energy functional for water, improving its description of hydrogen bonding. We examine the effect of this improvement by studying two hard solutes (a hard hydrophobic rod and a hard sphere) and a Lennard-Jones approximation of a krypton atom solute. The improved functional leads to a moderate change in the density profile and a large decrease in the number of hydrogen bonds broken in the vicinity of the hard solutes. We find an improvement of the partial radial distribution for a krypton atom in water when compared with experiment.
Optimized Effective Potential for Quantum Electrodynamical Time-Dependent Density Functional Theory.
Pellegrini, Camilla; Flick, Johannes; Tokatly, Ilya V; Appel, Heiko; Rubio, Angel
2015-08-28
We propose an orbital exchange-correlation functional for applying time-dependent density functional theory to many-electron systems coupled to cavity photons. The time nonlocal equation for the electron-photon optimized effective potential (OEP) is derived. In the static limit our OEP energy functional reduces to the Lamb shift of the ground state energy. We test the new approximation in the Rabi model. It is shown that the OEP (i) reproduces quantitatively the exact ground-state energy from the weak to the deep strong coupling regime and (ii) accurately captures the dynamics entering the ultrastrong coupling regime. The present formalism opens the path to a first-principles description of correlated electron-photon systems, bridging the gap between electronic structure methods and quantum optics for real material applications. PMID:26371646
NASA Astrophysics Data System (ADS)
Farzanehpour, Mehdi; Tokatly, Ilya; Nano-Bio Spectroscopy Group; ETSF Scientific Development Centre Team
2015-03-01
We present a rigorous formulation of the time-dependent density functional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic mode, which is equivalent to the single mode spin-boson model or the quantum Rabi model. For this system we prove that the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate, provided the initial state and the density satisfy a set of well defined conditions. Then we generalize the formalism to many interacting electrons on a lattice coupled to multiple photonic modes and prove the general mapping theorem. We also show that for a system evolving from the ground state of a lattice Hamiltonian any density with a continuous second time derivative is locally v-representable. Spanish Ministry of Economy and Competitiveness (Grant No. FIS2013-46159-C3-1-P), Grupos Consolidados UPV/EHU del Gobierno Vasco (Grant No. IT578-13), COST Actions CM1204 (XLIC) and MP1306 (EUSpec).
Addressing spectroscopic quality of covariant density functional theory
NASA Astrophysics Data System (ADS)
Afanasjev, A. V.
2015-03-01
The spectroscopic quality of covariant density functional theory has been accessed by analyzing the accuracy and theoretical uncertainties in the description of spectroscopic observables. Such analysis is first presented for the energies of the single-particle states in spherical and deformed nuclei. It is also shown that the inclusion of particle-vibration coupling improves the description of the energies of predominantly single-particle states in medium and heavy-mass spherical nuclei. However, the remaining differences between theory and experiment clearly indicate missing physics and missing terms in covariant energy density functionals. The uncertainties in the predictions of the position of two-neutron drip line sensitively depend on the uncertainties in the prediction of the energies of the single-particle states. On the other hand, many spectroscopic observables in well deformed nuclei at ground state and finite spin only weakly depend on the choice of covariant energy density functional.
Kinetic-energy density functional: Atoms and shell structure
Garcia-Gonzalez, P.; Alvarellos, J.E.; Chacon, E. |
1996-09-01
We present a nonlocal kinetic-energy functional which includes an anisotropic average of the density through a symmetrization procedure. This functional allows a better description of the nonlocal effects of the electron system. The main consequence of the symmetrization is the appearance of a clear shell structure in the atomic density profiles, obtained after the minimization of the total energy. Although previous results with some of the nonlocal kinetic functionals have given incipient structures for heavy atoms, only our functional shows a clear shell structure for most of the atoms. The atomic total energies have a good agreement with the exact calculations. Discussion of the chemical potential and the first ionization potential in atoms is included. The functional is also extended to spin-polarized systems. {copyright} {ital 1996 The American Physical Society.}
Exploration of a modified density dependence in the Skyrme functional
Erler, J.; Reinhard, P.-G.; Kluepfel, P.
2010-10-15
A variant of the basic Skyrme-Hartree-Fock functional is considered dealing with a new form of density dependence. It employs only integer powers and thus will allow a more sound basis for projection schemes (particle number, angular momentum). We optimize the new functional with exactly the same adjustment strategy as used in an earlier study with a standard Skyrme functional. This allows direct comparisons of the performance of the new functional relative to the standard one. We discuss various observables: bulk properties of finite nuclei, nuclear matter, giant resonances, superheavy elements, and energy systematics. The new functional performs at least as well as the standard one, but offers a wider range of applicability (e.g., for projection) and more flexibility in the regime of high densities.
NASA Astrophysics Data System (ADS)
MacLaren, J. M.; Clougherty, D. P.; McHenry, M. E.; Donovan, M. M.
1991-09-01
Commonly used approximate forms for the exchange-correlation energy and potential within the local density approximation are summarised, and FORTRAN code is included for the evaluation of these various forms. Included are the following: Xα, Kohn-Sham-Gaspàr, Hedin-Lundqvist-Wilkins, Janak-Moruzzi-Williams, Von Barth-Hedin, Ceperley-Alder (Perdew-Zunger), and Ceperley-Alder (Vosko-Wilk-Nusair). Both the Vosko-Wilk-Nusair and the Von Barth-Hedin expressions for spin interpolation between paramagnetic and ferromagnetic limits are also provided.
An Accurate Density Functional from Exchange-Correlation Hole
NASA Astrophysics Data System (ADS)
Tao, Jianmin; Mo, Yuxiang
The exchange-correlation hole is most fundamentally important in the development and understanding of density functional theory (DFT). However, due to the nonlocal nature of the exchange-correlation hole, development of DFT from the underlying hole presents a great challenge, and the works along this direction are limited. Here I will discuss a novel nonempirical DFT based on a semilocal hole, which is obtained from the density matrix expansion. Extensive tests on molecules and solids show that this functional can achieve remarkable accuracy for wide-ranging properties in condensed matter physics and quantum chemistry. This work was supported by NSF under Grant No. CHE-1261918.
Nonlinear eigenvalue problems in Density Functional Theory calculations
Fattebert, J
2009-08-28
Developed in the 1960's by W. Kohn and coauthors, Density Functional Theory (DFT) is a very popular quantum model for First-Principles simulations in chemistry and material sciences. It allows calculations of systems made of hundreds of atoms. Indeed DFT reduces the 3N-dimensional Schroedinger electronic structure problem to the search for a ground state electronic density in 3D. In practice it leads to the search for N electronic wave functions solutions of an energy minimization problem in 3D, or equivalently the solution of an eigenvalue problem with a non-linear operator.
Constrained Density Functional Calculations of alpha and delta Pu
NASA Astrophysics Data System (ADS)
Eriksson, Olle
2002-03-01
The electronic structure of α and δ Pu are described using a modified density functional theory that incorporates localization effects of the 5f shell. It is argued that a Russel-Saunders coupled state involving a 5f^4 multiplet, together with one itinerant 5f electron explains most of the observed ground state properties of δ Pu (equilibrium volume, elastic constants, near degeneracy with the alpha phase). This 5f electrons in the α phase are argued to form itinerant states, that are well described in density functional theory. The two distinctly different electronic ground states give rise to different excitation spectra and a comparison with experimental data is made.
Actinide electronic structure based on the Dirac equation and density functional theory
NASA Astrophysics Data System (ADS)
Wills, John M.; Mattsson, Ann E.
2013-03-01
Density functional theory (DFT) provides a formally predictive basis for predicting the structural properties of actinides. Although available approximations to the exchange/correlation functional provide accurate predictions for many materials, they fail qualitatively and sometimes quantitatively when applied to actinides. Major contributors to this deficiency are an inadequate treatment of confinement physics and an incomplete treatment of relativity in the underlying equations. The development of a functional correctly incorporating confinement physics with a proper treatment of relativity would provide definitive, internally consistent predictions of actinide properties. To enable the development of such a functional and quantify the predictions of currently available functionals, we have developed an efficient first-principles electronic structure method based on the Dirac equation. Results are compared with current methods, and the implications for relativistic density functionals discussed. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Direct propagation of probability density functions in hydrological equations
NASA Astrophysics Data System (ADS)
Kunstmann, Harald; Kastens, Marko
2006-06-01
Sustainable decisions in hydrological risk management require detailed information on the probability density function ( pdf) of the model output. Only then probabilities for the failure of a specific management option or the exceedance of critical thresholds (e.g. of pollutants) can be derived. A new approach of uncertainty propagation in hydrological equations is developed that directly propagates the probability density functions of uncertain model input parameters into the corresponding probability density functions of model output. The basics of the methodology are presented and central applications to different disciplines in hydrology are shown. This work focuses on the following basic hydrological equations: (1) pumping test analysis (Theis-equation, propagation of uncertainties in recharge and transmissivity), (2) 1-dim groundwater contaminant transport equation (Gauss-equation, propagation of uncertainties in decay constant and dispersivity), (3) evapotranspiration estimation (Penman-Monteith-equation, propagation of uncertainty in roughness length). The direct propagation of probability densities is restricted to functions that are monotonically increasing or decreasing or that can be separated in corresponding monotonic branches so that inverse functions can be derived. In case no analytic solutions for inverse functions could be derived, semi-analytical approximations were used. It is shown that the results of direct probability density function propagation are in perfect agreement with results obtained from corresponding Monte Carlo derived frequency distributions. Direct pdf propagation, however, has the advantage that is yields exact solutions for the resulting hydrological pdfs rather than approximating discontinuous frequency distributions. It is additionally shown that the type of the resulting pdf depends on the specific values (order of magnitude, respectively) of the standard deviation of the input pdf. The dependency of skewness and kurtosis
The exact density functional for two electrons in one dimension
NASA Astrophysics Data System (ADS)
Cohen, Aron; Mori-Sanchez, Paula
The exact universal density functional F [ ρ ] is calculated for real space two-electron densities in one dimension ρ (x) with a soft-Coulomb interaction. It is calculated by the Levy constrained search F [ ρ ] =minΨ-->ρ < Ψ | \\Tcirc +\\Vcircee | Ψ > over wavefunctions of a two-dimensional Hilbert space Ψ (x1 ,x2) --> ρ (x1) and can be directly visualized. We do an approximate constrained search via density matrices and a direct approximation to natural orbitals. This allows us to make an accurate approximation to the exact functional that is calculated using a search over potentials. We investigate the exact functional and the performance of many approximations on some of the most challenging electronic structure in two-electron systems, from strongly-correlated electron transfer to the description of a localized-delocalized transition. The exact Kohn-Sham potential, vs (x) , and exact Kohn-Sham eigenvalues, ɛi, are calculated and this allows us to discuss the band-gap problem versus the perspective of the exact density functional F [ ρ ] for all numbers of electrons. We calculate the derivative discontinuity of the exact functional in an example of a Mott-Insulator, one-dimensional stretched H2.
Bakosi, Jozsef; Ristorcelli, Raymond J
2010-01-01
Probability density function (PDF) methods are extended to variable-density pressure-gradient-driven turbulence. We apply the new method to compute the joint PDF of density and velocity in a non-premixed binary mixture of different-density molecularly mixing fluids under gravity. The full time-evolution of the joint PDF is captured in the highly non-equilibrium flow: starting from a quiescent state, transitioning to fully developed turbulence and finally dissipated by molecular diffusion. High-Atwood-number effects (as distinguished from the Boussinesq case) are accounted for: both hydrodynamic turbulence and material mixing are treated at arbitrary density ratios, with the specific volume, mass flux and all their correlations in closed form. An extension of the generalized Langevin model, originally developed for the Lagrangian fluid particle velocity in constant-density shear-driven turbulence, is constructed for variable-density pressure-gradient-driven flows. The persistent small-scale anisotropy, a fundamentally 'non-Kolmogorovian' feature of flows under external acceleration forces, is captured by a tensorial diffusion term based on the external body force. The material mixing model for the fluid density, an active scalar, is developed based on the beta distribution. The beta-PDF is shown to be capable of capturing the mixing asymmetry and that it can accurately represent the density through transition, in fully developed turbulence and in the decay process. The joint model for hydrodynamics and active material mixing yields a time-accurate evolution of the turbulent kinetic energy and Reynolds stress anisotropy without resorting to gradient diffusion hypotheses, and represents the mixing state by the density PDF itself, eliminating the need for dubious mixing measures. Direct numerical simulations of the homogeneous Rayleigh-Taylor instability are used for model validation.
NASA Astrophysics Data System (ADS)
Grüning, M.; Sangalli, D.; Attaccalite, C.
2016-07-01
In the presence of a (time-dependent) macroscopic electric field the electron dynamics of dielectrics cannot be described by the time-dependent density only. We present a real-time formalism that has the density and the macroscopic polarization P as key quantities. We show that a simple local function of P already captures long-range correlation in linear and nonlinear optical response functions. Specifically, after detailing the numerical implementation, we examine the optical absorption, the second- and third-harmonic generation of bulk Si, GaAs, AlAs, and CdTe, at different levels of approximation. We highlight links with ultranonlocal exchange-correlation functional approximations proposed within a linear response time-dependent density functional theory framework.
On the Evolution of the Density Probability Density Function in Strongly Self-gravitating Systems
NASA Astrophysics Data System (ADS)
Girichidis, Philipp; Konstandin, Lukas; Whitworth, Anthony P.; Klessen, Ralf S.
2014-02-01
The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple approximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form PV (ρ)vpropρ-1.54 for the (volume-weighted) PDF and PM (ρ)vpropρ-0.54 for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates (SFRs). Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured SFRs are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall.
On the evolution of the density probability density function in strongly self-gravitating systems
Girichidis, Philipp; Konstandin, Lukas; Klessen, Ralf S.; Whitworth, Anthony P.
2014-02-01
The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple approximate function for the collapse of a sphere. We demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form P{sub V} (ρ)∝ρ{sup –1.54} for the (volume-weighted) PDF and P{sub M} (ρ)∝ρ{sup –0.54} for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates (SFRs). Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured SFRs are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall.
Self-Averaging Stochastic Kohn-Sham Density-Functional Theory
NASA Astrophysics Data System (ADS)
Baer, Roi; Neuhauser, Daniel; Rabani, Eran
2013-09-01
We formulate the Kohn-Sham density functional theory (KS-DFT) as a statistical theory in which the electron density is determined from an average of correlated stochastic densities in a trace formula. The key idea is that it is sufficient to converge the total energy per electron to within a predefined statistical error in order to obtain reliable estimates of the electronic band structure, the forces on nuclei, the density and its moments, etc. The fluctuations in the total energy per electron are guaranteed to decay to zero as the system size increases. This facilitates “self-averaging” which leads to the first ever report of sublinear scaling KS-DFT electronic structure. The approach sidesteps calculation of the density matrix and thus, is insensitive to its evasive sparseness, as demonstrated here for silicon nanocrystals. The formalism is not only appealing in terms of its promise to far push the limits of application of KS-DFT, but also represents a cognitive change in the way we think of electronic structure calculations as this stochastic theory seamlessly converges to the thermodynamic limit.
Accurate hydrogen bond energies within the density functional tight binding method.
Domínguez, A; Niehaus, T A; Frauenheim, T
2015-04-01
The density-functional-based tight-binding (DFTB) approach has been recently extended by incorporating one-center exchange-like terms in the expansion of the multicenter integrals. This goes beyond the Mulliken approximation and leads to a scheme which treats in a self-consistent way the fluctuations of the whole dual density matrix and not only its diagonal elements (Mulliken charges). To date, only the performance of this new formalism to reproduce excited-state properties has been assessed (Domínguez et al. J. Chem. Theory Comput., 2013, 9, 4901-4914). Here we study the effect of our corrections on the computation of hydrogen bond energies for water clusters and water-containing systems. The limitations of traditional DFTB to reproduce hydrogen bonds has been acknowledged often. We compare our results for a set of 22 small water clusters and water-containing systems as well as for five water hexadecamers to those obtained with the DFTB3 method. Additionally, we combine our extension with a third-order energy expansion in the charge fluctuations. Our results show that the new formalisms significantly improve upon original DFTB. PMID:25763597
Simulation of X-ray absorption spectra with orthogonality constrained density functional theory†
Derricotte, Wallace D.; Evangelista, Francesco A.
2015-01-01
Orthogonality constrained density functional theory (OCDFT) is a variational time-independent approach for the computation of electronic excited states. In this work we extend OCDFT to compute core-excited states and generalize the original formalism to determine multiple excited states. Benchmark computations on a set of 13 small molecules and 40 excited states show that unshifted OCDFT/B3LYP excitation energies have a mean absolute error of 1.0 eV. Contrary to time-dependent DFT, OCDFT excitation energies for first- and second-row elements are computed with near-uniform accuracy. OCDFT core excitation energies are insensitive to the choice of the functional and the amount of Hartree–Fock exchange. We show that OCDFT is a powerful tool for the assignment of X-ray absorption spectra of large molecules by simulating the gas-phase near-edge spectrum of adenine and thymine. PMID:25690350
Subsystem real-time time dependent density functional theory
NASA Astrophysics Data System (ADS)
Krishtal, Alisa; Ceresoli, Davide; Pavanello, Michele
2015-04-01
We present the extension of Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) to real-time Time Dependent Density Functional Theory (rt-TDDFT). FDE is a DFT-in-DFT embedding method that allows to partition a larger Kohn-Sham system into a set of smaller, coupled Kohn-Sham systems. Additional to the computational advantage, FDE provides physical insight into the properties of embedded systems and the coupling interactions between them. The extension to rt-TDDFT is done straightforwardly by evolving the Kohn-Sham subsystems in time simultaneously, while updating the embedding potential between the systems at every time step. Two main applications are presented: the explicit excitation energy transfer in real time between subsystems is demonstrated for the case of the Na4 cluster and the effect of the embedding on optical spectra of coupled chromophores. In particular, the importance of including the full dynamic response in the embedding potential is demonstrated.
External orthogonality in subsystem time-dependent density functional theory.
Chulhai, Dhabih V; Jensen, Lasse
2016-08-01
Subsystem density functional theory (subsystem DFT) is a DFT partitioning method that is exact in principle, but depends on approximations to the kinetic energy density functional (KEDF). One may avoid the use of approximate KEDFs by ensuring that the inter-subsystem molecular orbitals are orthogonal, termed external orthogonality (EO). We present a method that extends a subsystem DFT method, that includes EO, into the time-dependent DFT (TDDFT) regime. This method therefore removes the need for approximations to the kinetic energy potential and kernel, and we show that it can accurately reproduce the supermolecular TDDFT results for weakly and strongly coupled subsystems, and for systems with strongly overlapping densities (where KEDF approximations traditionally fail). PMID:26932176
Applying Density Functional Theory for Atomic Vacancies in Solids
NASA Astrophysics Data System (ADS)
Zhou, Xiaolan; Perdew, John P.
2008-03-01
We use a new generalized gradient approximation of density functional theory -- PBEsol, a revised Perdew-Burke-Ernzerhof GGA, to calculate the vacancy formation energies and other properties of metals and semiconductors: Al, Pt, Pd, GaN [1], etc. By restoring the gradient expansion over a wide range of density gradients, PBEsol [2] yields excellent jellium exchange and correlation surface energies. We expect that this new functional will improve the description of vacancies in real materials, since the vacancy formation energy is essentially the work needed to create an interior surface. [1] Thomas R.Mattsson and Ann E. Mattson. Phys. Rev. B 66, 214410 (2002). [2] John P. Perdew, Adrienn Ruzsinszky, Gabor I. Csonka, Oleg A. Vydrov, Gustavo E. Scuseria, Lucian A. Constantin, Xiaolan Zhou, and Kieron Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, http://arxiv.org/abs/0711.0156
Catalytic activities of platinum nanotubes: a density functional study
NASA Astrophysics Data System (ADS)
Mukherjee, Prajna; Gupta, Bikash C.; Jena, Puru
2015-10-01
In this work we investigate the catalytic properties of platinum nanotubes using density functional theory based calculations. In particular, we study the dissociation of hydrogen and oxygen molecules as well as oxidation of CO molecules. The results indicate that platinum nanotubes have good catalytic properties and can be effectively used in converting CO molecule to CO2.
NASA Astrophysics Data System (ADS)
Manzhos, Sergei
2016-01-01
A comparative DFTB (density functional tight binding)-DFT (density functional theory) study of several adsorption modes of 2-anthroic acid on titania is presented. Two parameterizations of DFTB previously used for dye-TiO2 interfaces are tested. DFTB predicts adsorption energies which differ from those computed by DFT not only in magnitude (by up to 0.5 eV) but also in the order among different configurations. The band alignment computed with DFTB is not consistent with DFT results and with experimental data. The strategy of geometry optimization with DFTB followed by single-point DFT calculations also does not necessarily result in plausible adsorption energies.
Reduced density-matrix functionals applied to the Hubbard dimer
NASA Astrophysics Data System (ADS)
Kamil, Ebad; Schade, Robert; Pruschke, Thomas; Blöchl, Peter E.
2016-02-01
Common density-matrix functionals, the Müller and the power functional, have been benchmarked for the half-filled Hubbard dimer, which allows us to model the bond dissociation problem and the transition from the weakly to the strongly correlated limit. Unbiased numerical calculations are combined with analytical results. Despite the well known successes of the Müller functional, the ground state is degenerate with a one-dimensional manifold of ferromagnetic solutions. The resulting infinite magnetic susceptibility indicates another qualitative flaw of the Müller functional. The derivative discontinuity with respect to particle number is not present indicating an incorrect metal-like behavior. The power functional actually favors the ferromagnetic state for weak interaction. Analogous to the Hartree-Fock approximation, the power functional undergoes a transition beyond a critical interaction strength, in this case, however, to a noncollinear antiferromagnetic state.
Density Functional Study of Perovskite Superconductor MgCNi3
NASA Astrophysics Data System (ADS)
Kumar, Jagdish; Sharma, Devina; Kumar, Ranjan; Awana, V. P. S.; Ahluwalia, P. K.
2011-12-01
We here report the first principle density functional study of MgCNi3 which crystallize in cubic perovskite structure having critical transition temperature of 8 K. The interesting aspect of this compound is that in normal state it is non magnetic in nature despite conduction electrons in it are derived from partially filled Ni d states, which typically lead to ferromagnetism in metallic Ni and many Ni-based binary alloys. To investigate the detailed microscopic origin of the non magnetic nature we have done density functional based calculations on this compound. The lattice constant is calculated using minimum energy criteria from total energy versus lattice constant plot. By taking the calculated values of lattice constant we have done the precise calculations on the compound using Full Potential Linear Augmented Plane Wave (FP-LAPW) method implemented in ELK code. The electronic density of states is found spin degenerate that corresponds to a non-magnetic ground state. The density of states (DOS) at Fermi level, N(EF) is dominated by Ni-d states. The sharp peak observed just below Fermi level corresponds to van Hove singularity (vHs). The projected density of states (PDOS) suggests a strong hybridization of Ni-3d and C-2p states which is responsible for the observed non magnetic nature of MgCNi3.
Density functional calculations of point defects in InAs
NASA Astrophysics Data System (ADS)
Moussa, Jonathan; Schultz, Peter
2013-03-01
Standard semilocal density functionals do not generate a gap in the Kohn-Sham eigenvalues for InAs, a semiconductor with an experimental gap of 0.4 eV. Without a theoretical band gap, it becomes difficult to identify, specify, and characterize pure localized states of point defects with energy levels within the experimental band gap. The bulk band gap problem can be alleviated with screened hybrid density functionals, such as the Heyd-Scuseria-Ernzerhof (HSE) functional, that open the generalized Kohn-Sham eigenvalue gap of InAs to near the experimental value. However, even without a Kohn-Sham gap, the local moment countercharge (LMCC) method [Phys. Rev. Lett. 96, 246401 (2006)] is able to predict charge transition energy levels of localized defect states, using standard semi-local functionals. We present an LMCC-based study of standard point defects in InAs using semilocal density functionals and compare the results to HSE-based calculations to assess the validity of LMCC calculations in this situation. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. DOE's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Density Functional Theory of Biologically Relevant Metal Centers
NASA Astrophysics Data System (ADS)
Siegbahn, Per E. M.; Blomberg, Margareta R. A.
1999-10-01
Recent applications of density functional theory to biologically relevant metal centers are reviewed. The emphasis is on reaction mechanisms, structures, and modeling. The accuracy of different functionals is discussed for standard benchmark tests of first- and second-row molecules and for transition metal systems. Modeling aspects of the protein metal complexes are discussed regarding both the size of the model being treated quantum mechanically and the treatment of the protein surrounding it. To illustrate the effects, structures computed without the effects of the protein are compared with experimental structures from enzymes, and results from simple dielectric models of the protein for electron transfer processes are described. The choice of spin state is discussed for multimetal complexes. Examples of mechanisms studied recently by density functional theory are described, such as O2 and methane activation in methane monooxygenase and O2 formation in photosystem II.
Ab initio derivation of model energy density functionals
NASA Astrophysics Data System (ADS)
Dobaczewski, Jacek
2016-08-01
I propose a simple and manageable method that allows for deriving coupling constants of model energy density functionals (EDFs) directly from ab initio calculations performed for finite fermion systems. A proof-of-principle application allows for linking properties of finite nuclei, determined by using the nuclear nonlocal Gogny functional, to the coupling constants of the quasilocal Skyrme functional. The method does not rely on properties of infinite fermion systems but on the ab initio calculations in finite systems. It also allows for quantifying merits of different model EDFs in describing the ab initio results.
Perspective: Fundamental aspects of time-dependent density functional theory
NASA Astrophysics Data System (ADS)
Maitra, Neepa T.
2016-06-01
In the thirty-two years since the birth of the foundational theorems, time-dependent density functional theory has had a tremendous impact on calculations of electronic spectra and dynamics in chemistry, biology, solid-state physics, and materials science. Alongside the wide-ranging applications, there has been much progress in understanding fundamental aspects of the functionals and the theory itself. This Perspective looks back to some of these developments, reports on some recent progress and current challenges for functionals, and speculates on future directions to improve the accuracy of approximations used in this relatively young theory.
Modal density function and number of propagating modes in ducts
NASA Technical Reports Server (NTRS)
Rice, E. J.
1976-01-01
The question of the number of propagating modes within a small range of mode cut off ratio was raised. The population density of modes were shown to be greatest near cut off and least for the well propagating modes. It was shown that modes of nearly the same cut off ratio behave nearly the same in a sound absorbing duct as well as in the way they propagate to the far. Handling all of the propagating modes individually, they can be grouped into several cut off ratio ranges. It is important to know the modal density function to estimate acoustic power distribution.
Yushkov, Konstantin B; Molchanov, Vladimir Ya
2013-09-15
We demonstrate use of the modulation transfer function method in the spectral domain for dynamic measurement of the spectral resolution and modulation contrast of acousto-optic light dispersive delay lines and programmable filters with synthesized transmission. The method is useful for performance characterization of acousto-optic devices for ultrafast pulse shaping and adaptive spectroscopy. PMID:24104818
NASA Astrophysics Data System (ADS)
Xia, Junchao
Orbital-free (OF) density functional theory (DFT) is a powerful and numerically efficient first principles quantum mechanics method. Its application has contributed to understanding a diverse set of materials properties in recent decades. However, most previous studies were confined to simple metals. In this thesis, we focus on extending OFDFT to describe covalently-bonded materials and aiming for a balance between accuracy and efficiency. We first apply OFDFT to study diatomic molecules, with the Huang-Carter (HC) kinetic energy density functional (KEDF). OFDFT predicts reasonable equilibrium bond lengths, bond dissociation energies, and vibrational frequencies compared to Kohn-Sham (KS) DFT benchmarks. This work indicates significant progress of OFDFT in describing molecules. However, we find that the HC KEDF is computationally expensive and thus inapplicable for large-scale simulations. Consequently, we propose an electron density decomposition formalism for covalent materials. Based on local density information, the total density is decomposed into localized and delocalized electron densities, which are then described by different KEDF models separately. The resulting Wang--Govind--Carter-decomposition (WGCD) KEDF gives accurate properties for bulk semiconductors and isolated molecules. Furthermore, it offers far superior numerical efficiency compared to the previous HC KEDF. We then test the HC and WGCD KEDFs on Li-Si alloys and obtain accurate structures and bulk properties. The OFDFT Li adsorption energies on the Si(100) surface are also close to KSDFT values. OFDFT is thus promising to study mechanical properties of Li-Si alloys and the mixing mechanism during lithiation and delithiation processes. We next focus on single-point KEDFs for localized densities and pointwise quantities including the local kinetic energy density (KED) and the electron localization function (ELF). Based on a transferable correlation between the reduced density and the KED
Fragment approach to constrained density functional theory calculations using Daubechies wavelets
Ratcliff, Laura E.; Genovese, Luigi; Mohr, Stephan; Deutsch, Thierry
2015-06-21
In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.
Fragment approach to constrained density functional theory calculations using Daubechies wavelets.
Ratcliff, Laura E; Genovese, Luigi; Mohr, Stephan; Deutsch, Thierry
2015-06-21
In a recent paper, we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions are optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper, we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e., without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments. PMID:26093548
Numerical density-to-potential inversions in time-dependent density functional theory.
Jensen, Daniel S; Wasserman, Adam
2016-08-01
We treat the density-to-potential inverse problem of time-dependent density functional theory as an optimization problem with a partial differential equation constraint. The unknown potential is recovered from a target density by applying a multilevel optimization method controlled by error estimates. We employ a classical optimization routine using gradients efficiently computed by the discrete adjoint method. The inverted potential has both a real and imaginary part to reduce reflections at the boundaries and other numerical artifacts. We demonstrate this method on model one-dimensional systems. The method can be straightforwardly extended to a variety of numerical solvers of the time-dependent Kohn-Sham equations and to systems in higher dimensions. PMID:26984427
SURFACE SYMMETRY ENERGY OF NUCLEAR ENERGY DENSITY FUNCTIONALS
Nikolov, N; Schunck, N; Nazarewicz, W; Bender, M; Pei, J
2010-12-20
We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy density functionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutron-rich matter and description of fission rates for r-process nucleosynthesis.
No need for external orthogonality in subsystem density-functional theory.
Unsleber, Jan P; Neugebauer, Johannes; Jacob, Christoph R
2016-08-01
Recent reports on the necessity of using externally orthogonal orbitals in subsystem density-functional theory (SDFT) [Annu. Rep. Comput. Chem., 8, 2012, 53; J. Phys. Chem. A, 118, 2014, 9182] are re-investigated. We show that in the basis-set limit, supermolecular Kohn-Sham-DFT (KS-DFT) densities can exactly be represented as a sum of subsystem densities, even if the subsystem orbitals are not externally orthogonal. This is illustrated using both an analytical example and in basis-set free numerical calculations for an atomic test case. We further show that even with finite basis sets, SDFT calculations using accurate reconstructed potentials can closely approach the supermolecular KS-DFT density, and that the deviations between SDFT and KS-DFT decrease as the basis-set limit is approached. Our results demonstrate that formally, there is no need to enforce external orthogonality in SDFT, even though this might be a useful strategy when developing projection-based DFT embedding schemes. PMID:26878703
Scrutinizing "Invisible" astatine: A challenge for modern density functionals.
Sergentu, Dumitru-Claudiu; David, Grégoire; Montavon, Gilles; Maurice, Rémi; Galland, Nicolas
2016-06-01
The main-group 6p elements did not receive much attention in the development of recent density functionals. In many cases it is still difficult to choose among the modern ones a relevant functional for various applications. Here, we illustrate the case of astatine species (At, Z = 85) and we report the first, and quite complete, benchmark study on several properties concerning such species. Insights on geometries, transition energies and thermodynamic properties of a set of 19 astatine species, for which reference experimental or theoretical data has been reported, are obtained with relativistic (two-component) density functional theory calculations. An extensive set of widely used functionals is employed. The hybrid meta-generalized gradient approximation (meta-GGA) PW6B95 functional is overall the best choice. It is worth noting that the range-separated HSE06 functional as well as the old and very popular B3LYP and PBE0 hybrid-GGAs appear to perform quite well too. Moreover, we found that astatine chemistry in solution can accurately be predicted using implicit solvent models, provided that specific parameters are used to build At cavities. © 2016 Wiley Periodicals, Inc. PMID:27059181
Verreck, Devin Groeseneken, Guido; Verhulst, Anne S.; Mocuta, Anda; Collaert, Nadine; Thean, Aaron; Van de Put, Maarten; Magnus, Wim; Sorée, Bart
2015-10-07
Efficient quantum mechanical simulation of tunnel field-effect transistors (TFETs) is indispensable to allow for an optimal configuration identification. We therefore present a full-zone 15-band quantum mechanical solver based on the envelope function formalism and employing a spectral method to reduce computational complexity and handle spurious solutions. We demonstrate the versatility of the solver by simulating a 40 nm wide In{sub 0.53}Ga{sub 0.47}As lineTFET and comparing it to p-n-i-n configurations with various pocket and body thicknesses. We find that the lineTFET performance is not degraded compared to semi-classical simulations. Furthermore, we show that a suitably optimized p-n-i-n TFET can obtain similar performance to the lineTFET.
Marin, F. P.
2014-01-01
We study the I-V characteristic of mesoscopic systems or quantum dot (QD) attached to a pair of superconducting leads. Interaction effects in the QD are considered through the charging energy of the QD; that is, the treatment of current transport under a voltage bias is performed within a coupled Poisson nonequilibrium Green function (PNEGF) formalism. We derive the expression for the current in full generality but consider only the regime where transport occurs only via a single particle current. We show for this case and for various charging energies values U 0 and associated capacitances of the QD the effect on the I-V characteristic. Also the influence of the coupling constants on the I-V characteristic is investigated. Our approach puts forward a novel interpretation of experiments in the strong Coulomb regime. PMID:24977220
What Density Functional Theory could do for Quantum Information
NASA Astrophysics Data System (ADS)
Mattsson, Ann
2015-03-01
The Hohenberg-Kohn theorem of Density Functional Theory (DFT), and extensions thereof, tells us that all properties of a system of electrons can be determined through their density, which uniquely determines the many-body wave-function. Given access to the appropriate, universal, functionals of the density we would, in theory, be able to determine all observables of any electronic system, without explicit reference to the wave-function. On the other hand, the wave-function is at the core of Quantum Information (QI), with the wave-function of a set of qubits being the central computational resource in a quantum computer. While there is seemingly little overlap between DFT and QI, reliance upon observables form a key connection. Though the time-evolution of the wave-function and associated phase information is fundamental to quantum computation, the initial and final states of a quantum computer are characterized by observables of the system. While observables can be extracted directly from a system's wave-function, DFT tells us that we may be able to intuit a method for extracting them from its density. In this talk, I will review the fundamentals of DFT and how these principles connect to the world of QI. This will range from DFT's utility in the engineering of physical qubits, to the possibility of using it to efficiently (but approximately) simulate Hamiltonians at the logical level. The apparent paradox of describing algorithms based on the quantum mechanical many-body wave-function with a DFT-like theory based on observables will remain a focus throughout. The ultimate goal of this talk is to initiate a dialog about what DFT could do for QI, in theory and in practice. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Dynamical density functional theory for colloidal dispersions including hydrodynamic interactions
NASA Astrophysics Data System (ADS)
Rex, M.; Löwen, H.
2009-02-01
A dynamical density functional theory (DDFT) for translational Brownian dynamics is derived which includes hydrodynamic interactions. The theory reduces to the simple Brownian DDFT proposed by Marconi and Tarazona (U. Marini Bettolo Marconi and P. Tarazona, J. Chem. Phys. 110, 8032 (1999); J. Phys.: Condens. Matter 12, A413 (2000)) when hydrodynamic interactions are neglected. The derivation is based on Smoluchowski’s equation for the time evolution of the probability density with pairwise hydrodynamic interactions. The theory is applied to hard-sphere colloids in an oscillating spherical optical trap which switches periodically in time from a stable confining to an unstable potential. Rosenfeld’s fundamental measure theory for the equilibrium density functional is used and hydrodynamics are incorporated on the Rotne-Prager level. The results for the time-dependent density profiles are compared to extensive Brownian dynamics simulations which are performed on the same Rotne-Prager level and excellent agreement is obtained. It is further found that hydrodynamic interactions damp and slow the dynamics of the confined colloid cluster in comparison to the same situation with neglected hydrodynamic interactions.
A formal approach to detect functionally irrelevant barriers in MPI programs.
Sharma, S.; Vakkalanka, S.; Gopalakrishnan, G.; Kirby, R. M.; Thakur, R.; Gropp, W.
2008-01-01
We examine the unsolved problem of automatically and efficiently detecting functionally irrelevant barriers in MPI programs. A functionally irrelevant barrier is a set of MPI-Barrier calls, one per MPI process, such that their removal does not alter the overall MPI communication structure of the program. Static analysis methods are incapable of solving this problem, as MPI programs can compute many quantities at runtime, including send targets, receive sources, tags, and communicators, and also can have data-dependent control flows. We offer an algorithm called Fib to solve this problem based on dynamic (runtime) analysis. Fib applies to MPI programs that employ 24 widely used two-sided MPI operations. We show that it is sufficient to detect barrier calls whose removal causes a wildcard receive statement placed before or after a barrier to now begin matching a send statement with which it did not match before. Fib determines whether a barrier becomes relevant in any interleaving of the MPI processes of a given MPI program. Since the number of interleavings can grow exponentially with the number of processes, Fib employs a sound method to drastically reduce this number, by computing only the relevant interleavings. We show that many MPI programs do not have data dependent control flows, thus making the results of Fib applicable to all the input data the program can accept.
Density Functional Theory for Steady-State Nonequilibrium Molecular Junctions
NASA Astrophysics Data System (ADS)
Liu, Shuanglong; Nurbawono, Argo; Zhang, Chun
2015-10-01
We present a density functional theory (DFT) for steady-state nonequilibrium quantum systems such as molecular junctions under a finite bias. Based on the steady-state nonequilibrium statistics that maps nonequilibrium to an effective equilibrium, we show that ground-state DFT (GS-DFT) is not applicable in this case and two densities, the total electron density and the density of current-carrying electrons, are needed to uniquely determine the properties of the corresponding nonequilibrium system. A self-consistent mean-field approach based on two densities is then derived. The theory is implemented into SIESTA computational package and applied to study nonequilibrium electronic/transport properties of a realistic carbon-nanotube (CNT)/Benzene junction. Results obtained from our steady-state DFT (SS-DFT) are compared with those of conventional GS-DFT based transport calculations. We show that SS-DFT yields energetically more stable nonequilibrium steady state, predicts significantly lower electric current, and is able to produce correct electronic structures in local equilibrium under a limiting case.
Excitations and benchmark ensemble density functional theory for two electrons
Pribram-Jones, Aurora; Burke, Kieron; Yang, Zeng-hui; Ullrich, Carsten A.; Trail, John R.; Needs, Richard J.
2014-05-14
A new method for extracting ensemble Kohn-Sham potentials from accurate excited state densities is applied to a variety of two-electron systems, exploring the behavior of exact ensemble density functional theory. The issue of separating the Hartree energy and the choice of degenerate eigenstates is explored. A new approximation, spin eigenstate Hartree-exchange, is derived. Exact conditions that are proven include the signs of the correlation energy components and the asymptotic behavior of the potential for small weights of the excited states. Many energy components are given as a function of the weights for two electrons in a one-dimensional flat box, in a box with a large barrier to create charge transfer excitations, in a three-dimensional harmonic well (Hooke's atom), and for the He atom singlet-triplet ensemble, singlet-triplet-singlet ensemble, and triplet bi-ensemble.
Analyzing the financial crisis using the entropy density function
NASA Astrophysics Data System (ADS)
Oh, Gabjin; Kim, Ho-yong; Ahn, Seok-Won; Kwak, Wooseop
2015-02-01
The risk that is created by nonlinear interactions among subjects in economic systems is assumed to increase during an abnormal state of a financial market. Nevertheless, investigating the systemic risk in financial markets following the global financial crisis is not sufficient. In this paper, we analyze the entropy density function in the return time series for several financial markets, such as the S&P500, KOSPI, and DAX indices, from October 2002 to December 2011 and analyze the variability in the entropy value over time. We find that the entropy density function of the S&P500 index during the subprime crisis exhibits a significant decrease compared to that in other periods, whereas the other markets, such as those in Germany and Korea, exhibit no significant decrease during the market crisis. These findings demonstrate that the S&P500 index generated a regular pattern in the return time series during the financial crisis.
Covariant density functional theory: The role of the pion
Lalazissis, G. A.; Karatzikos, S.; Serra, M.; Otsuka, T.; Ring, P.
2009-10-15
We investigate the role of the pion in covariant density functional theory. Starting from conventional relativistic mean field (RMF) theory with a nonlinear coupling of the {sigma} meson and without exchange terms we add pions with a pseudovector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of density functionals does not destroy the overall description of the bulk properties by RMF. On the other hand, the noncentral contribution of the pion (tensor coupling) does have effects on single particle energies and on binding energies of certain nuclei.
Neutrinoless double-beta decay in covariant density functional theory
Ring, P.; Yao, J. M.; Song, L. S.; Hagino, K.; Meng, J.
2015-10-15
We use covariant density functional theory beyond mean field in order to describe neutrinoless double-beta decay in a fully relativistic way. The dynamic effects of particle-number and angular-momentum conservations as well as shape fluctuations of quadrupole character are taken into account within the generator coordinate method for both initial and final nuclei. The calculations are based on the full relativistic transition operator. The nuclear matrix elements (NME’s) for a large number of possible transitions are investigated. The results are compared with various non-relativistic calculations, in particular also with the density functional theory based on the Gogny force. We find that the non-relativistic approximation is justified and that the total NME’s can be well approximated by the pure axial-vector coupling term. This corresponds to a considerable reduction of the computational effort.
Density-functional theory of inhomogeneous systems of hard spherocylinders
Velasco; Mederos; Sullivan
2000-09-01
The smectic-A phase boundaries of a hard-spherocylinder fluid are calculated using a density-functional theory based on one proposed earlier by Somoza and Tarazona [Phys. Rev. A 41, 965 (1990)]. Our calculations do not employ the translation-rotation decoupling approximation used in previous density-functional theories. The calculated phase boundaries agree well with computer simulation results up to aspect ratios L/D approximately 5 and are in better agreement with the simulations than are previous theories. We generalize the model fluid by including long-range interactions with quadrupolar orientational symmetry, which are taken into account by mean-field approximation. For sufficiently large strength, these interactions produce a smectic-C phase, which undergoes either a continuous or weakly first-order transition to the smectic-A phase. The theory and numerical methods discussed here can be applied to the analysis of interfacial phenomena. PMID:11088887
Neutrinoless double-beta decay in covariant density functional theory
NASA Astrophysics Data System (ADS)
Ring, P.; Yao, J. M.; Song, L. S.; Hagino, K.; Meng, J.
2015-10-01
We use covariant density functional theory beyond mean field in order to describe neutrinoless double-beta decay in a fully relativistic way. The dynamic effects of particle-number and angular-momentum conservations as well as shape fluctuations of quadrupole character are taken into account within the generator coordinate method for both initial and final nuclei. The calculations are based on the full relativistic transition operator. The nuclear matrix elements (NME's) for a large number of possible transitions are investigated. The results are compared with various non-relativistic calculations, in particular also with the density functional theory based on the Gogny force. We find that the non-relativistic approximation is justified and that the total NME's can be well approximated by the pure axial-vector coupling term. This corresponds to a considerable reduction of the computational effort.
Density versus spin-density functional in DFT+U and DFT+DMFT
NASA Astrophysics Data System (ADS)
Park, Hyowon; Millis, Andrew; Marianetti, Chris
2015-03-01
The construction of multi-variable effective action theories such as DFT+U and DFT+DMFT requires the choice of a local subspace of correlated orbitals and an additional variable being either the charge density or spin density. This talk examines the differences between using charge-only and spin-dependent exchange-correlation functionals with the aim of providing guidance for constructing more sophisticated beyond-density functional theories. The widely used spin-dependent approximations to the exchange-correlation functional are found to lead to a large and in some cases unphysical effective exchange coupling within the correlated subspace. Additionally, the differences between Wannier and Projector based definitions of the correlated orbitals are examined, and only small differences are found provided that the orbitals are orthonormal and strongly localized. These results are documented in the context of the rare earth nickelates. This work is supported under the Grant DOE-ER-046169 and under the FAME grant, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA.
Śmiga, Szymon; Fabiano, Eduardo; Laricchia, Savio; Constantin, Lucian A; Della Sala, Fabio
2015-04-21
We analyze the methodology and the performance of subsystem density functional theory (DFT) with meta-generalized gradient approximation (meta-GGA) exchange-correlation functionals for non-bonded molecular systems. Meta-GGA functionals depend on the Kohn-Sham kinetic energy density (KED), which is not known as an explicit functional of the density. Therefore, they cannot be directly applied in subsystem DFT calculations. We propose a Laplacian-level approximation to the KED which overcomes this limitation and provides a simple and accurate way to apply meta-GGA exchange-correlation functionals in subsystem DFT calculations. The so obtained density and energy errors, with respect to the corresponding supermolecular calculations, are comparable with conventional approaches, depending almost exclusively on the approximations in the non-additive kinetic embedding term. An embedding energy error decomposition explains the accuracy of our method. PMID:25903880
Autoionization in time-dependent density-functional theory
NASA Astrophysics Data System (ADS)
Kapoor, V.
2016-06-01
We compute the exact exchange-correlation potential of the time-dependent density-functional theory (TDDFT) for the correlated process of autoionization. The potential develops barriers which regulate the autoionization rate. TDDFT employing known and practicable exchange-correlation potentials does not capture any autoionization dynamics. Approximate exchange-correlation potentials capturing such dynamics would necessarily require memory effects and are unlikely to be developed, as will be illustrated.
Density functional theory across chemistry, physics and biology
van Mourik, Tanja; Bühl, Michael; Gaigeot, Marie-Pierre
2014-01-01
The past decades have seen density functional theory (DFT) evolve from a rising star in computational quantum chemistry to one of its major players. This Theme Issue, which comes half a century after the publication of the Hohenberg–Kohn theorems that laid the foundations of modern DFT, reviews progress and challenges in present-day DFT research. Rather than trying to be comprehensive, this Theme Issue attempts to give a flavour of selected aspects of DFT. PMID:24516181
Association between lung function and airway wall density
NASA Astrophysics Data System (ADS)
Leader, J. Ken; Zheng, Bin; Fuhrman, Carl R.; Tedrow, John; Park, Sang C.; Tan, Jun; Pu, Jiantao; Drescher, John M.; Gur, David; Sciurba, Frank C.
2009-02-01
Computed tomography (CT) examination is often used to quantify the relation between lung function and airway remodeling in chronic obstructive pulmonary disease (COPD). In this preliminary study, we examined the association between lung function and airway wall computed attenuation ("density") in 200 COPD screening subjects. Percent predicted FVC (FVC%), percent predicted FEV1 (FEV1%), and the ratio of FEV1 to FVC as a percentage (FEV1/FVC%) were measured post-bronchodilator. The apical bronchus of the right upper lobe was manually selected from CT examinations for evaluation. Total airway area, lumen area, wall area, lumen perimeter and wall area as fraction of the total airway area were computed. Mean HU (meanHU) and maximum HU (maxHU) values were computed across pixels assigned membership in the wall and with a HU value greater than -550. The Pearson correlation coefficients (PCC) between FVC%, FEV1%, and FEV1/FVC% and meanHU were -0.221 (p = 0.002), -0.175 (p = 0.014), and -0.110 (p = 0.123), respectively. The PCCs for maxHU were only significant for FVC%. The correlations between lung function and the airway morphometry parameters were slightly stronger compared to airway wall density. MeanHU was significantly correlated with wall area (PCC = 0.720), airway area (0.498) and wall area percent (0.611). This preliminary work demonstrates that airway wall density is associated with lung function. Although the correlations in our study were weaker than a recent study, airway wall density initially appears to be an important parameter in quantitative CT analysis of COPD.
Probability Density Function Method for Langevin Equations with Colored Noise
Wang, Peng; Tartakovsky, Alexandre M.; Tartakovsky, Daniel M.
2013-04-05
We present a novel method to derive closed-form, computable PDF equations for Langevin systems with colored noise. The derived equations govern the dynamics of joint or marginal probability density functions (PDFs) of state variables, and rely on a so-called Large-Eddy-Diffusivity (LED) closure. We demonstrate the accuracy of the proposed PDF method for linear and nonlinear Langevin equations, describing the classical Brownian displacement and dispersion in porous media.
Density functional theory across chemistry, physics and biology.
van Mourik, Tanja; Bühl, Michael; Gaigeot, Marie-Pierre
2014-03-13
The past decades have seen density functional theory (DFT) evolve from a rising star in computational quantum chemistry to one of its major players. This Theme Issue, which comes half a century after the publication of the Hohenberg-Kohn theorems that laid the foundations of modern DFT, reviews progress and challenges in present-day DFT research. Rather than trying to be comprehensive, this Theme Issue attempts to give a flavour of selected aspects of DFT. PMID:24516181
Probability density function modeling for sub-powered interconnects
NASA Astrophysics Data System (ADS)
Pater, Flavius; Amaricǎi, Alexandru
2016-06-01
This paper proposes three mathematical models for reliability probability density function modeling the interconnect supplied at sub-threshold voltages: spline curve approximations, Gaussian models,and sine interpolation. The proposed analysis aims at determining the most appropriate fitting for the switching delay - probability of correct switching for sub-powered interconnects. We compare the three mathematical models with the Monte-Carlo simulations of interconnects for 45 nm CMOS technology supplied at 0.25V.
Next generation high density self assembling functional protein arrays
Ramachandran, Niroshan; Raphael, Jacob V.; Hainsworth, Eugenie; Demirkan, Gokhan; Fuentes, Manuel G.; Rolfs, Andreas; Hu, Yanhui; LaBaer, Joshua
2009-01-01
We report a high-density self assembling protein microarray that displays thousands of proteins, produced and captured in situ from immobilized cDNA templates. Over 1500 unique cDNAs were tested with > 90% success with nearly all proteins displaying yields within 2 fold of the mean, minimal sample variation and good day to day reproducibility. The displayed proteins revealed selective protein interactions. This method will enable various experimental approaches to study protein function in high throughput. PMID:18469824
Plato: A localised orbital based density functional theory code
NASA Astrophysics Data System (ADS)
Kenny, S. D.; Horsfield, A. P.
2009-12-01
The Plato package allows both orthogonal and non-orthogonal tight-binding as well as density functional theory (DFT) calculations to be performed within a single framework. The package also provides extensive tools for analysing the results of simulations as well as a number of tools for creating input files. The code is based upon the ideas first discussed in Sankey and Niklewski (1989) [1] with extensions to allow high-quality DFT calculations to be performed. DFT calculations can utilise either the local density approximation or the generalised gradient approximation. Basis sets from minimal basis through to ones containing multiple radial functions per angular momenta and polarisation functions can be used. Illustrations of how the package has been employed are given along with instructions for its utilisation. Program summaryProgram title: Plato Catalogue identifier: AEFC_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEFC_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 219 974 No. of bytes in distributed program, including test data, etc.: 1 821 493 Distribution format: tar.gz Programming language: C/MPI and PERL Computer: Apple Macintosh, PC, Unix machines Operating system: Unix, Linux and Mac OS X Has the code been vectorised or parallelised?: Yes, up to 256 processors tested RAM: Up to 2 Gbytes per processor Classification: 7.3 External routines: LAPACK, BLAS and optionally ScaLAPACK, BLACS, PBLAS, FFTW Nature of problem: Density functional theory study of electronic structure and total energies of molecules, crystals and surfaces. Solution method: Localised orbital based density functional theory. Restrictions: Tight-binding and density functional theory only, no exact exchange. Unusual features: Both atom centred and uniform meshes available
Advances in time-dependent current-density functional theory
NASA Astrophysics Data System (ADS)
Berger, Arjan
In this work we solve the problem of the gauge dependence of molecular magnetic properties (magnetizabilities, circular dichroism) using time-dependent current-density functional theory [1]. We also present a new functional that accurately describes the optical absorption spectra of insulators, semiconductors and metals [2] N. Raimbault, P.L. de Boeij, P. Romaniello, and J.A. Berger Phys. Rev. Lett. 114, 066404 (2015) J.A. Berger, Phys. Rev. Lett. 115, 137402 (2015) This study has been partially supported through the Grant NEXT No. ANR-10-LABX-0037 in the framework of the Programme des Investissements d'Avenir.
Thermal Corrections to Density Functional Simulations of Warm Dense Matter
NASA Astrophysics Data System (ADS)
Smith, Justin; Pribram-Jones, Aurora; Burke, Kieron
Present density functional calculations of warm dense matter often use the Mermin-Kohn-Sham (MKS) scheme at finite temperature, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable non-trivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies, the exact Mermin-Kohn-Sham functionals for this system, and extract the exact XC free energy. For moderate temperatures and weak correlation, we show this approximation is excellent, but fails for stronger correlations. Additionally, we use this system to test various conditions that must be satisfied.
Linear Scaling Density Functional Calculations with Gaussian Orbitals
NASA Technical Reports Server (NTRS)
Scuseria, Gustavo E.
1999-01-01
Recent advances in linear scaling algorithms that circumvent the computational bottlenecks of large-scale electronic structure simulations make it possible to carry out density functional calculations with Gaussian orbitals on molecules containing more than 1000 atoms and 15000 basis functions using current workstations and personal computers. This paper discusses the recent theoretical developments that have led to these advances and demonstrates in a series of benchmark calculations the present capabilities of state-of-the-art computational quantum chemistry programs for the prediction of molecular structure and properties.
Conformational Analysis of Thioether Musks Using Density Functional Theory
Setzer, William N.
2009-01-01
A conformational analysis of nine macrocyclic thioether musks has been carried out using molecular mechanics (MMFF), density functional theory (DFT) using both B3LYP and M06 functionals, as well as Hartree-Fock and post-Hartree-Fock (MP2) ab initio methods. 6-Thia-, 10-thia- and 4-methyl-5-thia-14-tetradecananolide, 4-thia-, 7-thia-, 11-thia- and 12-thia-15-pentadecanolide and 6-thia- and 12-thia-16-hexadecanolide were modeled. Unfortunately, there was little agreement between the computational methods at the levels of theory used in this study. PMID:20111690
Atomistic force field for alumina fit to density functional theory
Sarsam, Joanne; Finnis, Michael W.; Tangney, Paul
2013-11-28
We present a force field for bulk alumina (Al{sub 2}O{sub 3}), which has been parametrized by fitting the energies, forces, and stresses of a large database of reference configurations to those calculated with density functional theory (DFT). We use a functional form that is simpler and computationally more efficient than some existing models of alumina parametrized by a similar technique. Nevertheless, we demonstrate an accuracy of our potential that is comparable to those existing models and to DFT. We present calculations of crystal structures and energies, elastic constants, phonon spectra, thermal expansion, and point defect formation energies.
Franco-Pérez, Marco; Ayers, Paul W; Gázquez, José L; Vela, Alberto
2015-12-28
We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model. PMID:26723661
Franco-Pérez, Marco E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx; Ayers, Paul W. E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx; Gázquez, José L. E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx; Vela, Alberto E-mail: ayers@mcmaster.ca E-mail: avela@cinvestav.mx
2015-12-28
We explore the local and nonlocal response functions of the grand canonical potential density functional at nonzero temperature. In analogy to the zero-temperature treatment, local (e.g., the average electron density and the local softness) and nonlocal (e.g., the softness kernel) intrinsic response functions are defined as partial derivatives of the grand canonical potential with respect to its thermodynamic variables (i.e., the chemical potential of the electron reservoir and the external potential generated by the atomic nuclei). To define the local and nonlocal response functions of the electron density (e.g., the Fukui function, the linear density response function, and the dual descriptor), we differentiate with respect to the average electron number and the external potential. The well-known mathematical relationships between the intrinsic response functions and the electron-density responses are generalized to nonzero temperature, and we prove that in the zero-temperature limit, our results recover well-known identities from the density functional theory of chemical reactivity. Specific working equations and numerical results are provided for the 3-state ensemble model.
Adsorption of Ar on planar surfaces studied with a density functional theory.
Sartarelli, Salvador A; Szybisz, Leszek
2009-11-01
The adsorption of Ar on planar structureless substrates of alkali metals, alkaline-earth metal Mg, CO2 , and Au was analyzed by applying a density functional formalism which includes a recently proposed effective attractive pair potential conditioned to Ar. It is shown that this approach reproduces the experimental surface tension of the liquid-vapor interface over the entire bulk coexistence curve for temperatures T spanning from the triple point Tt up to the critical point Tc. The wetting properties were studied over the entire range temperatures Tt<-->Tc. It was found that Ar wets all the investigated surfaces. The adsorption isotherms for alkali metals exhibit first-order phase transitions. Prewetting lines were resolved even for the less attractive surfaces. In the cases of Mg, CO2 , and Au a continuous growth for T> or =Tt was obtained. A comparison with experimental data and other microscopic calculations is reported. PMID:20365027
NASA Astrophysics Data System (ADS)
Zhou, Shan-Gui
2016-06-01
The intrinsic nuclear shapes deviating from a sphere not only manifest themselves in nuclear collective states but also play important roles in determining nuclear potential energy surfaces (PES’s) and fission barriers. In order to describe microscopically and self-consistently nuclear shapes and PES’s with as many shape degrees of freedom as possible included, we developed multidimensionally constrained covariant density functional theories (MDC-CDFTs). In MDC-CDFTs, the axial symmetry and the reflection symmetry are both broken and all deformations characterized by {β }λ μ with even μ are considered. We have used the MDC-CDFTs to study PES’s and fission barriers of actinides, the non-axial octupole Y 32 correlations in N = 150 isotones and shapes of hypernuclei. In this Review we will give briefly the formalism of MDC-CDFTs and present the applications to normal nuclei.
Analytic cubic and quartic force fields using density-functional theory
Ringholm, Magnus; Gao, Bin; Thorvaldsen, Andreas J.; Ruud, Kenneth; Jonsson, Dan; Bast, Radovan; Ekström, Ulf; Helgaker, Trygve
2014-01-21
We present the first analytic implementation of cubic and quartic force constants at the level of Kohn–Sham density-functional theory. The implementation is based on an open-ended formalism for the evaluation of energy derivatives in an atomic-orbital basis. The implementation relies on the availability of open-ended codes for evaluation of one- and two-electron integrals differentiated with respect to nuclear displacements as well as automatic differentiation of the exchange–correlation kernels. We use generalized second-order vibrational perturbation theory to calculate the fundamental frequencies of methane, ethane, benzene, and aniline, comparing B3LYP, BLYP, and Hartree–Fock results. The Hartree–Fock anharmonic corrections agree well with the B3LYP corrections when calculated at the B3LYP geometry and from B3LYP normal coordinates, suggesting that the inclusion of electron correlation is not essential for the reliable calculation of cubic and quartic force constants.
Impact ionization in GaAs: A screened exchange density-functional approach
Picozzi, S.; Asahi, R.; Geller, C. B.; Continenza, A.; Freeman, A. J.
2001-08-13
Results are presented of a fully ab initio calculation of impact ionization rates in GaAs within the density functional theory framework, using a screened-exchange formalism and the highly precise all-electron full-potential linearized augmented plane wave method. The calculated impact ionization rates show a marked orientation dependence in k space, indicating the strong restrictions imposed by the conservation of energy and momentum. This anisotropy diminishes as the impacting electron energy increases. A Keldysh type fit performed on the energy-dependent rate shows a rather soft edge and a threshold energy greater than the direct band gap. The consistency with available Monte Carlo and empirical pseudopotential calculations shows the reliability of our approach and paves the way to ab initio calculations of pair production rates in new and more complex materials.
Analytic cubic and quartic force fields using density-functional theory.
Ringholm, Magnus; Jonsson, Dan; Bast, Radovan; Gao, Bin; Thorvaldsen, Andreas J; Ekström, Ulf; Helgaker, Trygve; Ruud, Kenneth
2014-01-21
We present the first analytic implementation of cubic and quartic force constants at the level of Kohn-Sham density-functional theory. The implementation is based on an open-ended formalism for the evaluation of energy derivatives in an atomic-orbital basis. The implementation relies on the availability of open-ended codes for evaluation of one- and two-electron integrals differentiated with respect to nuclear displacements as well as automatic differentiation of the exchange-correlation kernels. We use generalized second-order vibrational perturbation theory to calculate the fundamental frequencies of methane, ethane, benzene, and aniline, comparing B3LYP, BLYP, and Hartree-Fock results. The Hartree-Fock anharmonic corrections agree well with the B3LYP corrections when calculated at the B3LYP geometry and from B3LYP normal coordinates, suggesting that the inclusion of electron correlation is not essential for the reliable calculation of cubic and quartic force constants. PMID:25669359
Density functional theory and chromium: Insights from the dimers
Würdemann, Rolf; Kristoffersen, Henrik H.; Moseler, Michael; Walter, Michael
2015-03-28
The binding in small Cr clusters is re-investigated, where the correct description of the dimer in three charge states is used as criterion to assign the most suitable density functional theory approximation. The difficulty in chromium arises from the subtle interplay between energy gain from hybridization and energetic cost due to exchange between s and d based molecular orbitals. Variations in published bond lengths and binding energies are shown to arise from insufficient numerical representation of electron density and Kohn-Sham wave-functions. The best functional performance is found for gradient corrected (GGA) functionals and meta-GGAs, where we find severe differences between functionals from the same family due to the importance of exchange. Only the “best fit” from Bayesian error estimation is able to predict the correct energetics for all three charge states unambiguously. With this knowledge, we predict small bond-lengths to be exclusively present in Cr{sub 2} and Cr{sub 2}{sup −}. Already for the dimer cation, solely long bond-lengths appear, similar to what is found in the trimer and in chromium bulk.
Curvature and Frontier Orbital Energies in Density Functional Theory
Stein, Tamar; Autschbach, Jochen; Govind, Niranjan; Kronik, Leeor; Baer, Roi
2012-12-20
Perdew et al. [Phys. Rev. Lett 49, 1691 (1982)] discovered and proved two different properties that exact Kohn-Sham density functional theory (DFT) must obey: (i) The exact total energy versus particle number must be a series of linear segments between integer electron points; (ii) Across an integer number of electrons, the exchange-correlation potential may ``jump’’ by a constant, known as the derivative discontinuity (DD). Here, we show analytically that in both the original and the generalized Kohn-Sham formulation of DFT, the two are in fact two sides of the same coin. Absence of a derivative discontinuity necessitates deviation from piecewise linearity, and the latter can be used to correct for the former, thereby restoring the physical meaning of the orbital energies. Using selected small molecules, we show that this results in a simple correction scheme for any underlying functional, including semi-local and hybrid functionals as well as Hartree-Fock theory, suggesting a practical correction for the infamous gap problem of density functional theory. Moreover, we show that optimally-tuned range-separated hybrid functionals can inherently minimize both DD and curvature, thus requiring no correction, and show that this can be used as a sound theoretical basis for novel tuning strategies.
Van der Waals Density Functional Theory with Applications
NASA Astrophysics Data System (ADS)
Langreth, David C.
2004-03-01
We discuss the development of electronic density functionals that are applicable for weakly bound systems where the van der Waals interaction and its ramifications become important. Our current functionals approach the correct asymptotic dependence at large distances and are seamless at small distances. The first form of the functional, appropriate for layered systems, has been recently applied to graphite, boron nitride, and molybdenum sulfide [H. Rydberg et al., Phys. Rev. Lett. 91, 126402 (2003) and D. C. Langreth, Int. J. Quant. Chem. (submitted), see http//:www.physics.rutgers.edu/ ˜langreth/preprints/dft2003.pdf]. The second form of the functional [M. Dion it et al. (to be published)] is appropriate for arbitrary geometries. Recent results on rare gas dimers and the benzene dimer suggest promise for this method as well.
Theoretical and numerical assessments of spin-flip time-dependent density functional theory
NASA Astrophysics Data System (ADS)
Li, Zhendong; Liu, Wenjian
2012-01-01
Spin-flip time-dependent density functional theory (SF-TD-DFT) with the full noncollinear hybrid exchange-correlation kernel and its approximate variants are critically assessed, both formally and numerically. As demonstrated by the ethylene torsion and the C2v ring-opening of oxirane, SF-TD-DFT is very useful for describing nearly degenerate situations. However, it may occasionally yield unphysical results. This stems from the noncollinear form of the generalized gradient approximation, which becomes numerically instable in the presence of spin-flip excitations from the closed- to vacant-shell orbitals of an open-shell reference. To cure this defect, a simple modification, dubbed as ALDA0, is proposed in the spirit of adiabatic local density approximation (ALDA). It is applicable to all kinds of density functionals and yields stable results without too much loss of accuracy. In particular, the combination of ALDA0 with the Tamm-Dancoff approximation is a promising tool for studying global potential energy surfaces. In addition to the kernel problem, SF-TD-DFT is also rather sensitive to the choice of reference states, as demonstrated by the spin multiplet states of closed-shell molecules of H2O, CH2O, and C2H4. Surprisingly, SF-TD-DFT with pure density functionals may also fail for valance excitations with large orbital overlaps, at variance with the spin-conserving counterpart (SC-TD-DFT). In this case, the inclusion of a large amount of Hartree-Fock exchange is mandatory for quantitative results. Nonetheless, for spatially degenerate cases such as CF, CH, and NH+, SF-TD-DFT is more advantageous than SC-TD-DFT, unless the latter is also space adapted. These findings are very instructive for future development and applications of TD-DFT.
2007 Time_Dependent Density-Functional Therory (July 15-20, 2007 Colby College, Maine)
Ullrich Carsten Nancy Ryan Gray
2008-09-19
Time-dependent density-functional theory (TDDFT) provides an efficient, elegant, and formally exact way of describing the dynamics of interacting many-body quantum systems, circumventing the need for solving the full time-dependent Schroedinger equation. In the 20 years since it was first rigorously established in 1984, the field of TDDFT has made rapid and significant advances both formally as well as in terms of successful applications in chemistry, physics and materials science. Today, TDDFT has become the method of choice for calculating excitation energies of complex molecules, and is becoming increasingly popular for describing optical and spectroscopic properties of a variety of materials such as bulk solids, clusters and nanostructures. Other growing areas of applications of TDDFT are nonlinear dynamics of strongly excited electronic systems and molecular electronics. The purpose and scope of this Gordon Research Conference is to provide a platform for discussing the current state of the art of the rapidly progressing, highly interdisciplinary field of TDDFT, to identify and debate open questions, and to point out new promising research directions. The conference will bring together experts with a diverse background in chemistry, physics, and materials science.
Generalized Pauli constraints in reduced density matrix functional theory
Theophilou, Iris; Helbig, Nicole; Lathiotakis, Nektarios N.; Marques, Miguel A. L.
2015-04-21
Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman’s ensemble N-representability conditions. Recently, the topic of pure-state N-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble N-representability conditions violates the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.
Density-dependence of functional spiking networks in vitro
Ham, Michael I; Gintautuas, Vadas; Rodriguez, Marko A; Bettencourt, Luis M A; Bennett, Ryan; Santa Maria, Cara L
2008-01-01
During development, the mammalian brain differentiates into specialized regions with unique functional abilities. While many factors contribute to this functional specialization, we explore the effect neuronal density can have on neuronal interactions. Two types of networks, dense (50,000 neurons and glia support cells) and sparse (12,000 neurons and glia support cells), are studied. A competitive first response model is applied to construct activation graphs that represent pairwise neuronal interactions. By observing the evolution of these graphs during development in vitro we observe that dense networks form activation connections earlier than sparse networks, and that link-!llltropy analysis of the resulting dense activation graphs reveals that balanced directional connections dominate. Information theoretic measures reveal in addition that early functional information interactions (of order 3) are synergetic in both dense and sparse networks. However, during development in vitro, such interactions become redundant in dense, but not sparse networks. Large values of activation graph link-entropy correlate strongly with redundant ensembles observed in the dense networks. Results demonstrate differences between dense and sparse networks in terms of informational groups, pairwise relationships, and activation graphs. These differences suggest that variations in cell density may result in different functional specialization of nervous system tissue also in vivo.
Downlink Probability Density Functions for EOS-McMurdo Sound
NASA Technical Reports Server (NTRS)
Christopher, P.; Jackson, A. H.
1996-01-01
The visibility times and communication link dynamics for the Earth Observations Satellite (EOS)-McMurdo Sound direct downlinks have been studied. The 16 day EOS periodicity may be shown with the Goddard Trajectory Determination System (GTDS) and the entire 16 day period should be simulated for representative link statistics. We desire many attributes of the downlink, however, and a faster orbital determination method is desirable. We use the method of osculating elements for speed and accuracy in simulating the EOS orbit. The accuracy of the method of osculating elements is demonstrated by closely reproducing the observed 16 day Landsat periodicity. An autocorrelation function method is used to show the correlation spike at 16 days. The entire 16 day record of passes over McMurdo Sound is then used to generate statistics for innage time, outage time, elevation angle, antenna angle rates, and propagation loss. The levation angle probability density function is compared with 1967 analytic approximation which has been used for medium to high altitude satellites. One practical result of this comparison is seen to be the rare occurrence of zenith passes. The new result is functionally different than the earlier result, with a heavy emphasis on low elevation angles. EOS is one of a large class of sun synchronous satellites which may be downlinked to McMurdo Sound. We examine delay statistics for an entire group of sun synchronous satellites ranging from 400 km to 1000 km altitude. Outage probability density function results are presented three dimensionally.
Revealing the density of encoded functions in a viral RNA
Patel, Nikesh; Dykeman, Eric C.; Coutts, Robert H. A.; Lomonossoff, George P.; Rowlands, David J.; Phillips, Simon E. V.; Ranson, Neil; Twarock, Reidun; Tuma, Roman; Stockley, Peter G.
2015-01-01
We present direct experimental evidence that assembly of a single-stranded RNA virus occurs via a packaging signal-mediated mechanism. We show that the sequences of coat protein recognition motifs within multiple, dispersed, putative RNA packaging signals, as well as their relative spacing within a genomic fragment, act collectively to influence the fidelity and yield of capsid self-assembly in vitro. These experiments confirm that the selective advantages for viral yield and encapsidation specificity, predicted from previous modeling of packaging signal-mediated assembly, are found in Nature. Regions of the genome that act as packaging signals also function in translational and transcriptional enhancement, as well as directly coding for the coat protein, highlighting the density of encoded functions within the viral RNA. Assembly and gene expression are therefore direct molecular competitors for different functional folds of the same RNA sequence. The strongest packaging signal in the test fragment, encodes a region of the coat protein that undergoes a conformational change upon contact with packaging signals. A similar phenomenon occurs in other RNA viruses for which packaging signals are known. These contacts hint at an even deeper density of encoded functions in viral RNA, which if confirmed, would have profound consequences for the evolution of this class of pathogens. PMID:25646435
Current density partitioning in time-dependent current density functional theory
Mosquera, Martín A.; Wasserman, Adam; Department of Physics, Purdue University, West Lafayette, Indiana 47907
2014-05-14
We adapt time-dependent current density functional theory to allow for a fragment-based solution of the many-electron problem of molecules in the presence of time-dependent electric and magnetic fields. Regarding a molecule as a set of non-interacting subsystems that individually evolve under the influence of an auxiliary external electromagnetic vector-scalar potential pair, the partition 4-potential, we show that there are one-to-one mappings between this auxiliary potential, a sharply-defined set of fragment current densities, and the total current density of the system. The partition electromagnetic (EM) 4-potential is expressed in terms of the real EM 4-potential of the system and a gluing EM 4-potential that accounts for exchange-correlation effects and mutual interaction forces between fragments that are required to yield the correct electron dynamics. We prove the zero-force theorem for the fragmented system, establish a variational formulation in terms of action functionals, and provide a simple illustration for a charged particle in a ring.
Stochastic Optimally Tuned Range-Separated Hybrid Density Functional Theory.
Neuhauser, Daniel; Rabani, Eran; Cytter, Yael; Baer, Roi
2016-05-19
We develop a stochastic formulation of the optimally tuned range-separated hybrid density functional theory that enables significant reduction of the computational effort and scaling of the nonlocal exchange operator at the price of introducing a controllable statistical error. Our method is based on stochastic representations of the Coulomb convolution integral and of the generalized Kohn-Sham density matrix. The computational cost of the approach is similar to that of usual Kohn-Sham density functional theory, yet it provides a much more accurate description of the quasiparticle energies for the frontier orbitals. This is illustrated for a series of silicon nanocrystals up to sizes exceeding 3000 electrons. Comparison with the stochastic GW many-body perturbation technique indicates excellent agreement for the fundamental band gap energies, good agreement for the band edge quasiparticle excitations, and very low statistical errors in the total energy for large systems. The present approach has a major advantage over one-shot GW by providing a self-consistent Hamiltonian that is central for additional postprocessing, for example, in the stochastic Bethe-Salpeter approach. PMID:26651840
Subsystem real-time time dependent density functional theory.
Krishtal, Alisa; Ceresoli, Davide; Pavanello, Michele
2015-04-21
We present the extension of Frozen Density Embedding (FDE) formulation of subsystem Density Functional Theory (DFT) to real-time Time Dependent Density Functional Theory (rt-TDDFT). FDE is a DFT-in-DFT embedding method that allows to partition a larger Kohn-Sham system into a set of smaller, coupled Kohn-Sham systems. Additional to the computational advantage, FDE provides physical insight into the properties of embedded systems and the coupling interactions between them. The extension to rt-TDDFT is done straightforwardly by evolving the Kohn-Sham subsystems in time simultaneously, while updating the embedding potential between the systems at every time step. Two main applications are presented: the explicit excitation energy transfer in real time between subsystems is demonstrated for the case of the Na4 cluster and the effect of the embedding on optical spectra of coupled chromophores. In particular, the importance of including the full dynamic response in the embedding potential is demonstrated. PMID:25903875
Applications of large-scale density functional theory in biology
NASA Astrophysics Data System (ADS)
Cole, Daniel J.; Hine, Nicholas D. M.
2016-10-01
Density functional theory (DFT) has become a routine tool for the computation of electronic structure in the physics, materials and chemistry fields. Yet the application of traditional DFT to problems in the biological sciences is hindered, to a large extent, by the unfavourable scaling of the computational effort with system size. Here, we review some of the major software and functionality advances that enable insightful electronic structure calculations to be performed on systems comprising many thousands of atoms. We describe some of the early applications of large-scale DFT to the computation of the electronic properties and structure of biomolecules, as well as to paradigmatic problems in enzymology, metalloproteins, photosynthesis and computer-aided drug design. With this review, we hope to demonstrate that first principles modelling of biological structure-function relationships are approaching a reality.
Applications of large-scale density functional theory in biology.
Cole, Daniel J; Hine, Nicholas D M
2016-10-01
Density functional theory (DFT) has become a routine tool for the computation of electronic structure in the physics, materials and chemistry fields. Yet the application of traditional DFT to problems in the biological sciences is hindered, to a large extent, by the unfavourable scaling of the computational effort with system size. Here, we review some of the major software and functionality advances that enable insightful electronic structure calculations to be performed on systems comprising many thousands of atoms. We describe some of the early applications of large-scale DFT to the computation of the electronic properties and structure of biomolecules, as well as to paradigmatic problems in enzymology, metalloproteins, photosynthesis and computer-aided drug design. With this review, we hope to demonstrate that first principles modelling of biological structure-function relationships are approaching a reality. PMID:27494095
Van der Waals Interactions in Density Functional Theory: Intermolecular Complexes
NASA Astrophysics Data System (ADS)
Kannemann, Felix; Becke, Axel
2010-03-01
Conventional density functional theory (GGA and hybrid functionals) fails to account for dispersion interactions and is therefore not applicable to systems where van der Waals interactions play a dominant role, such as intermolecular complexes and biomolecules. The exchange-hole dipole moment (XDM) dispersion model of Becke and Johnson [A. D. Becke and E. R. Johnson, J. Chem. Phys. 127, 154108 (2007)] corrects for this deficiency. We have previously shown that the XDM dispersion model can be combined with standard GGA functionals (PW86 for exchange and PBE for correlation) to give accurate binding energy curves for rare-gas diatomics [F. O. Kannemann and A. D. Becke, J. Chem. Theory Comput. 5, 719 (2009)]. Here we present further tests of the GGA-XDM method using benchmark sets including hydrogen bonding, electrostatic, dispersion and stacking interactions, and systems ranging from rare-gas diatomics to biomolecular complexes.
Baczewski, Andrew David; Shulenburger, Luke; Desjarlais, Michael Paul; Magyar, Rudolph J.
2014-02-01
In recent years, DFT-MD has been shown to be a useful computational tool for exploring the properties of WDM. These calculations achieve excellent agreement with shock compression experiments, which probe the thermodynamic parameters of the Hugoniot state. New X-ray Thomson Scattering diagnostics promise to deliver independent measurements of electronic density and temperature, as well as structural information in shocked systems. However, they require the development of new levels of theory for computing the associated observables within a DFT framework. The experimentally observable x-ray scattering cross section is related to the electronic density-density response function, which is obtainable using TDDFT - a formally exact extension of conventional DFT that describes electron dynamics and excited states. In order to develop a capability for modeling XRTS data and, more generally, to establish a predictive capability for rst principles simulations of matter in extreme conditions, real-time TDDFT with Ehrenfest dynamics has been implemented in an existing PAW code for DFT-MD calculations. The purpose of this report is to record implementation details and benchmarks as the project advances from software development to delivering novel scienti c results. Results range from tests that establish the accuracy, e ciency, and scalability of our implementation, to calculations that are veri ed against accepted results in the literature. Aside from the primary XRTS goal, we identify other more general areas where this new capability will be useful, including stopping power calculations and electron-ion equilibration.
Dipole polarizability of 120Sn and nuclear energy density functionals
NASA Astrophysics Data System (ADS)
Hashimoto, T.; Krumbholz, A. M.; Reinhard, P.-G.; Tamii, A.; von Neumann-Cosel, P.; Adachi, T.; Aoi, N.; Bertulani, C. A.; Fujita, H.; Fujita, Y.; GanioÇ§lu, E.; Hatanaka, K.; Ideguchi, E.; Iwamoto, C.; Kawabata, T.; Khai, N. T.; Krugmann, A.; Martin, D.; Matsubara, H.; Miki, K.; Neveling, R.; Okamura, H.; Ong, H. J.; Poltoratska, I.; Ponomarev, V. Yu.; Richter, A.; Sakaguchi, H.; Shimbara, Y.; Shimizu, Y.; Simonis, J.; Smit, F. D.; Süsoy, G.; Suzuki, T.; Thies, J. H.; Yosoi, M.; Zenihiro, J.
2015-09-01
The electric dipole strength distribution in 120Sn between 5 and 22 MeV has been determined at the Research Center for Nuclear Physics, Osaka, from polarization transfer observables measured in proton inelastic scattering at E0=295 MeV and forward angles including 0∘. Combined with photoabsorption data, a highly precise electric dipole polarizability αD(120Sn) =8.93 (36 ) fm3 is extracted. The dipole polarizability as isovector observable par excellence carries direct information on nuclear symmetry energy and its density dependence. The correlation of the new value with the well-established αD(208Pb) serves as a test of its prediction by nuclear energy density functionals. Models based on modern Skyrme interactions describe the data fairly well while most calculations based on relativistic Hamiltonians cannot.
Dynamic density functional theory of solid tumor growth: Preliminary models.
Chauviere, Arnaud; Hatzikirou, Haralambos; Kevrekidis, Ioannis G; Lowengrub, John S; Cristini, Vittorio
2012-03-01
Cancer is a disease that can be seen as a complex system whose dynamics and growth result from nonlinear processes coupled across wide ranges of spatio-temporal scales. The current mathematical modeling literature addresses issues at various scales but the development of theoretical methodologies capable of bridging gaps across scales needs further study. We present a new theoretical framework based on Dynamic Density Functional Theory (DDFT) extended, for the first time, to the dynamics of living tissues by accounting for cell density correlations, different cell types, phenotypes and cell birth/death processes, in order to provide a biophysically consistent description of processes across the scales. We present an application of this approach to tumor growth. PMID:22489279
Sublinear scaling for time-dependent stochastic density functional theory
Gao, Yi; Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2015-01-21
A stochastic approach to time-dependent density functional theory is developed for computing the absorption cross section and the random phase approximation (RPA) correlation energy. The core idea of the approach involves time-propagation of a small set of stochastic orbitals which are first projected on the occupied space and then propagated in time according to the time-dependent Kohn-Sham equations. The evolving electron density is exactly represented when the number of random orbitals is infinite, but even a small number (≈16) of such orbitals is enough to obtain meaningful results for absorption spectrum and the RPA correlation energy per electron. We implement the approach for silicon nanocrystals using real-space grids and find that the overall scaling of the algorithm is sublinear with computational time and memory.
Hubbard operator density functional theory for Fermionic lattice models
NASA Astrophysics Data System (ADS)
Cheng, Zhengqian; Marianetti, Chris
We formulate an effective action as a functional of Hubbard operator densities whose stationary point delivers all local static information of the interacting lattice model. Using the variational principle, we get a self-consistent equation for Hubbard operator densities. The computational cost of our approach is set by diagonalizing the local Fock space. We apply our method to the one and two band Hubbard model (including crystal field and on-site exchange) in infinite dimensions where the exact solution is known. Excellent agreement is obtained for the one-band model. In the two-band model, good agreement is obtained in the metallic region of the phase diagram in addition to the metal-insulator transition. While our approach does not address frequency dependent observables, it has a negligible computational cost as compared to dynamical mean field theory and could be highly applicable in the context total energies of strongly correlated materials and molecules.
Progress at the interface of wave-function and density-functional theories
Gidopoulos, Nikitas I.
2011-04-15
The Kohn-Sham (KS) potential of density-functional theory (DFT) emerges as the minimizing effective potential in a variational scheme that does not involve fixing the unknown single-electron density. Using Rayleigh Schroedinger (RS) perturbation theory (PT), we construct ab initio approximations for the energy difference, the minimization of which determines the KS potential directly - thereby bypassing DFT's traditional algorithm to search for the density that minimizes the total energy. From second-order RS PT, we obtain variationally stable energy differences to be minimized, solving the severe problem of variational collapse of orbital-dependent exchange-correlation functionals based on second-order RS PT.
Characterizing the Spatial Density Functions of Neural Arbors
NASA Astrophysics Data System (ADS)
Teeter, Corinne Michelle
Recently, it has been proposed that a universal function describes the way in which all arbors (axons and dendrites) spread their branches over space. Data from fish retinal ganglion cells as well as cortical and hippocampal arbors from mouse, rat, cat, monkey and human provide evidence that all arbor density functions (adf) can be described by a Gaussian function truncated at approximately two standard deviations. A Gaussian density function implies that there is a minimal set of parameters needed to describe an adf: two or three standard deviations (depending on the dimensionality of the arbor) and an amplitude. However, the parameters needed to completely describe an adf could be further constrained by a scaling law found between the product of the standard deviations and the amplitude of the function. In the following document, I examine the scaling law relationship in order to determine the minimal set of parameters needed to describe an adf. First, I find that the at, two-dimensional arbors of fish retinal ganglion cells require only two out of the three fundamental parameters to completely describe their density functions. Second, the three-dimensional, volume filling, cortical arbors require four fundamental parameters: three standard deviations and the total length of an arbor (which corresponds to the amplitude of the function). Next, I characterize the shape of arbors in the context of the fundamental parameters. I show that the parameter distributions of the fish retinal ganglion cells are largely homogenous. In general, axons are bigger and less dense than dendrites; however, they are similarly shaped. The parameter distributions of these two arbor types overlap and, therefore, can only be differentiated from one another probabilistically based on their adfs. Despite artifacts in the cortical arbor data, different types of arbors (apical dendrites, non-apical dendrites, and axons) can generally be differentiated based on their adfs. In addition, within
NASA Astrophysics Data System (ADS)
Muzy, J. F.; Bacry, E.; Arneodo, A.
1993-02-01
Several attempts have been made recently to generalize the multifractal formalism, originally introduced for singular measures, to fractal signals. We report on a systematic comparison between the structure-function approach, pioneered by Parisi and Frisch [in 2 Proceedings of the International School on Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics, edited by M. Ghil, R. Benzi, and G. Parisi (North-Holland, Amsterdam, 1985), p. 84] to account for the multifractal nature of fully developed turbulent signals, and an alternative method we have developed within the framework of the wavelet-transform analysis. We comment on the intrinsic limitations of the structure-function approach; this technique has fundamental drawbacks and does not provide a full characterization of the singularities of a signal in many cases. We demonstrate that our method, based on the wavelet-transform modulus-maxima representation, works in most situations and is likely to be the ground of a unified multifractal description of self-affine distributions. Our theoretical considerations are both illustrated on pedagogical examples and supported by numerical simulations.
Asaadi, Sina; Ashrafi, Farzad; Omidbeigi, Mahmoud; Nasiri, Zahra; Pakdaman, Hossein; Amini-Harandi, Ali
2016-01-01
Background: Cognitive impairment in patients with Parkinson’s disease (PD) mainly involves executive function (EF). The frontal assessment battery (FAB) is an efficient tool for the assessment of EFs. The aims of this study were to determine the validity and reliability of the psychometric properties of the Persian version of FAB and assess its correlation with formal measures of EFs to provide normative data for the Persian version of FAB in patients with PD. Methods: The study recruited 149 healthy participants and 49 patients with idiopathic PD. In PD patients, FAB results were compared to their performance on EF tests. Reliability analysis involved test-retest reliability and internal consistency, whereas validity analysis involved convergent validity approach. FAB scores compared in normal controls and in PD patients matched for age, education, and Mini-Mental State Examination (MMSE) score. Results: In PD patients, FAB scores were significantly decreased compared to normal controls, and correlated with Stroop test and Wisconsin Card Sorting Test (WCST). In healthy subjects, FAB scores varied according to the age, education, and MMSE. In the FAB subtest analysis, the performances of PD patients were worse than the healthy participants on similarities, fluency tasks, and Luria’s motor series. Conclusion: Persian version of FAB could be used as a reliable scale for the assessment of frontal lobe functions in Iranian patients with PD. Furthermore, normative data provided for the Persian version of this test improve the accuracy and confidence in the clinical application of the FAB. PMID:27141272
Chukhovskii, F N; Polyakov, A M
2010-11-01
The Green function formalism is applied to the problem of grazing-incidence small-angle X-ray scattering from statistically rough surfaces. Kirchhoff's integral equation is used to describe the X-ray wavefield propagation through a single rough surface separating vacuum and medium. Taking into account multiple diffuse X-ray scattering effects, the reflection R(coh)(θ) and transmission T(coh)(θ) coefficients of the specular wave are obtained using the Gaussian statistical model of rough surfaces in terms of the two-point height-height correlation function. In the limiting cases when the correlation length xi is equal to zero or infinity, analytical formulae for the reflection R(coh)(θ) and transmission T(coh)(θ) coefficients of the specular wave are obtained. It is important that in the case xi --> infinity they coincide with the corresponding reflection R(DW)(θ) and transmission T(DW)(θ) coefficients related to the conventional Debye-Waller approximation for describing the grazing X-ray scattering from a rough surface. In the case of finite values of correlation length \\xi the reflection |R(coh)(θ)|(2) and transmission |T(coh)(θ)|(2) scans are numerically calculated. PMID:20962372
NASA Astrophysics Data System (ADS)
Shkolnik, Evgenya; Walker, Gordon A. H.; Rucinski, Slavek M.; Bohlender, David A.; Davidge, Tim J.
2005-08-01
The synchronously rotating G stars in the detached, short-period (0.7 days), partially eclipsing binary ER Vul are the most chromospherically active solar-type stars known. We have monitored activity in the Ca II H and K reversals for almost an entire orbit. Rucinski's broadening function formalism allows the photospheric contribution to be objectively subtracted from the highly blended spectra. The power of the broadening function technique is also demonstrated by the good agreement of radial velocities with those measured by others from less crowded spectral regions. In addition to strong Ca II emission from the primary and secondary, there appears to be a high-velocity stream flowing onto the secondary, where it stimulates a large active region on the surface 30°-40° in advance of the subbinary longitude. A model light curve with a spot centered on the same longitude also gives the best fit to the observed light curve. A flare with ~13% more power than at other phases was detected in one spectrum. We suggest that ER Vul may offer a magnified view of the more subtle chromospheric effects synchronized to planetary revolution seen in certain 51 Peg-type systems.
SUMO1 Affects Synaptic Function, Spine Density and Memory
Matsuzaki, Shinsuke; Lee, Linda; Knock, Erin; Srikumar, Tharan; Sakurai, Mikako; Hazrati, Lili-Naz; Katayama, Taiichi; Staniszewski, Agnieszka; Raught, Brian; Arancio, Ottavio; Fraser, Paul E.
2015-01-01
Small ubiquitin-like modifier-1 (SUMO1) plays a number of roles in cellular events and recent evidence has given momentum for its contributions to neuronal development and function. Here, we have generated a SUMO1 transgenic mouse model with exclusive overexpression in neurons in an effort to identify in vivo conjugation targets and the functional consequences of their SUMOylation. A high-expressing line was examined which displayed elevated levels of mono-SUMO1 and increased high molecular weight conjugates in all brain regions. Immunoprecipitation of SUMOylated proteins from total brain extract and proteomic analysis revealed ~95 candidate proteins from a variety of functional classes, including a number of synaptic and cytoskeletal proteins. SUMO1 modification of synaptotagmin-1 was found to be elevated as compared to non-transgenic mice. This observation was associated with an age-dependent reduction in basal synaptic transmission and impaired presynaptic function as shown by altered paired pulse facilitation, as well as a decrease in spine density. The changes in neuronal function and morphology were also associated with a specific impairment in learning and memory while other behavioral features remained unchanged. These findings point to a significant contribution of SUMO1 modification on neuronal function which may have implications for mechanisms involved in mental retardation and neurodegeneration. PMID:26022678
SUMO1 Affects Synaptic Function, Spine Density and Memory.
Matsuzaki, Shinsuke; Lee, Linda; Knock, Erin; Srikumar, Tharan; Sakurai, Mikako; Hazrati, Lili-Naz; Katayama, Taiichi; Staniszewski, Agnieszka; Raught, Brian; Arancio, Ottavio; Fraser, Paul E
2015-01-01
Small ubiquitin-like modifier-1 (SUMO1) plays a number of roles in cellular events and recent evidence has given momentum for its contributions to neuronal development and function. Here, we have generated a SUMO1 transgenic mouse model with exclusive overexpression in neurons in an effort to identify in vivo conjugation targets and the functional consequences of their SUMOylation. A high-expressing line was examined which displayed elevated levels of mono-SUMO1 and increased high molecular weight conjugates in all brain regions. Immunoprecipitation of SUMOylated proteins from total brain extract and proteomic analysis revealed ~95 candidate proteins from a variety of functional classes, including a number of synaptic and cytoskeletal proteins. SUMO1 modification of synaptotagmin-1 was found to be elevated as compared to non-transgenic mice. This observation was associated with an age-dependent reduction in basal synaptic transmission and impaired presynaptic function as shown by altered paired pulse facilitation, as well as a decrease in spine density. The changes in neuronal function and morphology were also associated with a specific impairment in learning and memory while other behavioral features remained unchanged. These findings point to a significant contribution of SUMO1 modification on neuronal function which may have implications for mechanisms involved in mental retardation and neurodegeneration. PMID:26022678
Dynamic density functional theory with hydrodynamic interactions and fluctuations.
Donev, Aleksandar; Vanden-Eijnden, Eric
2014-06-21
We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic Density Functional Theory (DDFT) [M. Rex and H. Löwen, "Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps," Phys. Rev. Lett. 101(14), 148302 (2008)], and, at the same time, it also describes the microscopic fluctuations around the mean behavior. We suggest separating the ideal (non-interacting) contribution from additional corrections due to pairwise interactions. We find that, for an incompressible fluid and in the absence of direct interactions, the mean concentration follows Fick's law just as for uncorrelated walkers. At the same time, the nature of the stochastic terms in fluctuating DDFT is shown to be distinctly different for hydrodynamically-correlated and uncorrelated walkers. This leads to striking differences in the behavior of the fluctuations around Fick's law, even in the absence of pairwise interactions. We connect our own prior work [A. Donev, T. G. Fai, and E. Vanden-Eijnden, "A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law," J. Stat. Mech.: Theory Exp. (2014) P04004] on fluctuating hydrodynamics of diffusion in liquids to the DDFT literature, and demonstrate that the fluid cannot easily be eliminated from consideration if one wants to describe the collective diffusion in colloidal suspensions. PMID:24952531
Dynamic density functional theory with hydrodynamic interactions and fluctuations
NASA Astrophysics Data System (ADS)
Donev, Aleksandar; Vanden-Eijnden, Eric
2014-06-01
We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic Density Functional Theory (DDFT) [M. Rex and H. Löwen, "Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps," Phys. Rev. Lett. 101(14), 148302 (2008)], and, at the same time, it also describes the microscopic fluctuations around the mean behavior. We suggest separating the ideal (non-interacting) contribution from additional corrections due to pairwise interactions. We find that, for an incompressible fluid and in the absence of direct interactions, the mean concentration follows Fick's law just as for uncorrelated walkers. At the same time, the nature of the stochastic terms in fluctuating DDFT is shown to be distinctly different for hydrodynamically-correlated and uncorrelated walkers. This leads to striking differences in the behavior of the fluctuations around Fick's law, even in the absence of pairwise interactions. We connect our own prior work [A. Donev, T. G. Fai, and E. Vanden-Eijnden, "A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law," J. Stat. Mech.: Theory Exp. (2014) P04004] on fluctuating hydrodynamics of diffusion in liquids to the DDFT literature, and demonstrate that the fluid cannot easily be eliminated from consideration if one wants to describe the collective diffusion in colloidal suspensions.
Dynamic density functional theory with hydrodynamic interactions and fluctuations
Donev, Aleksandar Vanden-Eijnden, Eric
2014-06-21
We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic Density Functional Theory (DDFT) [M. Rex and H. Löwen, “Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps,” Phys. Rev. Lett. 101(14), 148302 (2008)], and, at the same time, it also describes the microscopic fluctuations around the mean behavior. We suggest separating the ideal (non-interacting) contribution from additional corrections due to pairwise interactions. We find that, for an incompressible fluid and in the absence of direct interactions, the mean concentration follows Fick's law just as for uncorrelated walkers. At the same time, the nature of the stochastic terms in fluctuating DDFT is shown to be distinctly different for hydrodynamically-correlated and uncorrelated walkers. This leads to striking differences in the behavior of the fluctuations around Fick's law, even in the absence of pairwise interactions. We connect our own prior work [A. Donev, T. G. Fai, and E. Vanden-Eijnden, “A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law,” J. Stat. Mech.: Theory Exp. (2014) P04004] on fluctuating hydrodynamics of diffusion in liquids to the DDFT literature, and demonstrate that the fluid cannot easily be eliminated from consideration if one wants to describe the collective diffusion in colloidal suspensions.
Graphene oxide and adsorption of chloroform: A density functional study
NASA Astrophysics Data System (ADS)
Kuisma, Elena; Hansson, C. Fredrik; Lindberg, Th. Benjamin; Gillberg, Christoffer A.; Idh, Sebastian; Schröder, Elsebeth
2016-05-01
Chlorinated hydrocarbon compounds are of environmental concerns, since they are toxic to humans and other mammals, and are widespread, and exposure is hard to avoid. Understanding and improving methods to reduce the amount of the substances are important. We present an atomic-scale calculational study of the adsorption of chlorine-based substance chloroform (CHCl3) on graphene oxide, as a step in estimating the capacity of graphene oxide for filtering out such substances, e.g., from drinking water. The calculations are based on density functional theory, and the recently developed consistent-exchange functional for the van der Waals density-functional method is employed. We obtain values of the chloroform adsorption energy varying from roughly 0.2 to 0.4 eV per molecule. This is comparable to previously found results for chloroform adsorbed directly on clean graphene, using similar calculations. In a wet environment, like filters for drinking water, the graphene will not stay clean and will likely oxidize, and thus adsorption onto graphene oxide, rather than clean graphene, is a more relevant process to study.
Graphene oxide and adsorption of chloroform: A density functional study.
Kuisma, Elena; Hansson, C Fredrik; Lindberg, Th Benjamin; Gillberg, Christoffer A; Idh, Sebastian; Schröder, Elsebeth
2016-05-14
Chlorinated hydrocarbon compounds are of environmental concerns, since they are toxic to humans and other mammals, and are widespread, and exposure is hard to avoid. Understanding and improving methods to reduce the amount of the substances are important. We present an atomic-scale calculational study of the adsorption of chlorine-based substance chloroform (CHCl3) on graphene oxide, as a step in estimating the capacity of graphene oxide for filtering out such substances, e.g., from drinking water. The calculations are based on density functional theory, and the recently developed consistent-exchange functional for the van der Waals density-functional method is employed. We obtain values of the chloroform adsorption energy varying from roughly 0.2 to 0.4 eV per molecule. This is comparable to previously found results for chloroform adsorbed directly on clean graphene, using similar calculations. In a wet environment, like filters for drinking water, the graphene will not stay clean and will likely oxidize, and thus adsorption onto graphene oxide, rather than clean graphene, is a more relevant process to study. PMID:27179497
Relativistic cosmology number densities and the luminosity function
NASA Astrophysics Data System (ADS)
Iribarrem, A. S.; Lopes, A. R.; Ribeiro, M. B.; Stoeger, W. R.
2012-03-01
Aims: This paper studies the connection between the relativistic number density of galaxies down the past light cone in a Friedmann-Lemaître-Robertson-Walker spacetime with non-vanishing cosmological constant and the galaxy luminosity function (LF) data. It extends the redshift range of previous results presented in Albani et al. (2007, ApJ, 657, 760), where the galaxy distribution was studied out to z = 1. Observational inhomogeneities were detected at this range. This research also searches for LF evolution in the context of the framework advanced by Ribeiro and Stoeger (2003, ApJ, 592, 1), further developing the theory linking relativistic cosmology theory and LF data. Methods: Selection functions are obtained using the Schechter parameters and redshift parametrization of the galaxy LF obtained from an I-band selected dataset of the FORS deep field galaxy survey in the redshift range 0.5 ≤ z ≤ 5.0 for its blue bands and 0.75 ≤ z ≤ 3.0 for its red ones. Differential number counts, densities and other related observables are obtained, and then used with the calculated selection functions to study the empirical radial distribution of the galaxies in a fully relativistic framework. Results: The redshift range of the dataset used in this work, which is up to five times larger than the one used in previous studies, shows an increased relevance of the relativistic effects of expansion when compared to the evolution of the LF at the higher redshifts. The results also agree with the preliminary ones presented in Albani et al., suggesting a power-law behavior of relativistic densities at high redshifts when they are defined in terms of the luminosity distance.
Adsorption of Ne on alkali surfaces studied with a density functional theory.
Sartarelli, Salvador A; Szybisz, Leszek; Urrutia, Ignacio
2009-01-01
A density functional formalism is applied to investigate the wetting behavior of Ne adsorbed on planar substrates. The study is performed over the complete range of temperatures spanned from the triple point T_{t} up to the critical one T_{c} . For this purpose, an effective attractive pair potential was built on the basis of a separation procedure. This approach yields a good description of properties of the liquid-vapor interface at coexistence in the whole range of temperatures T_{t} < or = T < or = T_{c} . The adsorption of Ne on alkali metals and the alkaline-earth metal Mg is analyzed. This sequence of substrates exhibit increasing attractive strength leading to a variety of wetting situations throughout the interval T_{t}<-->T_{c} . A comparison with experimental data and other microscopic calculations is done. The predictions of a simple model are discussed. For NeRb we were able to resolve prewetting lines. Results obtained from a density functional are reported for NeK and NeMg . In the case of the latter system the interesting behavior occurs close to T_{t} . According to our results, Ne wets surfaces of Na and Li, and this statement is in agreement with the whole picture of the analyzed substrates. PMID:19257041
Zhang, Xing; Herbert, John M.
2015-02-14
We revisit the formalism for analytic derivative couplings between excited states in time-dependent density functional theory (TDDFT). We derive and implement these couplings using quadratic response theory, then numerically compare this response-theory formulation to couplings implemented previously based on a pseudo-wavefunction formalism and direct differentiation of the Kohn-Sham determinant. Numerical results, including comparison to full configuration interaction calculations, suggest that the two approaches perform equally well for many molecular systems, provided that the underlying DFT method affords accurate potential energy surfaces. The response contributions are found to be important for certain systems with high symmetry, but can be calculated with only a moderate increase in computational cost beyond what is required for the pseudo-wavefunction approach. In the case of spin-flip TDDFT, we provide a formal proof that the derivative couplings obtained using response theory are identical to those obtained from the pseudo-wavefunction formulation, which validates our previous implementation based on the latter formalism.
Nuclear clustering in the energy density functional approach
Ebran, J.-P.; Khan, E.; Nikšić, T.; Vretenar, D.
2015-10-15
Nuclear Energy Density Functionals (EDFs) are a microscopic tool of choice extensively used over the whole chart to successfully describe the properties of atomic nuclei ensuing from their quantum liquid nature. In the last decade, they also have proved their ability to deal with the cluster phenomenon, shedding a new light on its fundamental understanding by treating on an equal footing both quantum liquid and cluster aspects of nuclei. Such a unified microscopic description based on nucleonic degrees of freedom enables to tackle the question pertaining to the origin of the cluster phenomenon and emphasizes intrinsic mechanisms leading to the emergence of clusters in nuclei.
Application of Density Functional Theory to Systems Containing Metal Atoms
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Arnold, James O. (Technical Monitor)
1997-01-01
The accuracy of density functional theory (DFT) for problems involving metal atoms is considered. The DFT results are compared with experiment as well as results obtained using the coupled cluster approach. The comparisons include geometries, frequencies, and bond energies. The systems considered include MO2, M(OH)+(sub n), MNO+, and MCO+(sub 2). The DFT works well for frequencies and geometries, even in cases with symmetry breaking; however, some examples have been found where the symmetry breaking is quite severe and the DFT methods do not work well. The calculation of bond energies is more difficult and examples of the successes as well as failures of DFT will be given.
Quantification of Uncertainties in Nuclear Density Functional Theory
Schunck, N.; McDonnell, J.D.; Higdon, D.; Sarich, J.; Wild, S.
2015-01-15
Reliable predictions of nuclear properties are needed as much to answer fundamental science questions as in applications such as reactor physics or data evaluation. Nuclear density functional theory is currently the only microscopic, global approach to nuclear structure that is applicable throughout the nuclear chart. In the past few years, a lot of effort has been devoted to setting up a general methodology to assess theoretical uncertainties in nuclear DFT calculations. In this paper, we summarize some of the recent progress in this direction. Most of the new material discussed here will be be published in separate articles.
Application of Density Functional Theory to Systems Containing Metal Atoms
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.
2006-01-01
The accuracy of density functional theory (DFT) for problems involving metal atoms is considered. The DFT results are compared with experiment as well as results obtained using the coupled cluster approach. The comparisons include geometries, frequencies, and bond energies. The systems considered include MO2, M(OH)+n, MNO+, and MCO+2. The DFT works well for frequencies and geometries, even in case with symmetry breaking; however, some examples have been found where the symmetry breaking is quite severe and the DFT methods do not work well. The calculation of bond energies is more difficult and examples of successes as well as failures of DFT will be given.
Momentum distribution function of the electron gas at metallic densities
NASA Astrophysics Data System (ADS)
Takada, Yasutami; Yasuhara, H.
1991-10-01
The momentum distribution function n(k) of the electron gas is calculated in the effective-potential-expansion method at metallic densities. The recently established self-consistency relation between n(k) and the correlation energy [Y. Takada and T. Kita, J. Phys. Soc. Jpn. 60, 25 (1991)] is employed to check the accuracy of our results. This check shows that the effective-potential-expansion method provides probably the exact and at least more accurate results of n(k) than all the other methods that have given n(k) thus far.
Density functional study of the cysteine adsorption on Au nanoclusters
NASA Astrophysics Data System (ADS)
Pérez, L. A.; López-Lozano, X.; Garzón, I. L.
2009-04-01
The adsorption of the cysteine amino acid (H-SCβH2-CαH-NH2-COOH) on the Au55 cluster is investigated through density functional theory calculations. Two isomers, with icosahedral (Ih) and chiral (C1) geometries, of the Au55 cluster are used to calculate the adsorption energy of the cysteine on different facets of these isomers. Results, only involving the S(thiolate)-Au bonding show that the higher adsorption energies are obtained when the sulfur atom is bonded to an asymmetrical bridge site at the facet containing Au atoms with the lowest coordination of the C1 cluster isomer.
Nuclear clustering in the energy density functional approach
NASA Astrophysics Data System (ADS)
Ebran, J.-P.; Khan, E.; Nikšić, T.; Vretenar, D.
2015-10-01
Nuclear Energy Density Functionals (EDFs) are a microscopic tool of choice extensively used over the whole chart to successfully describe the properties of atomic nuclei ensuing from their quantum liquid nature. In the last decade, they also have proved their ability to deal with the cluster phenomenon, shedding a new light on its fundamental understanding by treating on an equal footing both quantum liquid and cluster aspects of nuclei. Such a unified microscopic description based on nucleonic degrees of freedom enables to tackle the question pertaining to the origin of the cluster phenomenon and emphasizes intrinsic mechanisms leading to the emergence of clusters in nuclei.
Density functional theory for strongly-correlated ultracold dipolar gases
NASA Astrophysics Data System (ADS)
Malet Giralt, Francesc; Reimann, Stephanie; Gori-Giorgi, Paola; Lund University Collaboration
2014-03-01
We address quasi-one-dimensional strongly-correlated dipolar ultracold gases by means of density functional theory. We make use of an approximation for the Hartree-exchange-correlation that has been shown to be very accurate for electronic systems with coulombic interactions. We show that this approach allows to treat systems with very large particle numbers at relatively low computational cost. This work has been supported by a VIDI grant of the NWO and a Marie Curie grant within the FP7 programme.
Density Functional Study of the structural properties in Tamoxifen
NASA Astrophysics Data System (ADS)
de Coss-Martinez, Romeo; Tapia, Jorge A.; Quijano-Quiñones, Ramiro F.; Canto, Gabriel I.
2013-03-01
Using the density functional theory, we have studied the structural properties of Tamoxifen. The calculations were performed with two methodological approaches, which were implemented in SIESTA and Spartan codes. For SIESTA, we considerate a linear combination of atomic orbitals method, using pseudopotentials and the van der Waals approximation for the exchange-correlation potential. Here we analyzed and compared the atomic structure between our results and other theoretical study. We found differences in the bond lengths between the results, that could be attributed to code approaches in each one. This work was supported under Grant FOMIX 2011-09 N: 170297 of Ph.D. A. Tapia.
Determining Ionospheric Irregularity Spectral Density Function from Japan GEONET
NASA Astrophysics Data System (ADS)
Lay, E. H.; Light, M. E.; Parker, P. A.; Carrano, C. S.; Haaser, R. A.
2015-12-01
Japan's GEONET GPS network is the densest GPS monitoring network in the world, with 1200+ receivers over the area of Japan. Measuring and calibrating the integrated total electron content (TEC) from each station has been done in many cases to provide detailed maps of ionospheric disturbances over Japan. We use TEC measurements from Japan's GEONET array to determine an empirically derived description of the 2-dimensional scale sizes of spatial irregularities above Japan. The contributions from various scale sizes will be included in a statistical description for the irregularity spectral density (ISD) function. We will compare the statistics of the spatial irregularities between calm and moderately scintillated conditions.
Density functional theory calculations of Rh-β-diketonato complexes.
Conradie, J
2015-01-28
Density functional theory (DFT) results on the geometry, energies and charges of selected Rh-β-diketonato reactants, products and transition states are discussed. Various DFT techniques are used to increase our understanding of the orientation of ligands coordinated to Rh, to identify the lowest energy geometry of possible geometrical isomers and to get a molecular orbital understanding of ground and transition states. Trends and relationships obtained between DFT calculated energies and charges, experimentally measured values and electronic parameters describing the electron donating power of groups and ligands, enable the design of ligands and complexes of specific reactivity. PMID:25429658
Relativistic Energy Density Functionals: Exotic modes of excitation
Vretenar, D.; Paar, N.; Marketin, T.
2008-11-11
The framework of relativistic energy density functionals has been applied to the description of a variety of nuclear structure phenomena, not only in spherical and deformed nuclei along the valley of {beta}-stability, but also in exotic systems with extreme isospin values and close to the particle drip-lines. Dynamical aspects of exotic nuclear structure have been investigated with the relativistic quasiparticle random-phase approximation. We present results for the evolution of low-lying dipole (pygmy) strength in neutron-rich nuclei, and charged-current neutrino-nucleus cross sections.
Strained graphene: tight-binding and density functional calculations
NASA Astrophysics Data System (ADS)
Ribeiro, R. M.; Pereira, Vitor M.; Peres, N. M. R.; Briddon, P. R.; Castro Neto, A. H.
2009-11-01
We determine the band structure of graphene under strain using density functional calculations. The ab initio band structure is then used to extract the best fit to the tight-binding hopping parameters used in a recent microscopic model of strained graphene. It is found that the hopping parameters may increase or decrease upon increasing strain, depending on the orientation of the applied stress. The fitted values are compared with an available parameterization for the dependence of the orbital overlap on the distance separating the two carbon atoms. It is also found that strain does not induce a gap in graphene, at least for deformations up to 10%.
Garcia-Aldea, David; Alvarellos, J. E.
2008-02-15
We propose a kinetic energy density functional scheme with nonlocal terms based on the von Weizsaecker functional, instead of the more traditional approach where the nonlocal terms have the structure of the Thomas-Fermi functional. The proposed functionals recover the exact kinetic energy and reproduce the linear response function of homogeneous electron systems. In order to assess their quality, we have tested the total kinetic energies as well as the kinetic energy density for atoms. The results show that these nonlocal functionals give as good results as the most sophisticated functionals in the literature. The proposed scheme for constructing the functionals means a step ahead in the field of fully nonlocal kinetic energy functionals, because they are capable of giving better local behavior than the semilocal functionals, yielding at the same time accurate results for total kinetic energies. Moreover, the functionals enjoy the possibility of being evaluated as a single integral in momentum space if an adequate reference density is defined, and then quasilinear scaling for the computational cost can be achieved.
Analysis of the local-density approximation of density-functional theory
NASA Astrophysics Data System (ADS)
Sahni, Viraht; Bohnen, K.-P.; Harbola, Manoj K.
1988-03-01
In this paper we perform a configuration-space analysis of the local-density approximation (LDA) for the exchange-correlation energy functional of Kohn-Sham density-functional theory in terms of the corresponding average exchange-correlation charge (hole) and energy densities. According to our analysis, the explanation for the quantitative success of the LDA based on the hole charge-conservation sum rule and the assumed consequent cancellation of errors in the spherical averages of the hole is inadequate. The principal conclusion of our work is that the constraint of charge neutrality is a necessary but not sufficient condition for an approximate energy functional to lead to accurate ground-state energies and ionization potentials. The significant additional requirement for the functional is that it must, at least qualitatively, reproduce correctly the structure of the hole as a function of electron position. We perform our calculations within the exchange-only approximation as applied to atoms and jellium metal surfaces. In atoms the Fermi hole is localized about the nucleus; as a consequence the LDA Fermi hole is accurate only for electron positions close to it. However, we show that the spherically averaged LDA hole is accurate for electron positions in the shell regions; it is substantially in error in the intershell and classically forbidden regions. The fact that the principal contribution to the exchange energy comes from the inner-shell region of the atom, where the LDA hole is accurate, explains why the errors in the LDA ground-state energies are small. However, the ionization potential, which depends on the structure of the hole in the outer regions of the atom, is substantially in error in the LDA since here the LDA hole differs significantly from the exact one. For metallic surfaces, on the other hand, as an electron is pulled from within the metal to infinity outside, the Fermi hole is delocalized and spread throughout the crystal. As a consequence
Krawczyk, Przemysław
2015-05-01
The absorption and emission spectra of three azo sulfonamide compounds in different solvents were investigated theoretically by using response functions combined with density functional theory (DFT), while the solvent effect on the structure and the electronic transitions was determined using the integral equation formalism for the polarizable continuum model (IEF-PCM). The results show that the applied different exchange-correlation functionals can reproduce the experimental values well. DFT calculations of the title compounds showed that the H-bond formed between the solute and solvent molecules is one of the major causes of the reversible solvatochromism observed in measured spectra. This is due to a better stabilization of the neutral form than the zwitterionic form in the polar protic solvents, which is characteristic of the hypsochromic shift. On the other hand, the molecules considered exhibit a monotonic behavior regarding the polarity of the low-lying excited state (Δμg-CT) as a function of the solvent polarity. This dependence occurs in the case of the positive solvatochromism and confirms the thesis regarding the H-bond solute-solvent interactions. Theoretically determined values of the two-photon cross section revealed that the (σOF(2)) shows similar trends with changes in λabs, in contrast to <δ(OF)> values. In conclusion, the results demonstrate that the investigated molecules can be used successfully as fluorochromes in bioimaging. PMID:25877526
Lithium adsorption on graphite from density functional theory calculations.
Valencia, Felipe; Romero, Aldo H; Ancilotto, Francesco; Silvestrelli, Pier Luigi
2006-08-01
The structural, energetic, and electronic properties of the Li/graphite system are studied through density functional theory (DFT) calculations using both the local spin density approximation (LSDA), and the gradient-corrected Perdew-Burke-Ernzerhof (PBE) approximation to the exchange-correlation energy. The calculations were performed using plane waves basis, and the electron-core interactions are described using pseudopotentials. We consider a disperse phase of the adsorbate comprising one Li atom for each 16 graphite surface cells, in a slab geometry. The close contact between the Li nucleus and the graphene plane results in a relatively large binding energy (larger than 1.1 eV). A detailed analysis of the electronic charge distribution, density difference distribution, and band structures indicates that one valence electron is entirely transferred from the atom to the surface, which gives rise to a strong interaction between the resulting lithium ion and the cloud of pi electrons in the substrate. We show that it is possible to explain the differences in the binding of Li, Na, and K adatoms on graphite considering the properties of the corresponding cation/aromatic complexes. PMID:16869593
Constrained Density Functional Theory by Imaginary Time-Step Method
NASA Astrophysics Data System (ADS)
Kidd, Daniel
Constrained Density Functional Theory (CDFT) has been a popular choice within the last decade for sidestepping the self interaction problem within long-range charge transfer calculations. Typically an inner constraint loop is added within the self-consistent field iterations of DFT in order to enforce this charge transfer state by means of a Lagrange multiplier method. In this work, an alternate implementation of CDFT is introduced, that of the imaginary time-step method, which lends itself more readily to real space calculations in the ability to solve numerically for 3D local external potentials which enforce arbitrary given densities. This method has been shown to reproduce the proper 1 / R dependence of charge transfer systems in real space calculations as well as the ability to generate useful constraint potentials. As an example application, this method is shown to be capable of describing defects within periodic systems using finite calculations by constraining the 3D density to that of the periodically calculated perfect system at the boundaries.
Antisites in III-V semiconductors: Density functional theory calculations
NASA Astrophysics Data System (ADS)
Chroneos, A.; Tahini, H. A.; Schwingenschlögl, U.; Grimes, R. W.
2014-07-01
Density functional based simulation, corrected for finite size effects, is used to investigate systematically the formation of antisite defects in III-V semiconductors (III = Al, Ga, and In and V = P, As, and Sb). Different charge states are modelled as a function of the Fermi level and under different growth conditions. The formation energies of group III antisites ( III V q) decrease with increasing covalent radius of the group V atom though not group III radius, whereas group V antisites ( V I I I q) show a consistent decrease in formation energies with increase in group III and group V covalent radii. In general, III V q defects dominate under III-rich conditions and V I I I q under V-rich conditions. Comparison with equivalent vacancy formation energy simulations shows that while antisite concentrations are always dominant under stoichiometric conditions, modest variation in growth or doping conditions can lead to a significantly higher concentration of vacancies.
A numerical efficient way to minimize classical density functional theory
NASA Astrophysics Data System (ADS)
Edelmann, Markus; Roth, Roland
2016-02-01
The minimization of the functional of the grand potential within the framework of classical density functional theory in three spatial dimensions can be numerically very demanding. The Picard iteration, that is often employed, is very simple and robust but can be rather slow. While a number of different algorithms for optimization problems have been suggested, there is still great need for additional strategies. Here, we present an approach based on the limited memory Broyden algorithm that is efficient and relatively simple to implement. We demonstrate the performance of this algorithm with the minimization of an inhomogeneous bulk structure of a fluid with competing interactions. For the problems we studied, we find that the presented algorithm improves performance by roughly a factor of three.
Computational predictions of energy materials using density functional theory
NASA Astrophysics Data System (ADS)
Jain, Anubhav; Shin, Yongwoo; Persson, Kristin A.
2016-01-01
In the search for new functional materials, quantum mechanics is an exciting starting point. The fundamental laws that govern the behaviour of electrons have the possibility, at the other end of the scale, to predict the performance of a material for a targeted application. In some cases, this is achievable using density functional theory (DFT). In this Review, we highlight DFT studies predicting energy-related materials that were subsequently confirmed experimentally. The attributes and limitations of DFT for the computational design of materials for lithium-ion batteries, hydrogen production and storage materials, superconductors, photovoltaics and thermoelectric materials are discussed. In the future, we expect that the accuracy of DFT-based methods will continue to improve and that growth in computing power will enable millions of materials to be virtually screened for specific applications. Thus, these examples represent a first glimpse of what may become a routine and integral step in materials discovery.
Density functional theory an effective method to model polythiophenes
NASA Astrophysics Data System (ADS)
Venkateswaran, S.
The luminescent polymer, poly[2-(3-thienyl)ethanol butoxycarbonyl-methyl urethane, called popularly as PURET, has rekindled research interests due to the recent discovery of its ability for detection of explosives at trace levels of molecules in their vapor phase. In this computational study, Hartree-Fock and/or Density Functional Theory (DFT) methods are applied, using Gaussian09 W software, for calculating the HOMO-LUMO energy levels, the Dipole Moment, and the UV-Vis and IR spectra for the Oligomers of PURET monomer, dimer, and trimer. Similar calculations for a few other Thiophene derivatives, such as TAA. TMA, 3HT, and TTZ, are also shown. DFT-based calculations, employing especially the B3LYP functional, are shown to systematically converge to experimental levels of accuracy for PURET Oligomers.
Density functional theory study of rutile VO2 surfaces
NASA Astrophysics Data System (ADS)
Mellan, Thomas A.; Grau-Crespo, Ricardo
2012-10-01
We present the results of a density functional theory investigation of the surfaces of rutile-like vanadium dioxide, VO2(R). We calculate the surface energies of low Miller index planes and find that the most stable surface orientation is the (110). The equilibrium morphology of a VO2(R) particle has an acicular shape, laterally confined by (110) planes and topped by (011) planes. The redox properties of the (110) surface are investigated by calculating the relative surface free energies of the non-stoichiometric compositions as a function of oxygen chemical potential. It is found that the VO2(110) surface is oxidized with respect to the stoichiometric composition, not only at ambient conditions but also at the more reducing conditions under which bulk VO2 is stable in comparison with bulk V2O5. The adsorbed oxygen forms surface vanadyl species much more favorably than surface peroxo species.
Towards the island of stability with relativistic energy density functionals
Prassa, V.; Niksic, T.; Lalazissis, G. A.; Vretenar, D.
2012-10-20
Relativistic energy density functionals (REDF) provide a complete and accurate, global description of nuclear structure phenomena. Modern semi-empirical functionals, adjusted to the nuclear matter equation of state and to empirical masses of deformed nuclei, are applied to studies of shapes of superheavy nuclei. The theoretical framework is tested in a comparison to empirical masses, quadrupole deformations, and energy barriers of actinide nuclei. The model is used in a self-consistent mean-field calculation of spherical, axial and triaxial shapes of superheavy nuclei, alpha-decay energies and lifetimes. The effect of explicit treatment of collective correlations is analyzed in calculations that consistently use a collective Hamiltonian model based on REDFs.
Electronic properties of graphene nanoribbons: A density functional investigation
Kumar, Sandeep Sharma, Hitesh
2015-05-15
Density functional theory calculations have been performed on graphene nano ribbons (GNRs) to investigate the electronic properties as a function of chirality, size and hydrogenation on the edges. The calculations were performed on GNRs with armchair and zigzag configurations with 28, 34, 36, 40, 50, 56, 62, 66 carbon atoms. The structural stability of AGNR and ZGNR increases with the size of nanoribbon where as hydrogenation of GNR tends to lowers their structural stability. All GNRs considered have shown semiconducting behavior with HOMO-LUMO gap decreasing with the increase in the GNR size. The hydrogenation of GNR decreases its HOMO-LUMO gap significantly. The results are in agreement with the available experimental and theoretical results.
Uncertainty Quantification and Propagation in Nuclear Density Functional Theory
Schunck, N; McDonnell, J D; Higdon, D; Sarich, J; Wild, S M
2015-03-17
Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going eff orts seek to better root nuclear DFT in the theory of nuclear forces, energy functionals remain semi-phenomenological constructions that depend on a set of parameters adjusted to experimental data in fi nite nuclei. In this paper, we review recent eff orts to quantify the related uncertainties, and propagate them to model predictions. In particular, we cover the topics of parameter estimation for inverse problems, statistical analysis of model uncertainties and Bayesian inference methods. Illustrative examples are taken from the literature.
BUILDING A UNIVERSAL NUCLEAR ENERGY DENSITY FUNCTIONAL (UNEDF)
Nazarewicz, Witold
2012-07-01
The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: First, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties. Second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data. Third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory.
Hybrid Density Functionals Tuned towards Fulfillment of Fundamental DFT Conditions
NASA Astrophysics Data System (ADS)
Scheffler, Matthias
2014-03-01
Hybrid exchange-correlation functionals (XC), e.g. PBE0 and HSE, have significantly improved the theoretical description of molecules and solids. Their degree of exact-exchange admixture (α) is in principle a functional of the electron density, but the functional form is not known. In this talk, I will discuss fundamental conditions of exact density-functional theory (DFT) that enable us to find the optimal choice of α for ground-state calculations. In particular, I will discuss the fact that the highest occupied Kohn-Sham level of an N-electron system (ɛHOMO(N)) should be constant for fractional particle numbers between N and N-1 and equals the ionization potential (IP), as given by the total-energy difference. In practice, we realize this in three different ways. XC(α) will be optimized (opt-XC) until it (i) fulfills the condition: ɛHOMO(N) =ɛHOMO (N-1/2) or the Kohn-Sham HOMO agrees with the ionization potential computed in a more sophisticated approach ɛHOMO(N) = IP such as (ii) the G0W0 @opt-XC method or (iii) CCSD(T) or full CI. Using such an opt-XC is essential for describing electron transfer between (organic) molecules, as exemplified by the TTF/TCNQ dimer. It also yields vertical ionization energies of the G2 test set of quantum chemistry with a mean absolute percentage error of only ~3%. Furthermore, our approach removes the starting-point uncertainty of GW calculations and thus bears some resemblance to the consistent starting point scheme and quasiparticle self-consistent GW. While our opt-XC approach yields large α values for small molecules in the gas phase, we find that α needs to be 0.25 or less for organic molecules adsorbed on metals. Work performed in collaboration with V. Atalla, N.A. Richter, S.V. Levchenko, and P. Rinke
Hydroxyl functionalized thermosensitive microgels with quadratic crosslinking density distribution.
Elmas, Begum; Tuncel, Murvet; Senel, Serap; Patir, S; Tuncel, Ali
2007-09-01
N-isopropylacrylamide (NIPA) based uniform thermosensitive microgels were synthesized by dispersion polymerization by using relatively hydrophilic crosslinking agents with hydroxyl functionality. Glycerol dimethacrylate (GDMA), pentaerythritol triacrylate (PETA) and pentaerythritol propoxylate triacrylate (PEPTA) were used as crosslinking agents with different hydrophilicities. A protocol was first proposed to determine the crosslinking density distribution in the thermosensitive microgel particles by confocal laser scanning microscopy (CLSM). The microgels were fluorescently labeled by using hydroxyl group of the crosslinking agent. The CLSM observations performed with the microgels synthesized by three different crosslinking agents showed that the crosslinking density exhibited a quadratic decrease with the increasing radial distance in the spherical microgel particles. This structure led to the formation of more loose gel structure on the particle surface with respect to the center. Then the use of hydrophilic crosslinking agents in the dispersion polymerization of NIPA made possible the synthesis of thermosensitive microgels carrying long, flexible and chemically derivatizable (i.e., hydroxyl functionalized) fringes on the surface by a single-stage dispersion polymerization. The microgels with all crosslinking agents exhibited volume phase transition with the increasing temperature. The microgel obtained by the most hydrophilic crosslinking agent, GDMA exhibited higher hydrodynamic diameters in the fully swollen form at low temperatures than those obtained by PETA and PEPTA. Higher hydrodynamic size decrease from fully swollen form to the fully shrunken form was also observed with the same microgel. PMID:17532327
Probability density function transformation using seeded localized averaging
Dimitrov, N. B.; Jordanov, V. T.
2011-07-01
Seeded Localized Averaging (SLA) is a spectrum acquisition method that averages pulse-heights in dynamic windows. SLA sharpens peaks in the acquired spectra. This work investigates the transformation of the original probability density function (PDF) in the process of applying SLA procedure. We derive an analytical expression for the resulting probability density function after an application of SLA. In addition, we prove the following properties: 1) for symmetric distributions, SLA preserves both the mean and symmetry. 2) for uni-modal symmetric distributions, SLA reduces variance, sharpening the distributions peak. Our results are the first to prove these properties, reinforcing past experimental observations. Specifically, our results imply that in the typical case of a spectral peak with Gaussian PDF the full width at half maximum (FWHM) of the transformed peak becomes narrower even with averaging of only two pulse-heights. While the Gaussian shape is no longer preserved, our results include an analytical expression for the resulting distribution. Examples of the transformation of other PDFs are presented. (authors)
Density functional study of silver defects in telluride thermoelectric materials
NASA Astrophysics Data System (ADS)
Ryu, Byungki; Oh, Min-Wook; Park, Su-Dong
2015-03-01
Silver impurity in telluride thermoelectric materials forms various defect and impurity structures, such as AgSb rich nanoregion in Ag-Sb-Pb-Te, Ag2Te and metallic silver in PbTe. To understand the atomic, electronic, energetic, and diffusion properties of silver impurities in telluride systems, we have performed the density functional theory and density functional perturbation theory calculations of silver doped PbTe. Under Te and Ag rich condition, silver telluride impurity phase or Ag-dimer defects are expected to be easily formed. Under Te poor condition, silver point defects are calculated to be easily formed and they are more stable than native point defects of PbTe, implying that silver point defect might be the major dopant responsible for the carrier generation in PbTe. We also calculated the diffusion coefficient and diffusion length of silver point defect in PbTe. Based on the results, we discussed the electrical and thermoelectric properties of silver doped PbTe. This work was supported by the National Institute of Supercomputing and Network/Korea Institute of Science and Technology Information with supercomputing resources including technical support (KSC-2014-C1-022).
Direct Neutron Capture Calculations with Covariant Density Functional Theory Inputs
NASA Astrophysics Data System (ADS)
Zhang, Shi-Sheng; Peng, Jin-Peng; Smith, Michael S.; Arbanas, Goran; Kozub, Ray L.
2014-09-01
Predictions of direct neutron capture are of vital importance for simulations of nucleosynthesis in supernovae, merging neutron stars, and other astrophysical environments. We calculate the direct capture cross sections for E1 transitions using nuclear structure information from a covariant density functional theory as input for the FRESCO coupled-channels reaction code. We find good agreement of our predictions with experimental cross section data on the double closed-shell targets 16O, 48Ca, and 90Zr, and the exotic nucleus 36S. Extensions of the technique for unstable nuclei and for large-scale calculations will be discussed. Predictions of direct neutron capture are of vital importance for simulations of nucleosynthesis in supernovae, merging neutron stars, and other astrophysical environments. We calculate the direct capture cross sections for E1 transitions using nuclear structure information from a covariant density functional theory as input for the FRESCO coupled-channels reaction code. We find good agreement of our predictions with experimental cross section data on the double closed-shell targets 16O, 48Ca, and 90Zr, and the exotic nucleus 36S. Extensions of the technique for unstable nuclei and for large-scale calculations will be discussed. Supported by the U.S. Dept. of Energy, Office of Nuclear Physics.
Towards simple orbital-dependent density functionals for molecular dissociation
NASA Astrophysics Data System (ADS)
Zhang, Igor Ying; Richter, Patrick; Scheffler, Matthias
2015-03-01
Density functional theory (DFT) is one of the leading first-principles electronic-structure theories. However, molecular dissociation remains a challenge, because it requires a well-balanced description of the drastically different electronic structure at different bond lengths. One typical and well-documented case is the dissociation of both H2+ and H2, for which all popular DFT functionals fail. We start from the Bethe-Goldstone equation to propose a simple orbital-dependent correlation functional which generalizes the linear adiabatic connection approach. The resulting scheme is based on second-order perturbation theory (PT2), but includes the self-consistent coupling of electron-hole pairs, which ensures the correct H2 dissociation limit and gives a finite correlation energy for systems with a (near)-degenerate energy gap. This coupling PT2-like (CPT2) approximation delivers a significant improvement over all existing functionals for both H2 and H2+ dissociation. We will demonstrate the reason for this improvement analytically for H2 in a minimal basis.
Medium density polyethylene composites with functionalized carbon nanotubes
NASA Astrophysics Data System (ADS)
Pulikkathara, Merlyn X.; Kuznetsov, Oleksandr V.; Peralta, Ivana R. G.; Wei, Xin; Khabashesku, Valery N.
2009-05-01
A strong interface between the single-walled carbon nanotubes (SWNTs) and polymer matrix is necessary to achieve enhanced mechanical properties of composites. In this work a series of sidewall-functionalized SWNTs have been investigated in order to evaluate the effect of functionalization on SWNT aspect ratio and composite interfacial chemistry and their role on mechanical properties of a medium density polyethylene (MDPE) matrix. Fluorinated nanotubes (F-SWNTs) were used as precursors for subsequent sidewall functionalization with long chain alkyl groups to produce an F-SWNT- C11H23 derivative. The latter was refluorinated to yield a new perfluorinated derivative, F-SWNT- C11FxHy. The functionalized SWNTs as well as the pristine SWNTs were integrated into an MDPE matrix at a 1 wt% loading. The nanotubes and composite materials were characterized with FTIR, Raman spectroscopy, NMR, XPS, AFM, SEM, TGA, DSC and tensile tests. When incorporated into polyethylene, the new perfluorinated derivative, F-SWNT- C11FxHy, yielded the highest tensile strength value among all nanotube/MDPE composite samples, showing a 52% enhancement in comparison with the neat MDPE. The 1 wt% SWNT/MDPE composite contained nanotubes with a larger aspect ratio but, due to a lack of interfacial chemistry, it resulted in less improvement in mechanical properties compared to the composites made with the fluorinated SWNT derivatives.
Medium density polyethylene composites with functionalized carbon nanotubes.
Pulikkathara, Merlyn X; Kuznetsov, Oleksandr V; Peralta, Ivana R G; Wei, Xin; Khabashesku, Valery N
2009-05-13
A strong interface between the single-walled carbon nanotubes (SWNTs) and polymer matrix is necessary to achieve enhanced mechanical properties of composites. In this work a series of sidewall-functionalized SWNTs have been investigated in order to evaluate the effect of functionalization on SWNT aspect ratio and composite interfacial chemistry and their role on mechanical properties of a medium density polyethylene (MDPE) matrix. Fluorinated nanotubes (F-SWNTs) were used as precursors for subsequent sidewall functionalization with long chain alkyl groups to produce an F-SWNT- C(11)H(23) derivative. The latter was refluorinated to yield a new perfluorinated derivative, F-SWNT- C(11)F(x)H(y). The functionalized SWNTs as well as the pristine SWNTs were integrated into an MDPE matrix at a 1 wt% loading. The nanotubes and composite materials were characterized with FTIR, Raman spectroscopy, NMR, XPS, AFM, SEM, TGA, DSC and tensile tests. When incorporated into polyethylene, the new perfluorinated derivative, F-SWNT- C(11)F(x)H(y), yielded the highest tensile strength value among all nanotube/MDPE composite samples, showing a 52% enhancement in comparison with the neat MDPE. The 1 wt% SWNT/MDPE composite contained nanotubes with a larger aspect ratio but, due to a lack of interfacial chemistry, it resulted in less improvement in mechanical properties compared to the composites made with the fluorinated SWNT derivatives. PMID:19420641
Abnormal Functional Connectivity Density in Post-traumatic Stress Disorder.
Zhang, Youxue; Xie, Bing; Chen, Heng; Li, Meiling; Liu, Feng; Chen, Huafu
2016-05-01
Post-traumatic stress disorder (PTSD) is a psychiatric disorder that occurs in individuals who have experienced life-threatening mental traumas. Previous neuroimaging studies have indicated that the pathology of PTSD may be associated with the abnormal functional integration among brain regions. In the current study, we used functional connectivity density (FCD) mapping, a novel voxel-wise data-driven approach based on graph theory, to explore aberrant FC through the resting-state functional magnetic resonance imaging of the PTSD. We calculated both short- and long-range FCD in PTSD patients and healthy controls (HCs). Compared with HCs, PTSD patients showed significantly increased long-range FCD in the left dorsolateral prefrontal cortex (DLPFC), but no abnormal short-range FCD was found in PTSD. Furthermore, seed-based FC analysis of the left DLPFC showed increased connectivity in the left superior parietal lobe and visual cortex of PTSD patients. The results suggested that PTSD patients experienced a disruption of intrinsic long-range functional connections in the fronto-parietal network and visual cortex, which are associated with attention control and visual information processing. PMID:26830769
Daubechies wavelets for linear scaling density functional theory.
Mohr, Stephan; Ratcliff, Laura E; Boulanger, Paul; Genovese, Luigi; Caliste, Damien; Deutsch, Thierry; Goedecker, Stefan
2014-05-28
We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10,000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems. PMID:24880269
Daubechies wavelets for linear scaling density functional theory
Mohr, Stephan; Ratcliff, Laura E.; Genovese, Luigi; Caliste, Damien; Deutsch, Thierry; Boulanger, Paul; Goedecker, Stefan
2014-05-28
We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10 000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.
Structural stability and functional remodeling of high-density lipoproteins.
Gursky, Olga
2015-09-14
Lipoproteins are protein-lipid nanoparticles that transport lipids in circulation and are central in atherosclerosis and other disorders of lipid metabolism. Apolipoproteins form flexible structural scaffolds and important functional ligands on the particle surface and direct lipoprotein metabolism. Lipoproteins undergo multiple rounds of metabolic remodeling that is crucial to lipid transport. Important aspects of this remodeling, including apolipoprotein dissociation and particle fusion, are mimicked in thermal or chemical denaturation and are modulated by free energy barriers. Here we review the biophysical studies that revealed the kinetic mechanism of lipoprotein stabilization and unraveled its structural basis. The main focus is on high-density lipoprotein (HDL). An inverse correlation between stability and functions of various HDLs in cholesterol transport suggests the functional role of structural disorder. A mechanism for the conformational adaptation of the major HDL proteins, apoA-I and apoA-II, to the increasing lipid load is proposed. Together, these studies help understand why HDL forms discrete subclasses separated by kinetic barriers, which have distinct composition, conformation and functional properties. Understanding these properties may help improve HDL quality and develop novel therapies for cardiovascular disease. PMID:25749369
NASA Astrophysics Data System (ADS)
Holas, A.; March, N. H.; Rubio, Angel
2005-11-01
Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force Fxc(r)=-∇υxc(r) associated with the xc potential υxc(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule ⟨nFxc⟩=0 relating the xc force with the ground-state density n(r ). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions.
Holas, A; March, N H; Rubio, Angel
2005-11-15
Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force F(xc)(r)= -inverted Deltaupsilon(xc)(r) associated with the xc potential upsilon(xc)(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule nF(xc)=0 relating the xc force with the ground-state density n(r). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions. PMID:16321073
NASA Astrophysics Data System (ADS)
Mattsson, Thomas R.
2007-06-01
Atomistic simulations employing Density Functional Theory (DFT) have recently emerged as a powerful way of increasing our understanding of materials and processes in high energy density physics. Knowledge of the properties of water (equation of state, electrical conductivity, diffusion, low-energy opacity) is essential for correctly describing the physics of giant planets as well as shock waves in water. Although a qualitative picture of water electrical conductivity has emerged, the necessary quantitative information is scarce over a wide range of temperature and density. Since experiments can only access certain areas of phase space, and often require modeling as a part of the analysis, Quantum Molecular Dynamics simulations play a vital role. Using finite-temperature density functional theory (FT-DFT), we have investigated the structure and electronic conductivity of water across three phase transitions (molecular liquid/ ionic liquid/ superionic/ electronic liquid). The ionic contribution to the conduction is calculated from proton diffusion and the electronic contribution is calculated using the Kubo-Greenwood formula. The calculations are performed with VASP, a plane-wave pseudo-potential code. There is a rapid transition to ionic conduction at 2000 K and 2 g/cm^3, whereas electronic conduction dominates at temperatures at and above 6000 K&[tilde;1]. Contrary to earlier results using the Car-Parrinello method&[tilde;2], we predict that the fluid bordering the superionic phase is conducting above 4000 K and 100 GPa. Our comprehensive use of FT-DFT explains the new findings. The calculated conductivity is compared to experimental data. I gratefully acknowledge Mike Desjarlais, my collaborator in this effort. The LDRD office at Sandia supported this work. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL
Mossahebi, Sina; Zhu, Simeng; Chen, Howard; Shmuylovich, Leonid; Ghosh, Erina; Kovács, Sándor J
2014-01-01
Quantitative cardiac function assessment remains a challenge for physiologists and clinicians. Although historically invasive methods have comprised the only means available, the development of noninvasive imaging modalities (echocardiography, MRI, CT) having high temporal and spatial resolution provide a new window for quantitative diastolic function assessment. Echocardiography is the agreed upon standard for diastolic function assessment, but indexes in current clinical use merely utilize selected features of chamber dimension (M-mode) or blood/tissue motion (Doppler) waveforms without incorporating the physiologic causal determinants of the motion itself. The recognition that all left ventricles (LV) initiate filling by serving as mechanical suction pumps allows global diastolic function to be assessed based on laws of motion that apply to all chambers. What differentiates one heart from another are the parameters of the equation of motion that governs filling. Accordingly, development of the Parametrized Diastolic Filling (PDF) formalism has shown that the entire range of clinically observed early transmitral flow (Doppler E-wave) patterns are extremely well fit by the laws of damped oscillatory motion. This permits analysis of individual E-waves in accordance with a causal mechanism (recoil-initiated suction) that yields three (numerically) unique lumped parameters whose physiologic analogues are chamber stiffness (k), viscoelasticity/relaxation (c), and load (xo). The recording of transmitral flow (Doppler E-waves) is standard practice in clinical cardiology and, therefore, the echocardiographic recording method is only briefly reviewed. Our focus is on determination of the PDF parameters from routinely recorded E-wave data. As the highlighted results indicate, once the PDF parameters have been obtained from a suitable number of load varying E-waves, the investigator is free to use the parameters or construct indexes from the parameters (such as stored
Mossahebi, Sina; Zhu, Simeng; Chen, Howard; Shmuylovich, Leonid; Ghosh, Erina; Kovács, Sándor J.
2014-01-01
Quantitative cardiac function assessment remains a challenge for physiologists and clinicians. Although historically invasive methods have comprised the only means available, the development of noninvasive imaging modalities (echocardiography, MRI, CT) having high temporal and spatial resolution provide a new window for quantitative diastolic function assessment. Echocardiography is the agreed upon standard for diastolic function assessment, but indexes in current clinical use merely utilize selected features of chamber dimension (M-mode) or blood/tissue motion (Doppler) waveforms without incorporating the physiologic causal determinants of the motion itself. The recognition that all left ventricles (LV) initiate filling by serving as mechanical suction pumps allows global diastolic function to be assessed based on laws of motion that apply to all chambers. What differentiates one heart from another are the parameters of the equation of motion that governs filling. Accordingly, development of the Parametrized Diastolic Filling (PDF) formalism has shown that the entire range of clinically observed early transmitral flow (Doppler E-wave) patterns are extremely well fit by the laws of damped oscillatory motion. This permits analysis of individual E-waves in accordance with a causal mechanism (recoil-initiated suction) that yields three (numerically) unique lumped parameters whose physiologic analogues are chamber stiffness (k), viscoelasticity/relaxation (c), and load (xo). The recording of transmitral flow (Doppler E-waves) is standard practice in clinical cardiology and, therefore, the echocardiographic recording method is only briefly reviewed. Our focus is on determination of the PDF parameters from routinely recorded E-wave data. As the highlighted results indicate, once the PDF parameters have been obtained from a suitable number of load varying E-waves, the investigator is free to use the parameters or construct indexes from the parameters (such as stored
NASA Astrophysics Data System (ADS)
Bocharov, Dmitry; Chollet, Melanie; Krack, Matthias; Bertsch, Johannes; Grolimund, Daniel; Martin, Matthias; Kuzmin, Alexei; Purans, Juris; Kotomin, Eugene
2016-05-01
X-ray absorption spectroscopy is employed to study the local structure of pure and Cr-doped UO2 at 300 K. The U L3-edge EXAFS spectrum is interpreted within the multiplescattering (MS) theory using the results of the classical and ab initio molecular dynamics simulations, allowing us to validate the accuracy of theoretical models. The Cr K-edge XANES is simulated within the full-multiple-scattering formalism considering a substitutional model (Cr at U site). It is shown that both unrelaxed and relaxed structures, produced by ab initio density functional theory (DFT) calculations, fail to describe the experiment.
NASA Astrophysics Data System (ADS)
Sadoudi, J.; Duguet, T.; Meyer, J.; Bender, M.
2013-12-01
Background: In one way or another, all modern parametrizations of the nuclear energy density functional (EDF) do not respect the exchange symmetry associated with Pauli's principle. It has been recently shown that this practice jeopardizes multireference (MR) EDF calculations by contaminating the energy with spurious self-interactions that, for example, lead to finite steps or even divergences when plotting it as a function of collective coordinates [J. Dobaczewski , Phys. Rev. CPRVCAN0556-281310.1103/PhysRevC.76.054315 76, 054315 (2007); D. Lacroix , Phys. Rev. CPRVCAN0556-281310.1103/PhysRevC.79.044318 79, 044318 (2009)]. As of today, the only viable option to bypass these pathologies is to rely on EDF kernels that enforce Pauli's principle from the outset by strictly and exactly deriving from a genuine, i.e., density-independent, Hamilton operator.Purpose: The objective is to build cutting-edge parametrizations of the EDF kernel deriving from a pseudopotential that can be safely employed in symmetry restoration and configuration mixing calculations.Methods: We wish to develop the most general Skyrme-like EDF parametrization containing linear, bilinear, and trilinear terms in the density matrices with up to two gradients, under the key constraint that it derives strictly from an effective Hamilton operator. While linear and bilinear terms are obtained from a standard one-body kinetic energy operator and a (density-independent) two-body Skyrme pseudopotential, the most general three-body Skyrme-like pseudopotential containing up to two gradient operators is constructed to generate the trilinear part. The present study is limited to central terms. Spin orbit and tensor will be addressed in a forthcoming paper.Results: The most general central Skyrme-type zero-range three-body interaction is built up to second order in derivatives. The complete trilinear EDF, including time-odd and T=1 pairing parts, is derived along with the corresponding normal and anomalous
Perspective: Fifty years of density-functional theory in chemical physics
Becke, Axel D.
2014-05-14
Since its formal inception in 1964–1965, Kohn-Sham density-functional theory (KS-DFT) has become the most popular electronic structure method in computational physics and chemistry. Its popularity stems from its beautifully simple conceptual framework and computational elegance. The rise of KS-DFT in chemical physics began in earnest in the mid 1980s, when crucial developments in its exchange-correlation term gave the theory predictive power competitive with well-developed wave-function methods. Today KS-DFT finds itself under increasing pressure to deliver higher and higher accuracy and to adapt to ever more challenging problems. If we are not mindful, however, these pressures may submerge the theory in the wave-function sea. KS-DFT might be lost. I am hopeful the Kohn-Sham philosophical, theoretical, and computational framework can be preserved. This Perspective outlines the history, basic concepts, and present status of KS-DFT in chemical physics, and offers suggestions for its future development.
Density functional theory based generalized effective fragment potential method
Nguyen, Kiet A. E-mail: ruth.pachter@wpafb.af.mil; Pachter, Ruth E-mail: ruth.pachter@wpafb.af.mil; Day, Paul N.
2014-06-28
We present a generalized Kohn-Sham (KS) density functional theory (DFT) based effective fragment potential (EFP2-DFT) method for the treatment of solvent effects. Similar to the original Hartree-Fock (HF) based potential with fitted parameters for water (EFP1) and the generalized HF based potential (EFP2-HF), EFP2-DFT includes electrostatic, exchange-repulsion, polarization, and dispersion potentials, which are generated for a chosen DFT functional for a given isolated molecule. The method does not have fitted parameters, except for implicit parameters within a chosen functional and the dispersion correction to the potential. The electrostatic potential is modeled with a multipolar expansion at each atomic center and bond midpoint using Stone's distributed multipolar analysis. The exchange-repulsion potential between two fragments is composed of the overlap and kinetic energy integrals and the nondiagonal KS matrices in the localized molecular orbital basis. The polarization potential is derived from the static molecular polarizability. The dispersion potential includes the intermolecular D3 dispersion correction of Grimme et al. [J. Chem. Phys. 132, 154104 (2010)]. The potential generated from the CAMB3LYP functional has mean unsigned errors (MUEs) with respect to results from coupled cluster singles, doubles, and perturbative triples with a complete basis set limit (CCSD(T)/CBS) extrapolation, of 1.7, 2.2, 2.0, and 0.5 kcal/mol, for the S22, water-benzene clusters, water clusters, and n-alkane dimers benchmark sets, respectively. The corresponding EFP2-HF errors for the respective benchmarks are 2.41, 3.1, 1.8, and 2.5 kcal/mol. Thus, the new EFP2-DFT-D3 method with the CAMB3LYP functional provides comparable or improved results at lower computational cost and, therefore, extends the range of applicability of EFP2 to larger system sizes.
Density functional theory based generalized effective fragment potential method.
Nguyen, Kiet A; Pachter, Ruth; Day, Paul N
2014-06-28
We present a generalized Kohn-Sham (KS) density functional theory (DFT) based effective fragment potential (EFP2-DFT) method for the treatment of solvent effects. Similar to the original Hartree-Fock (HF) based potential with fitted parameters for water (EFP1) and the generalized HF based potential (EFP2-HF), EFP2-DFT includes electrostatic, exchange-repulsion, polarization, and dispersion potentials, which are generated for a chosen DFT functional for a given isolated molecule. The method does not have fitted parameters, except for implicit parameters within a chosen functional and the dispersion correction to the potential. The electrostatic potential is modeled with a multipolar expansion at each atomic center and bond midpoint using Stone's distributed multipolar analysis. The exchange-repulsion potential between two fragments is composed of the overlap and kinetic energy integrals and the nondiagonal KS matrices in the localized molecular orbital basis. The polarization potential is derived from the static molecular polarizability. The dispersion potential includes the intermolecular D3 dispersion correction of Grimme et al. [J. Chem. Phys. 132, 154104 (2010)]. The potential generated from the CAMB3LYP functional has mean unsigned errors (MUEs) with respect to results from coupled cluster singles, doubles, and perturbative triples with a complete basis set limit (CCSD(T)/CBS) extrapolation, of 1.7, 2.2, 2.0, and 0.5 kcal/mol, for the S22, water-benzene clusters, water clusters, and n-alkane dimers benchmark sets, respectively. The corresponding EFP2-HF errors for the respective benchmarks are 2.41, 3.1, 1.8, and 2.5 kcal/mol. Thus, the new EFP2-DFT-D3 method with the CAMB3LYP functional provides comparable or improved results at lower computational cost and, therefore, extends the range of applicability of EFP2 to larger system sizes. PMID:24985612
Zhang, Huan-Huan; Luo, Yong-Chun; Wang, Hua-Peng; Chen, Wei; Xu, Peng-Fei
2014-09-19
A TiCl4 promoted formal [3 + 3] cycloaddition of cyclopropane 1,1-diesters with azides has been developed for the synthesis of highly functionalized triazinines. Both stoichiometric and substoichiometric versions of this reaction were accomplished dependent on the choice of solvent. It is noteworthy that the corresponding products could be easily converted to biologically important azetidines by simple thermolysis. PMID:25192042
NASA Astrophysics Data System (ADS)
Schoonmaker, Robert; Clark, Stewart; Lancaster, Tom; Frawley, Thomas; Hatton, Peter
Iron arsenide intersects interesting physics between novel superconductors and other helical magnetic ordering in Pnma metal arsenide materials. Recent diffraction data has found a more complex ordering than a simple helical incommensurate spin density wave. Instead iron arsenide exhibits a definite chirality to the helimagnetism, an ellipticity in the spiral not aligned with the crystal axis, and resonant diffraction peaks forbidden by the Pnma symmetry. From non-magnetic and collinear density functional theory calculations we present insight into the mechanisms for the formation of this helimagnetic state. We find that ferromagnetic superexchange is a likely mechanism for the spin ordering and that the noncollinear ordering under this regime is caused by the spins on neighbouring irons arranging to minimise direct exchange between iron atoms, and also minimize disruption of the ferromagnetic superexchange between priveleged iron-arsenic pairs. To explain the forbidden peaks in the diffraction we have performed second-order spin-orbit perturbation calculations on the nonmagnetic calculation, which finds that the orbital ordering on the iron atoms coupled to the helimagnetism will lead to the otherwise symmetry-forbidden peaks.
Open Quantum Transport and Non-Hermitian Real-Time Time-Dependent Density Functional Theory
NASA Astrophysics Data System (ADS)
Elenewski, Justin; Zhao, Yanxiang; Chen, Hanning
Sub-nanometer electronic devices are notoriously difficult to simulate, with the most widely adopted transport schemes predicting currents that diverge from experiment by several orders of magnitude. This deviation arises from numerous factors, including the inability of these methods to accommodate dynamic processes such as charge reorganization. A promising alternative entails the direct propagation of an electronic structure calculation, as exemplified by real-time time-dependent density functional theory (RT-TDDFT). Unfortunately this framework is inherently that of a closed system, and modifications must be made to handle incoming and outgoing particle fluxes. To this end, we establish a formal correspondence between the quantum master equation for an open, many-particle system and its description in terms of RT-TDDFT and non-Hermitian boundary potentials. By dynamically constraining the particle density within the boundary regions corresponding to the device leads, a simulation may be selectively converged to the non-equilibrium steady state associated with a given electrostatic bias. Our numerical tests demonstrate that this algorithm is both highly stable and readily integrated into existing electronic structure frameworks
Specification of optical components using the power spectral density function
Lawson, J.K.; Wolfe, C.R.; Manes, K.R.; Trenholme, J.B.; Aikens, D.M.; English, R.E. Jr.
1995-06-20
This paper describes the use of Fourier techniques to characterize the wavefront of optical components, specifically, the use of the power spectral density, (PSD), function. The PSDs of several precision optical components will be shown. Many of the optical components of interest to us have square, rectangular or irregularly shaped apertures with major dimensions up-to 800 mm. The wavefronts of components with non-circular apertures cannot be analyzed with Zernicke polynomials since these functions are an orthogonal set for circular apertures only. Furthermore, Zernicke analysis is limited to treating low frequency wavefront aberrations; mid-spatial scale and high frequency error are expressed only as ``residuals.`` A more complete and powerful representation of the optical wavefront can be obtained by Fourier analysis in 1 or 2 dimensions. The PSD is obtained from the amplitude of frequency components present in the Fourier spectrum. The PSD corresponds to the scattered intensity as a function of scattering angle in the wavefront and can be used to describe the intensity distribution at focus. The shape of a resultant wavefront or the focal spot of a complex multi-component laser system can be calculated and optimized using the PSDs of individual optical components which comprise it.
Effective quadrupole-quadrupole interaction from density functional theory
NASA Astrophysics Data System (ADS)
Alhassid, Y.; Bertsch, G. F.; Fang, L.; Sabbey, B.
2006-09-01
The density functional theory of nuclear structure provides a many-particle wave function that is useful for static properties, but an extension of the theory is necessary to describe correlation effects or other dynamic properties. We propose a procedure to extend the theory by mapping the properties of a self-consistent mean-field theory onto an effective shell-model Hamiltonian with quadrupole-quadrupole interaction. In this initial study, we consider the sd-shell nuclei Ne20, Mg24, Si28, and Ar36. The method is first tested with the USD shell-model Hamiltonian, using its mean-field approximation to construct an effective Hamiltonian and partially recover correlation effects. We find that more than half of the correlation energy is due to the quadrupole interaction. We then follow a similar procedure but using the SLy4 Skyrme energy functional as our starting point and truncating the space to the spherical sd shell. The constructed shell-model Hamiltonian is found to satisfy minimal consistency requirements to reproduce the properties of the mean-field solution. The quadrupolar correlation energies computed with the mapped Hamiltonian are reasonable compared with those computed by other methods. The method also provides a well-defined renormalization of the quadrupole operator in the shell-model space, the “effective charge” of the phenomenological shell model.
Density-functional theory: time to move up?
NASA Astrophysics Data System (ADS)
Marzari, Nicola
2013-03-01
Materials' simulations based on density-functional theory (DFT) have become an extremely powerful and widely used tool for scientific discovery and technological advancement. Still, in the current approximations, they remain an imperfect tool for predicting materials' properties, with open and urgent challenges in the quest towards qualitative and quantitative accuracy. Several of these challenges stem from the remnants of self-interaction in the electronic-structure framework, leading to qualitative failures in describing some of the fundamental processes involved e.g. in energy applications - from charge-transfer excitations to photoemission spectra to the structure and reactivity of transition-metal complexes. I'll discuss these challenges in realistic case studies, and present a brief overview of some of our suggestions for possible solutions - including constrained DFT, DFT + onsite and intersite Hubbard terms, and Koopmans' compliant energy functionals. In particular, I'll highlight how Koopmans' compliant functionals point to a beyond-DFT formulation where both total energies and spectroscopic properties can be accounted for. Such framework will be illustrated with applications to real systems and with simplified models that can be solved exactly. Work done in collaboration with Patrick H-L Sit, Heather Kulik, Damian Scherlis, Matteo Cococcioni, Ismaila Dabo, Andrea Ferretti, Nicolas Poilvert, Cheol-Hwan Park, Giovanni Borghi, and Linh Nguyen.
Probability Density Functions of Observed Rainfall in Montana
NASA Technical Reports Server (NTRS)
Larsen, Scott D.; Johnson, L. Ronald; Smith, Paul L.
1995-01-01
The question of whether a rain rate probability density function (PDF) can vary uniformly between precipitation events is examined. Image analysis on large samples of radar echoes is possible because of advances in technology. The data provided by such an analysis easily allow development of radar reflectivity factors (and by extension rain rate) distribution. Finding a PDF becomes a matter of finding a function that describes the curve approximating the resulting distributions. Ideally, one PDF would exist for all cases; or many PDF's that have the same functional form with only systematic variations in parameters (such as size or shape) exist. Satisfying either of theses cases will, validate the theoretical basis of the Area Time Integral (ATI). Using the method of moments and Elderton's curve selection criteria, the Pearson Type 1 equation was identified as a potential fit for 89 percent of the observed distributions. Further analysis indicates that the Type 1 curve does approximate the shape of the distributions but quantitatively does not produce a great fit. Using the method of moments and Elderton's curve selection criteria, the Pearson Type 1 equation was identified as a potential fit for 89% of the observed distributions. Further analysis indicates that the Type 1 curve does approximate the shape of the distributions but quantitatively does not produce a great fit.
Building A Universal Nuclear Energy Density Functional (UNEDF)
Joe Carlson; Dick Furnstahl; Mihai Horoi; Rusty Lusk; Witek Nazarewicz; Esmond Ng; Ian Thompson; James Vary
2012-09-30
During the period of Dec. 1 2006 - Jun. 30, 2012, the UNEDF collaboration carried out a comprehensive study of all nuclei, based on the most accurate knowledge of the strong nuclear interaction, the most reliable theoretical approaches, the most advanced algorithms, and extensive computational resources, with a view towards scaling to the petaflop platforms and beyond. The long-term vision initiated with UNEDF is to arrive at a comprehensive, quantitative, and unified description of nuclei and their reactions, grounded in the fundamental interactions between the constituent nucleons. We seek to replace current phenomenological models of nuclear structure and reactions with a well-founded microscopic theory that delivers maximum predictive power with well-quantified uncertainties. Specifically, the mission of this project has been three-fold: first, to find an optimal energy density functional (EDF) using all our knowledge of the nucleonic Hamiltonian and basic nuclear properties; second, to apply the EDF theory and its extensions to validate the functional using all the available relevant nuclear structure and reaction data; third, to apply the validated theory to properties of interest that cannot be measured, in particular the properties needed for reaction theory. The main physics areas of UNEDF, defined at the beginning of the project, were: ab initio structure; ab initio functionals; DFT applications; DFT extensions; reactions.
A Density Functional Theory Study of Formaldehyde Adsorption on Ceria
Mei, Donghai; Deskins, N. Aaron; Dupuis, Michel
2007-11-01
Molecular adsorption of formaldehyde on the stoichiometric CeO2(111) and CeO2(110) surfaces was studied using periodic density functional theory. Two adsorption modes (strong chemisorbed and weak physisorbed) were identified on both surfaces. This is consistent with recent experimental observations. On the (111) surface, formaldehyde strongly chemisorbs with an adsorption energy of 0.86 eV to form a dioxymethylene-like structure, in which a surface O lifts from the surface to bind with the C of formaldehyde. A weak physisorbed state with adsorption energy of 0.28 eV was found with the O of formaldehyde interacting with a surface Ce. On the (110) surface, dioxymethyelene formation was also observed, with an adsorption energy of 1.31 eV. The weakly adsorbed state of formaldehyde on the (110) surface was energetically comparable to the weak adsorption state on the (111) surface, but adsorption occurred through a formaldehyde C and surface O interaction. Analysis of the local density of states and charge density differences after adsorption shows that strong covalent bonding occurs between the C of formaldehyde and surface O when dioxymethylene forms. Calculated vibrational frequencies also confirm dioxymethylene formation. Our results also show that as the coverage increases, the adsorption of formaldehyde on the (111) surface becomes weak, but is nearly unaffected on the (110) surface. This work was supported by a Laboratory Directed Research and Development (LDRD) project of the Pacific Northwest National Laboratory (PNNL). The computations were performed using the Molecular Science Computing Facility in the William R. Wiley Environmental Molecular Sciences Laboratory, which is a U.S. Department of Energy national scientific user facility located at PNNL in Richland, Washington. Computing time was made under a Computational Grand Challenge “Computational Catalysis”. Part of the computing time was also granted by the National Energy Research Scientific Computing
Rethinking Formalisms in Formal Education
ERIC Educational Resources Information Center
Nathan, Mitchell J.
2012-01-01
I explore a belief about learning and teaching that is commonly held in education and society at large that nonetheless is deeply flawed. The belief asserts that mastery of "formalisms"--specialized representations such as symbolic equations and diagrams with no inherent meaning except that which is established by convention--is prerequisite to…
Hierarchy of equations for the energy functional of the density-functional theory
NASA Astrophysics Data System (ADS)
Nagy, Á.
1993-04-01
A hierarchy of equations has been derived for the energy functionals of the density-functional theory using the virial theorem and the Levy-Perdew relation. In the local-density approximation, the solution of the equations of hierarchy for the kinetic and exchange energies provides the well-known Thomas-Fermi expression for the kinetic energy and the Slater-Gáspár-Kohn-Sham expression for the exchange. The truncation of the hierarchies of the kinetic and exchange energies results in rigorous lower bounds to the kinetic energy and upper bounds to the exchange energy in the plane-wave approximation.
Ionospheric mapping functions based on electron density fields
NASA Astrophysics Data System (ADS)
Zus, Florian; Deng, Zhiguo; Heise, Stefan; Wickert, Jens
2016-04-01
We developed an ionospheric Mapping Function (MF) for the Global Navigation Satellite System (GNSS) which is based on the electron density field of the International Reference Ionosphere (IRI). The station specific MF utilizes a look-up table which contains a set of ray-traced ionospheric delays. Hence, unlike the simple MFs that are currently in use, the developed MF depends on the time, location, elevation and azimuth angle. Ray-bending is taken into account, which implies that the MF depends on the carrier frequency as well. This frequency dependency of the MF can be readily used to examine higher-order ionospheric effects due to ray-bending. We compare the proposed MF with the so-called single layer model MF and find significant differences in particular around the equatorial anomaly. In so-far as the proposed MF is based on a realistic electron density field (IRI) our comparison shows the potential error of the single-layer model MF in practice. We conclude that the developed MF concept might be valuable in the GNSS Total Electron Content estimation. The frequency dependency of the MF can be used to mitigate higher-order ionospheric effects.
Density functional theory and phytochemical study of 8-hydroxyisodiospyrin
NASA Astrophysics Data System (ADS)
Ullah, Zakir; Ata-ur-Rahman; Fazl-i-Sattar; Rauf, Abdur; Yaseen, Muhammad; Hassan, Waseem; Tariq, Muhammad; Ayub, Khurshid; Tahir, Asif Ali; Ullah, Habib
2015-09-01
Comprehensive theoretical and experimental studies of a natural product, 8-hydroxyisodiospyrin (HDO) have been carried out. Based on the correlation of experimental and theoretical data, an appropriate computational model was developed for obtaining the electronic, spectroscopic, and thermodynamic parameters of HDO. First of all, the exact structure of HDO is confirmed from the nice correlation of theory and experiment, prior to determination of its electroactive nature. Hybrid density functional theory (DFT) is employed for all theoretical simulations. The experimental and predicted IR and UV-vis spectra [B3LYP/6-31+G(d,p) level of theory] have excellent correlation. Inter-molecular non-covalent interaction of HDO with different gases such as NH3, CO2, CO, H2O is investigated through geometrical counterpoise (gCP) i.e., B3LYP-gCP-D3/6-31G∗ method. Furthermore, the inter-molecular interaction is also supported by geometrical parameters, electronic properties, thermodynamic parameters and charge analysis. All these characterizations have corroborated each other and confirmed the electroactive nature (non-covalent interaction ability) of HDO for the studied gases. Electronic properties such as Ionization Potential (IP), Electron Affinities (EA), electrostatic potential (ESP), density of states (DOS), HOMO, LUMO, and band gap of HDO have been estimated for the first time theoretically.
Accurate ionization potential of semiconductors from efficient density functional calculations
NASA Astrophysics Data System (ADS)
Ye, Lin-Hui
2016-07-01
Despite its huge successes in total-energy-related applications, the Kohn-Sham scheme of density functional theory cannot get reliable single-particle excitation energies for solids. In particular, it has not been able to calculate the ionization potential (IP), one of the most important material parameters, for semiconductors. We illustrate that an approximate exact-exchange optimized effective potential (EXX-OEP), the Becke-Johnson exchange, can be used to largely solve this long-standing problem. For a group of 17 semiconductors, we have obtained the IPs to an accuracy similar to that of the much more sophisticated G W approximation (GWA), with the computational cost of only local-density approximation/generalized gradient approximation. The EXX-OEP, therefore, is likely as useful for solids as for finite systems. For solid surfaces, the asymptotic behavior of the vx c has effects similar to those of finite systems which, when neglected, typically cause the semiconductor IPs to be underestimated. This may partially explain why standard GWA systematically underestimates the IPs and why using the same GWA procedures has not been able to get an accurate IP and band gap at the same time.
Kinetic Density Functional Theory: A Microscopic Approach to Fluid Mechanics
NASA Astrophysics Data System (ADS)
Umberto Marini Bettolo, Marconi; Simone, Melchionna
2014-10-01
In the present paper we give a brief summary of some recent theoretical advances in the treatment of inhomogeneous fluids and methods which have applications in the study of dynamical properties of liquids in situations of extreme confinement, such as nanopores, nanodevices, etc. The approach obtained by combining kinetic and density functional methods is microscopic, fully self-consistent and allows to determine both configurational and flow properties of dense fluids. The theory predicts the correct hydrodynamic behavior and provides a practical and numerical tool to determine how the transport properties are modified when the length scales of the confining channels are comparable with the size of the molecules. The applications range from the dynamics of simple fluids under confinement, to that of neutral binary mixtures and electrolytes where the theory in the limit of slow gradients reproduces the known phenomenological equations such as the Planck—Nernst—Poisson and the Smolochowski equations. The approach here illustrated allows for fast numerical solution of the evolution equations for the one-particle phase-space distributions by means of the weighted density lattice Boltzmann method and is particularly useful when one considers flows in complex geometries.
Nitrotyrosine adsorption on defective graphene: A density functional theory study
NASA Astrophysics Data System (ADS)
Majidi, R.; Karami, A. R.
2015-06-01
We have applied density functional theory to study adsorption of nitrotyrosine on perfect and defective graphene sheets. The graphene sheets with Stone-Wales (SW) defect, pentagon-nonagon (5-9) single vacancy, and pentagon-octagon-pentagon (5-8-5) double vacancy were considered. The calculations of adsorption energy showed that nitrotyrosine presents a more strong interaction with defective graphene rather than with perfect graphene sheet. The order of interaction strength is: SW>5-9>5-8-5>perfect graphene. It is found that the electronic properties of perfect and defective graphene are sensitive to the presence of nitrotyrosine. Hence, graphene sheets can be considered as a good sensor for detection of nitrotyrosine molecule which is observed in connection with several human disorders, such as Parkinson's and Alzheimer's disease.
Band Anticrossing in Dilute Germanium Carbides Using Hybrid Density Functionals
NASA Astrophysics Data System (ADS)
Stephenson, Chad A.; O'brien, William A.; Qi, Meng; Penninger, Michael; Schneider, William F.; Wistey, Mark A.
2016-04-01
Dilute germanium carbides (Ge1- x C x ) offer a direct bandgap for compact silicon photonics, but widely varying properties have been reported. This work reports improved band structure calculations for Ge1- x C x using ab initio simulations that employ the HSE06 exchange-correlation density functional. Contrary to Vegard's law, the conduction band minimum at Γ is consistently found to decrease with increasing C content, while L and X valleys change much more slowly. The calculated Ge bandgap is within 11% of experimental values. A decrease in energy at the Γ conduction band valley of (170 meV ± 50)/%C is predicted, leading to a direct bandgap for x > 0.008. These results indicate a promising material for Group IV lasers.
Native defects in Tl6SI4: Density functional calculations
Shi, Hongliang; Du, Mao -Hua
2015-05-05
In this study, Tl6SI4 is a promising room-temperature semiconductor radiation detection material. Here, we report density functional calculations of native defects and dielectric properties of Tl6SI4. Formation energies and defect levels of native point defects and defect complexes are calculated. Donor-acceptor defect complexes are shown to be abundant in Tl6SI4. High resistivity can be obtained by Fermi level pinning by native donor and acceptor defects. Deep donors that are detrimental to electron transport are identified and methods to mitigate such problem are discussed. Furthermore, we show that mixed ionic-covalent character of Tl6SI4 gives rise to enhanced Born effective charges andmore » large static dielectric constant, which provides effective screening of charged defects and impurities.« less
Periodic Density Functional Theory Solver using Multiresolution Analysis with MADNESS
NASA Astrophysics Data System (ADS)
Harrison, Robert; Thornton, William
2011-03-01
We describe the first implementation of the all-electron Kohn-Sham density functional periodic solver (DFT) using multi-wavelets and fast integral equations using MADNESS (multiresolution adaptive numerical environment for scientific simulation; http://code.google.com/p/m-a-d-n-e-s-s). The multiresolution nature of a multi-wavelet basis allows for fast computation with guaranteed precision. By reformulating the Kohn-Sham eigenvalue equation into the Lippmann-Schwinger equation, we can avoid using the derivative operator which allows better control of overall precision for the all-electron problem. Other highlights include the development of periodic integral operators with low-rank separation, an adaptable model potential for nuclear potential, and an implementation for Hartree Fock exchange. This work was supported by NSF project OCI-0904972 and made use of resources at the Center for Computational Sciences at Oak Ridge National Laboratory under contract DE-AC05-00OR22725.
Self-consistent polarization density functional theory: Application to Argon
Maerzke, Katie A.; Murdachaew, Garold; Mundy, Christopher J.; Schenter, Gregory K.; Siepmann, J. I.
2009-03-12
We present a comprehensive set of results for argon, a case study in weak interactions, using the selfconsistent polarization density functional theory (SCP-DFT). With minimal parameterization, SCPDFT is found is give excellent results for the dimer interaction energy, the second virial coefficient, the liquid structure, and the lattice constant and cohesion energy of the face-centered cubic (fcc) crystal compared to both accurate theoretical and experimental benchmarks. Thus, SCP-DFT holds promise as a fast, efficient, and accurate method for performing ab initio dynamics that include additional polarization and dispersion interactions for large, complex systems involving solvation and bond breaking. This work was supported by the U.S. Department of Energy's (DOE) Office of Basic Energy Sciences, Chemical Sciences program. The Pacific Northwest National Laboratory is operated by Battelle for DOE.
Native defects in Tl6SI4: Density functional calculations
NASA Astrophysics Data System (ADS)
Shi, Hongliang; Du, Mao-Hua
2015-05-01
Tl6SI4 is a promising room-temperature semiconductor radiation detection material. Here, we report density functional calculations of native defects and dielectric properties of Tl6SI4. Formation energies and defect levels of native point defects and defect complexes are calculated. Donor-acceptor defect complexes are shown to be abundant in Tl6SI4. High resistivity can be obtained by Fermi level pinning by native donor and acceptor defects. Deep donors that are detrimental to electron transport are identified and methods to mitigate such problem are discussed. Furthermore, we show that mixed ionic-covalent character of Tl6SI4 gives rise to enhanced Born effective charges and large static dielectric constant, which provides effective screening of charged defects and impurities.
Density functional calculations of Hubbard parameter in actinide series
Puri, A.; Sen, K.D.
1993-05-01
The calculations of Hubbard parameter, U, which defines the polar state formation energy of the reaction 2(5f{sup n} 6d{sup 1} 7d{sup 2}) {yields} 5f{sup n-1} 6d{sup 2}7s{sup 2} + 5f{sup n+1} 7s{sup 2} for the actinide atoms, Th-No, have been carried out using the self-interaction-corrected (SIC) quasi-relativistic local spin density (LSD) functional due to Perdew and Zunger. Based on the available bandwidth calculations for the 5f metals and its monotonically decreasing trend with increasing nuclear charge it is predicted that the 5f state is iterent in Th-Np beyond which it becomes localized. These calculations agree with the conclusions drawn earlier by Johansson using the semiempirical data.
Density Functional Exploration of C4H3N Isomers.
Custer, Thomas; Szczepaniak, Urszula; Gronowski, Marcin; Fabisiewicz, Emilia; Couturier-Tamburelli, Isabelle; Kołos, Robert
2016-07-28
Molecules having C4H3N stoichiometry are of astrophysical interest. Two of these, methylcyanoacetylene (CH3C3N) and its structural isomer allenyl cyanide (H2CCCHN), have been observed in interstellar space, while several more have been examined in laboratories. Here we describe, for a broad range of C4H3N isomers, density functional calculations (B3LYP/aug-cc-pVTZ) of molecular parameters including the energetics, geometries, rotational constants, electric dipole moments, polarizabilities, vibrational IR frequencies, IR absorption intensities, and Raman activities. Singlet-triplet splittings as well as singlet vertical electronic excitation energies are given for selected species. The identification of less stable C4H3N molecules, generated in ongoing spectroscopic experiments, relies heavily on these quantum chemical predictions. PMID:27341606
Fundamental gap of molecular crystals via constrained density functional theory
NASA Astrophysics Data System (ADS)
Droghetti, Andrea; Rungger, Ivan; Das Pemmaraju, Chaitanya; Sanvito, Stefano
2016-05-01
The energy gap of a molecular crystal is one of the most important properties since it determines the crystal charge transport when the material is utilized in electronic devices. This is, however, a quantity difficult to calculate and standard theoretical approaches based on density functional theory (DFT) have proven unable to provide accurate estimates. In fact, besides the well-known band-gap problem, DFT completely fails in capturing the fundamental gap reduction occurring when molecules are packed in a crystal structures. The failure has to be associated with the inability of describing the electronic polarization and the real space localization of the charged states. Here we describe a scheme based on constrained DFT, which can improve upon the shortcomings of standard DFT. The method is applied to the benzene crystal, where we show that accurate results can be achieved for both the band gap and also the energy level alignment.
Descriptions of carbon isotopes within the energy density functional theory
Ismail, Atef; Cheong, Lee Yen; Yahya, Noorhana; Tammam, M.
2014-10-24
Within the energy density functional (EDF) theory, the structure properties of Carbon isotopes are systematically studied. The shell model calculations are done for both even-A and odd-A nuclei, to study the structure of rich-neutron Carbon isotopes. The EDF theory indicates the single-neutron halo structures in {sup 15}C, {sup 17}C and {sup 19}C, and the two-neutron halo structures in {sup 16}C and {sup 22}C nuclei. It is also found that close to the neutron drip-line, there exist amazing increase in the neutron radii and decrease on the binding energies BE, which are tightly related with the blocking effect and correspondingly the blocking effect plays a significant role in the shell model configurations.
Time-Dependent Density Functional Theory for Universal Quantum Computation
NASA Astrophysics Data System (ADS)
Tempel, David
2015-03-01
In this talk, I will discuss how the theorems of TDDFT can be applied to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practical standpoint this opens the possibility of approximating observables of interest in quantum computations directly in terms of single-qubit quantities (i.e. as density functionals). Additionally, I will discuss how TDDFT provides an exact prescription for simulating universal Hamiltonians with other universal Hamiltonians that have different, and possibly easier-to-realize two-qubit interactions.
Density functional theory studies of HCOOH decomposition on Pd(111)
NASA Astrophysics Data System (ADS)
Scaranto, Jessica; Mavrikakis, Manos
2016-08-01
The investigation of formic acid (HCOOH) decomposition on transition metal surfaces is important to derive useful insights for vapor phase catalysis involving HCOOH and for the development of direct HCOOH fuel cells (DFAFC). Here we present the results obtained from periodic, self-consistent, density functional theory (DFT-GGA) calculations for the elementary steps involved in the gas-phase decomposition of HCOOH on Pd(111). Accordingly, we analyzed the minimum energy paths for HCOOH dehydrogenation to CO2 + H2 and dehydration to CO + H2O through the carboxyl (COOH) and formate (HCOO) intermediates. Our results suggest that HCOO formation is easier than COOH formation, but HCOO decomposition is more difficult than COOH decomposition, in particular in the presence of co-adsorbed O and OH species. Therefore, both paths may contribute to HCOOH decomposition. CO formation goes mainly through COOH decomposition.
Kappa distribution and Probability Density Functions in Solar Wind
NASA Astrophysics Data System (ADS)
Jurac, S.
2004-12-01
A signature of a statistical intermittency is the presence of large deviations from the average value: this increased probability of finding extreme deviations is characterized by Probability Density Functions (PDFs) which exhibit non Gaussian power-law tails. Such power-law distributions were observed over decades in biology, chemistry, finance and other fields. Known examples include heartbeat histograms, price distribution, turbulent fluid flow and many other non-equilibrium systems. It is shown that the Kappa distribution represents a good description of PDFs observed in Solar wind. The asymmetric fluctuations in variance over time observed in solar wind PDFs are Gamma distributed. It is shown that, by assuming such a distribution of variance, the Kappa distribution can be analitically derived.
Origin of anomeric effect: A density functional steric analysis
Huang, Ying; Zhong, Ai-Guo; Yang, Qinsong; Liu, Shubin
2011-01-01
The anomeric effect (the tendency of heteroatomic substituents adjacent to a heteroatom within the cyclohexane ring to prefer the axial orientation instead of the sterically less hindered equatorial position) is traditionally explained through either the dipole moment repulsion or the hyperconjugation effect. In this work, by employing our recent work in density functional steric analysis, we provide a novel two-component explanation, which is consistent with the common belief in chemistry that the effect has a stereoelectronic origin. With α-D-glucopyranose as the prototype, we systematically explore its conformational space and generate 32 isomers, leading to a total of 80 axial–equatorial conformation pairs. The energy difference analysis of these pairs shows that while statistically speaking the tendency is valid, the anomeric effect is not always true and can be violated. Three energy components, exchange–correlation, classical electrostatic, and density functional steric, are found to be directly proportional to the total energy difference between axial and equatorial isomers. We also found that the total dipole moment change, not the hyperconjugation effect, is a reasonable indicator of the total energy difference. However, all these correlations alone are not strong enough to provide a compellingly convincing explanation for the general validity of the effect. With the help of strong correlations between energy components, an explanation with two energy components, steric and electrostatic, was proposed in this work. We show that the axial–equatorial energy difference in general, with the anomeric effect as a special case, is dictated by two factors of the stereoelectronic origin, steric hindrance and classical electrostaticinteractions, synchronously working together. Another explanation in terms of exchange–correlation and electrostaticinteractions has also been obtained in this work.
Experimental assessment of presumed filtered density function models
NASA Astrophysics Data System (ADS)
Stetsyuk, V.; Soulopoulos, N.; Hardalupas, Y.; Taylor, A. M. K. P.
2015-06-01
Measured filtered density functions (FDFs) as well as assumed beta distribution model of mixture fraction and "subgrid" scale (SGS) scalar variance z '' 2 ¯ , used typically in large eddy simulations, were studied by analysing experimental data, obtained from two-dimensional planar, laser induced fluorescence measurements in isothermal swirling turbulent flows at a constant Reynolds number of 29 000 for different swirl numbers (0.3, 0.58, and 1.07). Two-dimensional spatial filtering, by using a box filter, was performed in order to obtain the filtered variables, namely, resolved mean and "subgrid" scale scalar variance. These were used as inputs for assumed beta distribution of mixture fraction and top-hat FDF shape estimates. The presumed beta distribution model, top-hat FDF, and the measured filtered density functions were used to integrate a laminar flamelet solution in order to calculate the corresponding resolved temperature. The experimentally measured FDFs varied with the flow swirl number and both axial and radial positions in the flow. The FDFs were unimodal at flow regions with low SGS scalar variance, z '' 2 ¯ < 0.01, and bimodal at regions with high SGS variance, z '' 2 ¯ > 0.02. Bimodal FDF could be observed for a filter size of approximately 1.5-2 times the Batchelor scale. Unimodal FDF could be observed for a filter size as large as four times the Batchelor scale under well-mixed conditions. In addition, two common computational models (a gradient assumption and a scale similarity model) for the SGS scalar variance were used with the aim to evaluate their validity through comparison with the experimental data. It was found that the gradient assumption model performed generally better than the scale similarity one.
NASA Astrophysics Data System (ADS)
Yu, Kuang; Libisch, Florian; Carter, Emily A.
2015-09-01
We report a new implementation of the density functional embedding theory (DFET) in the VASP code, using the projector-augmented-wave (PAW) formalism. Newly developed algorithms allow us to efficiently perform optimized effective potential optimizations within PAW. The new algorithm generates robust and physically correct embedding potentials, as we verified using several test systems including a covalently bound molecule, a metal surface, and bulk semiconductors. We show that with the resulting embedding potential, embedded cluster models can reproduce the electronic structure of point defects in bulk semiconductors, thereby demonstrating the validity of DFET in semiconductors for the first time. Compared to our previous version, the new implementation of DFET within VASP affords use of all features of VASP (e.g., a systematic PAW library, a wide selection of functionals, a more flexible choice of U correction formalisms, and faster computational speed) with DFET. Furthermore, our results are fairly robust with respect to both plane-wave and Gaussian type orbital basis sets in the embedded cluster calculations. This suggests that the density functional embedding method is potentially an accurate and efficient way to study properties of isolated defects in semiconductors.
Yu, Kuang; Libisch, Florian
2015-09-14
We report a new implementation of the density functional embedding theory (DFET) in the VASP code, using the projector-augmented-wave (PAW) formalism. Newly developed algorithms allow us to efficiently perform optimized effective potential optimizations within PAW. The new algorithm generates robust and physically correct embedding potentials, as we verified using several test systems including a covalently bound molecule, a metal surface, and bulk semiconductors. We show that with the resulting embedding potential, embedded cluster models can reproduce the electronic structure of point defects in bulk semiconductors, thereby demonstrating the validity of DFET in semiconductors for the first time. Compared to our previous version, the new implementation of DFET within VASP affords use of all features of VASP (e.g., a systematic PAW library, a wide selection of functionals, a more flexible choice of U correction formalisms, and faster computational speed) with DFET. Furthermore, our results are fairly robust with respect to both plane-wave and Gaussian type orbital basis sets in the embedded cluster calculations. This suggests that the density functional embedding method is potentially an accurate and efficient way to study properties of isolated defects in semiconductors.
Current Density Functional Theory Using Meta-Generalized Gradient Exchange-Correlation Functionals.
Furness, James W; Verbeke, Joachim; Tellgren, Erik I; Stopkowicz, Stella; Ekström, Ulf; Helgaker, Trygve; Teale, Andrew M
2015-09-01
We present the self-consistent implementation of current-dependent (hybrid) meta-generalized gradient approximation (mGGA) density functionals using London atomic orbitals. A previously proposed generalized kinetic energy density is utilized to implement mGGAs in the framework of Kohn-Sham current density functional theory (KS-CDFT). A unique feature of the nonperturbative implementation of these functionals is the ability to seamlessly explore a wide range of magnetic fields up to 1 au (∼235 kT) in strength. CDFT functionals based on the TPSS and B98 forms are investigated, and their performance is assessed by comparison with accurate coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) data. In the weak field regime, magnetic properties such as magnetizabilities and nuclear magnetic resonance shielding constants show modest but systematic improvements over generalized gradient approximations (GGA). However, in the strong field regime, the mGGA-based forms lead to a significantly improved description of the recently proposed perpendicular paramagnetic bonding mechanism, comparing well with CCSD(T) data. In contrast to functionals based on the vorticity, these forms are found to be numerically stable, and their accuracy at high field suggests that the extension of mGGAs to CDFT via the generalized kinetic energy density should provide a useful starting point for further development of CDFT approximations. PMID:26575912
Hoyer, Chad E; Gagliardi, Laura; Truhlar, Donald G
2015-11-01
Time-dependent Kohn-Sham density functional theory (TD-KS-DFT) is useful for calculating electronic excitation spectra of large systems, but the low-energy spectra are often complicated by artificially lowered higher-energy states. This affects even the lowest energy excited states. Here, by calculating the lowest energy spin-conserving excited state for atoms from H to K and for formaldehyde, we show that this problem does not occur in multiconfiguration pair-density functional theory (MC-PDFT). We use the tPBE on-top density functional, which is a translation of the PBE exchange-correlation functional. We compare to a robust multireference method, namely, complete active space second-order perturbation theory (CASPT2), and to TD-KS-DFT with two popular exchange-correlation functionals, PBE and PBE0. We find for atoms that the mean unsigned error (MUE) of MC-PDFT with the tPBE functional improves from 0.42 to 0.40 eV with a double set of diffuse functions, whereas the MUEs for PBE and PBE0 drastically increase from 0.74 to 2.49 eV and from 0.45 to 1.47 eV, respectively. PMID:26722961
A density functional for core-valence correlation energy
NASA Astrophysics Data System (ADS)
Ranasinghe, Duminda S.; Frisch, Michael J.; Petersson, George A.
2015-12-01
A density functional, ɛCV-DFT(ρc, ρv), describing the core-valence correlation energy has been constructed as a linear combination of ɛLY Pcorr(ρc), ɛV WN5corr(ρc, ρv), ɛPBEcorr(ρc, ρv), ɛSlaterex(ρc, ρv), ɛHCTHex(ρc, ρv), ɛHFex(ρc, ρv), and F CV -DFT (" separators=" N i , Z i ) , a function of the nuclear charges. This functional, with 6 adjustable parameters, reproduces (±0.27 kcal/mol rms error) a benchmark set of 194 chemical energy changes including 9 electron affinities, 18 ionization potentials, and 167 total atomization energies covering the first- and second-rows of the periodic table. This is almost twice the rms error (±0.16 kcal/mol) obtained with CCSD(T)/MTsmall calculations, but less than half the rms error (±0.65 kcal/mol) obtained with MP2/GTlargeXP calculations, and somewhat smaller than the rms error (±0.39 kcal/mol) obtained with CCSD/MTsmall calculations. The largest positive and negative errors from ɛCV-DFT(ρc, ρv) were 0.88 and -0.75 kcal/mol with the set of 194 core-valence energy changes ranging from +3.76 kcal/mol for the total atomization energy of propyne to -9.05 kcal/mol for the double ionization of Mg. Evaluation of the ɛCV-DFT(ρc, ρv) functional requires less time than a single SCF iteration, and the accuracy is adequate for any model chemistry based on the CCSD(T) level of theory.
Reduced density-matrix functional theory: Correlation and spectroscopy
Di Sabatino, S.; Romaniello, P.; Berger, J. A.; Reining, L.
2015-07-14
In this work, we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard dimer at 1/4 and 1/2 fillings as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison, we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis is made concerning the approximations of the observables. In particular, we focus on the atomic limit, where the two sites of the dimer are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard dimer at 1/2 filling with or without a spin-symmetry-broken ground state allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW, the signature of strong correlation is present, when looking at the removal/addition energies and spectral function from the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover, we show how the spectroscopic properties change from one spin structure to the other.
Electrochemical phase diagrams for Ti oxides from density functional calculations
NASA Astrophysics Data System (ADS)
Huang, Liang-Feng; Rondinelli, James M.
2015-12-01
Developing an accurate simulation method for the electrochemical stability of solids, as well as understanding the physics related with its accuracy, is critically important for improving the performance of compounds and predicting the stability of new materials in aqueous environments. Herein we propose a workflow for the accurate calculation of first-principles electrochemical phase (Pourbaix) diagrams. With this scheme, we study the electrochemical stabilities of Ti and Ti oxides using density-functional theory. First, we find the accuracy of an exchange-correlation functional in predicting formation energies and electrochemical stabilities is closely related with the electronic exchange interaction therein. Second, the metaGGA and hybrid functionals with a more precise description of the electronic exchange interaction lead to a systematic improvement in the accuracy of the Pourbaix diagrams. Furthermore, we show that accurate Ti Pourbaix diagrams also require that thermal effects are included through vibrational contributions to the free energy. We then use these diagrams to explain various experimental electrochemical phenomena for the Ti-O system, and show that if experimental formation energies for Ti oxides, which contain contributions from defects owing to their generation at high (combustion) temperatures, are directly used to predict room temperature Pourbaix diagrams then significant inaccuracies result. In contrast, the formation energies from accurate first-principles calculations, e.g., using metaGGA and hybrid functionals, are found to be more reliable. Finally, to facilitate the future application of our accurate electrochemical phase equilibria diagrams, the variation of the Ti Pourbaix diagrams with aqueous ion concentration is also provided.
A density functional for core-valence correlation energy.
Ranasinghe, Duminda S; Frisch, Michael J; Petersson, George A
2015-12-01
A density functional, εCV-DFT(ρc, ρv), describing the core-valence correlation energy has been constructed as a linear combination of εLY P (corr)(ρc), εV WN5 (corr)(ρc, ρv), εPBE (corr)(ρc, ρv), εSlater (ex)(ρc, ρv), εHCTH (ex)(ρc, ρv), εHF (ex)(ρc, ρv), and FCV-DFTNi,Zi, a function of the nuclear charges. This functional, with 6 adjustable parameters, reproduces (±0.27 kcal/mol rms error) a benchmark set of 194 chemical energy changes including 9 electron affinities, 18 ionization potentials, and 167 total atomization energies covering the first- and second-rows of the periodic table. This is almost twice the rms error (±0.16 kcal/mol) obtained with CCSD(T)/MTsmall calculations, but less than half the rms error (±0.65 kcal/mol) obtained with MP2/GTlargeXP calculations, and somewhat smaller than the rms error (±0.39 kcal/mol) obtained with CCSD/MTsmall calculations. The largest positive and negative errors from εCV-DFT(ρc, ρv) were 0.88 and -0.75 kcal/mol with the set of 194 core-valence energy changes ranging from +3.76 kcal/mol for the total atomization energy of propyne to -9.05 kcal/mol for the double ionization of Mg. Evaluation of the εCV-DFT(ρc, ρv) functional requires less time than a single SCF iteration, and the accuracy is adequate for any model chemistry based on the CCSD(T) level of theory. PMID:26646873
Minimizing density functional failures for non-covalent interactions beyond van der Waals complexes.
Corminboeuf, Clemence
2014-11-18
CONSPECTUS: Kohn-Sham density functional theory offers a powerful and robust formalism for investigating the electronic structure of many-body systems while providing a practical balance of accuracy and computational cost unmatched by other methods. Despite this success, the commonly used semilocal approximations have difficulties in properly describing attractive dispersion interactions that decay with R(-6) at large intermolecular distances. Even in the short to medium range, most semilocal density functionals fail to give an accurate description of weak interactions. The omnipresence of dispersion interactions, which are neglected in the most popular electronic structure framework, has stimulated intense developments during the past decade. In this Account, we summarize our effort to develop and implement dispersion corrections that dramatically reduce the failures of both inter- and intramolecular interaction energies. The proposed schemes range from improved variants of empirical atom pairwise dispersion correction (e.g., dD10) to robust formulations dependent upon the electron density. Emphasis has been placed on introducing more physics into a modified Tang and Toennies damping function and deriving accurate dispersion coefficients. Our most sophisticated and established density-dependent correction, dDsC, is based on a simple generalized gradient approximation (GGA)-like reformulation of the exchange hole dipole moment introduced by Becke and Johnson. Akin to its empirical precursor, dDsC dramatically improves the interaction energy of a variety of standard density functionals simultaneously for typical intermolecular complexes and shorter-range interactions occurring within molecules. The broad applicability and robustness of the dDsC scheme is demonstrated on various representative reaction energies, geometries, and molecular dynamic simulations. The suitability of the a posteriori correction is also established through comparisons with the more
The QTP family of consistent functionals and potentials in Kohn-Sham density functional theory.
Jin, Yifan; Bartlett, Rodney J
2016-07-21
This manuscript presents the second, consistent density functional in the QTP (Quantum Theory Project) family, that is, the CAM-QTP(01). It is a new range-separated exchange-correlation functional in which the non-local exchange contribution is 100% at large separation. It follows the same basic principles of this family that the Kohn-Sham eigenvalues of the occupied orbitals approximately equal the vertical ionization energies, which is not fulfilled by most of the traditional density functional methods. This new CAM-QTP(01) functional significantly improves the accuracy of the vertical excitation energies especially for the Rydberg states in the test set. It also reproduces many other properties such as geometries, reaction barrier heights, and atomization energies. PMID:27448874
Designing Meaningful Density Functional Theory Calculations in Materials Science
NASA Astrophysics Data System (ADS)
Mattsson, A. E.
2005-07-01
Density functional theory (DFT) methods for calculating the quantum mechanical ground states of condensed matter systems are now a common and significant component of materials research. These methods are also increasingly used in Equation of State work, in particular in the warm dense matter regime. The growing importance of DFT reflects the development of sufficiently accurate functionals, efficient algorithms, and continuing improvements in computing capabilities. As the materials problems to which DFT is applied have become large and complex, so have the sets of calculations necessary to investigate a given problem. Highly versatile, powerful codes exist to serve the practitioner, but designing useful simulations is a complicated task, involving intricate manipulation of many variables, with many pitfalls for the unwary and the inexperienced. We give an overview of DFT and discuss several of the most important issues that go into designing a meaningful DFT calculation. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000.
Metallophilic interactions from dispersion-corrected density-functional theory
Otero-de-la-Roza, Alberto Mallory, Joel D.; Johnson, Erin R.
2014-05-14
In this article, we present the first comprehensive study of metallophilic (aurophilic) interactions using dispersion-corrected density-functional theory. Dispersion interactions (an essential component of metallophilicity) are treated using the exchange-hole dipole moment (XDM) model. By comparing against coupled-cluster benchmark calculations on simple dimers, we show that LC-ωPBE-XDM is a viable functional to study interactions between closed-shell transition metals and that it performs uniformly better than second-order Møller-Plesset theory, the basic computational technique used in previous works. We apply LC-ωPBE-XDM to address several open questions regarding metallophilicity, such as the interplay between dispersion and relativistic effects, the interaction strength along group 11, the additivity of homo- and hetero-metallophilic effects, the stability of [E(AuPH{sub 3}){sub 4}]{sup +} cations (E = N, P, As, Sb), and the role of metallophilic effects in crystal packing. We find that relativistic effects explain the prevalence of aurophilicity not by stabilizing metal-metal contacts, but by preventing gold from forming ionic structures involving bridge anions (which are otherwise common for Ag and Cu) as a result of the increased electron affinity of the metal. Dispersion effects are less important than previously assumed and their stabilization contribution is relatively independent of the metal.
Acrolein Impairs the Cholesterol Transport Functions of High Density Lipoproteins
Chadwick, Alexandra C.; Holme, Rebecca L.; Chen, Yiliang; Thomas, Michael J.; Sorci-Thomas, Mary G.; Silverstein, Roy L.; Pritchard, Kirkwood A.; Sahoo, Daisy
2015-01-01
High density lipoproteins (HDL) are considered athero-protective, primarily due to their role in reverse cholesterol transport, where they transport cholesterol from peripheral tissues to the liver for excretion. The current study was designed to determine the impact of HDL modification by acrolein, a highly reactive aldehyde found in high abundance in cigarette smoke, on the cholesterol transport functions of HDL. HDL was chemically-modified with acrolein and immunoblot and mass spectrometry analyses confirmed apolipoprotein crosslinking, as well as acrolein adducts on apolipoproteins A-I and A-II. The ability of acrolein-modified HDL (acro-HDL) to serve as an acceptor of free cholesterol (FC) from COS-7 cells transiently expressing SR-BI was significantly decreased. Further, in contrast to native HDL, acro-HDL promotes higher neutral lipid accumulation in murine macrophages as judged by Oil Red O staining. The ability of acro-HDL to mediate efficient selective uptake of HDL-cholesteryl esters (CE) into SR-BI-expressing cells was reduced compared to native HDL. Together, the findings from our studies suggest that acrolein modification of HDL produces a dysfunctional particle that may ultimately promote atherogenesis by impairing functions that are critical in the reverse cholesterol transport pathway. PMID:25849485
Density functional steric analysis of linear and branched alkanes.
Ess, Daniel H; Liu, Shubin; De Proft, Frank
2010-12-16
Branched alkane hydrocarbons are thermodynamically more stable than straight-chain linear alkanes. This thermodynamic stability is also manifest in alkane bond separation energies. To understand the physical differences between branched and linear alkanes, we have utilized a novel density functional theory (DFT) definition of steric energy based on the Weizäcker kinetic energy. Using the M06-2X functional, the total DFT energy was partitioned into a steric energy term (E(s)[ρ]), an electrostatic energy term (E(e)[ρ]), and a fermionic quantum energy term (E(q)[ρ]). This analysis revealed that branched alkanes have less (destabilizing) DFT steric energy than linear alkanes. The lower steric energy of branched alkanes is mitigated by an equal and opposite quantum energy term that contains the Pauli component of the kinetic energy and exchange-correlation energy. Because the steric and quantum energy terms cancel, this leaves the electrostatic energy term that favors alkane branching. Electrostatic effects, combined with correlation energy, explains why branched alkanes are more stable than linear alkanes. PMID:21086970
Effects of Methylation on Zebularine Studied by Density Functional Theory
NASA Astrophysics Data System (ADS)
Selvam, Lalitha; Vasilyev, Vladislav; Wang, Feng; Vasilyev, Vladislav
2009-06-01
1-(β -D-ribofuranosyl)-2-pyrimidone (zebularine or zeb) and 1-(β -D-ribofuranosyl)-5-methyl-2-pyrimidinone (d5) are effective inhibitors of cytidine deaminases (CDA). Methyl modification of zeb at the C(5) position in the base moiety produces d5. A density functional theory (DFT) study reveals the impact of the methyl group on the electronic structures and spectra of the nucleoside pair. It is found that the addition of methyl group has little effect on the geometry of the nucleosides as well as their sugar puckering, but affects anisotropic properties such as dihedral angles, condensed Fukui functions and charge distribution can be seen in their molecular electrostatic potentials (MEPs). Electron spectra serve as the fingerprint for the methyl group. The valence spectra clearly indicate that the molecular pair is related in the inner valence space of IP > 20 eV, whereas the outer valence space reveals the methyl associated electronic structural modifications of the molecular pair. In the present study, the molecular orbitals (MO) such as MO8, MO18 and MO37 (HOMO as MO1) are identified as the fingerprint MOs for methyl, whereas other MOs marked in the figure are secondary methyl related MOs. Chemical shift in the inner shell and their spectra are also calculated. It reveals the similarities and differences of methyl effect to large nucleosides and small amino acids such as L-alanine.
Physical basis for constrained lattice density functional theory.
Men, Yumei; Zhang, Xianren
2012-03-28
To study nucleation phenomena in an open system, a constrained lattice density functional theory (LDFT) method has been developed before to identify the unstable directions of grand potential functional and to stabilize nuclei by imposing a suitable constraint. In this work, we answer several questions about the method on a fundamental level, and give a firmer basis for the constrained LDFT method. First, we demonstrate that the nucleus structure and free energy barrier from a volume constraint method are equivalent to those from a surface constraint method. Then, we show that for the critical nucleus, the constrained LDFT method in fact produces a bias-free solution for both the nucleus structure and nucleation barrier. Finally, we give a physical interpretation of the Lagrange multiplier in the constraint method, which provides the generalized force to stabilize a nucleus in an open system. The Lagrange multiplier is found to consist of two parts: part I of the constraint produces an effective pressure, and part II imposes a constraint to counteract the supersaturation. PMID:22462885
Self-interaction corrections in density functional theory
Tsuneda, Takao; Hirao, Kimihiko
2014-05-14
Self-interaction corrections for Kohn-Sham density functional theory are reviewed for their physical meanings, formulations, and applications. The self-interaction corrections get rid of the self-interaction error, which is the sum of the Coulomb and exchange self-interactions that remains because of the use of an approximate exchange functional. The most frequently used self-interaction correction is the Perdew-Zunger correction. However, this correction leads to instabilities in the electronic state calculations of molecules. To avoid these instabilities, several self-interaction corrections have been developed on the basis of the characteristic behaviors of self-interacting electrons, which have no two-electron interactions. These include the von Weizsäcker kinetic energy and long-range (far-from-nucleus) asymptotic correction. Applications of self-interaction corrections have shown that the self-interaction error has a serious effect on the states of core electrons, but it has a smaller than expected effect on valence electrons. This finding is supported by the fact that the distribution of self-interacting electrons indicates that they are near atomic nuclei rather than in chemical bonds.
Antisites in III-V semiconductors: Density functional theory calculations
Chroneos, A.; Tahini, H. A.; Schwingenschlögl, U.; Grimes, R. W.
2014-07-14
Density functional based simulation, corrected for finite size effects, is used to investigate systematically the formation of antisite defects in III-V semiconductors (III = Al, Ga, and In and V = P, As, and Sb). Different charge states are modelled as a function of the Fermi level and under different growth conditions. The formation energies of group III antisites (III{sub V}{sup q}) decrease with increasing covalent radius of the group V atom though not group III radius, whereas group V antisites (V{sub III}{sup q}) show a consistent decrease in formation energies with increase in group III and group V covalent radii. In general, III{sub V}{sup q} defects dominate under III-rich conditions and V{sub III}{sup q} under V-rich conditions. Comparison with equivalent vacancy formation energy simulations shows that while antisite concentrations are always dominant under stoichiometric conditions, modest variation in growth or doping conditions can lead to a significantly higher concentration of vacancies.
Metallophilic interactions from dispersion-corrected density-functional theory.
Otero-de-la-Roza, Alberto; Mallory, Joel D; Johnson, Erin R
2014-05-14
In this article, we present the first comprehensive study of metallophilic (aurophilic) interactions using dispersion-corrected density-functional theory. Dispersion interactions (an essential component of metallophilicity) are treated using the exchange-hole dipole moment (XDM) model. By comparing against coupled-cluster benchmark calculations on simple dimers, we show that LC-ωPBE-XDM is a viable functional to study interactions between closed-shell transition metals and that it performs uniformly better than second-order Møller-Plesset theory, the basic computational technique used in previous works. We apply LC-ωPBE-XDM to address several open questions regarding metallophilicity, such as the interplay between dispersion and relativistic effects, the interaction strength along group 11, the additivity of homo- and hetero-metallophilic effects, the stability of [E(AuPH3)4](+) cations (E = N, P, As, Sb), and the role of metallophilic effects in crystal packing. We find that relativistic effects explain the prevalence of aurophilicity not by stabilizing metal-metal contacts, but by preventing gold from forming ionic structures involving bridge anions (which are otherwise common for Ag and Cu) as a result of the increased electron affinity of the metal. Dispersion effects are less important than previously assumed and their stabilization contribution is relatively independent of the metal. PMID:24832312
Density Functional Steric Analysis of Linear and Branched Alkanes
Ess, Daniel H.; Liu, Shubin; De Proft, Frank
2010-11-18
Branched alkane hydrocarbons are thermodynamically more stable than straight-chain linear alkanes. This thermodynamic stability is also manifest in alkane bond separation energies. To understand the physical differences between branched and linear alkanes, we have utilized a novel density functional theory (DFT) definition of steric energy based on the Weizäcker kinetic energy. Using the M06-2X functional, the total DFT energy was partitioned into a steric energy term (E_{e}[[ρ]), an electrostatic energy term (E_{e}[ρ]), and a fermionic quantum energy term (E_{q}[[ρ]). This analysis revealed that branched alkanes have less (destabilizing) DFT steric energy than linear alkanes. The lower steric energy of branched alkanes is mitigated by an equal and opposite quantum energy term that contains the Pauli component of the kinetic energy and exchange-correlation energy. Because the steric and quantum energy terms cancel, this leaves the electrostatic energy term that favors alkane branching. Electrostatic effects, combined with correlation energy, explains why branched alkanes are more stable than linear alkanes.
Augmented Lagrangian formulation of orbital-free density functional theory
Suryanarayana, Phanish Phanish, Deepa
2014-10-15
We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic Orbital-Free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas–Fermi–von Weizsacker (TFW) kinetic energy functional in the framework of higher-order finite-differences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higher-order finite-differences represent a computationally efficient discretization for performing OF-DFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane-wave methods.
A solvation-free-energy functional: a reference-modified density functional formulation.
Sumi, Tomonari; Mitsutake, Ayori; Maruyama, Yutaka
2015-07-01
The three-dimensional reference interaction site model (3D-RISM) theory, which is one of the most applicable integral equation theories for molecular liquids, overestimates the absolute values of solvation-free-energy (SFE) for large solute molecules in water. To improve the free-energy density functional for the SFE of solute molecules, we propose a reference-modified density functional theory (RMDFT) that is a general theoretical approach to construct the free-energy density functional systematically. In the RMDFT formulation, hard-sphere (HS) fluids are introduced as the reference system instead of an ideal polyatomic molecular gas, which has been regarded as the appropriate reference system of the interaction-site-model density functional theory for polyatomic molecular fluids. We show that using RMDFT with a reference HS system can significantly improve the absolute values of the SFE for a set of neutral amino acid side-chain analogues as well as for 504 small organic molecules. PMID:26032201
Benchmarking FeCr empirical potentials against density functional theory data
NASA Astrophysics Data System (ADS)
Klaver, T. P. C.; Bonny, G.; Olsson, P.; Terentyev, D.
2010-10-01
Three semi-empirical force field FeCr potentials, two within the formalism of the two-band model and one within the formalism of the concentration dependent model, have been benchmarked against a wide variety of density functional theory (DFT) structures. The benchmarking allows an assessment of how reliable empirical potential results are in different areas relevant to radiation damage modelling. The DFT data consist of defect-free structures, structures with single interstitials and structures with small di- and tri-interstitial clusters. All three potentials reproduce the general trend of the heat of formation (h.o.f.) quite well. The most important shortcomings of the original two-band model potential are the low or even negative h.o.f. for Cr-rich structures and the lack of a strong repulsion when moving two solute Cr atoms from being second-nearest neighbours to nearest neighbours. The newer two-band model potential partly solves the first problem. The most important shortcoming in the concentration dependent model potential is the magnitude of the Cr-Cr repulsion, being too strong at short distances and mostly absent at longer distances. Both two-band model potentials do reproduce long-range Cr-Cr repulsion. For interstitials the two-band model potentials reproduce a number of Cr-interstitial binding energies surprisingly well, in contrast to the concentration dependent model potential. For Cr interacting with clusters, the result can sometimes be directly extrapolated from Cr interacting with single interstitials, both according to DFT and the three empirical potentials.
A mixed basis density functional approach for one-dimensional systems with B-splines
NASA Astrophysics Data System (ADS)
Ren, Chung-Yuan; Chang, Yia-Chung; Hsue, Chen-Shiung
2016-05-01
A mixed basis approach based on density functional theory is extended to one-dimensional (1D) systems. The basis functions here are taken to be the localized B-splines for the two finite non-periodic dimensions and the plane waves for the third periodic direction. This approach will significantly reduce the number of the basis and therefore is computationally efficient for the diagonalization of the Kohn-Sham Hamiltonian. For 1D systems, B-spline polynomials are particularly useful and efficient in two-dimensional spatial integrations involved in the calculations because of their absolute localization. Moreover, B-splines are not associated with atomic positions when the geometry structure is optimized, making the geometry optimization easy to implement. With such a basis set we can directly calculate the total energy of the isolated system instead of using the conventional supercell model with artificial vacuum regions among the replicas along the two non-periodic directions. The spurious Coulomb interaction between the charged defect and its repeated images by the supercell approach for charged systems can also be avoided. A rigorous formalism for the long-range Coulomb potential of both neutral and charged 1D systems under the mixed basis scheme will be derived. To test the present method, we apply it to study the infinite carbon-dimer chain, graphene nanoribbon, carbon nanotube and positively-charged carbon-dimer chain. The resulting electronic structures are presented and discussed in detail.
NASA Astrophysics Data System (ADS)
Basurto, Luis; Zope, Rajendra R.; Baruah, Tunna
2016-05-01
We report an electronic structure study of a multichromophoric molecular complex containing two of each borondipyrromethane dye, Zn-tetraphenyl-porphyrin, bisphenyl anthracene and a fullerene. The snowflake shaped molecule behaves like an antenna capturing photon at different frequencies and transferring the photon energy to the porphyrin where electron transfer occurs from the porphyrin to the fullerene. The study is performed within density functional formalism using large polarized Guassian basis sets (12,478 basis functions in total). The energies of the HOMO and LUMO states in the complex, as adjudged by the ionization potential and the electron affinity values, show significant differences with respect to their values in participating subunits in isolation. These differences are also larger than the variations of the ionization potential and electron affinity values observed in non-bonded C60-ZnTPP complexes in co-facial arrangement or end-on orientations. An understanding of the origin of these differences is obtained by a systematic study of the effect of structural strain, the presence of ligands, the effect of orbital delocalization on the ionization energy and the electron affinity. Finally, a few lowest charge transfer energies involving electronic transitions from the porphyrin component to the fullerene subunit of the complex are predicted.
On the evaluation of the non-interacting kinetic energy in density functional theory.
Peach, Michael J G; Griffiths, David G J; Tozer, David J
2012-04-14
The utility of both an orbital-free and a single-orbital expression for computing the non-interacting kinetic energy in density functional theory is investigated for simple atomic systems. The accuracy of both expressions is governed by the extent to which the Kohn-Sham equation is solved for the given exchange-correlation functional and so special attention is paid to the influence of finite Gaussian basis sets. The orbital-free expression is a statement of the virial theorem and its accuracy is quantified. The accuracy of the single-orbital expression is sensitive to the choice of Kohn-Sham orbital. The use of particularly compact orbitals is problematic because the failure to solve the Kohn-Sham equation exactly in regions where the orbital has decayed to near-zero leads to unphysical behaviour in regions that contribute to the kinetic energy, rendering it inaccurate. This problem is particularly severe for core orbitals, which would otherwise appear attractive due to their formally nodeless nature. The most accurate results from the single-orbital expression are obtained using the relatively diffuse, highest occupied orbitals, although special care is required at orbital nodes. PMID:22502495
Understanding density functional theory (DFT) and completing it in practice
Bagayoko, Diola
2014-12-15
We review some salient points in the derivation of density functional theory (DFT) and of the local density approximation (LDA) of it. We then articulate an understanding of DFT and LDA that seems to be ignored in the literature. We note the well-established failures of many DFT and LDA calculations to reproduce the measured energy gaps of finite systems and band gaps of semiconductors and insulators. We then illustrate significant differences between the results from self consistent calculations using single trial basis sets and those from computations following the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). Unlike the former, the latter calculations verifiably attain the absolute minima of the occupied energies, as required by DFT. These minima are one of the reasons for the agreement between their results and corresponding, experimental ones for the band gap and a host of other properties. Further, we note predictions of DFT BZW-EF calculations that have been confirmed by experiment. Our subsequent description of the BZW-EF method ends with the application of the Rayleigh theorem in the selection, among the several calculations the method requires, of the one whose results have a full, physics content ascribed to DFT. This application of the Rayleigh theorem adds to or completes DFT, in practice, to preserve the physical content of unoccupied, low energy levels. Discussions, including implications of the method, and a short conclusion follow the description of the method. The successive augmentation of the basis set in the BZW-EF method, needed for the application of the Rayleigh theorem, is also necessary in the search for the absolute minima of the occupied energies, in practice.
NASA Astrophysics Data System (ADS)
Perron, H.; Mellier, T.; Domain, C.; Roques, J.; Simoni, E.; Drot, R.; Catalette, H.
2007-08-01
Periodic density functional theory (DFT) calculations using plane-wave basis sets were performed in order to study the bulk of nickel ferrite NiFe2O4. The local spin density approximation (LSDA) and the generalized gradient approximation (GGA) formalism were used, and it appeared that the LSDA failed to describe the magnetic structure of this compound. However, the GGA formalism gave reliable results in good agreement with experimental data for the lattice parameters, the electronic properties and the bulk modulus. In addition, the calculated density of states of the metallic species d block as well as their local magnetic moments were correlated to the crystal-field theory. Then, a charge deformation map was computed and, as expected from the electronegativity scale, the electron excess is localized around oxygen atoms along the bond axes. The formation energies of metallic vacancies are in good agreement with the inverse spinel structure experimentally observed.
NASA Astrophysics Data System (ADS)
Pham, Thinh H.; Ramprasad, Rampi; Nguyen, Huy-Viet
2016-06-01
Due to the lack of treatment of long-range dispersion energies, density functional theory with local and semilocal approximations of exchange-correlation energy is known to fail in describing van der Waals complexes, including polymer crystals. This limitation can be overcome by using a different class of functionals, called van der Waals density functional (vdW-DF), originally developed by Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)]. In this work, we performed a systematic study of structural properties of polymeric crystals using the original vdW-DF functional by Dion et al. and its variants and refinements. Our study shows that this class of functional outperforms the conventional LDA or PBE functionals and gives results with similar accuracy to that of empirical dispersion-corrected schemes such as DFT-D. This study suggests the use of vdW-DF2 functional — a revised version of vdW-DF functional — to obtain a high-fidelity prediction of structural and other properties of polymeric materials.
Pham, Thinh H; Ramprasad, Rampi; Nguyen, Huy-Viet
2016-06-01
Due to the lack of treatment of long-range dispersion energies, density functional theory with local and semilocal approximations of exchange-correlation energy is known to fail in describing van der Waals complexes, including polymer crystals. This limitation can be overcome by using a different class of functionals, called van der Waals density functional (vdW-DF), originally developed by Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)]. In this work, we performed a systematic study of structural properties of polymeric crystals using the original vdW-DF functional by Dion et al. and its variants and refinements. Our study shows that this class of functional outperforms the conventional LDA or PBE functionals and gives results with similar accuracy to that of empirical dispersion-corrected schemes such as DFT-D. This study suggests the use of vdW-DF2 functional - a revised version of vdW-DF functional - to obtain a high-fidelity prediction of structural and other properties of polymeric materials. PMID:27276968
Filtered density function approach for reactive transport in groundwater
NASA Astrophysics Data System (ADS)
Suciu, Nicolae; Schüler, Lennart; Attinger, Sabine; Knabner, Peter
2016-04-01
Spatial filtering may be used in coarse-grained simulations (CGS) of reactive transport in groundwater, similar to the large eddy simulations (LES) in turbulence. The filtered density function (FDF), stochastically equivalent to a probability density function (PDF), provides a statistical description of the sub-grid, unresolved, variability of the concentration field. Besides closing the chemical source terms in the transport equation for the mean concentration, like in LES-FDF methods, the CGS-FDF approach aims at quantifying the uncertainty over the whole hierarchy of heterogeneity scales exhibited by natural porous media. Practically, that means estimating concentration PDFs on coarse grids, at affordable computational costs. To cope with the high dimensionality of the problem in case of multi-component reactive transport and to reduce the numerical diffusion, FDF equations are solved by particle methods. But, while trajectories of computational particles are modeled as stochastic processes indexed by time, the concentration's heterogeneity is modeled as a random field, with multi-dimensional, spatio-temporal sets of indices. To overcome this conceptual inconsistency, we consider FDFs/PDFs of random species concentrations weighted by conserved scalars and we show that their evolution equations can be formulated as Fokker-Planck equations describing stochastically equivalent processes in concentration-position spaces. Numerical solutions can then be approximated by the density in the concentration-position space of an ensemble of computational particles governed by the associated Itô equations. Instead of sequential particle methods we use a global random walk (GRW) algorithm, which is stable, free of numerical diffusion, and practically insensitive to the increase of the number of particles. We illustrate the general FDF approach and the GRW numerical solution for a reduced complexity problem consisting of the transport of a single scalar in groundwater
Spin propensities of octahedral complexes from density functional theory.
Mortensen, Sara R; Kepp, Kasper P
2015-04-30
The fundamental balance between high- and low-spin states of transition metal systems depends on both the metal ion and the ligands surrounding it, as often visualized by the spectrochemical series. Most density functionals do not reproduce this balance, and real spin state propensities depend on orbital pairing and vibrational entropies absent in the spectrochemical series. Thus, we systematically computed the tendency toward high or low spin of "text-book" octahedral metal complexes versus ligand and metal type, using eight density functionals. Dispersion effects were generally <5 kJ/mol, favoring low-spin states. Zero-point energies favored high-spin states up to 33 kJ/mol for strong ligands, but down to a few kilojoules per mole for weak ligands. Vibrational entropy also favored high-spin states up to 40 kJ/mol, most for strong ligands. Jahn-Teller distortion in Co(II) low-spin states, particularly stable d(6) low-spin states, and entropy corrections were consistent with experiment. Entropy and zero-point energy corrections were markedly lower for Co(II) and Mn(III), viz., the differential ligand field stabilization energy, and can only be ignored for weak ligands. The data enable simple assessment of spin state propensities versus ligand and metal type and reveal, e.g., that CN(-) is consistently weaker than CO for M(II) but stronger than CO for M(III) and SCN(-) and NCS(-) change order in M(II) versus M(III) complexes. Contrary to expectation based on the spectrochemical series, Cl(-) and Br(-) are very close in spin state propensity because the pairing penalty for low spin is smaller in Br(-). Thus, for the M(II) complexes, we find a consensus order of Br(-) ∼ Cl(-) < H2O < SCN(-) < NCS(-) ∼ NH3 < CN(-) < CO, whereas for the M(III) complexes, an approximate order is Br(-) ∼ Cl(-) < H2O ∼ NCS(-) ∼ SCN(-)< NH3 < CO < CN(-). PMID:25856244
Wilken, F.; Bauer, D.
2006-11-17
The ionization of a one-dimensional model helium atom in short laser pulses using time-dependent density-functional theory is investigated. We calculate ionization probabilities as a function of laser intensity by approximating the correlation function of the system adiabatically with an explicit dependence on the fractional number of bound electrons. For the correlation potential we take the derivative discontinuity at integer numbers of bound electrons explicitly into account. This approach reproduces ionization probabilities from the solution of the time-dependent Schroedinger equation, in particular, the so-called knee due to nonsequential ionization.
Tensor part of the Skyrme energy density functional: Spherical nuclei
NASA Astrophysics Data System (ADS)
Lesinski, T.; Bender, M.; Bennaceur, K.; Duguet, T.; Meyer, J.
2007-07-01
the single-particle spectra in doubly-magic nuclei is deteriorated, which can be traced back to features of the single-particle spectra that are not related to the tensor terms. We conclude that the currently used central and spin-orbit parts of the Skyrme energy density functional are not flexible enough to allow for the presence of large tensor terms.
ERIC Educational Resources Information Center
Herrera, D.; Valencia, A. M.; Pennini, F.; Curilef, S.
2008-01-01
In this work, we review two formalisms of coherent states for the case of a particle in a magnetic field. We focus our revision on both pioneering (Feldman and Kahn 1970 "Phys. Rev." B 1 4584) and recent (Kowalski and Rembielinski 2005 "J. Phys. A: Math. Gen." 38 8247) formulations of coherent states for this problem. We introduce a general…
Global and local curvature in density functional theory
NASA Astrophysics Data System (ADS)
Zhao, Qing; Ioannidis, Efthymios I.; Kulik, Heather J.
2016-08-01
Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density functional theory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a "+U" correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc-Cu) and ligand strength (CO, NH3, and H2O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide.
Global and local curvature in density functional theory.
Zhao, Qing; Ioannidis, Efthymios I; Kulik, Heather J
2016-08-01
Piecewise linearity of the energy with respect to fractional electron removal or addition is a requirement of an electronic structure method that necessitates the presence of a derivative discontinuity at integer electron occupation. Semi-local exchange-correlation (xc) approximations within density functional theory (DFT) fail to reproduce this behavior, giving rise to deviations from linearity with a convex global curvature that is evidence of many-electron, self-interaction error and electron delocalization. Popular functional tuning strategies focus on reproducing piecewise linearity, especially to improve predictions of optical properties. In a divergent approach, Hubbard U-augmented DFT (i.e., DFT+U) treats self-interaction errors by reducing the local curvature of the energy with respect to electron removal or addition from one localized subshell to the surrounding system. Although it has been suggested that DFT+U should simultaneously alleviate global and local curvature in the atomic limit, no detailed study on real systems has been carried out to probe the validity of this statement. In this work, we show when DFT+U should minimize deviations from linearity and demonstrate that a "+U" correction will never worsen the deviation from linearity of the underlying xc approximation. However, we explain varying degrees of efficiency of the approach over 27 octahedral transition metal complexes with respect to transition metal (Sc-Cu) and ligand strength (CO, NH3, and H2O) and investigate select pathological cases where the delocalization error is invisible to DFT+U within an atomic projection framework. Finally, we demonstrate that the global and local curvatures represent different quantities that show opposing behavior with increasing ligand field strength, and we identify where these two may still coincide. PMID:27497541
Mukamel, Shaul
2005-02-01
Time-ordered superoperators are used to develop a unified description of nonlinear density response and spontaneous fluctuations of many-electron systems. The pth-order density response functions are decomposed into 2{sup p+1} non-causal Liouville space pathways. Individual pathways are symmetric to the interchange of their space, time, and superoperator indices and can thus be calculated as functional derivatives. Other combinations of these pathways represent spontaneous density fluctuations and the response of such fluctuations to an external field. The resolution of the causality paradox of time-dependent density-functional theory (TDDFT) is shown to be intimately connected with the nonretarded nature of fluctuations.
Numerical methods for high-dimensional probability density function equations
NASA Astrophysics Data System (ADS)
Cho, H.; Venturi, D.; Karniadakis, G. E.
2016-01-01
In this paper we address the problem of computing the numerical solution to kinetic partial differential equations involving many phase variables. These types of equations arise naturally in many different areas of mathematical physics, e.g., in particle systems (Liouville and Boltzmann equations), stochastic dynamical systems (Fokker-Planck and Dostupov-Pugachev equations), random wave theory (Malakhov-Saichev equations) and coarse-grained stochastic systems (Mori-Zwanzig equations). We propose three different classes of new algorithms addressing high-dimensionality: The first one is based on separated series expansions resulting in a sequence of low-dimensional problems that can be solved recursively and in parallel by using alternating direction methods. The second class of algorithms relies on truncation of interaction in low-orders that resembles the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) framework of kinetic gas theory and it yields a hierarchy of coupled probability density function equations. The third class of algorithms is based on high-dimensional model representations, e.g., the ANOVA method and probabilistic collocation methods. A common feature of all these approaches is that they are reducible to the problem of computing the solution to high-dimensional equations via a sequence of low-dimensional problems. The effectiveness of the new algorithms is demonstrated in numerical examples involving nonlinear stochastic dynamical systems and partial differential equations, with up to 120 variables.
Parameterizing deep convection using the assumed probability density function method
Storer, R. L.; Griffin, B. M.; Hoft, Jan; Weber, J. K.; Raut, E.; Larson, Vincent E.; Wang, Minghuai; Rasch, Philip J.
2015-01-06
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method.The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and mid-latitude deep convection.These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing is weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.
Predicting Stability Constants for Uranyl Complexes Using Density Functional Theory
Vukovic, Sinisa; Hay, Benjamin P.; Bryantsev, Vyacheslav S.
2015-04-02
The ability to predict the equilibrium constants for the formation of 1:1 uranyl:ligand complexes (log K_{1 }values) provides the essential foundation for the rational design of ligands with enhanced uranyl affinity and selectivity. We also use density functional theory (B3LYP) and the IEFPCM continuum solvation model to compute aqueous stability constants for UO_{2}^{2+} complexes with 18 donor ligands. Theoretical calculations permit reasonably good estimates of relative binding strengths, while the absolute log K_{1} values are significantly overestimated. Accurate predictions of the absolute log K_{1} values (root mean square deviation from experiment < 1.0 for log K_{1} values ranging from 0 to 16.8) can be obtained by fitting the experimental data for two groups of mono and divalent negative oxygen donor ligands. The utility of correlations is demonstrated for amidoxime and imide dioxime ligands, providing a useful means of screening for new ligands with strong chelate capability to uranyl.
Predicting Stability Constants for Uranyl Complexes Using Density Functional Theory
Vukovic, Sinisa; Hay, Benjamin P.; Bryantsev, Vyacheslav S.
2015-04-02
The ability to predict the equilibrium constants for the formation of 1:1 uranyl:ligand complexes (log K1 values) provides the essential foundation for the rational design of ligands with enhanced uranyl affinity and selectivity. We also use density functional theory (B3LYP) and the IEFPCM continuum solvation model to compute aqueous stability constants for UO22+ complexes with 18 donor ligands. Theoretical calculations permit reasonably good estimates of relative binding strengths, while the absolute log K1 values are significantly overestimated. Accurate predictions of the absolute log K1 values (root mean square deviation from experiment < 1.0 for log K1 values ranging from 0more » to 16.8) can be obtained by fitting the experimental data for two groups of mono and divalent negative oxygen donor ligands. The utility of correlations is demonstrated for amidoxime and imide dioxime ligands, providing a useful means of screening for new ligands with strong chelate capability to uranyl.« less
Parameterizing deep convection using the assumed probability density function method
NASA Astrophysics Data System (ADS)
Storer, R. L.; Griffin, B. M.; Höft, J.; Weber, J. K.; Raut, E.; Larson, V. E.; Wang, M.; Rasch, P. J.
2015-01-01
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method. The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and midlatitude deep convection. These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing is weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.
Large Eddy Simulation and the Filtered Probability Density Function Method
NASA Astrophysics Data System (ADS)
Jones, W. P.; Navarro-Martinez, S.
2009-12-01
Recently there is has been increased interest in modelling combustion processes with high-levels of extinction and re-ignition. Such system often lie beyond the scope of conventional single scalar-based models. Large Eddy Simulation (LES) has shown a large potential for describing turbulent reactive systems, though combustion occurs at the smallest unresolved scales of the flow and must be modelled. In the sub-grid Probability Density Function (pdf) method approximations are devised to close the evolution equation for the joint-pdf which is then solved directly. The paper describes such an approach and concerns, in particular, the Eulerian stochastic field method of solving the pdf equation. The paper examines the capabilities of the LES-pdf method in capturing auto-ignition and extinction events in different partially premixed configurations with different fuels (hydrogen, methane and n-heptane). The results show that the LES-pdf formulation can capture different regimes without any parameter adjustments, independent of Reynolds numbers and fuel type.
Parameterizing deep convection using the assumed probability density function method
Storer, R. L.; Griffin, B. M.; Höft, J.; Weber, J. K.; Raut, E.; Larson, V. E.; Wang, M.; Rasch, P. J.
2014-06-11
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method. The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and mid-latitude deep convection. These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing ismore » weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.« less
Parameterizing deep convection using the assumed probability density function method
Storer, R. L.; Griffin, B. M.; Höft, J.; Weber, J. K.; Raut, E.; Larson, V. E.; Wang, M.; Rasch, P. J.
2015-01-06
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method. The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and midlatitude deep convection. These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing ismore » weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.« less
Density functional theory study of oxygen migration in molten carbonate
NASA Astrophysics Data System (ADS)
Lei, Xueling; Haines, Kahla; Huang, Kevin; Qin, Changyong
2016-02-01
The process of oxygen migration in alkali molten carbonate salts has been examined using density functional theory method. All geometries were optimized at the B3LYP/6-31G(d) level, while single point energy corrections were performed using MP4 and CCSD(T). At TS, a O-O-O linkage is formed and O-O bond forming and breaking is concerted. A cooperative "cogwheel" mechanism as described in the equation of CO42- + CO32- → CO32- ⋯O ⋯ CO32- → CO32- + CO42- is involved. The energy barrier is calculated to be 103.0, 136.3 and 127.9 kJ/mol through an intra-carbonate pathway in lithium, sodium and potassium carbonate, respectively. The reliability and accuracy of B3LYP/6-31G(d) were confirmed by CCSD(T). The calculated low values of activation energy indicate that the oxygen transfer in molten carbonate salts is fairly easy. In addition, it is found that lithium carbonate is not only a favorable molten carbonate salt for better cathode kinetics, but also it is widely used for reducing the melting point of Li/Na and Li/K eutectic MC mixtures. The current results imply that the process of oxygen reduction in MC modified cathodes is facilitated by the presence of MC, resulting in an enhancement of cell performance at low operating temperatures.
Dynamical Density Functional Theory and Hydrodynamic Interactions in Confined Systems
NASA Astrophysics Data System (ADS)
Goddard, Benjamin; Kalliadasis, Serafim; Nold, Andreas
Colloidal systems consist of nano-micrometer sized particles suspended in a bath of many more, much smaller and much lighter particles. When the colloidal particles move through the bath, e.g. when driven by external forces such as gravity, flows are induced in the bath. These flows in turn impart forces on the colloid particles. These bath-mediated forces, known as Hydrodynamic Interactions (HI) strongly influence the dynamics of the colloid particles. This is particularly true in confined systems, in which the presence of walls substantially modifies the HI compared to unbounded geometries. For many-particle systems, the number of degrees of freedom prohibit a direct solution of the underlying stochastic equations and a reduced model is necessary. We model such systems through Dynamical Density Functional Theory (DDFT), the computational complexity of which is independent of the number of particles. We include both inter-particle and particle-wall HI, demonstrating both their combined and relative effects. Funded by EPSRC Grant No. EP/L025159/1.
Efficiency issues related to probability density function comparison
Kelly, P.M.; Cannon, M.; Barros, J.E.
1996-03-01
The CANDID project (Comparison Algorithm for Navigating Digital Image Databases) employs probability density functions (PDFs) of localized feature information to represent the content of an image for search and retrieval purposes. A similarity measure between PDFs is used to identify database images that are similar to a user-provided query image. Unfortunately, signature comparison involving PDFs is a very time-consuming operation. In this paper, we look into some efficiency considerations when working with PDFS. Since PDFs can take on many forms, we look into tradeoffs between accurate representation and efficiency of manipulation for several data sets. In particular, we typically represent each PDF as a Gaussian mixture (e.g. as a weighted sum of Gaussian kernels) in the feature space. We find that by constraining all Gaussian kernels to have principal axes that are aligned to the natural axes of the feature space, computations involving these PDFs are simplified. We can also constrain the Gaussian kernels to be hyperspherical rather than hyperellipsoidal, simplifying computations even further, and yielding an order of magnitude speedup in signature comparison. This paper illustrates the tradeoffs encountered when using these constraints.
Van der Waals interactions in density functional theory
NASA Astrophysics Data System (ADS)
Langreth, David C.
2009-03-01
The van der Waals density functional which we introduced half a decade agoootnotetextM. Dion et al. Phys. Rev. Lett. 92, 246401 (2004). and its self-consistent generalizationootnotetextT. Thonhauser et al., Phys. Rev. B 76, 125112 (2007). will be briefly reviewed. There are many collaborators in the application review that will follow, not only those who worked in the physics department at Rutgers% ootnotetextMaxime Dion, Aaron Puzder, T. Thonhauser, Valentino R. Cooper, Shen Li, Eamonn Murray, Lingzhu Kong, and Kyuho Lee. and at Chalmers,% ootnotetextHenrik Rydberg, Svetla Chakarova-K"ack, Jesper Kleis, Elsebeth Schr"oder, Per Hyldgaard, and Bengt I. Lundqvist. but also at Denmarks Technical University,% ootnotetextAndrei Kelkkanen, Poul G. Moses, Jesper Kleis, and Bengt I. Lundqvist. the chemistry department at Rutgers,% ootnotetextKonhoa Li, Jing Li, Yves Chabal, and Wilma K. Olson. and most recently at the University of Texas at Dallas.% ootnotetextNour Nijem and Yves Chabal. I will expand on our recent review article,ootnotetextD. C. Langreth et al., J. Phys. Cond. Mat. (in press). which hopefully will be published before the present talk, and include applications by other groups not listed below. If possible, I will also review results from a more recent collaboration to study nucleosomal DNA and beyond.
A probability density function method for acoustic field uncertainty analysis
NASA Astrophysics Data System (ADS)
James, Kevin R.; Dowling, David R.
2005-11-01
Acoustic field predictions, whether analytical or computational, rely on knowledge of the environmental, boundary, and initial conditions. When knowledge of these conditions is uncertain, acoustic field predictions will also be uncertain, even if the techniques for field prediction are perfect. Quantifying acoustic field uncertainty is important for applications that require accurate field amplitude and phase predictions, like matched-field techniques for sonar, nondestructive evaluation, bio-medical ultrasound, and atmospheric remote sensing. Drawing on prior turbulence research, this paper describes how an evolution equation for the probability density function (PDF) of the predicted acoustic field can be derived and used to quantify predicted-acoustic-field uncertainties arising from uncertain environmental, boundary, or initial conditions. Example calculations are presented in one and two spatial dimensions for the one-point PDF for the real and imaginary parts of a harmonic field, and show that predicted field uncertainty increases with increasing range and frequency. In particular, at 500 Hz in an ideal 100 m deep underwater sound channel with a 1 m root-mean-square depth uncertainty, the PDF results presented here indicate that at a range of 5 km, all phases and a 10 dB range of amplitudes will have non-negligible probability. Evolution equations for the two-point PDF are also derived.
Time-dependent density functional theory of extreme environments
NASA Astrophysics Data System (ADS)
Shulenburger, Luke; Desjarlais, Michael; Magyar, Rudolph
2013-04-01
We describe the challenges involved when using time-dependent density functional theory (TDDFT) to describe warm dense matter (WDM) within a plane-wave, real-time formulation. WDM occurs under conditions of temperature and pressure (over 1000 K and 1 Mbar) where plasma physics meets condensed matter physics. TDDFT is especially important in this regime as it can describe ions and electrons strongly out of equilibrium. Several theoretical challenges must be overcome including assignment of initial state orbitals, choice of time-propogation scheme, treatment of PAW potentials, and inclusion of non-adiabatic effects in the potential energy surfaces. The results of these simulations are critical in several applications. For example, we will explain how the TDDFT calculation can resolve modeling inconsistencies in X-ray Thompson cross-sections, thereby improving an important temperature diagnostic in experiments. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Density Functional Study for Homodendrimers and Amphiphilic Dendrimers.
Chen, Cangyi; Tang, Ping; Qiu, Feng; Shi, An-Chang
2016-06-23
The conformation of homodendrimers and amphiphilic dendrimers in various solvents is studied using classical density functional theory (DFT), in which the excluded-volume effects are treated explicitly. For homodendrimers in an athermal solvent, DFT results predict a remarkable fold-back behavior for the outer generation of segments, supporting the dense-core model. A coil-to-globule transition is observed for homodendrimers in a poor solvent. The size of the dendrimers, characterized by the radius of gyration, ⟨Rg⟩, is found to follow the scaling relationship, ⟨Rg⟩ ∼ N(ν), where N is the total number of segments of the dendrimers. For amphiphilic dendrimers, DFT results show that chemical modification in the outermost generation is an effective method to drive the ends toward the periphery of the dendrimers. In particular, a conformation with a hollow interior structure could be formed for amphiphilic dendrimers with longer end spacers in a selective solvent. The resulting unimolecular micelles with a hollow core and dense shell could serve as a unique candidate for encapsulation applications, such as sustained-drug-release nanocontainers. PMID:27243274
Excess electrons in ice: a density functional theory study.
Bhattacharya, Somesh Kr; Inam, Fakharul; Scandolo, Sandro
2014-02-21
We present a density functional theory study of the localization of excess electrons in the bulk and on the surface of crystalline and amorphous water ice. We analyze the initial stages of electron solvation in crystalline and amorphous ice. In the case of crystalline ice we find that excess electrons favor surface states over bulk states, even when the latter are localized at defect sites. In contrast, in amorphous ice excess electrons find it equally favorable to localize in bulk and in surface states which we attribute to the preexisting precursor states in the disordered structure. In all cases excess electrons are found to occupy the vacuum regions of the molecular network. The electron localization in the bulk of amorphous ice is assisted by its distorted hydrogen bonding network as opposed to the crystalline phase. Although qualitative, our results provide a simple interpretation of the large differences observed in the dynamics and localization of excess electrons in crystalline and amorphous ice films on metals. PMID:24401958
Simple preconditioning for time-dependent density functional perturbation theory.
Lehtovaara, Lauri; Marques, Miguel A L
2011-07-01
By far, the most common use of time-dependent density functional theory is in the linear-reponse regime, where it provides information about electronic excitations. Ideally, the linear-response equations should be solved by a method that avoids the use of the unoccupied Kohn-Sham states--such as the Sternheimer method--as this reduces the complexity and increases the precision of the calculation. However, the Sternheimer equation becomes ill-conditioned near and indefinite above the first resonant frequency, seriously hindering the use of efficient iterative solution methods. To overcome this serious limitation, and to improve the general convergence properties of the iterative techniques, we propose a simple preconditioning strategy. In our method, the Sternheimer equation is solved directly as a linear equation using an iterative Krylov subspace method, i.e., no self-consistent cycle is required. Furthermore, the preconditioner uses the information of just a few unoccupied states and requires simple and minimal modifications to existing implementations. In this way, convergence can be reached faster and in a considerably wider frequency range than the traditional approach. PMID:21744884
Density functional theory simulation of liquid helium-4 in aerogel
NASA Astrophysics Data System (ADS)
Lysogorskiy, Yu. V.; Tayurskii, D. A.
2013-10-01
The distribution of liquid 4He in different types of confinements—adsorbing and nonadsorbing aerogel on the basis of silicon dioxide SiO2 and an absorbing homogeneous strand—has been studied using the density functional theory. It has been demonstrated that the helium atoms tend to be adsorbed on the concave aerogel surface. It has been shown that, in the confinement with fractional mass dimension within certain scales, liquid helium also has a fractional mass dimension within these scales. The dependence of the energy of liquid helium on the number of atoms has been studied for different types of adsorbing surfaces. It has been established that the specific energy of liquid helium behaves differently in the cases of attractive and unattractive potentials with decreasing number of particles. This indicates that the system under consideration is nonextensive. Thus, the necessity of taking into account the surface effects and the fractional mass dimension in the studies of the properties of liquid helium in the restricted space geometry has been demonstrated.
Applications of density functional theory in materials science and engineering
NASA Astrophysics Data System (ADS)
Alvarado, Manuel, Jr.
Density Functional Theory (DFT) is a powerful tool that can be used to model various systems in materials science. Our research applies DFT to two problems of interest. First, an organic/inorganic complex dye system known as a Mayan pigment is modeled to determine chemical binding sites, verifying each model with physical data such as UV/Vis spectra. Preliminary studies on palygorskite-based mayan pigments (mayacrom blue, mayacrom purple) show excellent agreement with experimental studies when using a dimer dye geometry binding with tetrahedrally-coordinated aluminum impurity sites in palygorksite. This approach is applied to a sepiolite-based organic/inorganic dye system using thioindigo attached to a tetrahedral aluminum impurity site with an additional aluminum impurity site in close proximity to the binding site. As a second application of DFT, various grain orientations in beta-Sn are modeled under imposed strains in order to calculate elastic properties of this system. These calculations are intended to clarify discrepancies in published, experimental crystal compliance values.
Price, A. Martinez, A.
2015-04-28
Using quantum transport simulations, the impact of electron-phonon scattering on the transfer characteristic of a gate-all-around nanowire (GaAs) field effect transistor (NWFET) has been thoroughly investigated. The Non-Equilibrium Green's Function formalism in the effective mass approximation using a decoupled mode decomposition has been deployed. NWFETs of different dimensions have been considered, and scattering mechanisms including acoustic, optical and polar optical phonons have been included. The effective masses were extracted from tight binding simulations. High and low drain bias have been considered. We found substantial source to drain tunnelling current and significant impact of phonon scattering on the performance of the NWFET. At low drain bias, for a 2.2 × 2.2 nm{sup 2} cross-section transistor, scattering caused a 72%, 77%, and 81% decrease in the on-current for a 6 nm, 10 nm, and 20 nm channel length, respectively. This reduction in the current due to scattering is influenced by the increase in the tunnelling current. We include the percentage tunnelling for each valley at low and high drain bias. It was also found that the strong quantisation caused the relative position of the valleys to vary with the cross-section. This had a large effect on the overall tunnelling current. The phonon-limited mobility was also calculated, finding a mobility of 950 cm{sup 2}/V s at an inversion charge density of 10{sup 12 }cm{sup −2} for a 4.2 × 4.2 nm{sup 2} cross-section device.
Quantum Drude friction for time-dependent density functional theory
NASA Astrophysics Data System (ADS)
Neuhauser, Daniel; Lopata, Kenneth
2008-10-01
way to very simple finite grid description of scattering and multistage conductance using time-dependent density functional theory away from the linear regime, just as absorbing potentials and self-energies are useful for noninteracting systems and leads.
Assumed Probability Density Functions for Shallow and Deep Convection
NASA Astrophysics Data System (ADS)
Bogenschutz, Peter A.; Krueger, Steven K.; Khairoutdinov, Marat
2010-04-01
The assumed joint probability density function (PDF) between vertical velocity and conserved temperature and total water scalars has been suggested to be a relatively computationally inexpensive and unified subgrid-scale (SGS) parameterization for boundary layer clouds and turbulent moments. This paper analyzes the performance of five families of PDFs using large-eddy simulations of deep convection, shallow convection, and a transition from stratocumulus to trade wind cumulus. Three of the PDF families are based on the double Gaussian form and the remaining two are the single Gaussian and a Double Delta Function (analogous to a mass flux model). The assumed PDF method is tested for grid sizes as small as 0.4 km to as large as 204.8 km. In addition, studies are performed for PDF sensitivity to errors in the input moments and for how well the PDFs diagnose some higher-order moments. In general, the double Gaussian PDFs more accurately represent SGS cloud structure and turbulence moments in the boundary layer compared to the single Gaussian and Double Delta Function PDFs for the range of grid sizes tested. This is especially true for small SGS cloud fractions. While the most complex PDF, Lewellen-Yoh, better represents shallow convective cloud properties (cloud fraction and liquid water mixing ratio) compared to the less complex Analytic Double Gaussian 1 PDF, there appears to be no advantage in implementing Lewellen-Yoh for deep convection. However, the Analytic Double Gaussian 1 PDF better represents the liquid water flux, is less sensitive to errors in the input moments, and diagnoses higher order moments more accurately. Between the Lewellen-Yoh and Analytic Double Gaussian 1 PDFs, it appears that neither family is distinctly better at representing cloudy layers. However, due to the reduced computational cost and fairly robust results, it appears that the Analytic Double Gaussian 1 PDF could be an ideal family for SGS cloud and turbulence representation in coarse
Surfaces of complex intermetallic compounds: insights from density functional calculations.
Hafner, Jürgen; Krajčí, Marian
2014-11-18
CONSPECTUS: Complex intermetallic compounds are a class of ordered alloys consisting of quasicrystals and other ordered compounds with large unit cells; many of them are approximant phases to quasicrystals. Quasicrystals are the limiting case where the unit cell becomes infinitely large; approximants are series of periodic structures converging to the quasicrystal. While the unique properties of quasicrystals have inspired many investigations of their surfaces, relatively little attention has been devoted to the surface properties of the approximants. In general, complex intermetallic compounds display rather irregular, often strongly corrugated surfaces, making the determination of their atomic structure a very complex and challenging task. During recent years, scanning tunneling microscopy (STM) has been used to study the surfaces of several complex intermetallic compounds. If atomic resolution can be achieved, STM permits visualization of the local atomistic surface structure. However, the interpretation of the STM images is often ambiguous and sometimes even impossible without a realistic model of the structure of the surface and the distribution of the electronic density above the surface. Here we demonstrate that ab initio density functional theory (DFT) can be used to determine the energetics and the geometric and electronic structures of the stable surfaces of complex intermetallic compounds. Calculations for surfaces with different chemical compositions can be performed in the grand canonical ensemble. Simulated cleavage experiments permit us to determine the formation of the cleavage planes requiring the lowest energy. The investigation of the adsorption of molecular species permits a comparison with temperature-programmed thermal desorption experiments. Calculated surface electronic densities of state can be compared with the results of photoelectron spectroscopy. Simulations of detailed STM images can be directly confronted with the experimental results
Capillary wave Hamiltonian for the Landau-Ginzburg-Wilson density functional.
Chacón, Enrique; Tarazona, Pedro
2016-06-22
We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau-Ginzburg-Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers. PMID:27115912
Capillary wave Hamiltonian for the Landau–Ginzburg–Wilson density functional
NASA Astrophysics Data System (ADS)
Chacón, Enrique; Tarazona, Pedro
2016-06-01
We study the link between the density functional (DF) formalism and the capillary wave theory (CWT) for liquid surfaces, focused on the Landau–Ginzburg–Wilson (LGW) model, or square gradient DF expansion, with a symmetric double parabola free energy, which has been extensively used in theoretical studies of this problem. We show the equivalence between the non-local DF results of Parry and coworkers and the direct evaluation of the mean square fluctuations of the intrinsic surface, as is done in the intrinsic sampling method for computer simulations. The definition of effective wave-vector dependent surface tensions is reviewed and we obtain new proposals for the LGW model. The surface weight proposed by Blokhuis and the surface mode analysis proposed by Stecki provide consistent and optimal effective definitions for the extended CWT Hamiltonian associated to the DF model. A non-local, or coarse-grained, definition of the intrinsic surface provides the missing element to get the mesoscopic surface Hamiltonian from the molecular DF description, as had been proposed a long time ago by Dietrich and coworkers.
Describing long-range charge-separation processes with subsystem density-functional theory
Solovyeva, Alisa; Neugebauer, Johannes; Pavanello, Michele
2014-04-28
Long-range charge-transfer processes in extended systems are difficult to describe with quantum chemical methods. In particular, cost-effective (non-hybrid) approximations within time-dependent density functional theory (DFT) are not applicable unless special precautions are taken. Here, we show that the efficient subsystem DFT can be employed as a constrained DFT variant to describe the energetics of long-range charge-separation processes. A formal analysis of the energy components in subsystem DFT for such excitation energies is presented, which demonstrates that both the distance dependence and the long-range limit are correctly described. In addition, electronic couplings for these processes as needed for rate constants in Marcus theory can be obtained from this method. It is shown that the electronic structure of charge-separated states constructed by a positively charged subsystem interacting with a negatively charged one is difficult to converge — charge leaking from the negative subsystem to the positive one can occur. This problem is related to the delocalization error in DFT and can be overcome with asymptotically correct exchange–correlation (XC) potentials or XC potentials including a sufficiently large amount of exact exchange. We also outline an approximate way to obtain charge-transfer couplings between locally excited and charge-separated states.
Fattebert, J
2008-07-29
We describe an iterative algorithm to solve electronic structure problems in Density Functional Theory. The approach is presented as a Subspace Accelerated Inexact Newton (SAIN) solver for the non-linear Kohn-Sham equations. It is related to a class of iterative algorithms known as RMM-DIIS in the electronic structure community. The method is illustrated with examples of real applications using a finite difference discretization and multigrid preconditioning.
Density functional theory and phytochemical study of Pistagremic acid
NASA Astrophysics Data System (ADS)
Ullah, Habib; Rauf, Abdur; Ullah, Zakir; Fazl-i-Sattar; Anwar, Muhammad; Shah, Anwar-ul-Haq Ali; Uddin, Ghias; Ayub, Khurshid
2014-01-01
We report here for the first time a comparative theoretical and experimental study of Pistagremic acid (P.A). We have developed a theoretical model for obtaining the electronic and spectroscopic properties of P.A. The simulated data showed nice correlation with the experimental data. The geometric and electronic properties were simulated at B3LYP/6-31 G (d, p) level of density functional theory (DFT). The optimized geometric parameters of P.A were found consistent with those from X-ray crystal structure. Differences of about 0.01 and 0.15 Å in bond length and 0.19-1.30° degree in the angles, respectively; were observed between the experimental and theoretical data. The theoretical vibrational bands of P.A were found to correlate with the experimental IR spectrum after a common scaling factor of 0.963. The experimental and predicted UV-Vis spectra (at B3LYP/6-31+G (d, p)) have 36 nm differences. This difference from experimental results is because of the condensed phase nature of P.A. Electronic properties such as Ionization Potential (I.P), Electron Affinities (E.A), co-efficient of highest occupied molecular orbital (HOMO), co-efficient of lowest unoccupied molecular orbital (LUMO) of P.A were estimated for the first time however, no correlation can be made with experiment. Inter-molecular interaction and its effect on vibrational (IR), electronic and geometric parameters were simulated by using Formic acid as model for hydrogen bonding in P.A.
Density functional study of condensation in capped capillaries.
Yatsyshin, P; Savva, N; Kalliadasis, S
2015-07-15
We study liquid adsorption in narrow rectangular capped capillaries formed by capping two parallel planar walls (a slit pore) with a third wall orthogonal to the two planar walls. The most important transition in confined fluids is arguably condensation, where the pore becomes filled with the liquid phase which is metastable in the bulk. Depending on the temperature T, the condensation in capped capillaries can be first-order (at T≤Tcw) or continuous (at T>Tcw), where Tcw is the capillary wetting temperature. At T>Tcw, the capping wall can adsorb mesoscopic amounts of metastable under-condensed liquid. The onset of condensation is then manifested by the continuous unbinding of the interface between the liquid adsorbed on the capping wall and the gas filling the rest of the capillary volume. In wide capped capillaries there may be a remnant of wedge filling transition, which is manifested by the adsorption of liquid drops in the corners. Our classical statistical mechanical treatment predicts a possibility of three-phase coexistence between gas, corner drops and liquid slabs adsorbed on the capping wall. In sufficiently wide capillaries we find that thick prewetting films of finite length may be nucleated at the capping wall below the boundary of the prewetting transition. Prewetting then proceeds in a continuous manner manifested by the unbinding interface between the thick and thin films adsorbed on the side walls. Our analysis is based on a detailed numerical investigation of the density functional theory for the fluid equilibria for a number of illustrative case studies. PMID:26086161
Density functional study of condensation in capped capillaries
NASA Astrophysics Data System (ADS)
Yatsyshin, P.; Savva, N.; Kalliadasis, S.
2015-07-01
We study liquid adsorption in narrow rectangular capped capillaries formed by capping two parallel planar walls (a slit pore) with a third wall orthogonal to the two planar walls. The most important transition in confined fluids is arguably condensation, where the pore becomes filled with the liquid phase which is metastable in the bulk. Depending on the temperature T, the condensation in capped capillaries can be first-order (at T≤slant {{T}\\text{cw}} ) or continuous (at T\\gt {{T}\\text{cw}} ), where {{T}\\text{cw}} is the capillary wetting temperature. At T \\gt {{T}\\text{cw}} , the capping wall can adsorb mesoscopic amounts of metastable under-condensed liquid. The onset of condensation is then manifested by the continuous unbinding of the interface between the liquid adsorbed on the capping wall and the gas filling the rest of the capillary volume. In wide capped capillaries there may be a remnant of wedge filling transition, which is manifested by the adsorption of liquid drops in the corners. Our classical statistical mechanical treatment predicts a possibility of three-phase coexistence between gas, corner drops and liquid slabs adsorbed on the capping wall. In sufficiently wide capillaries we find that thick prewetting films of finite length may be nucleated at the capping wall below the boundary of the prewetting transition. Prewetting then proceeds in a continuous manner manifested by the unbinding interface between the thick and thin films adsorbed on the side walls. Our analysis is based on a detailed numerical investigation of the density functional theory for the fluid equilibria for a number of illustrative case studies.
Density functional theory study of neutral and oxidized thiophene oligomers
NASA Astrophysics Data System (ADS)
Dai, Yafei; Wei, Chengwei; Blaisten-Barojas, Estela
2013-11-01
The effect of oxidation on the energetics and structure of thiophene (Th) oligomers is studied with density functional theory at the B3PW91/6-311++G(d,p) level. Neutral n-Th oligomers (2 < n < 13) are gently curved planar chains. Ionization potential and electron affinity results show that n-Th oligomers are easier to be oxidized as their chain length increases. Oxidation states +2, +4, +6, and +8 are energetically stable in 12-Th. Upon oxidation the conjugated backbone of 12-Th switches from extended benzenoid phase to quinoid phase localized on groups of monomers regularly spaced along the chain. Oxidized states +2, +4, +6, and +8 of 12-Th display two +1e localized at the ends of their chains only because of the finite size of the chains. In 12-Th this end-effect extends over the two terminal monomers forming a positive-negative charge duet. This peculiar charge localization makes n-Th oligomers different from other conducting polymers with similar structure, such as polypyrrole. The spectrum of single-electron molecular states of oxidized 12-Th displays two localized single-electron states in the HOMO-LUMO energy gap per +2 oxidation state. Oligothiophene 12-Th doped with F atoms at 1:2 concentration presents a charge transfer of 3.4 e from oligomer to dopants that increases to 4.8 e in the presence of solvent. The charge distribution in these F-doped oligomers is similar to the +4 oxidation state of 12-Th. It is predicted that dopants produce an enhanced charge transfer localized in the proximity of their locations enhancing the formation of bipolarons in the central part of the oligomer chain.
Density functional theory and phytochemical study of Pistagremic acid.
Ullah, Habib; Rauf, Abdur; Ullah, Zakir; Fazl-i-Sattar; Anwar, Muhammad; Shah, Anwar-ul-Haq Ali; Uddin, Ghias; Ayub, Khurshid
2014-01-24
We report here for the first time a comparative theoretical and experimental study of Pistagremic acid (P.A). We have developed a theoretical model for obtaining the electronic and spectroscopic properties of P.A. The simulated data showed nice correlation with the experimental data. The geometric and electronic properties were simulated at B3LYP/6-31 G (d, p) level of density functional theory (DFT). The optimized geometric parameters of P.A were found consistent with those from X-ray crystal structure. Differences of about 0.01 and 0.15 Å in bond length and 0.19-1.30° degree in the angles, respectively; were observed between the experimental and theoretical data. The theoretical vibrational bands of P.A were found to correlate with the experimental IR spectrum after a common scaling factor of 0.963. The experimental and predicted UV-Vis spectra (at B3LYP/6-31+G (d, p)) have 36 nm differences. This difference from experimental results is because of the condensed phase nature of P.A. Electronic properties such as Ionization Potential (I.P), Electron Affinities (E.A), co-efficient of highest occupied molecular orbital (HOMO), co-efficient of lowest unoccupied molecular orbital (LUMO) of P.A were estimated for the first time however, no correlation can be made with experiment. Inter-molecular interaction and its effect on vibrational (IR), electronic and geometric parameters were simulated by using Formic acid as model for hydrogen bonding in P.A. PMID:24051292
Density Functional Theory applied to magnetic materials: Mn3O4 at different hybrid functionals
NASA Astrophysics Data System (ADS)
Ribeiro, R. A. P.; de Lazaro, S. R.; Pianaro, S. A.
2015-10-01
Antiferromagnetic Mn3O4 in spinel structure was investigated employing the Density Functional Theory at different hybrid functionals with default HF exchange percentage. Structural, electronic and magnetic properties were examined. Structural results were in agreement with experimental and Hartree-Fock results showing that the octahedral site was distorted by the Jahn-Teller effect, which changed the electron density distribution. Band-gap results for B3LYP and B3PW hybrid functionals were closer to the experimental when compared to PBE0. Mulliken Population Analysis revealed magnetic moments very close to ideal d4 and d5 electron configurations of Mn3+ and Mn2+, respectively. Electron density maps are useful to determine that oxygen atoms mediate the electron transfer between octahedral and tetrahedral clusters. Magnetic properties were investigated from theoretical results for exchange coupling constants. Intratetrahedral and tetra-octahedral interactions were observed to be antiferromagnetic, whereas, octahedral sites presented antiferromagnetic interactions in the same layer and ferromagnetic in adjacent layers. Results showed that only default B3LYP was successful to describe magnetic properties of antiferromagnetic materials in agreement with experimental results.
NASA Astrophysics Data System (ADS)
Putaja, A.; Eich, F. G.; Baldsiefen, T.; Räsänen, E.
2016-03-01
Physically valid and numerically efficient approximations for the exchange and correlation energy are critical for reduced-density-matrix-functional theory to become a widely used method in electronic structure calculations. Here we examine the physical limits of power functionals of the form f (n ,n') =(nn')α for the scaling function in the exchange-correlation energy. To this end we obtain numerically the minimizing momentum distributions for the three- and two-dimensional homogeneous electron gas, respectively. In particular, we examine the limiting values for the power α to yield physically sound solutions that satisfy the Lieb-Oxford lower bound for the exchange-correlation energy and exclude pinned states with the condition n (k )<1 for all wave vectors k . The results refine the constraints previously obtained from trial momentum distributions. We also compute the values for α that yield the exact correlation energy and its kinetic part for both the three- and two-dimensional electron gas. In both systems, narrow regimes of validity and accuracy are found at α ≳0.6 and at rs≳10 for the density parameter, corresponding to relatively low densities.
Symmetry Energy as a Function of Density and Mass
Danielewicz, Pawel; Lee, Jenny
2007-10-26
Energy in nuclear matter is, in practice, completely characterized at different densities and asymmetries, when the density dependencies of symmetry energy and of energy of symmetric matter are specified. The density dependence of the symmetry energy at subnormal densities produces mass dependence of nuclear symmetry coefficient and, thus, can be constrained by that latter dependence. We deduce values of the mass dependent symmetry coefficients, by using excitation energies to isobaric analog states. The coefficient systematic, for intermediate and high masses, is well described in terms of the symmetry coefficient values of a{sub a}{sup V} = (31.5-33.5) MeV for the volume coefficient and a{sub a}{sup S} = (9-12) MeV for the surface coefficient. These two further correspond to the parameter values describing density dependence of symmetry energy, of L{approx}95 MeV and K{sub sym}{approx}25 MeV.
Density functional theory modeling of multilayer "epitaxial" graphene oxide.
Zhou, Si; Bongiorno, Angelo
2014-11-18
CONSPECTUS: Graphene oxide (GO) is a complex material of both fundamental and applied interest. Elucidating the structure of GO is crucial to achieve control over its properties and technological applications. GO is a nonstoichiometric and hygroscopic material with a lamellar structure, and its physical chemical properties depend critically on synthesis procedures and postsynthesis treatments. Numerous efforts are in place to both understand and exploit this versatile layered carbon material. This Account reports on recent density functional theory (DFT) studies of "epitaxial" graphene oxide (hereafter EGO), a type of GO obtained by oxidation of graphene films grown epitaxially on silicon carbide. Here, we rely on selected X-ray photoelectron spectroscopy (XPS), infrared spectroscopy (IR), and X-ray diffraction (XRD) measurements of EGO, and we discuss in great detail how we utilized DFT-based techniques to project out from the experimental data basic atomistic information about the chemistry and structure of these films. This Account provides an example as to how DFT modeling can be used to elucidate complex materials such as GO from a limited set of experimental information. EGO exhibits a uniform layered structure, consisting of a stack of graphene planes hosting predominantly epoxide and hydroxyl groups, and water molecules intercalated between the oxidized carbon layers. Here, we first focus on XPS measurements of EGO, and we use DFT to generate realistic model structures, calculate core-level chemical shifts, and through the comparison with experiment, gain insight on the chemical composition and metastability characteristics of EGO. DFT calculations are then used to devise a simplistic but accurate simulation scheme to study thermodynamic and kinetic stability and to predict the intralayer structure of EGO films aged at room temperature. Our simulations show that aged EGO encompasses layers with nanosized oxidized domains presenting a high concentration of
Laser Spectroscopy and Density Functional Study on Niobium Dimer Cation
NASA Astrophysics Data System (ADS)
Aydin, Metin; Lombardi, John R.
2009-06-01
Resonant multiphoton fragmentation spectra of niobium dimer cation (Nb2+) have been obtained by utilizing laser vaporization of a Nb metal target. Ions are mass-selected with a time-of-flight mass spectrometer followed by a mass gate, then fragmented with a pulsed dye laser, and the resulting fragment ions are detected with a second time-of-flight reflectron mass spectrometer and multichannel plate. Photon resonances are detected by monitoring ion current as a function of fragmentation laser wavelength. A rich, but complex spectrum of the cation is obtained. The bands display a characteristic multiplet structure that may be interpreted as due to transitions from the ground state X^{4}{Σ}^{-}({Ω}g) to several excited states, X^{4}{Π}({Ω}u) and X^{4}{Σ}(^{-}{Ω}u). The ground state X^{4}{Σ}^{-}({Ω}g) is derived from the electron configuration ({π}{_u})^{4} (1{σ}{_g})^{2}(2{σ}{_g})^{1} ({δ}{_g})^{2}. The two spin-orbit components are split by 145 cm^{-1} due to a strong second-order isoconfigurational spin-orbit interaction with the low-lying ^{2}{Σ}^{+}({Ω}g) state. The vibrational frequencies of the ground sate and the excited state of Nb2+ are identified as well as molecular spin-orbit constants (A{_S}{_O}) in the excited state. The electronic structure of niobium dimer cation was investigated using density functional theory. For the electronic ground state, the predicted spectroscopic properties were in good agreement with experiment. Calculations on excited states reveal congested manifolds of quartet and doublet electronic states in the range 0-30,000 cm^{-1}, reflecting the multitude of possible electronic promotions among the 4d- and 5s-based molecular orbitals. Comparisons are drawn between Nb^{+}{_2} and the prevalent isoelectronic molecules V^{+}{_2}/NbV^{+}/Nb{_2}/V{_2}/NbV. M. Aydin and John R. Lombardi J. Phys. Chem. A. xx XXXX 2009.
Yang, Ke; Peverati, Roberto; Truhlar, Donald G; Valero, Rosendo
2011-07-28
A database containing 17 multiplicity-changing valence and Rydberg excitation energies of p-block elements is used to test the performance of density functional theory (DFT) with approximate density functionals for calculating relative energies of spin states. We consider only systems where both the low-spin and high-spin state are well described by a single Slater determinant, thereby avoiding complications due to broken-symmetry solutions. Because the excitations studied involve a spin change, they require a balanced treatment of exchange and correlation, thus providing a hard test for approximate density functionals. We test three formalisms for predicting the multiplicity-changing transition energies. First is the ΔSCF method; we also test time-dependent density functional theory (TDDFT), both in its conventional form starting from the low-spin state and in its collinear spin-flip form starting from the high-spin state. Very diffuse basis functions are needed to give a qualitatively correct description of the Rydberg excitations. The scalar relativistic effect needs to be considered when quantitative results are desired, and we include it in the comparisons. With the ΔSCF method, most of the tested functionals give mean unsigned errors (MUEs) larger than 6 kcal/mol for valence excitations and MUEs larger than 3 kcal/mol for Rydberg excitations, but the performance for the Rydberg states is much better than can be obtained with time-dependent DFT. It is surprising to see that the long-range corrected functionals, which have 100% Hartree-Fock exchange at large inter-electronic distance, do not improve the performance for Rydberg excitations. Among all tested density functionals, ΔSCF calculations with the O3LYP, M08-HX, and OLYP functionals give the best overall performance for both valence and Rydberg excitations, with MUEs of 2.1, 2.6, and 2.7 kcal/mol, respectively. This is very encouraging since the MUE of the CCSD(T) coupled cluster method with quintuple
Density functional study on the functionalization of BN nanotubes with nitramide
NASA Astrophysics Data System (ADS)
Kakemam, Jamal; Noei, M.
2014-10-01
Chemical functionalization of a boron nitride nanotube (BNNT) with nitramide molecule (H2NNO2) has been investigated using density functional theory. It was found that the molecule prefers to be adsorbed and dissociated on a diagonal B-N bond of the tube surface so that the -NH2 and -NO2 groups are attached on B and N atoms, releasing energy of 0.50 eV. The results show that the functionalized BNNT is more soluble than the pristine one which may render the chemical modification process to be an effective way for purification of the BNNTs. Depending on the cleavage behavior of nitramide on the tube, HOMO/LUMO gap of the system can be either decreased or increased while the chemically modified BNNT is still a semiconductor. Furthermore, the chemical functionalization results in hindered field emission in the tube by raising the potential barrier of the electron emission.
NASA Astrophysics Data System (ADS)
Mattsson, Ann E.; Wills, John M.
2013-03-01
The inability to computationally describe the physics governing the properties of actinides and their alloys is the poster child of failure of existing Density Functional Theory exchange-correlation functionals. The intricate competition between localization and delocalization of the electrons, present in these materials, exposes the limitations of functionals only designed to properly describe one or the other situation. We will discuss the manifestation of this competition in real materials and propositions on how to construct a functional able to accurately describe properties of these materials. I addition we will discuss both the importance of using the Dirac equation to describe the relativistic effects in these materials, and the connection to the physics of transition metal oxides. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Louie, S.G.
1988-10-01
Two recently developed approaches for calculating properties of materials going beyond the density functional formalism are discussed. For excited-state properties, a first-principles quasiparticle theory has been developed. The electron self-energy operator is calculated using the full dielectric matrix and the dressed Green's function. Electron excitation spectra are interpreted as transitions between quasiparticle states of an interacting many-electron system. For ground-state properties, a new method using nonlocal pseudopotentials in conjunction with the variational quantum Monte Carlo approach is introduced. Electron correlations are treated using the exact interaction with a correlated wavefunction of the Jastrow-Slater form. Selected examples from bulk, surface, and interface calculations are presented to illustrate the capabilities of these two approaches. 47 refs., 6 figs., 5 tabs.
Exact density functional and wave function embedding schemes based on orbital localization
NASA Astrophysics Data System (ADS)
Hégely, Bence; Nagy, Péter R.; Ferenczy, György G.; Kállay, Mihály
2016-08-01
Exact schemes for the embedding of density functional theory (DFT) and wave function theory (WFT) methods into lower-level DFT or WFT approaches are introduced utilizing orbital localization. First, a simple modification of the projector-based embedding scheme of Manby and co-workers [J. Chem. Phys. 140, 18A507 (2014)] is proposed. We also use localized orbitals to partition the system, but instead of augmenting the Fock operator with a somewhat arbitrary level-shift projector we solve the Huzinaga-equation, which strictly enforces the Pauli exclusion principle. Second, the embedding of WFT methods in local correlation approaches is studied. Since the latter methods split up the system into local domains, very simple embedding theories can be defined if the domains of the active subsystem and the environment are treated at a different level. The considered embedding schemes are benchmarked for reaction energies and compared to quantum mechanics (QM)/molecular mechanics (MM) and vacuum embedding. We conclude that for DFT-in-DFT embedding, the Huzinaga-equation-based scheme is more efficient than the other approaches, but QM/MM or even simple vacuum embedding is still competitive in particular cases. Concerning the embedding of wave function methods, the clear winner is the embedding of WFT into low-level local correlation approaches, and WFT-in-DFT embedding can only be more advantageous if a non-hybrid density functional is employed.
Modeling the Pauli potential in the pair density functional theory.
Amovilli, C; Nagy, A
2008-11-28
In the ground state the pair density can be determined by solving a single auxiliary equation of a two-particle problem. A novel method for determining the Pauli potential entering this equation is presented and, starting from a reliable description of the pair density, an analytical expression is derived for atomic systems. Test calculations are presented for Be and isoelectronic C(2+) and O(4+) ions. PMID:19045853
2010-01-01
The optoelectronic and excitonic properties in a series of linear acenes (naphthalene up to heptacene) are investigated using range-separated methods within time-dependent density functional theory (TDDFT). In these rather simple systems, it is well-known that TDDFT methods using conventional hybrid functionals surprisingly fail in describing the low-lying La and Lb valence states, resulting in large, growing errors for the La state and an incorrect energetic ordering as a function of molecular size. In this work, we demonstrate that the range-separated formalism largely eliminates both of these errors and also provides a consistent description of excitonic properties in these systems. We further demonstrate that reoptimizing the percentage of Hartree−Fock exchange in conventional hybrids to match wave function-based benchmark calculations still yields serious errors, and a full 100% Hartree−Fock range separation is essential for simultaneously describing both of the La and Lb transitions. From an analysis of electron−hole transition density matrices, we finally show that conventional hybrid functionals over-delocalize excitons and underestimate quasiparticle energy gaps in the acene systems. The results of our present study emphasize the importance of both a range-separated and asymptotically correct contribution of exchange in TDDFT for investigating optoelectronic and excitonic properties, even for these simple valence excitations. PMID:21170284
Density Functional Theory Calculations of Mass Transport in UO2
Andersson, Anders D.; Dorado, Boris; Uberuaga, Blas P.; Stanek, Christopher R.
2012-06-26
In this talk we present results of density functional theory (DFT) calculations of U, O and fission gas diffusion in UO{sub 2}. These processes all impact nuclear fuel performance. For example, the formation and retention of fission gas bubbles induce fuel swelling, which leads to mechanical interaction with the clad thereby increasing the probability for clad breach. Alternatively, fission gas can be released from the fuel to the plenum, which increases the pressure on the clad walls and decreases the gap thermal conductivity. The evolution of fuel microstructure features is strongly coupled to diffusion of U vacancies. Since both U and fission gas transport rates vary strongly with the O stoichiometry, it is also important to understand O diffusion. In order to better understand bulk Xe behavior in UO{sub 2{+-}x} we first calculate the relevant activation energies using DFT techniques. By analyzing a combination of Xe solution thermodynamics, migration barriers and the interaction of dissolved Xe atoms with U, we demonstrate that Xe diffusion predominantly occurs via a vacancy-mediated mechanism. Since Xe transport is closely related to diffusion of U vacancies, we have also studied the activation energy for this process. In order to explain the low value of 2.4 eV found for U migration from independent damage experiments (not thermal equilibrium) the presence of vacancy clusters must be included in the analysis. Next we investigate species transport on the (111) UO{sub 2} surface, which is motivated by the formation of small voids partially filled with fission gas atoms (bubbles) in UO{sub 2} under irradiation. Surface diffusion could be the rate-limiting step for diffusion of such bubbles, which is an alternative mechanism for mass transport in these materials. As expected, the activation energy for surface diffusion is significantly lower than for bulk transport. These results are further discussed in terms of engineering-scale fission gas release models
Zinc surface complexes on birnessite: A density functional theory study
Kwon, Kideok D.; Refson, Keith; Sposito, Garrison
2009-01-05
Biogeochemical cycling of zinc is strongly influenced by sorption on birnessite minerals (layer-type MnO2), which are found in diverse terrestrial and aquatic environments. Zinc has been observed to form both tetrahedral (Zn{sup IV}) and octahedral (Zn{sup VI}) triple-corner-sharing surface complexes (TCS) at Mn(IV) vacancy sites in hexagonal birnessite. The octahedral complex is expected to be similar to that of Zn in the Mn oxide mineral, chalcophanite (ZnMn{sub 3}O{sub 7} {center_dot} 3H{sub 2}O), but the reason for the occurrence of the four-coordinate Zn surface species remains unclear. We address this issue computationally using spin-polarized Density Functional Theory (DFT) to examine the Zn{sub IV}-TCS and Zn{sup VI}-TCS species. Structural parameters obtained by DFT geometry optimization were in excellent agreement with available experimental data on Zn-birnessites. Total energy, magnetic moments, and electron-overlap populations obtained by DFT for isolated Zn{sup IV}-TCS revealed that this species is stable in birnessite without a need for Mn(III) substitution in the octahedral sheet and that it is more effective in reducing undersaturation of surface O at a Mn vacancy than is Zn{sub VI}-TCS. Comparison between geometry-optimized ZnMn{sub 3}O{sub 7} {center_dot} 3H{sub 2}O (chalcophanite) and the hypothetical monohydrate mineral, ZnMn{sub 3}O{sub 7} {center_dot} H{sub 2}O, which contains only tetrahedral Zn, showed that the hydration state of Zn significantly affects birnessite structural stability. Finally, our study also revealed that, relative to their positions in an ideal vacancy-free MnO{sub 2}, Mn nearest to Zn in a TCS surface complex move toward the vacancy by 0.08-0.11 {angstrom}, while surface O bordering the vacancy move away from it by 0.16-0.21 {angstrom}, in agreement with recent X-ray absorption spectroscopic analyses.
Native defects in oxide semiconductors: a density functional approach.
Oba, Fumiyasu; Choi, Minseok; Togo, Atsushi; Seko, Atsuto; Tanaka, Isao
2010-09-29
We report a semilocal and hybrid Hartree-Fock density functional study of native defects in three oxide semiconductors: ZnO, SrTiO(3), and SnO. The defect that is responsible for the n-type conductivity of ZnO has been debated, in which the O vacancy, Zn interstitial, their complexes, and residual H impurity are considered candidates. Our results indicate that the O vacancy induces a deep and localized in-gap state, whereas the Zn interstitial is a shallow donor and hence can be a source of the carriers. In view of the formation energies, the O vacancy is likely to form with a substantial concentration under O-poor conditions, but the Zn interstitial is unlikely. We thus propose that the O vacancy is relevant to the nonstoichiometry of ZnO and that a source other than the native defects, such as the H impurity, needs to be considered for the n-type conductivity. For SrTiO(3), the O vacancy and its complexes have been regarded as the origins of some of the remarkable electrical and optical properties. We suggest significant roles of the Ti antisite for a new insight into the defect-induced properties. Two types of Ti antisite, both of which are off-centered from the Sr site but toward different directions, exhibit low formation energies under Ti-rich conditions as does the O vacancy. They can explain optical properties such as visible-light emission, deep-level absorption, and the ferroelectricity observed in reduced SrTiO(3). As an example of p-type conductors, SnO has been investigated with a focus on the acceptor-like native defects. Under O-rich conditions, the Sn vacancy and O interstitial are found to be energetically favorable. The Sn vacancy induces shallow acceptor levels and can therefore be a source of carriers. The O interstitial shows no in-gap levels and hence it is inactive in terms of the carrier generation and compensation. However, this defect is a key to the understanding of the structures of intermediate compounds between SnO and SnO(2). PMID
Probability density functions for use when calculating standardised drought indices
NASA Astrophysics Data System (ADS)
Svensson, Cecilia; Prosdocimi, Ilaria; Hannaford, Jamie
2015-04-01
Time series of drought indices like the standardised precipitation index (SPI) and standardised flow index (SFI) require a statistical probability density function to be fitted to the observed (generally monthly) precipitation and river flow data. Once fitted, the quantiles are transformed to a Normal distribution with mean = 0 and standard deviation = 1. These transformed data are the SPI/SFI, which are widely used in drought studies, including for drought monitoring and early warning applications. Different distributions were fitted to rainfall and river flow data accumulated over 1, 3, 6 and 12 months for 121 catchments in the United Kingdom. These catchments represent a range of catchment characteristics in a mid-latitude climate. Both rainfall and river flow data have a lower bound at 0, as rains and flows cannot be negative. Their empirical distributions also tend to have positive skewness, and therefore the Gamma distribution has often been a natural and suitable choice for describing the data statistically. However, after transformation of the data to Normal distributions to obtain the SPIs and SFIs for the 121 catchments, the distributions are rejected in 11% and 19% of cases, respectively, by the Shapiro-Wilk test. Three-parameter distributions traditionally used in hydrological applications, such as the Pearson type 3 for rainfall and the Generalised Logistic and Generalised Extreme Value distributions for river flow, tend to make the transformed data fit better, with rejection rates of 5% or less. However, none of these three-parameter distributions have a lower bound at zero. This means that the lower tail of the fitted distribution may potentially go below zero, which would result in a lower limit to the calculated SPI and SFI values (as observations can never reach into this lower tail of the theoretical distribution). The Tweedie distribution can overcome the problems found when using either the Gamma or the above three-parameter distributions. The
NASA Astrophysics Data System (ADS)
Tachikawa, Hiroto; Iyama, Tetsuji; Kawabata, Hiroshi
2016-05-01
Electronic structures and formation mechanism of hydrogen functionalized carbon nanotube (CNT) have been investigated by means of density functional theory (DFT) method. The mechanism of hydrogen addition reaction to the CNT surface was also investigated. Pure and boron-nitrogen (BN) substituted CNT (denoted by CNT and BN-CNT, respectively) were examined as the carbon nanotubes. It was found that the additions of hydrogen atom to B (boron atom) and C (carbon atom) sites of BN-CNT proceed without activation barrier, whereas the hydrogenation of N (nitrogen atom) site needs the activation energy. The electronic states of hydrogen functionalized CNT and BN-CNT were discussed on the basis of theoretical results.
Sundararajan, Mahesh; Sinha, Vivek; Bandyopadhyay, Tusar; Ghosh, Swapan K
2012-05-01
The feasibility of using cucurbituril host molecule as a probable actinyl cation binders candidate is investigated through density functional theory based calculations. Various possible binding sites of the cucurbit[5]uril host molecule to uranyl are analyzed and based on the binding energy evaluations, μ(5)-binding is predicted to be favored. For this coordination, the structure, vibrational spectra, and binding energies are evaluated for the binding of three actinyls in hexa-valent and penta-valent oxidation states with functionalized cucurbiturils. Functionalizing cucurbituril with methyl and cyclohexyl groups increases the binding affinities of actinyls, whereas fluorination decreases the binding affinities as compared to the native host molecule. Surprisingly hydroxylation of the host molecule does not distinguish the oxidation state of the three actinyls. PMID:22471316
LIBXC: A library of exchange and correlation functionals for density functional theory
NASA Astrophysics Data System (ADS)
Marques, Miguel A. L.; Oliveira, Micael J. T.; Burnus, Tobias
2012-10-01
The central quantity of density functional theory is the so-called exchange-correlation functional. This quantity encompasses all non-trivial many-body effects of the ground-state and has to be approximated in any practical application of the theory. For the past 50 years, hundreds of such approximations have appeared, with many successfully persisting in the electronic structure community and literature. Here, we present a library that contains routines to evaluate many of these functionals (around 180) and their derivatives. Program summary Program title: LIBXC Catalogue identifier: AEMU_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEMU_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU Lesser General Public License version 3 No. of lines in distributed program, including test data, etc.: 87455 No. of bytes in distributed program, including test data, etc.: 945365 Distribution format: tar.gz Programming language: C with Fortran bindings. Computer: All. Operating system: All. RAM: N.A. Classification: 7.3, 16.1. Nature of problem: Evaluation of the exchange-correlation energy functional and its derivatives. This is a fundamental part of any atomic, molecular, or solid-state code that uses density-functional theory. Solution method: The values of the energy functional and its derivatives are given in a real grid of mesh points. Running time: Typically much smaller than the remainder of the electronic structure code. The running time has a natural linear scaling with the number of grid points.
NASA Astrophysics Data System (ADS)
Duguet, T.; Bender, M.; Ebran, J.-P.; Lesinski, T.; Somà, V.
2015-12-01
This programmatic paper lays down the possibility to reconcile the necessity to resum many-body correlations into the energy kernel with the fact that safe multi-reference energy density functional (EDF) calculations cannot be achieved whenever the Pauli principle is not enforced, as is for example the case when many-body correlations are parametrized under the form of empirical density dependencies. Our proposal is to exploit a newly developed ab initio many-body formalism to guide the construction of safe, explicitly correlated and systematically improvable parametrizations of the off-diagonal energy and norm kernels that lie at the heart of the nuclear EDF method. The many-body formalism of interest relies on the concepts of symmetry breaking and restoration that have made the fortune of the nuclear EDF method and is, as such, amenable to this guidance. After elaborating on our proposal, we briefly outline the project we plan to execute in the years to come.
Density Dependent Functional Forms Drive Compensation in Populations Exposed to Stressors
The interaction between density dependence (DD) and environmental stressors can result in a compensatory or synergistic response in population growth, and population models that use density-independent demographic rates or generic DD functions may be introducing bias into managem...
Reimers, Jeffrey R; Solomon, Gemma C; Gagliardi, Alessio; Bilić, Ante; Hush, Noel S; Frauenheim, Thomas; Di Carlo, Aldo; Pecchia, Alessandro
2007-07-01
A review is presented of the nonequilibrium Green's function (NEGF) method "gDFTB" for evaluating elastic and inelastic conduction through single molecules employing the density functional tight-binding (DFTB) electronic structure method. This focuses on the possible advantages that DFTB implementations of NEGF have over conventional methods based on density functional theory, including not only the ability to treat large irregular metal-molecule junctions with high nonequilibrium thermal distributions but perhaps also the ability to treat dispersive forces, bond breakage, and open-shell systems and to avoid large band lineup errors. New results are presented indicating that DFTB provides a useful depiction of simple gold-thiol interactions. Symmetry is implemented in DFTB, and the advantages it brings in terms of large savings of computational resources with significant increase in numerical stability are described. The power of DFTB is then harnessed to allow the use of gDFTB as a real-time tool to discover the nature of the forces that control inelastic charge transport through molecules and the role of molecular symmetry in determining both elastic and inelastic transport. Future directions for the development of the method are discussed. PMID:17530826
How do azoles inhibit cytochrome P450 enzymes? A density functional study.
Balding, Philip R; Porro, Cristina S; McLean, Kirsty J; Sutcliffe, Michael J; Maréchal, Jean-Didier; Munro, Andrew W; de Visser, Sam P
2008-12-18
To examine how azole inhibitors interact with the heme active site of the cytochrome P450 enzymes, we have performed a series of density functional theory studies on azole binding. These are the first density functional studies on azole interactions with a heme center and give fundamental insight into how azoles inhibit the catalytic function of P450 enzymes. Since azoles come in many varieties, we tested three typical azole motifs representing a broad range of azole and azole-type inhibitors: methylimidazolate, methyltriazolate, and pyridine. These structural motifs represent typical azoles, such as econazole, fluconazole, and metyrapone. The calculations show that azole binding is a stepwise mechanism whereby first the water molecule from the resting state of P450 is released from the sixth binding site of the heme to create a pentacoordinated active site followed by coordination of the azole nitrogen to the heme iron. This process leads to the breaking of a hydrogen bond between the resting state water molecule and the approaching inhibitor molecule. Although, formally, the water molecule is released in the first step of the reaction mechanism and a pentacoordinated heme is created, this does not lead to an observed spin state crossing. Thus, we show that release of a water molecule from the resting state of P450 enzymes to create a pentacoordinated heme will lead to a doublet to quartet spin state crossing at an Fe-OH(2) distance of approximately 3.0 A, while the azole substitution process takes place at shorter distances. Azoles bind heme with significantly stronger binding energies than a water molecule, so that these inhibitors block the catalytic cycle of the enzyme and prevent oxygen binding and the catalysis of substrate oxidation. Perturbations within the active site (e.g., a polarized environment) have little effect on the relative energies of azole binding. Studies with an extra hydrogen-bonded ethanol molecule in the model, mimicking the active site