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
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.
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
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.
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.
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.
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.
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
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.
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.}
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.
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.
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.
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.
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.
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
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.
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.
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
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 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.
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 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
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.
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.
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
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.
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.
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.
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
2015-09-01
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
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.
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.
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.
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.
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.
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.
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.
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.
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).
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.
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.
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
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
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.
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
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.
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
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.
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
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
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.
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
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.
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.
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.
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,…
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.
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.
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.
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.
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…
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.
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.
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.
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
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.
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.
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.
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.}
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.
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.
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.
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