Stoessel, J.P.; Wolynes, P.G.
1989-01-01
With analogy to the ''highly accurate'' summation of cluster diagrams for hard sphere fluids a la Carnahan-Starling, we present a simple, real space free energy density functional for arbitrary potential systems, based on the generalization of the second virial coefficient to inhomogeneous systems which, when applied to hard sphere, soft-sphere, and Lennard-Jones freezing, yield melting characteristics in remarkable agreement with experiment. Implications for the liquid-glass transition in all three potential systems are also presented. 45 refs., 7 figs., 1 tab.
Modeling solvation effects in real-space and real-time within density functional approaches
Delgado, Alain; Corni, Stefano; Pittalis, Stefano; Rozzi, Carlo Andrea
2015-10-14
The Polarizable Continuum Model (PCM) can be used in conjunction with Density Functional Theory (DFT) and its time-dependent extension (TDDFT) to simulate the electronic and optical properties of molecules and nanoparticles immersed in a dielectric environment, typically liquid solvents. In this contribution, we develop a methodology to account for solvation effects in real-space (and real-time) (TD)DFT calculations. The boundary elements method is used to calculate the solvent reaction potential in terms of the apparent charges that spread over the van der Waals solute surface. In a real-space representation, this potential may exhibit a Coulomb singularity at grid points that are close to the cavity surface. We propose a simple approach to regularize such singularity by using a set of spherical Gaussian functions to distribute the apparent charges. We have implemented the proposed method in the OCTOPUS code and present results for the solvation free energies and solvatochromic shifts for a representative set of organic molecules in water.
ATLAS: A real-space finite-difference implementation of orbital-free density functional theory
NASA Astrophysics Data System (ADS)
Mi, Wenhui; Shao, Xuecheng; Su, Chuanxun; Zhou, Yuanyuan; Zhang, Shoutao; Li, Quan; Wang, Hui; Zhang, Lijun; Miao, Maosheng; Wang, Yanchao; Ma, Yanming
2016-03-01
Orbital-free density functional theory (OF-DFT) is a promising method for large-scale quantum mechanics simulation as it provides a good balance of accuracy and computational cost. Its applicability to large-scale simulations has been aided by progress in constructing kinetic energy functionals and local pseudopotentials. However, the widespread adoption of OF-DFT requires further improvement in its efficiency and robustly implemented software. Here we develop a real-space finite-difference (FD) method for the numerical solution of OF-DFT in periodic systems. Instead of the traditional self-consistent method, a powerful scheme for energy minimization is introduced to solve the Euler-Lagrange equation. Our approach engages both the real-space finite-difference method and a direct energy-minimization scheme for the OF-DFT calculations. The method is coded into the ATLAS software package and benchmarked using periodic systems of solid Mg, Al, and Al3Mg. The test results show that our implementation can achieve high accuracy, efficiency, and numerical stability for large-scale simulations.
Scalable real space pseudopotential-density functional codes for materials applications
NASA Astrophysics Data System (ADS)
Chelikowsky, James R.; Lena, Charles; Schofield, Grady; Saad, Yousef; Deslippe, Jack; Yang, Chao
2015-03-01
Real-space pseudopotential density functional theory has proven to be an efficient method for computing the properties of matter in many different states and geometries, including liquids, wires, slabs and clusters with and without spin polarization. Fully self-consistent solutions have been routinely obtained for systems with thousands of atoms. However, there are still systems where quantum mechanical accuracy is desired, but scalability proves to be a hindrance, such as large biological molecules or complex interfaces. We will present an overview of our work on new algorithms, which offer improved scalability by implementing another layer of parallelism, and by optimizing communication and memory management. Support provided by the SciDAC program, Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences. Grant Numbers DE-SC0008877 (Austin) and DE-FG02-12ER4 (Berkeley).
Oshiyama, Atsushi Iwata, Jun-Ichi; Uchida, Kazuyuki; Matsushita, Yu-Ichiro
2015-03-21
We show that our real-space finite-difference scheme allows us to perform density-functional calculations for nanometer-scale targets containing more than 100 000 atoms. This real-space scheme is applied to twisted bilayer graphene, clarifying that Moiré pattern induced in the slightly twisted bilayer graphene drastically modifies the atomic and electronic structures.
Scalable real space pseudopotential density functional codes for materials in the exascale regime
NASA Astrophysics Data System (ADS)
Lena, Charles; Chelikowsky, James; Schofield, Grady; Biller, Ariel; Kronik, Leeor; Saad, Yousef; Deslippe, Jack
Real-space pseudopotential density functional theory has proven to be an efficient method for computing the properties of matter in many different states and geometries, including liquids, wires, slabs, and clusters with and without spin polarization. Fully self-consistent solutions using this approach have been routinely obtained for systems with thousands of atoms. Yet, there are many systems of notable larger sizes where quantum mechanical accuracy is desired, but scalability proves to be a hindrance. Such systems include large biological molecules, complex nanostructures, or mismatched interfaces. We will present an overview of our new massively parallel algorithms, which offer improved scalability in preparation for exascale supercomputing. We will illustrate these algorithms by considering the electronic structure of a Si nanocrystal exceeding 104 atoms. Support provided by the SciDAC program, Department of Energy, Office of Science, Advanced Scientific Computing Research and Basic Energy Sciences. Grant Numbers DE-SC0008877 (Austin) and DE-FG02-12ER4 (Berkeley).
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.
Andrade, Xavier; Aspuru-Guzik, Alán
2013-10-01
We discuss the application of graphical processing units (GPUs) to accelerate real-space density functional theory (DFT) calculations. To make our implementation efficient, we have developed a scheme to expose the data parallelism available in the DFT approach; this is applied to the different procedures required for a real-space DFT calculation. We present results for current-generation GPUs from AMD and Nvidia, which show that our scheme, implemented in the free code Octopus, can reach a sustained performance of up to 90 GFlops for a single GPU, representing a significant speed-up when compared to the CPU version of the code. Moreover, for some systems, our implementation can outperform a GPU Gaussian basis set code, showing that the real-space approach is a competitive alternative for DFT simulations on GPUs. PMID:26589153
Flick, Johannes; Ruggenthaler, Michael; Appel, Heiko; Rubio, Angel
2015-01-01
The density-functional approach to quantum electrodynamics extends traditional density-functional theory and opens the possibility to describe electron–photon interactions in terms of effective Kohn–Sham potentials. In this work, we numerically construct the exact electron–photon Kohn–Sham potentials for a prototype system that consists of a trapped electron coupled to a quantized electromagnetic mode in an optical high-Q cavity. Although the effective current that acts on the photons is known explicitly, the exact effective potential that describes the forces exerted by the photons on the electrons is obtained from a fixed-point inversion scheme. This procedure allows us to uncover important beyond-mean-field features of the effective potential that mark the breakdown of classical light–matter interactions. We observe peak and step structures in the effective potentials, which can be attributed solely to the quantum nature of light; i.e., they are real-space signatures of the photons. Our findings show how the ubiquitous dipole interaction with a classical electromagnetic field has to be modified in real space to take the quantum nature of the electromagnetic field fully into account. PMID:26627715
Flick, Johannes; Ruggenthaler, Michael; Appel, Heiko; Rubio, Angel
2015-12-15
The density-functional approach to quantum electrodynamics extends traditional density-functional theory and opens the possibility to describe electron-photon interactions in terms of effective Kohn-Sham potentials. In this work, we numerically construct the exact electron-photon Kohn-Sham potentials for a prototype system that consists of a trapped electron coupled to a quantized electromagnetic mode in an optical high-Q cavity. Although the effective current that acts on the photons is known explicitly, the exact effective potential that describes the forces exerted by the photons on the electrons is obtained from a fixed-point inversion scheme. This procedure allows us to uncover important beyond-mean-field features of the effective potential that mark the breakdown of classical light-matter interactions. We observe peak and step structures in the effective potentials, which can be attributed solely to the quantum nature of light; i.e., they are real-space signatures of the photons. Our findings show how the ubiquitous dipole interaction with a classical electromagnetic field has to be modified in real space to take the quantum nature of the electromagnetic field fully into account. PMID:26627715
All-electron Kohn–Sham density functional theory on hierarchic finite element spaces
Schauer, Volker; Linder, Christian
2013-10-01
In this work, a real space formulation of the Kohn–Sham equations is developed, making use of the hierarchy of finite element spaces from different polynomial order. The focus is laid on all-electron calculations, having the highest requirement onto the basis set, which must be able to represent the orthogonal eigenfunctions as well as the electrostatic potential. A careful numerical analysis is performed, which points out the numerical intricacies originating from the singularity of the nuclei and the necessity for approximations in the numerical setting, with the ambition to enable solutions within a predefined accuracy. In this context the influence of counter-charges in the Poisson equation, the requirement of a finite domain size, numerical quadratures and the mesh refinement are examined as well as the representation of the electrostatic potential in a high order finite element space. The performance and accuracy of the method is demonstrated in computations on noble gases. In addition the finite element basis proves its flexibility in the calculation of the bond-length as well as the dipole moment of the carbon monoxide molecule.
Momentum-space properties from coordinate-space electron density
Harbola, Manoj K.; Zope, Rajendra R.; Kshirsagar, Anjali; Pathak, Rajeev K.
2005-05-22
Electron density and electron momentum density, while independently tractable experimentally, bear no direct connection without going through the many-electron wave function. However, invoking a variant of the constrained-search formulation of density-functional theory, we develop a general scheme (valid for arbitrary external potentials) yielding decent momentum-space properties, starting exclusively from the coordinate-space electron density. A numerical illustration of the scheme is provided for the closed-shell atomic systems He, Be, and Ne in their ground state and for 1s{sup 1} 2s{sup 1} singlet electronic excited state for helium by calculating the Compton profiles and the
expectation values derived from given coordinate-space electron densities.
Space race functional responses
Sjödin, Henrik; Brännström, Åke; Englund, Göran
2015-01-01
We derive functional responses under the assumption that predators and prey are engaged in a space race in which prey avoid patches with many predators and predators avoid patches with few or no prey. The resulting functional response models have a simple structure and include functions describing how the emigration of prey and predators depend on interspecific densities. As such, they provide a link between dispersal behaviours and community dynamics. The derived functional response is general but is here modelled in accordance with empirically documented emigration responses. We find that the prey emigration response to predators has stabilizing effects similar to that of the DeAngelis–Beddington functional response, and that the predator emigration response to prey has destabilizing effects similar to that of the Holling type II response. A stability criterion describing the net effect of the two emigration responses on a Lotka–Volterra predator–prey system is presented. The winner of the space race (i.e. whether predators or prey are favoured) is determined by the relationship between the slopes of the species' emigration responses. It is predicted that predators win the space race in poor habitats, where predator and prey densities are low, and that prey are more successful in richer habitats. PMID:25589602
Space race functional responses.
Sjödin, Henrik; Brännström, Åke; Englund, Göran
2015-02-22
We derive functional responses under the assumption that predators and prey are engaged in a space race in which prey avoid patches with many predators and predators avoid patches with few or no prey. The resulting functional response models have a simple structure and include functions describing how the emigration of prey and predators depend on interspecific densities. As such, they provide a link between dispersal behaviours and community dynamics. The derived functional response is general but is here modelled in accordance with empirically documented emigration responses. We find that the prey emigration response to predators has stabilizing effects similar to that of the DeAngelis-Beddington functional response, and that the predator emigration response to prey has destabilizing effects similar to that of the Holling type II response. A stability criterion describing the net effect of the two emigration responses on a Lotka-Volterra predator-prey system is presented. The winner of the space race (i.e. whether predators or prey are favoured) is determined by the relationship between the slopes of the species' emigration responses. It is predicted that predators win the space race in poor habitats, where predator and prey densities are low, and that prey are more successful in richer habitats. PMID:25589602
Zuzovski, Michael; Boag, Amir; Natan, Amir
2015-12-21
In this work we show the implementation of a linear scaling algorithm for the calculation of the Poisson integral. We use domain decomposition and non-uniform auxiliary grids (NGs) to calculate the electrostatic interaction. We demonstrate the approach within the PARSEC density functional theory code and perform calculations of long 1D carbon chains and other long molecules. Finally, we discuss possible applications to additional problems and geometries. PMID:26123448
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.
NASA Astrophysics Data System (ADS)
Shuai, Jing; Deog Yoo, Hyun; Liang, Yanliang; Li, Yifei; Yao, Yan; Grabow, Lars C.
2016-06-01
Layered materials, such as the transition metal dichalcogenide molybdenum disulfide (MoS2), are promising materials for ion storage in electrodes of rechargeable batteries. To extend the application range of these materials to ions beyond lithium-ions, we used van der Waals corrected density functional theory simulations to study the intercalation and diffusion of lithium (Li), sodium (Na), and magnesium (Mg) in the 2H structure of MoS2 as a function of interlayer spacing. All three species exhibit an optimal intercalation energy, which is reached at about 11% expansion for Li and Mg, and 23% expansion for Na. Similarly, the slow diffusion kinetics of large Na and divalent Mg-ions can be improved by layer expansion. When the interlayer spacing is increased by about 35% from its equilibrium value, the diffusion of Na and Mg-ions becomes more facile than the diffusion of small, monovalent Li-ions, with diffusion barriers similar to those of Li in graphene. Our results indicate that interlayer expansion is a promising technique to improve intercalation kinetics and thermodynamics for large and/or multivalent ions in MoS2, which can be a major limitation to battery performance. The rationalization of our results in terms of bonding geometries forms the basis of a battery electrode design framework with applications for a wide range of layered materials.
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.
West, J B; Elliott, A R; Guy, H J; Prisk, G K
1997-06-25
The lung is exquisitely sensitive to gravity, and so it is of interest to know how its function is altered in the weightlessness of space. Studies on National Aeronautics and Space Administration (NASA) Spacelabs during the last 4 years have provided the first comprehensive data on the extensive changes in pulmonary function that occur in sustained microgravity. Measurements of pulmonary function were made on astronauts during space shuttle flights lasting 9 and 14 days and were compared with extensive ground-based measurements before and after the flights. Compared with preflight measurements, cardiac output increased by 18% during space flight, and stroke volume increased by 46%. Paradoxically, the increase in stroke volume occurred in the face of reductions in central venous pressure and circulating blood volume. Diffusing capacity increased by 28%, and the increase in the diffusing capacity of the alveolar membrane was unexpectedly large based on findings in normal gravity. The change in the alveolar membrane may reflect the effects of uniform filling of the pulmonary capillary bed. Distributions of blood flow and ventilation throughout the lung were more uniform in space, but some unevenness remained, indicating the importance of nongravitational factors. A surprising finding was that airway closing volume was approximately the same in microgravity and in normal gravity, emphasizing the importance of mechanical properties of the airways in determining whether they close. Residual volume was unexpectedly reduced by 18% in microgravity, possibly because of uniform alveolar expansion. The findings indicate that pulmonary function is greatly altered in microgravity, but none of the changes observed so far will apparently limit long-term space flight. In addition, the data help to clarify how gravity affects pulmonary function in the normal gravity environment on Earth. PMID:9200637
NASA Technical Reports Server (NTRS)
West, J. B.; Elliott, A. R.; Guy, H. J.; Prisk, G. K.
1997-01-01
The lung is exquisitely sensitive to gravity, and so it is of interest to know how its function is altered in the weightlessness of space. Studies on National Aeronautics and Space Administration (NASA) Spacelabs during the last 4 years have provided the first comprehensive data on the extensive changes in pulmonary function that occur in sustained microgravity. Measurements of pulmonary function were made on astronauts during space shuttle flights lasting 9 and 14 days and were compared with extensive ground-based measurements before and after the flights. Compared with preflight measurements, cardiac output increased by 18% during space flight, and stroke volume increased by 46%. Paradoxically, the increase in stroke volume occurred in the face of reductions in central venous pressure and circulating blood volume. Diffusing capacity increased by 28%, and the increase in the diffusing capacity of the alveolar membrane was unexpectedly large based on findings in normal gravity. The change in the alveolar membrane may reflect the effects of uniform filling of the pulmonary capillary bed. Distributions of blood flow and ventilation throughout the lung were more uniform in space, but some unevenness remained, indicating the importance of nongravitational factors. A surprising finding was that airway closing volume was approximately the same in microgravity and in normal gravity, emphasizing the importance of mechanical properties of the airways in determining whether they close. Residual volume was unexpectedly reduced by 18% in microgravity, possibly because of uniform alveolar expansion. The findings indicate that pulmonary function is greatly altered in microgravity, but none of the changes observed so far will apparently limit long-term space flight. In addition, the data help to clarify how gravity affects pulmonary function in the normal gravity environment on Earth.
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
NASA Astrophysics Data System (ADS)
Li, Junfeng; Rinkevicius, Zilvinas; Cao, Zexing
2014-07-01
Time-dependent density-functional theory (TD-DFT) and complete active space multiconfiguration self-consistent field (CASSCF) calculations have been used to determine equilibrium structures and vibrational frequencies of the ground state and several singlet low-lying excited states of coumarin. Vertical and adiabatic transition energies of S1, S2, and S3 have been estimated by TD-B3LYP and CASSCF/PT2. Calculations predict that the dipole-allowed S1 and S3 states have a character of 1(ππ*), while the dipole-forbidden 1(nπ*) state is responsible for S2. The vibronic absorption and emission spectra of coumarin have been simulated by TD-B3LYP and CASSCF calculations within the Franck-Condon approximation, respectively. The simulated vibronic spectra show good agreement with the experimental observations available, which allow us to reasonably interpret vibronic features in the S0→S1 and S0→S3 absorption and the S0←S1 emission spectra. Based on the calculated results, activity, intensity, and density of the vibronic transitions and their contribution to the experimental spectrum profile have been discussed.
Li, Junfeng; Rinkevicius, Zilvinas; Cao, Zexing
2014-07-01
Time-dependent density-functional theory (TD-DFT) and complete active space multiconfiguration self-consistent field (CASSCF) calculations have been used to determine equilibrium structures and vibrational frequencies of the ground state and several singlet low-lying excited states of coumarin. Vertical and adiabatic transition energies of S1, S2, and S3 have been estimated by TD-B3LYP and CASSCF/PT2. Calculations predict that the dipole-allowed S1 and S3 states have a character of (1)(ππ*), while the dipole-forbidden (1)(nπ*) state is responsible for S2. The vibronic absorption and emission spectra of coumarin have been simulated by TD-B3LYP and CASSCF calculations within the Franck-Condon approximation, respectively. The simulated vibronic spectra show good agreement with the experimental observations available, which allow us to reasonably interpret vibronic features in the S0→S1 and S0→S3 absorption and the S0←S1 emission spectra. Based on the calculated results, activity, intensity, and density of the vibronic transitions and their contribution to the experimental spectrum profile have been discussed. PMID:25005288
Carbó-Dorca, Ramon
2013-04-01
A general algorithm implementing a useful variant of quantum quantitative structure-property relationships (QQSPR) theory is described. Based on quantum similarity framework and previous theoretical developments on the subject, the present QQSPR procedure relies on the possibility to perform geometrical origin shifts over molecular density function sets. In this way, molecular collections attached to known properties can be easily used over other quantum mechanically well-described molecular structures for the estimation of their unknown property values. The proposed procedure takes quantum mechanical expectation value as provider of causal relation background and overcomes the dimensionality paradox, which haunts classical descriptor space QSPR. Also, contrarily to classical procedures, which are also attached to heavy statistical gear, the present QQSPR approach might use a geometrical assessment only or just some simple statistical outline or both. From an applied point of view, several easily reachable computational levels can be set up. A Fortran 95 program: QQSPR-n is described with two versions, which might be downloaded from a dedicated web site. Various practical examples are provided, yielding excellent results. Finally, it is also shown that an equivalent molecular space classical QSPR formalism can be easily developed. PMID:23238931
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.
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.
Understanding redshift space distortions in density-weighted peculiar velocity
NASA Astrophysics Data System (ADS)
Sugiyama, Naonori S.; Okumura, Teppei; Spergel, David N.
2016-07-01
Observations of the kinetic Sunyaev-Zel'dovich (kSZ) effect measure the density-weighted velocity field, a potentially powerful cosmological probe. This paper presents an analytical method to predict the power spectrum and two-point correlation function of the density-weighted velocity in redshift space, the direct observables in kSZ surveys. We show a simple relation between the density power spectrum and the density-weighted velocity power spectrum that holds for both dark matter and halos. Using this relation, we can then extend familiar perturbation expansion techniques to the kSZ power spectrum. One of the most important features of density-weighted velocity statistics in redshift space is the change in sign of the cross-correlation between the density and density-weighted velocity at mildly small scales due to nonlinear redshift space distortions. Our model can explain this characteristic feature without any free parameters. As a result, our results can precisely predict the non-linear behavior of the density-weighted velocity field in redshift space up to ~ 30 h‑1 Mpc for dark matter particles at the redshifts of z=0.0, 0.5, and 1.0.
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
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.
]: 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.
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.
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.
Simple Fixed Functional Space Maintainer
Sarawgi, Aditi; Marwah, Nikhil; Gumber, Parvind; Dutta, Samir
2014-01-01
ABSTRACT% Premature loss of a primary tooth is one of the most common etiology for malocclusion. Space maintainers are employed to prevent this complication. In anterior region, esthetics is an important concern along with function and space management. Fiber-reinforced composite (FRC) retained space maintainer solves all these purposes ef ficiently and ef fectively. In addition, the technique is simple and the appliance is very comfortable inside the oral cavity. Here is a case of premature loss of anterior primary tooth which was replaced by FRC retained esthetic functional space maintainer. The appliance was found to be functioning satisfactorily inside the oral cavity till the last visit (1 Year). How to cite this article: Goenka P, Sarawgi A, Marwah N, Gumber P, Dutta S. Simple Fixed Functional Space Maintainer. Int J Clin Pediatr Dent 2014;7(3):225-228. PMID:25709309
Reanalysis of relativistic electron phase space density
NASA Astrophysics Data System (ADS)
Shprits, Yuri; Chen, Yue; Kondrashov, Dmitri
In this study we perform a reanalysis of the sparse relativistic electron data using a relatively simple one-dimensional radial diffusion model and a Kalman filtering approach. The results of the reanalysis clearly show pronounced peaks in the electron phase space density (PSD), which can not be explained by the variations in the outer boundary, and can only be produced by a local acceleration processes. The location of the innovation vector shows that local acceleration is most efficient at L* = 5.5. To verify that our results are not affected by the limitations of the satellite orbit and coverage, we performed an "identical twin" experiments with synthetic data specified only at the locations for which CRRES observations are available. Our results indicate that the model with data assimilation can accurately reproduce the underlying structure of the PSD even when data is sparse.
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.
Space: The Final Frontier of Bone Density
NASA Technical Reports Server (NTRS)
Sibonga, Jean D.
2011-01-01
It is a medical requirement at NASA to evaluate the skeletal integrity of "long-duration" astronauts by measuring bone mineral density [BMD] with DXA technology. A long-duration mission is a spaceflight that is greater than 30 days but is typically the continuous 120-180 day missions aboard the International Space Station [ISS]. Not only does NASA use the BMD index to monitor fracture risk in this astronaut population, but these measures are also used to describe the effects of spaceflight, to certify skeletal health readiness for flight, to monitor the recovery of lost bone mass after return to earth, and to evaluate the efficacy of countermeasures to bone loss. However, despite the fact that DXA-based BMD is a widely-applied surrogate for bone strength that is grounded in an abundance of population-based fracture data, its applicability to the long-duration astronaut is limited. The cohort of long-duration astronauts is not the typical group for evaluating osteoporosis or determining age-related fracture risk. The cohort is young (< 55 years), predominantly male and exposed to novel risk factors for bone loss besides the weightlessness of space. NASA is concerned about early onset osteoporosis in the astronaut exposed to long-duration spaceflight, especially since any detectable symptoms are likely to manifest after return to earth and perhaps years after space travel. This risk raises the question: is NASA doing enough now to mitigate a fracture event that may manifest later? This presentation will discuss the limitations and constraints to understanding skeletal changes due to prolonged spaceflight and the recommendations, by clinical experts in osteoporosis and BMD, to transition research technologies for clinical decision-making by NASA.
Distribution function approach to redshift space distortions
Seljak, Uroš; McDonald, Patrick E-mail: pvmcdonald@lbl.gov
2011-11-01
We develop a phase space distribution function approach to redshift space distortions (RSD), in which the redshift space density can be written as a sum over velocity moments of the distribution function. These moments are density weighted and have well defined physical interpretation: their lowest orders are density, momentum density, and stress energy density. The series expansion is convergent if kμu/aH < 1, where k is the wavevector, H the Hubble parameter, u the typical gravitational velocity and μ = cos θ, with θ being the angle between the Fourier mode and the line of sight. We perform an expansion of these velocity moments into helicity modes, which are eigenmodes under rotation around the axis of Fourier mode direction, generalizing the scalar, vector, tensor decomposition of perturbations to an arbitrary order. We show that only equal helicity moments correlate and derive the angular dependence of the individual contributions to the redshift space power spectrum. We show that the dominant term of μ{sup 2} dependence on large scales is the cross-correlation between the density and scalar part of momentum density, which can be related to the time derivative of the matter power spectrum. Additional terms contributing to μ{sup 2} and dominating on small scales are the vector part of momentum density-momentum density correlations, the energy density-density correlations, and the scalar part of anisotropic stress density-density correlations. The second term is what is usually associated with the small scale Fingers-of-God damping and always suppresses power, but the first term comes with the opposite sign and always adds power. Similarly, we identify 7 terms contributing to μ{sup 4} dependence. Some of the advantages of the distribution function approach are that the series expansion converges on large scales and remains valid in multi-stream situations. We finish with a brief discussion of implications for RSD in galaxies relative to dark matter
Space station functional relationships analysis
NASA Technical Reports Server (NTRS)
Tullis, Thomas S.; Bied, Barbra R.
1988-01-01
A systems engineering process is developed to assist Space Station designers to understand the underlying operational system of the facility so that it can be physically arranged and configured to support crew productivity. The study analyzes the operational system proposed for the Space Station in terms of mission functions, crew activities, and functional relationships in order to develop a quantitative model for evaluation of interior layouts, configuration, and traffic analysis for any Station configuration. Development of the model involved identification of crew functions, required support equipment, criteria of assessing functional relationships, and tools for analyzing functional relationship matrices, as well as analyses of crew transition frequency, sequential dependencies, support equipment requirements, potential for noise interference, need for privacy, and overall compatability of functions. The model can be used for analyzing crew functions for the Initial Operating Capability of the Station and for detecting relationships among these functions. Note: This process (FRA) was used during Phase B design studies to test optional layouts of the Space Station habitat module. The process is now being automated as a computer model for use in layout testing of the Space Station laboratory modules during Phase C.
A Safari Through Density Functional Theory
NASA Astrophysics Data System (ADS)
Dreizler, Reiner M.; Lüdde, Cora S.
Density functional theory is widely used to treat quantum many body problems in many areas of physics and related fields. A brief survey of this method covering foundations, functionals and applications is presented here.
Magnetic fields and density functional theory
Salsbury Jr., Freddie
1999-02-01
A major focus of this dissertation is the development of functionals for the magnetic susceptibility and the chemical shielding within the context of magnetic field density functional theory (BDFT). These functionals depend on the electron density in the absence of the field, which is unlike any other treatment of these responses. There have been several advances made within this theory. The first of which is the development of local density functionals for chemical shieldings and magnetic susceptibilities. There are the first such functionals ever proposed. These parameters have been studied by constructing functionals for the current density and then using the Biot-Savart equations to obtain the responses. In order to examine the advantages and disadvantages of the local functionals, they were tested numerically on some small molecules.
Density functional theory for carbon dioxide crystal
Chang, Yiwen; Mi, Jianguo Zhong, Chongli
2014-05-28
We present a density functional approach to describe the solid−liquid phase transition, interfacial and crystal structure, and properties of polyatomic CO{sub 2}. Unlike previous phase field crystal model or density functional theory, which are derived from the second order direct correlation function, the present density functional approach is based on the fundamental measure theory for hard-sphere repulsion in solid. More importantly, the contributions of enthalpic interactions due to the dispersive attractions and of entropic interactions arising from the molecular architecture are integrated in the density functional model. Using the theoretical model, the predicted liquid and solid densities of CO{sub 2} at equilibrium triple point are in good agreement with the experimental values. Based on the structure of crystal-liquid interfaces in different planes, the corresponding interfacial tensions are predicted. Their respective accuracies need to be tested.
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).
Cardiovascular function in space flight
NASA Technical Reports Server (NTRS)
Nicogossian, A. E.; Charles, J. B.; Bungo, M. W.; Leach-Huntoon, C. S.
1990-01-01
Postflight orthostatic intolerance and cardiac hemodynamics associated with manned space flight have been investigated on seven STS missions. Orthostatic heart rates appear to be influenced by the mission duration. The rates increase during the first 7-10 days of flight and recover partially after that. Fluid loading is used as a countermeasure to the postflight orthostatic intolerance. The carotid baroreceptor function shows only slight responsiveness to orthostatic stimulation. Plots of the baroreceptor function are presented. It is concluded that an early adaptation to the space flight conditions involves a fluid shift and that the subsequent alterations in the neutral controlling mechanisms contribute to the orthoststic intolerance.
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.
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
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.
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.
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.}
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.
Cardiovascular function in space flight
NASA Technical Reports Server (NTRS)
Nicogossian, A. E.; Charles, J. B.; Bungo, M. W.; Leach-Huntoon, C. S.; Nicgossian, A. E.
1991-01-01
Changes in orthostatic heart rate have been noted universally in Soviet and U.S. crewmembers post space flight. The magnitude of these changes appears to be influenced by mission duration, with increasing orthostatic intolerance for the first 7-10 days of flight and then a partial recovery in the orthostatic heart rate response. Fluid loading has been used as a countermeasure to this postflight orthostatic intolerance. Previous reports have documented the effectiveness of this technique, but it has also been noted that the effectiveness of volume expansion diminishes as flight duration exceeds one week. The response of carotid baroreceptor function was investigated utilizing a commercially available neck collar which could apply positive and negative pressure to effect receptor stimulation. Bedrest studies had validated the usefulness and validity of the device. In these studies it was shown that carotid baroreceptor function curves demonstrated less responsiveness to orthostatic stimulation than control individuals. Twelve Space Shuttle crewmembers were examined pre- and postflight from flights lasting from 4-5 days. Plots of baroreceptor function were constructed and plotted as change in R-R interval vs. carotid distending pressure (an orthostatic stimulus). Typical sigmoidal curves were obtained. Postflight the resting heart rate was higher (smaller R-R interval) and the range of R-R value and the slope of the carotid sigmoidal response were both depressed. These changes were not significant immediately postflight (L + O), but did become significant by the second day postflight (L + 2), and remained suppressed for several days thereafter. It is hypothesized that the early adaptation to space flight involves a central fluid shift during the initial days of flight, but subsequent alterations in neural controlling mechanisms (such as carotid baroreceptor function) contribute to orthostatic intolerance.
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.
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.
Space Shuttle critical function audit
NASA Technical Reports Server (NTRS)
Sacks, Ivan J.; Dipol, John; Su, Paul
1990-01-01
A large fault-tolerance model of the main propulsion system of the US space shuttle has been developed. This model is being used to identify single components and pairs of components that will cause loss of shuttle critical functions. In addition, this model is the basis for risk quantification of the shuttle. The process used to develop and analyze the model is digraph matrix analysis (DMA). The DMA modeling and analysis process is accessed via a graphics-based computer user interface. This interface provides coupled display of the integrated system schematics, the digraph models, the component database, and the results of the fault tolerance and risk analyses.
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.
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.
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.
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.
Mukamel, Shaul
2005-02-01
Time-ordered superoperators are used to develop a unified description of nonlinear density response and spontaneous fluctuations of many-electron systems. The pth-order density response functions are decomposed into 2{sup p+1} non-causal Liouville space pathways. Individual pathways are symmetric to the interchange of their space, time, and superoperator indices and can thus be calculated as functional derivatives. Other combinations of these pathways represent spontaneous density fluctuations and the response of such fluctuations to an external field. The resolution of the causality paradox of time-dependent density-functional theory (TDDFT) is shown to be intimately connected with the nonretarded nature of fluctuations.
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.
Spaces defined by the Paley function
Astashkin, S V; Semenov, E M
2013-07-31
The paper is concerned with Haar and Rademacher series in symmetric spaces, and also with the properties of spaces defined by the Paley function. In particular, the symmetric hull of the space of functions with uniformly bounded Paley function is found. Bibliography: 27 titles.
The Thermodynamic Functions in Curved Space of Neutron Star
NASA Astrophysics Data System (ADS)
Hussein, N. A.; Eisa, D. A.; Sayed, E. G.
2016-04-01
The aim of this article is to calculate the thermodynamic functions of a neutron star in curved space. We obtained equation of state (EOS) and the excess free energy for a neutron star in curved space up to order n4, where n is the density of particles.
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).
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
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.
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
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.
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.
Koga, T.; Yamamoto, Y. ); Kryachko, E.S.
1989-10-15
The recently proposed method of density mapping between momentum and position spaces is applied to the ground state of the helium atom. The Kellner densities and wave functions are used as reference, and the Eckart densities {gamma}({bold p}) and {rho}({bold r}) are employed as test densities keeping their parent wave functions in blind. From the momentum density {gamma}({bold p}), the corresponding position density {rho}{sub {gamma}}({bold r}) and the position moments {l angle}{ital r}{sup {ital n}}{r angle}{sub {gamma}} ({minus}2{le}{ital n}{le}4) are generated within a few percent error. The inverse procedure generates the momentum density {gamma}{sub {rho}}({bold p}) and the momentum moments {l angle}{ital p}{sup {ital n}}{r angle}{sub {rho}} ({minus}2{le}{ital n}{le}4) from the position density {rho}({bold r}) with a better accuracy. Density-functional calculations are performed in a simplified manner and the energies close to the Hartree--Fock limit value are obtained.
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
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.
Sublinear scaling for time-dependent stochastic density functional theory
Gao, Yi; Neuhauser, Daniel; Baer, Roi; Rabani, Eran
2015-01-21
A stochastic approach to time-dependent density functional theory is developed for computing the absorption cross section and the random phase approximation (RPA) correlation energy. The core idea of the approach involves time-propagation of a small set of stochastic orbitals which are first projected on the occupied space and then propagated in time according to the time-dependent Kohn-Sham equations. The evolving electron density is exactly represented when the number of random orbitals is infinite, but even a small number (≈16) of such orbitals is enough to obtain meaningful results for absorption spectrum and the RPA correlation energy per electron. We implement the approach for silicon nanocrystals using real-space grids and find that the overall scaling of the algorithm is sublinear with computational time and memory.
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
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
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
Immune function during space flight.
Sonnenfeld, Gerald; Shearer, William T
2002-10-01
It is very likely that the human immune system will be altered in astronauts exposed to the conditions of long-term space flight: isolation, containment, microgravity, radiation, microbial contamination, sleep disruption, and insufficient nutrition. In human and animal subjects flown in space, there is evidence of immune compromise, reactivation of latent virus infection, and possible development of a premalignant or malignant condition. Moreover, in ground-based space flight model investigations, there is evidence of immune compromise and reactivation of latent virus infection. All of these observations in space flight itself or in ground-based models of space flight have a strong resonance in a wealth of human pathologic conditions involving the immune system where reactivated virus infections and cancer appear as natural consequences. The clinical conditions of Epstein-Barr-driven lymphomas in transplant patients and Kaposi's sarcoma in patients with autoimmune deficiency virus come easily to mind in trying to identify these conditions. With these thoughts in mind, it is highly appropriate, indeed imperative, that careful investigations of human immunity, infection, and cancer be made by space flight researchers. PMID:12361785
Immune function during space flight
NASA Technical Reports Server (NTRS)
Sonnenfeld, Gerald; Shearer, William T.
2002-01-01
It is very likely that the human immune system will be altered in astronauts exposed to the conditions of long-term space flight: isolation, containment, microgravity, radiation, microbial contamination, sleep disruption, and insufficient nutrition. In human and animal subjects flown in space, there is evidence of immune compromise, reactivation of latent virus infection, and possible development of a premalignant or malignant condition. Moreover, in ground-based space flight model investigations, there is evidence of immune compromise and reactivation of latent virus infection. All of these observations in space flight itself or in ground-based models of space flight have a strong resonance in a wealth of human pathologic conditions involving the immune system where reactivated virus infections and cancer appear as natural consequences. The clinical conditions of Epstein-Barr-driven lymphomas in transplant patients and Kaposi's sarcoma in patients with autoimmune deficiency virus come easily to mind in trying to identify these conditions. With these thoughts in mind, it is highly appropriate, indeed imperative, that careful investigations of human immunity, infection, and cancer be made by space flight researchers.
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
Morphology Effects on Space Charge Characteristics of Low Density Polyethylene
NASA Astrophysics Data System (ADS)
Zhou; Yuanxiang; Wang; Yunshan; Zahn, Markus; Wang; Ninghua; Sun; Qinghua; Liang; Xidong; Guan; Zhichen
2011-01-01
Low density polyethylene (LDPE) film samples with different morphology were prepared by three kinds of annealing methods which were different in cooling rates in this study. A pulsed electro-acoustic (PEA) space charge measurement system was improved to solve the surface discharge problems for small samples applied with a high voltage. Negative direct current (DC) fields from 50 to above 220 kV/mm were applied to the samples. The influences of morphologies on space charge and space charge packet characteristics were measured by the improved high voltage withstand (HVW) PEA system. Mobility and trap depth of released charges were calculated by space charge decay. It was found that there is a different probability of space charge packet initiation under applied field from -60 to -100 kV/mm. Average velocity and mobility of the space charge packets were calculated by space charge packet dynamics. It was found that the lower cooling rate samples have higher crystallinity, more homo-charge accumulation, lower mobility and deeper trap depth. The mechanism of morphological effects on space charge phenomena have been presumed to give a plausible explanation for their inherent relationships. The morphology in the metal-dielectric interface and in the bulk is convincingly suggested to be responsible for the injection and propagation processes of space charge. A model of positive space charge initiation in LDPE samples was also suggested and analyzed. The mechanism of morphological effects and the charge injection model are well fit with the injection and propagation processes of space charge. The different effects of morphology in the metal-dielectric interface and in the bulk of polymers are stressed.
Polynomial approximation of functions in Sobolev spaces
Dupont, T.; Scott, R.
1980-04-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomical plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
Polynomial approximation of functions in Sobolev spaces
NASA Technical Reports Server (NTRS)
Dupont, T.; Scott, R.
1980-01-01
Constructive proofs and several generalizations of approximation results of J. H. Bramble and S. R. Hilbert are presented. Using an averaged Taylor series, we represent a function as a polynomial plus a remainder. The remainder can be manipulated in many ways to give different types of bounds. Approximation of functions in fractional order Sobolev spaces is treated as well as the usual integer order spaces and several nonstandard Sobolev-like spaces.
Probabilistic Q-function distributions in fermionic phase-space
NASA Astrophysics Data System (ADS)
Rosales-Zárate, Laura E. C.; Drummond, P. D.
2015-03-01
We obtain a positive probability distribution or Q-function for an arbitrary fermionic many-body system. This is different to previous Q-function proposals, which were either restricted to a subspace of the overall Hilbert space, or used Grassmann methods that do not give probabilities. The fermionic Q-function obtained here is constructed using normally ordered Gaussian operators, which include both non-interacting thermal density matrices and BCS states. We prove that the Q-function exists for any density matrix, is real and positive, and has moments that correspond to Fermi operator moments. It is defined on a finite symmetric phase-space equivalent to the space of real, antisymmetric matrices. This has the natural SO(2M) symmetry expected for Majorana fermion operators. We show that there is a physical interpretation of the Q-function: it is the relative probability for observing a given Gaussian density matrix. The distribution has a uniform probability across the space at infinite temperature, while for pure states it has a maximum value on the phase-space boundary. The advantage of probabilistic representations is that they can be used for computational sampling without a sign problem.
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).
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).
Lieleg, Corinna; Ketterer, Philip; Nuebler, Johannes; Ludwigsen, Johanna; Gerland, Ulrich; Dietz, Hendrik
2015-01-01
Arrays of regularly spaced nucleosomes are a hallmark of chromatin, but it remains unclear how they are generated. Recent genome-wide studies, in vitro and in vivo, showed constant nucleosome spacing even if the histone concentration was experimentally reduced. This counters the long-held assumption that nucleosome density determines spacing and calls for factors keeping spacing constant regardless of nucleosome density. We call this a clamping activity. Here, we show in a purified system that ISWI- and CHD1-type nucleosome remodelers have a clamping activity such that they not only generate regularly spaced nucleosome arrays but also generate constant spacing regardless of nucleosome density. This points to a functionally attractive nucleosome interaction that could be mediated either directly by nucleosome-nucleosome contacts or indirectly through the remodelers. Mutant Drosophila melanogaster ISWI without the HAND-SANT-SLIDE (HSS) domain had no detectable spacing activity even though it is known to remodel and slide nucleosomes. This suggests that the role of ISWI remodelers in generating constant spacing is not just to mediate nucleosome sliding; they actively contribute to the attractive interaction. Additional factors are necessary to set physiological spacing in absolute terms. PMID:25733687
Garcia-Aldea, David; Alvarellos, J. E.
2008-02-15
We propose a kinetic energy density functional scheme with nonlocal terms based on the von Weizsaecker functional, instead of the more traditional approach where the nonlocal terms have the structure of the Thomas-Fermi functional. The proposed functionals recover the exact kinetic energy and reproduce the linear response function of homogeneous electron systems. In order to assess their quality, we have tested the total kinetic energies as well as the kinetic energy density for atoms. The results show that these nonlocal functionals give as good results as the most sophisticated functionals in the literature. The proposed scheme for constructing the functionals means a step ahead in the field of fully nonlocal kinetic energy functionals, because they are capable of giving better local behavior than the semilocal functionals, yielding at the same time accurate results for total kinetic energies. Moreover, the functionals enjoy the possibility of being evaluated as a single integral in momentum space if an adequate reference density is defined, and then quasilinear scaling for the computational cost can be achieved.
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.
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.
Hubbard operator density functional theory for Fermionic lattice models
NASA Astrophysics Data System (ADS)
Cheng, Zhengqian; Marianetti, Chris
We formulate an effective action as a functional of Hubbard operator densities whose stationary point delivers all local static information of the interacting lattice model. Using the variational principle, we get a self-consistent equation for Hubbard operator densities. The computational cost of our approach is set by diagonalizing the local Fock space. We apply our method to the one and two band Hubbard model (including crystal field and on-site exchange) in infinite dimensions where the exact solution is known. Excellent agreement is obtained for the one-band model. In the two-band model, good agreement is obtained in the metallic region of the phase diagram in addition to the metal-insulator transition. While our approach does not address frequency dependent observables, it has a negligible computational cost as compared to dynamical mean field theory and could be highly applicable in the context total energies of strongly correlated materials and molecules.
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.
Constrained Density Functional Theory by Imaginary Time-Step Method
NASA Astrophysics Data System (ADS)
Kidd, Daniel
Constrained Density Functional Theory (CDFT) has been a popular choice within the last decade for sidestepping the self interaction problem within long-range charge transfer calculations. Typically an inner constraint loop is added within the self-consistent field iterations of DFT in order to enforce this charge transfer state by means of a Lagrange multiplier method. In this work, an alternate implementation of CDFT is introduced, that of the imaginary time-step method, which lends itself more readily to real space calculations in the ability to solve numerically for 3D local external potentials which enforce arbitrary given densities. This method has been shown to reproduce the proper 1 / R dependence of charge transfer systems in real space calculations as well as the ability to generate useful constraint potentials. As an example application, this method is shown to be capable of describing defects within periodic systems using finite calculations by constraining the 3D density to that of the periodically calculated perfect system at the boundaries.
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
Generalized Pauli constraints in reduced density matrix functional theory
Theophilou, Iris; Helbig, Nicole; Lathiotakis, Nektarios N.; Marques, Miguel A. L.
2015-04-21
Functionals of the one-body reduced density matrix (1-RDM) are routinely minimized under Coleman’s ensemble N-representability conditions. Recently, the topic of pure-state N-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of reduced density-matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble N-representability conditions violates the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.
Revealing the density of encoded functions in a viral RNA
Patel, Nikesh; Dykeman, Eric C.; Coutts, Robert H. A.; Lomonossoff, George P.; Rowlands, David J.; Phillips, Simon E. V.; Ranson, Neil; Twarock, Reidun; Tuma, Roman; Stockley, Peter G.
2015-01-01
We present direct experimental evidence that assembly of a single-stranded RNA virus occurs via a packaging signal-mediated mechanism. We show that the sequences of coat protein recognition motifs within multiple, dispersed, putative RNA packaging signals, as well as their relative spacing within a genomic fragment, act collectively to influence the fidelity and yield of capsid self-assembly in vitro. These experiments confirm that the selective advantages for viral yield and encapsidation specificity, predicted from previous modeling of packaging signal-mediated assembly, are found in Nature. Regions of the genome that act as packaging signals also function in translational and transcriptional enhancement, as well as directly coding for the coat protein, highlighting the density of encoded functions within the viral RNA. Assembly and gene expression are therefore direct molecular competitors for different functional folds of the same RNA sequence. The strongest packaging signal in the test fragment, encodes a region of the coat protein that undergoes a conformational change upon contact with packaging signals. A similar phenomenon occurs in other RNA viruses for which packaging signals are known. These contacts hint at an even deeper density of encoded functions in viral RNA, which if confirmed, would have profound consequences for the evolution of this class of pathogens. PMID:25646435
Wigner function for Klein-Gordon oscillator in commutative and noncommutative spaces
NASA Astrophysics Data System (ADS)
Hassanabadi, S.; Ghominejad, M.
2016-06-01
As a quasi-probability distribution function in phase-space and a special representation of the density matrix, the Wigner function is of great significance in physics. In this work, the Wigner function for the Klein-Gordon oscillator is studied in commutative and noncommutative spaces. We first study the Wigner function for Klein-Gordon oscillator in commutative space then, by using a generalized Bopp's shift method, we obtain the corresponding Wigner function in noncommutative space. The additional terms in Wigner function on a NC space is related to the noncommutativity of space.
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.
Bone Density Following Long Duration Space Flight and Recovery
NASA Technical Reports Server (NTRS)
Amin, Shreyasee; Achenbach, Sara J.; Atkinson, Elizabeth J.; Melton, L. Joseph; Khosla, Sundeep; Sibonga, Jean
2010-01-01
At approx.12 months, Bone Mineral Density (BMD) at most sites in men remained lower than would be predicted, raising concerns for long-term bone health consequences following space flight. Additional analyses based on longer follow-up are being conducted. Although the N is too small for definitive conclusions, women had lower rates of loss at load-bearing sites of the hip and spine immediately post-flight relative to men and smaller differences between observed vs. predicted BMD at most sites, both immediately and 12 months post-flight, relative to men. The role of other exposures/risk factors need to be explored to further understand these possible gender differences in BMD loss and recovery following long-duration space flight.
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.
Effective quadrupole-quadrupole interaction from density functional theory
NASA Astrophysics Data System (ADS)
Alhassid, Y.; Bertsch, G. F.; Fang, L.; Sabbey, B.
2006-09-01
The density functional theory of nuclear structure provides a many-particle wave function that is useful for static properties, but an extension of the theory is necessary to describe correlation effects or other dynamic properties. We propose a procedure to extend the theory by mapping the properties of a self-consistent mean-field theory onto an effective shell-model Hamiltonian with quadrupole-quadrupole interaction. In this initial study, we consider the sd-shell nuclei Ne20, Mg24, Si28, and Ar36. The method is first tested with the USD shell-model Hamiltonian, using its mean-field approximation to construct an effective Hamiltonian and partially recover correlation effects. We find that more than half of the correlation energy is due to the quadrupole interaction. We then follow a similar procedure but using the SLy4 Skyrme energy functional as our starting point and truncating the space to the spherical sd shell. The constructed shell-model Hamiltonian is found to satisfy minimal consistency requirements to reproduce the properties of the mean-field solution. The quadrupolar correlation energies computed with the mapped Hamiltonian are reasonable compared with those computed by other methods. The method also provides a well-defined renormalization of the quadrupole operator in the shell-model space, the “effective charge” of the phenomenological shell model.
Parker, Shane M.; Shiozaki, Toru
2014-12-07
We extend the active space decomposition method, recently developed by us, to more than two active sites using the density matrix renormalization group algorithm. The fragment wave functions are described by complete or restricted active-space wave functions. Numerical results are shown on a benzene pentamer and a perylene diimide trimer. It is found that the truncation errors in our method decrease almost exponentially with respect to the number of renormalization states M, allowing for numerically exact calculations (to a few μE{sub h} or less) with M = 128 in both cases. This rapid convergence is because the renormalization steps are used only for the interfragment electron correlation.
Multiple Streaming and the Probability Distribution of Density in Redshift Space
Hui, Lam; Kofman, Lev; Shandarin, Sergei F.
2000-07-01
We examine several aspects of redshift distortions by expressing the redshift-space density in terms of the eigenvalues and orientation of the local Lagrangian deformation tensor. We explore the importance of multiple streaming using the Zeldovich approximation (ZA), and compute the average number of streams in both real and redshift space. We find that multiple streaming can be significant in redshift space but negligible in real space, even at moderate values of the linear fluctuation amplitude ({sigma}{sub l}(less-or-similar sign)1). Moreover, unlike their real-space counterparts, redshift-space multiple streams can flow past each other with minimal interactions. Such nonlinear redshift-space effects, which are physically distinct from the fingers-of-God due to small-scale virialized motions, might in part explain the well-known departure of redshift distortions from the classic linear prediction by Kaiser, even at relatively large scales where the corresponding density field in real space is well described by linear perturbation theory. We also compute, using the ZA, the probability distribution function (PDF) of the density, as well as S{sub 3}, in real and redshift space, and compare it with the PDF measured from N-body simulations. The role of caustics in defining the character of the high-density tail is examined. We find that (non-Lagrangian) smoothing, due to both finite resolution or discreteness and small-scale velocity dispersions, is very effective in erasing caustic structures, unless the initial power spectrum is sufficiently truncated. (c) 2000 The American Astronomical Society.
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.
Hoyer, Chad E; Gagliardi, Laura; Truhlar, Donald G
2015-11-01
Time-dependent Kohn-Sham density functional theory (TD-KS-DFT) is useful for calculating electronic excitation spectra of large systems, but the low-energy spectra are often complicated by artificially lowered higher-energy states. This affects even the lowest energy excited states. Here, by calculating the lowest energy spin-conserving excited state for atoms from H to K and for formaldehyde, we show that this problem does not occur in multiconfiguration pair-density functional theory (MC-PDFT). We use the tPBE on-top density functional, which is a translation of the PBE exchange-correlation functional. We compare to a robust multireference method, namely, complete active space second-order perturbation theory (CASPT2), and to TD-KS-DFT with two popular exchange-correlation functionals, PBE and PBE0. We find for atoms that the mean unsigned error (MUE) of MC-PDFT with the tPBE functional improves from 0.42 to 0.40 eV with a double set of diffuse functions, whereas the MUEs for PBE and PBE0 drastically increase from 0.74 to 2.49 eV and from 0.45 to 1.47 eV, respectively. PMID:26722961
a 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.
Characterizing the Spatial Density Functions of Neural Arbors
NASA Astrophysics Data System (ADS)
Teeter, Corinne Michelle
Recently, it has been proposed that a universal function describes the way in which all arbors (axons and dendrites) spread their branches over space. Data from fish retinal ganglion cells as well as cortical and hippocampal arbors from mouse, rat, cat, monkey and human provide evidence that all arbor density functions (adf) can be described by a Gaussian function truncated at approximately two standard deviations. A Gaussian density function implies that there is a minimal set of parameters needed to describe an adf: two or three standard deviations (depending on the dimensionality of the arbor) and an amplitude. However, the parameters needed to completely describe an adf could be further constrained by a scaling law found between the product of the standard deviations and the amplitude of the function. In the following document, I examine the scaling law relationship in order to determine the minimal set of parameters needed to describe an adf. First, I find that the at, two-dimensional arbors of fish retinal ganglion cells require only two out of the three fundamental parameters to completely describe their density functions. Second, the three-dimensional, volume filling, cortical arbors require four fundamental parameters: three standard deviations and the total length of an arbor (which corresponds to the amplitude of the function). Next, I characterize the shape of arbors in the context of the fundamental parameters. I show that the parameter distributions of the fish retinal ganglion cells are largely homogenous. In general, axons are bigger and less dense than dendrites; however, they are similarly shaped. The parameter distributions of these two arbor types overlap and, therefore, can only be differentiated from one another probabilistically based on their adfs. Despite artifacts in the cortical arbor data, different types of arbors (apical dendrites, non-apical dendrites, and axons) can generally be differentiated based on their adfs. In addition, within
Effects of Methylation on Zebularine Studied by Density Functional Theory
NASA Astrophysics Data System (ADS)
Selvam, Lalitha; Vasilyev, Vladislav; Wang, Feng; Vasilyev, Vladislav
2009-06-01
1-(β -D-ribofuranosyl)-2-pyrimidone (zebularine or zeb) and 1-(β -D-ribofuranosyl)-5-methyl-2-pyrimidinone (d5) are effective inhibitors of cytidine deaminases (CDA). Methyl modification of zeb at the C(5) position in the base moiety produces d5. A density functional theory (DFT) study reveals the impact of the methyl group on the electronic structures and spectra of the nucleoside pair. It is found that the addition of methyl group has little effect on the geometry of the nucleosides as well as their sugar puckering, but affects anisotropic properties such as dihedral angles, condensed Fukui functions and charge distribution can be seen in their molecular electrostatic potentials (MEPs). Electron spectra serve as the fingerprint for the methyl group. The valence spectra clearly indicate that the molecular pair is related in the inner valence space of IP > 20 eV, whereas the outer valence space reveals the methyl associated electronic structural modifications of the molecular pair. In the present study, the molecular orbitals (MO) such as MO8, MO18 and MO37 (HOMO as MO1) are identified as the fingerprint MOs for methyl, whereas other MOs marked in the figure are secondary methyl related MOs. Chemical shift in the inner shell and their spectra are also calculated. It reveals the similarities and differences of methyl effect to large nucleosides and small amino acids such as L-alanine.
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.
Fundamental gap of molecular crystals via constrained density functional theory
NASA Astrophysics Data System (ADS)
Droghetti, Andrea; Rungger, Ivan; Das Pemmaraju, Chaitanya; Sanvito, Stefano
2016-05-01
The energy gap of a molecular crystal is one of the most important properties since it determines the crystal charge transport when the material is utilized in electronic devices. This is, however, a quantity difficult to calculate and standard theoretical approaches based on density functional theory (DFT) have proven unable to provide accurate estimates. In fact, besides the well-known band-gap problem, DFT completely fails in capturing the fundamental gap reduction occurring when molecules are packed in a crystal structures. The failure has to be associated with the inability of describing the electronic polarization and the real space localization of the charged states. Here we describe a scheme based on constrained DFT, which can improve upon the shortcomings of standard DFT. The method is applied to the benzene crystal, where we show that accurate results can be achieved for both the band gap and also the energy level alignment.
Density Functional Exploration of C4H3N Isomers.
Custer, Thomas; Szczepaniak, Urszula; Gronowski, Marcin; Fabisiewicz, Emilia; Couturier-Tamburelli, Isabelle; Kołos, Robert
2016-07-28
Molecules having C4H3N stoichiometry are of astrophysical interest. Two of these, methylcyanoacetylene (CH3C3N) and its structural isomer allenyl cyanide (H2CCCHN), have been observed in interstellar space, while several more have been examined in laboratories. Here we describe, for a broad range of C4H3N isomers, density functional calculations (B3LYP/aug-cc-pVTZ) of molecular parameters including the energetics, geometries, rotational constants, electric dipole moments, polarizabilities, vibrational IR frequencies, IR absorption intensities, and Raman activities. Singlet-triplet splittings as well as singlet vertical electronic excitation energies are given for selected species. The identification of less stable C4H3N molecules, generated in ongoing spectroscopic experiments, relies heavily on these quantum chemical predictions. PMID:27341606
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.
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.
The space density of mCVs: GROND observations
NASA Astrophysics Data System (ADS)
Burwitz, Vadim; Greiner, Jochen; Zengin Camurdan, Dicle
2016-07-01
We present the first results from a large project to improve our knowledge of the space density of magnetic cataclysmic variables (mCVs). Until now it has been difficult bring the results from theoretical predictions and measurement together due selection effects (the main one being flux limitation). To extend our sample to include fainter mCVs we are currently obtaining g'r'i'z'JHK measurements using the GROND 7 channel imaging instrument mounted on the 2.2m telescope at La Silla, Chile. From the light curves obtained with GROND we can determine the distance to objects by using the relationship between the distance and K-band surface brightness of the secondary star. In addition we will for the first time be able to characterize the IR light curves of a large sample of magnetic CVs homogeneously as well as improve the ephemerides for these objects.
The luminosity distribution and total space density of pulsars
NASA Technical Reports Server (NTRS)
Roberts, D. H.
1976-01-01
The detailed distribution of dispersion measures and spectral fluxes for a sample of 50 pulsars in part of the galactic plane near longitude 50 deg is analyzed, and the intrinsic luminosity distribution of the pulsars is obtained along with some constraints on their spatial distribution. Expressions for the observed distributions of spectral fluxes, distances, and directions are given in terms of the spatial and luminosity distributions of the sources as well as the sensitivity of the detector. A previous analysis of the same sample is reviewed, and the intrinsic luminosity distribution is determined from the distribution of observed distances as well as from the observed distribution of spectral fluxes. The results indicate that the scale height of pulsars cannot be significantly less than 400 pc, the total space density of active pulsars is about 30 per cu kpc, and the birthrate required to maintain this population is about one in the Galaxy every 980 (450-2600) years.
Density functional theory with spatial-symmetry breaking and configuration mixing
NASA Astrophysics Data System (ADS)
Lesinski, Thomas
2014-04-01
This article generalizes the notion of the local density of a many-body system to introduce collective coordinates as explicit degrees of freedom. It is shown that the energy of the system can be expressed as a functional of this object. The latter can in turn be factorized as the product of the square modulus of a collective wave function and a normalized collective-coordinate-dependent density. Energy minimization translates into a set of coupled equations, i.e., a local Schrödinger equation for the collective wave function and a set of Kohn-Sham equations for optimizing the normalized density at each point in the collective space. These equations reformulate the many-body problem exactly provided one is able to determine density- and collective-wave-function-dependent terms of the collective mass and potential which play a similar role to the exchange-correlation term in electronic Kohn-Sham density functional theory.
Filtered density function approach for reactive transport in groundwater
NASA Astrophysics Data System (ADS)
Suciu, Nicolae; Schüler, Lennart; Attinger, Sabine; Knabner, Peter
2016-04-01
Spatial filtering may be used in coarse-grained simulations (CGS) of reactive transport in groundwater, similar to the large eddy simulations (LES) in turbulence. The filtered density function (FDF), stochastically equivalent to a probability density function (PDF), provides a statistical description of the sub-grid, unresolved, variability of the concentration field. Besides closing the chemical source terms in the transport equation for the mean concentration, like in LES-FDF methods, the CGS-FDF approach aims at quantifying the uncertainty over the whole hierarchy of heterogeneity scales exhibited by natural porous media. Practically, that means estimating concentration PDFs on coarse grids, at affordable computational costs. To cope with the high dimensionality of the problem in case of multi-component reactive transport and to reduce the numerical diffusion, FDF equations are solved by particle methods. But, while trajectories of computational particles are modeled as stochastic processes indexed by time, the concentration's heterogeneity is modeled as a random field, with multi-dimensional, spatio-temporal sets of indices. To overcome this conceptual inconsistency, we consider FDFs/PDFs of random species concentrations weighted by conserved scalars and we show that their evolution equations can be formulated as Fokker-Planck equations describing stochastically equivalent processes in concentration-position spaces. Numerical solutions can then be approximated by the density in the concentration-position space of an ensemble of computational particles governed by the associated Itô equations. Instead of sequential particle methods we use a global random walk (GRW) algorithm, which is stable, free of numerical diffusion, and practically insensitive to the increase of the number of particles. We illustrate the general FDF approach and the GRW numerical solution for a reduced complexity problem consisting of the transport of a single scalar in groundwater
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.
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.
Song, Jiayu; Liu, Q H
2006-01-01
Non-Cartesian sampling is widely used for fast magnetic resonance imaging (MRI). The well known gridding method usually requires density compensation to adjust the non-uniform sampling density, which is a major source of reconstruction error. Minimum-norm least square (MNLS) reconstruction, on the other hand, does not need density compensation, but requires intensive computations. In this paper, a new version of MNLS reconstruction method is developed using maximum likelihood and is speeded up by incorporating novel non-uniform fast Fourier transform (NUFFT) and bi-conjugate gradient fast Fourier transform (BCG-FFT) techniques. Studies on computer-simulated phantoms and a physically scanned phantom show improved reconstruction accuracy and signal-to-noise ratio compared to gridding method. The method is shown applicable to arbitrary k-space trajectory. Furthermore, we find that the method in fact performs un-blurring in the image space as an equivalent of density compensation in the k-space. Equalizing MNLS solution with gridding algorithm leads to new approaches of finding optimal density compensation functions (DCF). The method has been applied to radially encoded cardiac imaging on small animals. Reconstructed dynamic images of an in vivo mouse heart are shown. PMID:17946203
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.
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…
Characterizing high-energy-density propellants for space propulsion applications
NASA Astrophysics Data System (ADS)
Kokan, Timothy
There exists wide ranging research interest in high-energy-density matter (HEDM) propellants as a potential replacement for existing industry standard fuels for liquid rocket engines. The U.S. Air Force Research Laboratory, the U.S. Army Research Lab, the NASA Marshall Space Flight Center, and the NASA Glenn Research Center each either recently concluded or currently has ongoing programs in the synthesis and development of these potential new propellants. In order to perform conceptual designs using these new propellants, most conceptual rocket engine powerhead design tools (e.g. NPSS, ROCETS, and REDTOP-2) require several thermophysical properties of a given propellant over a wide range of temperature and pressure. These properties include enthalpy, entropy, density, viscosity, and thermal conductivity. Very little thermophysical property data exists for most of these potential new HEDM propellants. Experimental testing of these properties is both expensive and time consuming and is impractical in a conceptual vehicle design environment. A new technique for determining these thermophysical properties of potential new rocket engine propellants is presented. The technique uses a combination of three different computational methods to determine these properties. Quantum mechanics and molecular dynamics are used to model new propellants at a molecular level in order to calculate density, enthalpy, and entropy. Additivity methods are used to calculate the kinematic viscosity and thermal conductivity of new propellants. This new technique is validated via a series of verification experiments of HEDM compounds. Results are provided for two HEDM propellants: quadricyclane and 2-azido-N,N-dimethylethanamine (DMAZ). In each case, the new technique does a better job than the best current computational methods at accurately matching the experimental data of the HEDM compounds of interest. A case study is provided to help quantify the vehicle level impacts of using HEDM
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.
Kinetic Density Functional Theory: A Microscopic Approach to Fluid Mechanics
NASA Astrophysics Data System (ADS)
Umberto Marini Bettolo, Marconi; Simone, Melchionna
2014-10-01
In the present paper we give a brief summary of some recent theoretical advances in the treatment of inhomogeneous fluids and methods which have applications in the study of dynamical properties of liquids in situations of extreme confinement, such as nanopores, nanodevices, etc. The approach obtained by combining kinetic and density functional methods is microscopic, fully self-consistent and allows to determine both configurational and flow properties of dense fluids. The theory predicts the correct hydrodynamic behavior and provides a practical and numerical tool to determine how the transport properties are modified when the length scales of the confining channels are comparable with the size of the molecules. The applications range from the dynamics of simple fluids under confinement, to that of neutral binary mixtures and electrolytes where the theory in the limit of slow gradients reproduces the known phenomenological equations such as the Planck—Nernst—Poisson and the Smolochowski equations. The approach here illustrated allows for fast numerical solution of the evolution equations for the one-particle phase-space distributions by means of the weighted density lattice Boltzmann method and is particularly useful when one considers flows in complex geometries.
Efficiency issues related to probability density function comparison
Kelly, P.M.; Cannon, M.; Barros, J.E.
1996-03-01
The CANDID project (Comparison Algorithm for Navigating Digital Image Databases) employs probability density functions (PDFs) of localized feature information to represent the content of an image for search and retrieval purposes. A similarity measure between PDFs is used to identify database images that are similar to a user-provided query image. Unfortunately, signature comparison involving PDFs is a very time-consuming operation. In this paper, we look into some efficiency considerations when working with PDFS. Since PDFs can take on many forms, we look into tradeoffs between accurate representation and efficiency of manipulation for several data sets. In particular, we typically represent each PDF as a Gaussian mixture (e.g. as a weighted sum of Gaussian kernels) in the feature space. We find that by constraining all Gaussian kernels to have principal axes that are aligned to the natural axes of the feature space, computations involving these PDFs are simplified. We can also constrain the Gaussian kernels to be hyperspherical rather than hyperellipsoidal, simplifying computations even further, and yielding an order of magnitude speedup in signature comparison. This paper illustrates the tradeoffs encountered when using these constraints.
Analysis of the local-density approximation of density-functional theory
NASA Astrophysics Data System (ADS)
Sahni, Viraht; Bohnen, K.-P.; Harbola, Manoj K.
1988-03-01
In this paper we perform a configuration-space analysis of the local-density approximation (LDA) for the exchange-correlation energy functional of Kohn-Sham density-functional theory in terms of the corresponding average exchange-correlation charge (hole) and energy densities. According to our analysis, the explanation for the quantitative success of the LDA based on the hole charge-conservation sum rule and the assumed consequent cancellation of errors in the spherical averages of the hole is inadequate. The principal conclusion of our work is that the constraint of charge neutrality is a necessary but not sufficient condition for an approximate energy functional to lead to accurate ground-state energies and ionization potentials. The significant additional requirement for the functional is that it must, at least qualitatively, reproduce correctly the structure of the hole as a function of electron position. We perform our calculations within the exchange-only approximation as applied to atoms and jellium metal surfaces. In atoms the Fermi hole is localized about the nucleus; as a consequence the LDA Fermi hole is accurate only for electron positions close to it. However, we show that the spherically averaged LDA hole is accurate for electron positions in the shell regions; it is substantially in error in the intershell and classically forbidden regions. The fact that the principal contribution to the exchange energy comes from the inner-shell region of the atom, where the LDA hole is accurate, explains why the errors in the LDA ground-state energies are small. However, the ionization potential, which depends on the structure of the hole in the outer regions of the atom, is substantially in error in the LDA since here the LDA hole differs significantly from the exact one. For metallic surfaces, on the other hand, as an electron is pulled from within the metal to infinity outside, the Fermi hole is delocalized and spread throughout the crystal. As a consequence
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
The local dark matter phase-space density and impact on WIMP direct detection
Catena, Riccardo; Ullio, Piero E-mail: ullio@sissa.it
2012-05-01
We present a new determination of the local dark matter phase-space density. This result is obtained implementing, in the limit of isotropic velocity distribution and spherical symmetry, Eddington's inversion formula, which links univocally the dark matter distribution function to the density profile, and applying, within a Bayesian framework, a Markov Chain Monte Carlo algorithm to sample mass models for the Milky Way against a broad and variegated sample of dynamical constraints. We consider three possible choices for the dark matter density profile, namely the Einasto, NFW and Burkert profiles, finding that the velocity dispersion, which characterizes the width in the distribution, tends to be larger for the Burkert case, while the escape velocity depends very weakly on the profile, with the mean value we obtain being in very good agreement with estimates from stellar kinematics. The derived dark matter phase-space densities differ significantly — most dramatically in the high velocity tails — from the model usually taken as a reference in dark matter detection studies, a Maxwell-Boltzmann distribution with velocity dispersion fixed in terms of the local circular velocity and with a sharp truncation at a given value of the escape velocity. We discuss the impact of astrophysical uncertainties on dark matter scattering rates and direct detection exclusion limits, considering a few sample cases and showing that the most sensitive ones are those for light dark matter particles and for particles scattering inelastically. As a general trend, regardless of the assumed profile, when adopting a self-consistent phase-space density, we find that rates are larger, and hence exclusion limits stronger, than with the standard Maxwell-Boltzmann approximation. Tools for applying our result on the local dark matter phase-space density to other dark matter candidates or experimental setups are provided.
A joint acceptance function for enclosed spaces
NASA Astrophysics Data System (ADS)
Koopmann, G. H.; Pollard, H. F.
1980-12-01
A method is proposed for quantifying the geometric coupling between the acoustic modes of an enclosure and the vibratory motion of the enclosing surfaces. A dimensionless quantity, called the joint acceptance function, is defined which gives the coupling efficiency of an enclosing surface within a range from zero to unity. The joint acceptance function is based on an integral solution to the wave equation which requires a knowledge of the Green function for an enclosed space. Section 2 of the paper is devoted to methods of generating Green functions for enclosed spaces as series expansions in terms of orthogonal eigenfunctions. Computer generated Green functions are shown to compare favorably with those obtained from experiments performed on a hard walled, rectangular box. Section 3 of the paper describes the method of calculating the joint acceptance function for arbitrarily shaped enclosures. Two applications of this function are presented: (a) a rectangular enclosure with surfaces vibrating as simply supported plates, and (b) a practical case involving the reduction of noise in a tractor cabin.
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.
NASA Astrophysics Data System (ADS)
Mattsson, Thomas R.
2007-06-01
Atomistic simulations employing Density Functional Theory (DFT) have recently emerged as a powerful way of increasing our understanding of materials and processes in high energy density physics. Knowledge of the properties of water (equation of state, electrical conductivity, diffusion, low-energy opacity) is essential for correctly describing the physics of giant planets as well as shock waves in water. Although a qualitative picture of water electrical conductivity has emerged, the necessary quantitative information is scarce over a wide range of temperature and density. Since experiments can only access certain areas of phase space, and often require modeling as a part of the analysis, Quantum Molecular Dynamics simulations play a vital role. Using finite-temperature density functional theory (FT-DFT), we have investigated the structure and electronic conductivity of water across three phase transitions (molecular liquid/ ionic liquid/ superionic/ electronic liquid). The ionic contribution to the conduction is calculated from proton diffusion and the electronic contribution is calculated using the Kubo-Greenwood formula. The calculations are performed with VASP, a plane-wave pseudo-potential code. There is a rapid transition to ionic conduction at 2000 K and 2 g/cm^3, whereas electronic conduction dominates at temperatures at and above 6000 K&[tilde;1]. Contrary to earlier results using the Car-Parrinello method&[tilde;2], we predict that the fluid bordering the superionic phase is conducting above 4000 K and 100 GPa. Our comprehensive use of FT-DFT explains the new findings. The calculated conductivity is compared to experimental data. I gratefully acknowledge Mike Desjarlais, my collaborator in this effort. The LDRD office at Sandia supported this work. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL
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.
Coulomb wave functions in momentum space
Eremenko, V; Upadhyay, N. J.; Thompson, I J; Elster, Charlotte; Nunes, F. M.; Arbanas, Goran; Escher, J.E.; Hlophe, L.
2015-01-01
An algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space is presented. The arguments are the Sommerfeld parameter eta, the angular momentum l, the asymptotic momentum q and the 'running' momentum p, where both momenta are real. Since the partial-wave Coulomb functions exhibit singular behavior when p -> q, different representations of the Legendre functions of the 2nd kind need to be implemented in computing the functions for the values of p close to the singularity and far away from it. The code for the momentum-space Coulomb wave functions is applicable for values of vertical bar eta vertical barmore » in the range of 10(-1) to 10, and thus is particularly suited for momentum space calculations of nuclear reactions. Program Summary Program title: libcwfn Catalogue identifier: AEUQ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEUQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 864503 No. of bytes in distributed program, including test data, etc.: 7178021 Distribution format: tar.gz Programming language: Fortran 90, Fortran 77, Python, make (GNU Make dialect), GNU Bash shell interpreter (available as /bin/bash). Computer: Apple Powermac (Intel Xeon), ASUS K53U (AMD E-350 (Dual Core)), DELL Precision T3500 (Intel Xeon), NERSC Carver (Intel Nehalem Quad Core). Operating system: Linux, Windows (using Cygwin). RAM: less than 512 Mbytes Classification: 17.8, 17.13, 17.16. Nature of problem: The calculation of partial wave Coulomb functions with integer land all other arguments real. Solution method: Computing the value of the function using explicit formulae and algorithms. Running time: Less than 10(-3) s. (C) 2014 Elsevier B.V. All rights reserved.« less
Coulomb wave functions in momentum space
Eremenko, V; Upadhyay, N. J.; Thompson, I J; Elster, Charlotte; Nunes, F. M.; Arbanas, Goran; Escher, J.E.; Hlophe, L.
2015-01-01
An algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space is presented. The arguments are the Sommerfeld parameter eta, the angular momentum l, the asymptotic momentum q and the 'running' momentum p, where both momenta are real. Since the partial-wave Coulomb functions exhibit singular behavior when p -> q, different representations of the Legendre functions of the 2nd kind need to be implemented in computing the functions for the values of p close to the singularity and far away from it. The code for the momentum-space Coulomb wave functions is applicable for values of vertical bar eta vertical bar in the range of 10(-1) to 10, and thus is particularly suited for momentum space calculations of nuclear reactions. Program Summary Program title: libcwfn Catalogue identifier: AEUQ_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEUQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 864503 No. of bytes in distributed program, including test data, etc.: 7178021 Distribution format: tar.gz Programming language: Fortran 90, Fortran 77, Python, make (GNU Make dialect), GNU Bash shell interpreter (available as /bin/bash). Computer: Apple Powermac (Intel Xeon), ASUS K53U (AMD E-350 (Dual Core)), DELL Precision T3500 (Intel Xeon), NERSC Carver (Intel Nehalem Quad Core). Operating system: Linux, Windows (using Cygwin). RAM: less than 512 Mbytes Classification: 17.8, 17.13, 17.16. Nature of problem: The calculation of partial wave Coulomb functions with integer land all other arguments real. Solution method: Computing the value of the function using explicit formulae and algorithms. Running time: Less than 10(-3) s. (C) 2014 Elsevier B.V. All rights reserved.
Origin of anomeric effect: A density functional steric analysis
Huang, Ying; Zhong, Ai-Guo; Yang, Qinsong; Liu, Shubin
2011-01-01
The anomeric effect (the tendency of heteroatomic substituents adjacent to a heteroatom within the cyclohexane ring to prefer the axial orientation instead of the sterically less hindered equatorial position) is traditionally explained through either the dipole moment repulsion or the hyperconjugation effect. In this work, by employing our recent work in density functional steric analysis, we provide a novel two-component explanation, which is consistent with the common belief in chemistry that the effect has a stereoelectronic origin. With α-D-glucopyranose as the prototype, we systematically explore its conformational space and generate 32 isomers, leading to a total of 80 axial–equatorial conformation pairs. The energy difference analysis of these pairs shows that while statistically speaking the tendency is valid, the anomeric effect is not always true and can be violated. Three energy components, exchange–correlation, classical electrostatic, and density functional steric, are found to be directly proportional to the total energy difference between axial and equatorial isomers. We also found that the total dipole moment change, not the hyperconjugation effect, is a reasonable indicator of the total energy difference. However, all these correlations alone are not strong enough to provide a compellingly convincing explanation for the general validity of the effect. With the help of strong correlations between energy components, an explanation with two energy components, steric and electrostatic, was proposed in this work. We show that the axial–equatorial energy difference in general, with the anomeric effect as a special case, is dictated by two factors of the stereoelectronic origin, steric hindrance and classical electrostaticinteractions, synchronously working together. Another explanation in terms of exchange–correlation and electrostaticinteractions has also been obtained in this work.
Augmented Lagrangian formulation of orbital-free density functional theory
Suryanarayana, Phanish Phanish, Deepa
2014-10-15
We present an Augmented Lagrangian formulation and its real-space implementation for non-periodic Orbital-Free Density Functional Theory (OF-DFT) calculations. In particular, we rewrite the constrained minimization problem of OF-DFT as a sequence of minimization problems without any constraint, thereby making it amenable to powerful unconstrained optimization algorithms. Further, we develop a parallel implementation of this approach for the Thomas–Fermi–von Weizsacker (TFW) kinetic energy functional in the framework of higher-order finite-differences and the conjugate gradient method. With this implementation, we establish that the Augmented Lagrangian approach is highly competitive compared to the penalty and Lagrange multiplier methods. Additionally, we show that higher-order finite-differences represent a computationally efficient discretization for performing OF-DFT simulations. Overall, we demonstrate that the proposed formulation and implementation are both efficient and robust by studying selected examples, including systems consisting of thousands of atoms. We validate the accuracy of the computed energies and forces by comparing them with those obtained by existing plane-wave methods.
Curtis, Robert O.; Bansal, Sheel; Harrington, Constance A.
2016-01-01
This report presents updated information on a 1981 Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco var. menziesii) plantation spacing trial at 33 years from planting. Stand statistics at the most recent measurement were compared for initial spacing of 1 through 6 meters and associated relative densities. There was no clear relationship of spacing to top height. Diameter, live crown ratio, and percent survival increased with spacing; basal area and relative density decreased with increase in spacing. Volume in trees ≥ 4 cm diameter was greatest at 2 m spacing, while utilizable volume (trees ≥20 cm dbh) was greatest at 4 m spacing. Live crown ratio decreased and total crown projectional area increased with increasing relative density indices. Total crown projectional area was more closely related to relative density than to basal area.
Space shuttle configuration accounting functional design specification
NASA Technical Reports Server (NTRS)
1974-01-01
An analysis is presented of the requirements for an on-line automated system which must be capable of tracking the status of requirements and engineering changes and of providing accurate and timely records. The functional design specification provides the definition, description, and character length of the required data elements and the interrelationship of data elements to adequately track, display, and report the status of active configuration changes. As changes to the space shuttle program levels II and III configuration are proposed, evaluated, and dispositioned, it is the function of the configuration management office to maintain records regarding changes to the baseline and to track and report the status of those changes. The configuration accounting system will consist of a combination of computers, computer terminals, software, and procedures, all of which are designed to store, retrieve, display, and process information required to track proposed and proved engineering changes to maintain baseline documentation of the space shuttle program levels II and III.
NASA Astrophysics Data System (ADS)
Erdinc, Ozgur; Willett, Peter; Bar-Shalom, Yaakov
2006-05-01
The probability hypothesis density (PHD) filter, an automatically track-managed multi-target tracker, is attracting increasing but cautious attention. Its derivation is elegant and mathematical, and thus of course many engineers fear it; perhaps that is currently limiting the number of researchers working on the subject. In this paper, we explore a physical-space approach - a bin model - which leads us to arrive the same filter equations as the PHD. Unlike the original derivation of the PHD filter, the concepts used are the familiar ones of conditional probability. The original PHD suffers from a "target-death" problem in which even a single missed detection can lead to the apparent disappearance of a target. To obviate this, PHD originator Mahler has recently developed a new "cardinalized" version of PHD (CPHD). We are able to extend our physical-space derivation to the CPHD case as well. We stress that the original derivations are mathematically correct, and need no embellishment from us; our contribution here is to offer an alternative derivation, one that we find appealing.
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…
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.
Carlson, Rebecca K; Li Manni, Giovanni; Sonnenberger, Andrew L; Truhlar, Donald G; Gagliardi, Laura
2015-01-13
Kohn-Sham density functional theory, resting on the representation of the electronic density and kinetic energy by a single Slater determinant, has revolutionized chemistry, but for open-shell systems, the Kohn-Sham Slater determinant has the wrong symmetry properties as compared to an accurate wave function. We have recently proposed a theory, called multiconfiguration pair-density functional theory (MC-PDFT), in which the electronic kinetic energy and classical Coulomb energy are calculated from a multiconfiguration wave function with the correct symmetry properties, and the rest of the energy is calculated from a density functional, called the on-top density functional, that depends on the density and the on-top pair density calculated from this wave function. We also proposed a simple way to approximate the on-top density functional by translation of Kohn-Sham exchange-correlation functionals. The method is much less expensive than other post-SCF methods for calculating the dynamical correlation energy starting with a multiconfiguration self-consistent-field wave function as the reference wave function, and initial tests of the theory were quite encouraging. Here, we provide a broader test of the theory by applying it to bond energies of main-group molecules and transition metal complexes, barrier heights and reaction energies for diverse chemical reactions, proton affinities, and the water dimerization energy. Averaged over 56 data points, the mean unsigned error is 3.2 kcal/mol for MC-PDFT, as compared to 6.9 kcal/mol for Kohn-Sham theory with a comparable density functional. MC-PDFT is more accurate on average than complete active space second-order perturbation theory (CASPT2) for main-group small-molecule bond energies, alkyl bond dissociation energies, transition-metal-ligand bond energies, proton affinities, and the water dimerization energy. PMID:26574206
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.
Tensor part of the Skyrme energy density functional: Spherical nuclei
NASA Astrophysics Data System (ADS)
Lesinski, T.; Bender, M.; Bennaceur, K.; Duguet, T.; Meyer, J.
2007-07-01
We perform a systematic study of the impact of the J2 tensor term in the Skyrme energy functional on properties of spherical nuclei. In the Skyrme energy functional, the tensor terms originate from both zero-range central and tensor forces. We build a set of 36 parametrizations, covering a wide range of the parameter space of the isoscalar and isovector tensor term coupling constants with a fit protocol very similar to that of the successful SLy parametrizations. We analyze the impact of the tensor terms on a large variety of observables in spherical mean-field calculations, such as the spin-orbit splittings and single-particle spectra of doubly-magic nuclei, the evolution of spin-orbit splittings along chains of semi-magic nuclei, mass residuals of spherical nuclei, and known anomalies of radii. The major findings of our study are as follows: (i) Tensor terms should not be added perturbatively to existing parametrizations; a complete refit of the entire parameter set is imperative. (ii) The free variation of the tensor terms does not lower the χ2 within a standard Skyrme energy functional. (iii) For certain regions of the parameter space of their coupling constants, the tensor terms lead to instabilities of the spherical shell structure, or even to the coexistence of two configurations with different spherical shell structures. (iv) The standard spin-orbit interaction does not scale properly with the principal quantum number, such that single-particle states with one or several nodes have too large spin-orbit splittings, whereas those of nodeless intruder levels are tentatively too small. Tensor terms with realistic coupling constants cannot cure this problem. (v) Positive values of the coupling constants of proton-neutron and like-particle tensor terms allow for a qualitative description of the evolution of spin-orbit splittings in chains of Ca, Ni, and Sn isotopes. (vi) For the same values of the tensor term coupling constants, however, the overall agreement of
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
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.
On Weighted Bloch Spaces of Quaternion-Valued Functions
NASA Astrophysics Data System (ADS)
Ahmed, A. El-Sayed; Ahmadi, Aydah
2011-09-01
In this paper, we give the definition of (α,β)-Bloch spaces of quaternion-valued functions, then we investigate the relation between (α,β)-Bloch spaces and the Dirichlet space in the unit ball of R3. Besides, we obtain characterizations for (α,β)-Bloch spaces by Qp spaces of quaternion-valued functions.
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.
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.
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
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.
[VESTIBULAR FUNCTION AFTER REPEATED SPACE FLIGHTS].
Naumov, I A; Kornilova, L N; Glukhikh, D O; Pavlova, A S; Khabarova, E V; Ekimovsky, G A; Vasin, A V
2015-01-01
Results of the vestibular function testing of 32 cosmonauts on return from repeated 125- to 215-day space flights (SF) on the International space station are presented. The cosmonauts were tested twice before flight (baseline data collection) and on days 1-2, 4-5 and 8-9 after landing. Electro- and video-oculography were used to register simultaneously eye and head movements. It was found that deadaptation following a repeated stay in long-duration SF takes statistically much shorter time. Most often, atypical vestibular disorders and changed patterns of the otolith-semicircular canal interaction are observed in cosmonauts who have made their maiden flights to microgravity. PMID:26934788
The Deep Space Network. [tracking and communication functions and facilities
NASA Technical Reports Server (NTRS)
1974-01-01
The objectives, functions, and organization of the Deep Space Network are summarized. The Deep Space Instrumentation Facility, the Ground Communications Facility, and the Network Control System are described.
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
Parameterizing deep convection using the assumed probability density function method
Storer, R. L.; Griffin, B. M.; Hoft, Jan; Weber, J. K.; Raut, E.; Larson, Vincent E.; Wang, Minghuai; Rasch, Philip J.
2015-01-06
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method.The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and mid-latitude deep convection.These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing is weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.
Parameterizing deep convection using the assumed probability density function method
NASA Astrophysics Data System (ADS)
Storer, R. L.; Griffin, B. M.; Höft, J.; Weber, J. K.; Raut, E.; Larson, V. E.; Wang, M.; Rasch, P. J.
2015-01-01
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method. The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and midlatitude deep convection. These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing is weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.
Parameterizing deep convection using the assumed probability density function method
Storer, R. L.; Griffin, B. M.; Höft, J.; Weber, J. K.; Raut, E.; Larson, V. E.; Wang, M.; Rasch, P. J.
2014-06-11
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method. The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and mid-latitude deep convection. These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing ismore » weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.« less
Parameterizing deep convection using the assumed probability density function method
Storer, R. L.; Griffin, B. M.; Höft, J.; Weber, J. K.; Raut, E.; Larson, V. E.; Wang, M.; Rasch, P. J.
2015-01-06
Due to their coarse horizontal resolution, present-day climate models must parameterize deep convection. This paper presents single-column simulations of deep convection using a probability density function (PDF) parameterization. The PDF parameterization predicts the PDF of subgrid variability of turbulence, clouds, and hydrometeors. That variability is interfaced to a prognostic microphysics scheme using a Monte Carlo sampling method. The PDF parameterization is used to simulate tropical deep convection, the transition from shallow to deep convection over land, and midlatitude deep convection. These parameterized single-column simulations are compared with 3-D reference simulations. The agreement is satisfactory except when the convective forcing ismore » weak. The same PDF parameterization is also used to simulate shallow cumulus and stratocumulus layers. The PDF method is sufficiently general to adequately simulate these five deep, shallow, and stratiform cloud cases with a single equation set. This raises hopes that it may be possible in the future, with further refinements at coarse time step and grid spacing, to parameterize all cloud types in a large-scale model in a unified way.« less
Density functional theory simulation of liquid helium-4 in aerogel
NASA Astrophysics Data System (ADS)
Lysogorskiy, Yu. V.; Tayurskii, D. A.
2013-10-01
The distribution of liquid 4He in different types of confinements—adsorbing and nonadsorbing aerogel on the basis of silicon dioxide SiO2 and an absorbing homogeneous strand—has been studied using the density functional theory. It has been demonstrated that the helium atoms tend to be adsorbed on the concave aerogel surface. It has been shown that, in the confinement with fractional mass dimension within certain scales, liquid helium also has a fractional mass dimension within these scales. The dependence of the energy of liquid helium on the number of atoms has been studied for different types of adsorbing surfaces. It has been established that the specific energy of liquid helium behaves differently in the cases of attractive and unattractive potentials with decreasing number of particles. This indicates that the system under consideration is nonextensive. Thus, the necessity of taking into account the surface effects and the fractional mass dimension in the studies of the properties of liquid helium in the restricted space geometry has been demonstrated.
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.
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.
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
Abstracting Attribute Space for Transfer Function Exploration and Design.
Maciejewski, Ross; Jang, Yun; Woo, Insoo; Jänicke, Heike; Gaither, Kelly P; Ebert, David S
2013-01-01
Currently, user centered transfer function design begins with the user interacting with a one or two-dimensional histogram of the volumetric attribute space. The attribute space is visualized as a function of the number of voxels, allowing the user to explore the data in terms of the attribute size/magnitude. However, such visualizations provide the user with no information on the relationship between various attribute spaces (e.g., density, temperature, pressure, x, y, z) within the multivariate data. In this work, we propose a modification to the attribute space visualization in which the user is no longer presented with the magnitude of the attribute; instead, the user is presented with an information metric detailing the relationship between attributes of the multivariate volumetric data. In this way, the user can guide their exploration based on the relationship between the attribute magnitude and user selected attribute information as opposed to being constrained by only visualizing the magnitude of the attribute. We refer to this modification to the traditional histogram widget as an abstract attribute space representation. Our system utilizes common one and two-dimensional histogram widgets where the bins of the abstract attribute space now correspond to an attribute relationship in terms of the mean, standard deviation, entropy, or skewness. In this manner, we exploit the relationships and correlations present in the underlying data with respect to the dimension(s) under examination. These relationships are often times key to insight and allow us to guide attribute discovery as opposed to automatic extraction schemes which try to calculate and extract distinct attributes a priori. In this way, our system aids in the knowledge discovery of the interaction of properties within volumetric data. PMID:22508900
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.}
Modelling the number density of Hα emitters for future spectroscopic near-IR space missions
NASA Astrophysics Data System (ADS)
Pozzetti, L.; Hirata, C. M.; Geach, J. E.; Cimatti, A.; Baugh, C.; Cucciati, O.; Merson, A.; Norberg, P.; Shi, D.
2016-05-01
Context. The future space missions Euclid and WFIRST-AFTA will use the Hα emission line to measure the redshifts of tens of millions of galaxies. The Hα luminosity function at z> 0.7 is one of the major sources of uncertainty in forecasting cosmological constraints from these missions. Aims: We construct unified empirical models of the Hα luminosity function spanning the range of redshifts and line luminosities relevant to the redshift surveys proposed with Euclid and WFIRST-AFTA. Methods: By fitting to observed luminosity functions from Hα surveys, we build three models for its evolution. Different fitting methodologies, functional forms for the luminosity function, subsets of the empirical input data, and treatment of systematic errors are considered to explore the robustness of the results. Results: Functional forms and model parameters are provided for all three models, along with the counts and redshift distributions up to z ~ 2.5 for a range of limiting fluxes (FHα> 0.5 - 3 × 10-16 erg cm-2 s-1) that are relevant for future space missions. For instance, in the redshift range 0.90
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.
Non-Periodic Finite-Element Formulation of Orbital-Free Density Functional Theory
Gavini, V; Knap, J; Bhattacharya, K; Ortiz, M
2006-10-06
We propose an approach to perform orbital-free density functional theory calculations in a non-periodic setting using the finite-element method. We consider this a step towards constructing a seamless multi-scale approach for studying defects like vacancies, dislocations and cracks that require quantum mechanical resolution at the core and are sensitive to long range continuum stresses. In this paper, we describe a local real space variational formulation for orbital-free density functional theory, including the electrostatic terms and prove existence results. We prove the convergence of the finite-element approximation including numerical quadratures for our variational formulation. Finally, we demonstrate our method using examples.
Density functional theory study of neutral and oxidized thiophene oligomers
NASA Astrophysics Data System (ADS)
Dai, Yafei; Wei, Chengwei; Blaisten-Barojas, Estela
2013-11-01
The effect of oxidation on the energetics and structure of thiophene (Th) oligomers is studied with density functional theory at the B3PW91/6-311++G(d,p) level. Neutral n-Th oligomers (2 < n < 13) are gently curved planar chains. Ionization potential and electron affinity results show that n-Th oligomers are easier to be oxidized as their chain length increases. Oxidation states +2, +4, +6, and +8 are energetically stable in 12-Th. Upon oxidation the conjugated backbone of 12-Th switches from extended benzenoid phase to quinoid phase localized on groups of monomers regularly spaced along the chain. Oxidized states +2, +4, +6, and +8 of 12-Th display two +1e localized at the ends of their chains only because of the finite size of the chains. In 12-Th this end-effect extends over the two terminal monomers forming a positive-negative charge duet. This peculiar charge localization makes n-Th oligomers different from other conducting polymers with similar structure, such as polypyrrole. The spectrum of single-electron molecular states of oxidized 12-Th displays two localized single-electron states in the HOMO-LUMO energy gap per +2 oxidation state. Oligothiophene 12-Th doped with F atoms at 1:2 concentration presents a charge transfer of 3.4 e from oligomer to dopants that increases to 4.8 e in the presence of solvent. The charge distribution in these F-doped oligomers is similar to the +4 oxidation state of 12-Th. It is predicted that dopants produce an enhanced charge transfer localized in the proximity of their locations enhancing the formation of bipolarons in the central part of the oligomer chain.
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
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.
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.
Garcia-Aldea, David; Alvarellos, J. E.
2007-11-15
We study two families of approximate nonlocal kinetic-energy functionals that include a full von Weizsaecker functional, and that have nonlocal terms with the mathematical structure of the Thomas-Fermi functional. The functionals recover the exact kinetic energy and the linear response function of a homogeneous electron system. The first family is a generalization of a successful previous nonlocal functional. The second family is proposed in the paper, and is designed to obtain functionals suitable for use in both localized and extended systems. Furthermore, this family has been designed to be evaluated by a single integration in momentum space when a constant reference density is used. The atomic total kinetic energies are in good agreement with the exact calculations. The kinetic-energy density corresponding to each functional has been assessed to control its quality. The results show that, in general, these functionals behave better than both the Thomas-Fermi and all semilocal generalized gradient approximation functionals when describing the kinetic-energy density of atoms, providing a better description of the nonlocal effects of the kinetic energy of electron systems.
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.
Density functional theory modeling of multilayer "epitaxial" graphene oxide.
Zhou, Si; Bongiorno, Angelo
2014-11-18
CONSPECTUS: Graphene oxide (GO) is a complex material of both fundamental and applied interest. Elucidating the structure of GO is crucial to achieve control over its properties and technological applications. GO is a nonstoichiometric and hygroscopic material with a lamellar structure, and its physical chemical properties depend critically on synthesis procedures and postsynthesis treatments. Numerous efforts are in place to both understand and exploit this versatile layered carbon material. This Account reports on recent density functional theory (DFT) studies of "epitaxial" graphene oxide (hereafter EGO), a type of GO obtained by oxidation of graphene films grown epitaxially on silicon carbide. Here, we rely on selected X-ray photoelectron spectroscopy (XPS), infrared spectroscopy (IR), and X-ray diffraction (XRD) measurements of EGO, and we discuss in great detail how we utilized DFT-based techniques to project out from the experimental data basic atomistic information about the chemistry and structure of these films. This Account provides an example as to how DFT modeling can be used to elucidate complex materials such as GO from a limited set of experimental information. EGO exhibits a uniform layered structure, consisting of a stack of graphene planes hosting predominantly epoxide and hydroxyl groups, and water molecules intercalated between the oxidized carbon layers. Here, we first focus on XPS measurements of EGO, and we use DFT to generate realistic model structures, calculate core-level chemical shifts, and through the comparison with experiment, gain insight on the chemical composition and metastability characteristics of EGO. DFT calculations are then used to devise a simplistic but accurate simulation scheme to study thermodynamic and kinetic stability and to predict the intralayer structure of EGO films aged at room temperature. Our simulations show that aged EGO encompasses layers with nanosized oxidized domains presenting a high concentration of
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.
Experimental study of high density foods for the Space Operations Center
NASA Technical Reports Server (NTRS)
Ahmed, S. M.
1981-01-01
The experimental study of high density foods for the Space Operations Center is described. A sensory evaluation of the high density foods was conducted first to test the acceptability of the products. A shelf-life study of the high density foods was also conducted for three different time lengths at three different temperatures. The nutritional analysis of the high density foods is at present incomplete.
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
Modal density function and number of propagating modes in ducts
NASA Technical Reports Server (NTRS)
Rice, E. J.
1976-01-01
The question of the number of propagating modes within a small range of mode cut off ratio was raised. The population density of modes were shown to be greatest near cut off and least for the well propagating modes. It was shown that modes of nearly the same cut off ratio behave nearly the same in a sound absorbing duct as well as in the way they propagate to the far. Handling all of the propagating modes individually, they can be grouped into several cut off ratio ranges. It is important to know the modal density function to estimate acoustic power distribution.
Weak Type Interpolation in Quasinormed Spaces of Measurable Functions
NASA Astrophysics Data System (ADS)
Pustylnik, Evgeniy
2003-04-01
We propose a general method for extending various interpolation theorems for Banach function spaces to corresponding quasi-Banach spaces. The method consists in a special measure transformation which states a homeomorphism between the cones of decreasing functions in considered spaces. We also give a quasi-Banach analog of the Krein-Semenov theorem on weak interpolation.
Numerical density-to-potential inversions in time-dependent density functional theory.
Jensen, Daniel S; Wasserman, Adam
2016-08-01
We treat the density-to-potential inverse problem of time-dependent density functional theory as an optimization problem with a partial differential equation constraint. The unknown potential is recovered from a target density by applying a multilevel optimization method controlled by error estimates. We employ a classical optimization routine using gradients efficiently computed by the discrete adjoint method. The inverted potential has both a real and imaginary part to reduce reflections at the boundaries and other numerical artifacts. We demonstrate this method on model one-dimensional systems. The method can be straightforwardly extended to a variety of numerical solvers of the time-dependent Kohn-Sham equations and to systems in higher dimensions. PMID:26984427
SURFACE SYMMETRY ENERGY OF NUCLEAR ENERGY DENSITY FUNCTIONALS
Nikolov, N; Schunck, N; Nazarewicz, W; Bender, M; Pei, J
2010-12-20
We study the bulk deformation properties of the Skyrme nuclear energy density functionals. Following simple arguments based on the leptodermous expansion and liquid drop model, we apply the nuclear density functional theory to assess the role of the surface symmetry energy in nuclei. To this end, we validate the commonly used functional parametrizations against the data on excitation energies of superdeformed band-heads in Hg and Pb isotopes, and fission isomers in actinide nuclei. After subtracting shell effects, the results of our self-consistent calculations are consistent with macroscopic arguments and indicate that experimental data on strongly deformed configurations in neutron-rich nuclei are essential for optimizing future nuclear energy density functionals. The resulting survey provides a useful benchmark for further theoretical improvements. Unlike in nuclei close to the stability valley, whose macroscopic deformability hangs on the balance of surface and Coulomb terms, the deformability of neutron-rich nuclei strongly depends on the surface-symmetry energy; hence, its proper determination is crucial for the stability of deformed phases of the neutron-rich matter and description of fission rates for r-process nucleosynthesis.
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.
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
Characterizing high-energy-density propellants for space propulsion applications
NASA Astrophysics Data System (ADS)
Kokan, Timothy S.; Olds, John R.; Seitzman, Jerry M.; Ludovice, Peter J.
2009-10-01
A technique for computationally determining the thermophysical properties of high-energy-density matter (HEDM) propellants is presented. HEDM compounds are of interest in the liquid rocket engine industry due to their high density and high energy content relative to existing industry-standard propellants. In order to accurately model rocket engine performance, cost and weight in a conceptual design environment, several thermodynamic and physical properties are required over a range of temperatures and pressures. The approach presented here combines quantum mechanical and molecular dynamic (MD) calculations and group additivity methods. A method for improving the force field model coefficients used in the MD is included. This approach is used to determine thermophysical properties for two HEDM compounds of interest: quadricyclane and 2-azido-N,N-dimethylethanamine (DMAZ). The modified force field approach provides results that more accurately match experimental data than the unmodified approach. Launch vehicle and Lunar lander case studies are presented to quantify the system level impact of employing quadricyclane and DMAZ rather than industry standard propellants. In both cases, the use of HEDM propellants provides reductions in vehicle mass compared to industry standard propellants. The results demonstrate that HEDM propellants can be an attractive technology for future launch vehicle and Lunar lander applications.
Scrutinizing "Invisible" astatine: A challenge for modern density functionals.
Sergentu, Dumitru-Claudiu; David, Grégoire; Montavon, Gilles; Maurice, Rémi; Galland, Nicolas
2016-06-01
The main-group 6p elements did not receive much attention in the development of recent density functionals. In many cases it is still difficult to choose among the modern ones a relevant functional for various applications. Here, we illustrate the case of astatine species (At, Z = 85) and we report the first, and quite complete, benchmark study on several properties concerning such species. Insights on geometries, transition energies and thermodynamic properties of a set of 19 astatine species, for which reference experimental or theoretical data has been reported, are obtained with relativistic (two-component) density functional theory calculations. An extensive set of widely used functionals is employed. The hybrid meta-generalized gradient approximation (meta-GGA) PW6B95 functional is overall the best choice. It is worth noting that the range-separated HSE06 functional as well as the old and very popular B3LYP and PBE0 hybrid-GGAs appear to perform quite well too. Moreover, we found that astatine chemistry in solution can accurately be predicted using implicit solvent models, provided that specific parameters are used to build At cavities. © 2016 Wiley Periodicals, Inc. PMID:27059181
Enabling Exploration of Deep Space: High Density Storage of Antimatter
NASA Technical Reports Server (NTRS)
Smith, Gerald A.; Kramer, Kevin J.
1999-01-01
Portable electromagnetic antiproton traps are now in a state of realization. This allows facilities like NASA Marshall Space Flight Center to conduct antimatter research remote to production sites. MSFC is currently developing a trap to store 10(exp 12) antiprotons for a twenty-day half-life period to be used in future experiments including antimatter plasma guns, antimatter-initiated microfusion, and the synthesis of antihydrogen for space propulsion applications. In 1998, issues including design, safety and transportation were considered for the MSFC High Performance Antimatter Trap (HiPAT). Radial diffusion and annihilation losses of antiprotons prompted the use of a 4 Tesla superconducting magnet and a 20 KV electrostatic potential at 10(exp -12) Torr pressure. Cryogenic fluids used to maintain a trap temperature of 4K were sized accordingly to provide twenty days of stand-alone storage time (half-life). Procurement of the superconducting magnet with associated cryostat has been completed. The inner, ultra-high vacuum system with electrode structures has been fabricated, tested and delivered to MSFC along with the magnet and cryostat. Assembly of these systems is currently in progress. Testing under high vacuum conditions, using electrons and hydrogen ions will follow in the months ahead.
What Density Functional Theory could do for Quantum Information
NASA Astrophysics Data System (ADS)
Mattsson, Ann
2015-03-01
The Hohenberg-Kohn theorem of Density Functional Theory (DFT), and extensions thereof, tells us that all properties of a system of electrons can be determined through their density, which uniquely determines the many-body wave-function. Given access to the appropriate, universal, functionals of the density we would, in theory, be able to determine all observables of any electronic system, without explicit reference to the wave-function. On the other hand, the wave-function is at the core of Quantum Information (QI), with the wave-function of a set of qubits being the central computational resource in a quantum computer. While there is seemingly little overlap between DFT and QI, reliance upon observables form a key connection. Though the time-evolution of the wave-function and associated phase information is fundamental to quantum computation, the initial and final states of a quantum computer are characterized by observables of the system. While observables can be extracted directly from a system's wave-function, DFT tells us that we may be able to intuit a method for extracting them from its density. In this talk, I will review the fundamentals of DFT and how these principles connect to the world of QI. This will range from DFT's utility in the engineering of physical qubits, to the possibility of using it to efficiently (but approximately) simulate Hamiltonians at the logical level. The apparent paradox of describing algorithms based on the quantum mechanical many-body wave-function with a DFT-like theory based on observables will remain a focus throughout. The ultimate goal of this talk is to initiate a dialog about what DFT could do for QI, in theory and in practice. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Dynamical density functional theory for colloidal dispersions including hydrodynamic interactions
NASA Astrophysics Data System (ADS)
Rex, M.; Löwen, H.
2009-02-01
A dynamical density functional theory (DDFT) for translational Brownian dynamics is derived which includes hydrodynamic interactions. The theory reduces to the simple Brownian DDFT proposed by Marconi and Tarazona (U. Marini Bettolo Marconi and P. Tarazona, J. Chem. Phys. 110, 8032 (1999); J. Phys.: Condens. Matter 12, A413 (2000)) when hydrodynamic interactions are neglected. The derivation is based on Smoluchowski’s equation for the time evolution of the probability density with pairwise hydrodynamic interactions. The theory is applied to hard-sphere colloids in an oscillating spherical optical trap which switches periodically in time from a stable confining to an unstable potential. Rosenfeld’s fundamental measure theory for the equilibrium density functional is used and hydrodynamics are incorporated on the Rotne-Prager level. The results for the time-dependent density profiles are compared to extensive Brownian dynamics simulations which are performed on the same Rotne-Prager level and excellent agreement is obtained. It is further found that hydrodynamic interactions damp and slow the dynamics of the confined colloid cluster in comparison to the same situation with neglected hydrodynamic interactions.
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.
Effects of high density on spacing behaviour and reproduction in Akodon azarae: A fencing experiment
NASA Astrophysics Data System (ADS)
Ávila, Belén; Bonatto, Florencia; Priotto, José; Steinmann, Andrea R.
2016-01-01
We studied the short term spacing behavioural responses of Pampean grassland mouse (Akodon azarae) with regard to population density in four 0.25 ha enclosures (two control and two experimental) in the 2011 breeding season. Based on the hypothesis that A. azarae breeding females exhibit spacing behaviour, and breeding males show a fusion spatial response, we tested the following predictions: (1) home range size and intrasexual overlap degree of females are independent of population density values; (2) at high population density, home range size of males decreases and the intrasexual home range overlap degree increases. To determine if female reproductive success decreases at high population density, we analyzed pregnancy rate, size and weight of litters, and period until fecundation in both low and high enclosure population density. We found that both males and females varied their home range size in relation to population density. Although male home ranges were always bigger than those of females in populations with high density, home range sizes of both sexes decreased. Females kept exclusive home ranges independent of density values meanwhile males decreased home range overlap in high breeding density populations. Although females produced litters of similar size in both treatments, weight of litter, pregnant rate and period until fecundation varied in relation to population density. Our results did not support the hypothesis that at high density females of A. azarae exhibit spacing behaviour neither that males exhibit a fusion spatial response.