The Experts below are selected from a list of 20214 Experts worldwide ranked by ideXlab platform
E Rasanen - One of the best experts on this subject based on the ideXlab platform.
-
validity of power functionals for a homogeneous electron gas in reduced density matrix functional theory
Physical Review A, 2016Co-Authors: E Rasanen, A Putaja, F G Eich, T BaldsiefenAbstract:Physically valid and numerically efficient approximations for the Exchange and Correlation Energy are critical for reduced-density-matrix-functional theory to become a widely used method in electronic structure calculations. Here we examine the physical limits of power functionals of the form $f(n,{n}^{\ensuremath{'}})={(n{n}^{\ensuremath{'}})}^{\ensuremath{\alpha}}$ for the scaling function in the Exchange-Correlation Energy. To this end we obtain numerically the minimizing momentum distributions for the three- and two-dimensional homogeneous electron gas, respectively. In particular, we examine the limiting values for the power $\ensuremath{\alpha}$ to yield physically sound solutions that satisfy the Lieb-Oxford lower bound for the Exchange-Correlation Energy and exclude pinned states with the condition $n(\mathbf{k})l1$ for all wave vectors $\mathbf{k}$. The results refine the constraints previously obtained from trial momentum distributions. We also compute the values for $\ensuremath{\alpha}$ that yield the exact Correlation Energy and its kinetic part for both the three- and two-dimensional electron gas. In both systems, narrow regimes of validity and accuracy are found at $\ensuremath{\alpha}\ensuremath{\gtrsim}0.6$ and at ${r}_{s}\ensuremath{\gtrsim}10$ for the density parameter, corresponding to relatively low densities.
-
laplacian level density functionals for the Exchange Correlation Energy of low dimensional nanostructures
Physical Review B, 2010Co-Authors: S Pittalis, E RasanenAbstract:In modeling low-dimensional electronic nanostructures, the evaluation of the electron-electron interaction is a challenging task. Here we present an accurate and practical density-functional approach to the two-dimensional many-electron problem. In particular, we show that spin-density functionals in the class of meta-generalized-gradient approximations can be greatly simplified by reducing the explicit dependence on the Kohn-Sham orbitals to the dependence on the electron spin density and its spatial derivatives. Tests on various quantum-dot systems show that the overall accuracy is well preserved, if not even improved, by the modifications.
-
semi local density functional for the Exchange Correlation Energy of electrons in two dimensions
International Journal of Quantum Chemistry, 2010Co-Authors: E Rasanen, S Pittalis, J G Vilhena, Miguel A L MarquesAbstract:We present a practical and accurate density functional for the Exchange-Correlation Energy of electrons in two dimensions. The Exchange part is based on a recent two-dimensional generalized-gradient approximation derived by considering the limits of small and large density gradients. The fully local Correlation part is constructed following the Colle-Salvetti scheme and a Gaussian approximation for the pair density. The combination of these expressions is shown to provide an efficient density functional to calculate the total energies of two-dimensional electron systems such as semiconductor quantum dots. Excellent performance of the functional with respect to numerically exact reference data for quantum dots is demonstrated. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110: 2308-2314, 2010
-
colle salvetti type local density functional for the Exchange Correlation Energy in two dimensions
Physical Review A, 2010Co-Authors: S şakiroglu, E RasanenAbstract:We derive an approximate local density functional for the Exchange-Correlation Energy to be used in density-functional calculations of two-dimensional systems. In the derivation we employ the Colle-Salvetti wave function within the scheme of Salvetti and Montagnani [Phys. Rev. A 63, 052109 (2001)] to satisfy the sum rule for the Exchange-Correlation hole. We apply the functional to the two-dimensional homogeneous electron gas as well as to a set of quantum dots and find a very good agreement with exact reference data.
-
lower bounds on the Exchange Correlation Energy in reduced dimensions
Physical Review Letters, 2009Co-Authors: E Rasanen, S Pittalis, K Capelle, C R ProettoAbstract:Bounds on the Exchange-Correlation Energy of many-electron systems are derived and tested. By using universal scaling properties of the electron-electron interaction, we obtain the exponent of the bounds in three, two, one, and quasione dimensions. From the properties of the electron gas in the dilute regime, the tightest estimate to date is given for the numerical prefactor of the bound, which is crucial in practical applications. Numerical tests on various low-dimensional systems are in line with the bounds obtained and give evidence of an interesting dimensional crossover between two and one dimensions.
Masahiko Higuchi - One of the best experts on this subject based on the ideXlab platform.
-
sum rules for the Exchange Correlation Energy functional of the extended constrained search theory application to checking the validity of the vorticity expansion approximation of the current density functional theory
Physical Review A, 2010Co-Authors: Masahiko Higuchi, Katsuhiko HiguchiAbstract:We present four kinds of sum rules for the Exchange-Correlation Energy functional of the extended constrained-search theory. They are applicable even to the conventional density functional theory. As an application of these sum rules, we utilize them to check the validity of the vorticity expansion approximation (VEA) of the current-density functional theory (CDFT). The VEA formula fulfils three of them, though the local density approximation formula of the CDFT fulfills only one. The validity of the VEA formula is thus confirmed successfully from the viewpoint of the sum rules.
-
kinetic Energy contribution to the Exchange Correlation Energy functional of the extended constrained search theory
Physical Review A, 2009Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:We present the kinetic Energy contribution to the Exchange-Correlation Energy functional of the extended constrained-search (ECS) theory by means of the generalized Bauer's relation. Due to the nature of the Exchange-Correlation Energy functional being a function of the Bohr radius and ${e}^{2}$, three kinds of expressions for the kinetic Energy contribution are obtained. These can be utilized as constraints in developing and/or evaluating the approximate form of the Exchange-Correlation Energy functional of the ECS theory. Furthermore, by combining three expressions with the virial relation, we derive other useful relations that include not the kinetic Energy contribution but only the Exchange-Correlation Energy functional.
-
vorticity expansion approximation of the Exchange Correlation Energy functional in current density functional theory
Physical Review B, 2006Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:We propose the vorticity expansion approximation VEA formulas of the Exchange and Correlation Energy functionals of the current density functional theory CDFT. They have a form of the second-order expansion with respect to the vorticity. Expansion coefficients are determined by requiring them to satisfy exact relations that have been derived from scaling properties of Exchange and Correlation Energy functionals. Resultant VEA formulas satisfy a larger number of exact relations than those of the local-density approximation of the CDFT. Due to the well-behaved forms, the VEA formulas can be in quite good agreement with the Exchange and Correlation energies of the homogeneous electron liquid under a uniform magnetic field.
-
Exchange Correlation Energy functional and virial theorem in the extended constrained search theory
Physical Review B, 2005Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:The coupling-constant expression and virial relation for the Exchange-Correlation Energy functional of the extended-constrained search theory [M. Higuchi and K. Higuchi, Phys. Rev. B 69, 035113 (2004)] are derived. These provide the guideline for developing and testing the approximate form of the Exchange-Correlation Energy functional.
-
Exchange and Correlation Energy functional in the current density functional theory
Physica B-condensed Matter, 2002Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:Abstract The exact conditions fulfilled by the Exchange–Correlation Energy functional E xc [ρ, j p ] of the current-density functional theory (CDFT) are investigated for the purpose of developing the approximate form of E xc [ρ, j p ] . A set of new exact conditions is obtained by considering the behavior of the Correlation Energy functional under a nonuniform coordinate scaling of electrons. We also compile certain known exact conditions for E xc [ρ, j p ] of the CDFT. By using some of the exact conditions as the constraint, we newly derive the approximation of the Exchange Energy functional in the form of the second-order vorticity expansion.
John P Perdew - One of the best experts on this subject based on the ideXlab platform.
-
Exchange Correlation Energy functional based on the airy gas reference system
Physical Review B, 2009Co-Authors: Lucian A Constantin, Adrienn Ruzsinszky, John P PerdewAbstract:In recent work, generalized gradient approximations (GGAs) have been constructed from the Energy density of the Airy gas for Exchange but not for Correlation. We report the random-phase approximation (RPA) conventional Correlation Energy density of the Airy gas, the simplest edge electron gas, in which the auxiliary noninteracting electrons experience a linear potential. By fitting the Airy-gas RPA Exchange-Correlation Energy density and making an accurate short-range correction to RPA, we propose a simple beyond RPA GGA density functional (``$\text{ARPA}+$'') for the Exchange-Correlation Energy. Our functional, tested for jellium surfaces, atoms, molecules, and solids, improves mildly over the local spin-density approximation for atomization energies and lattice constants without much worsening the already good surface Exchange-Correlation energies.
-
Exchange Correlation Energy functional based on the airy gas reference system
arXiv: Materials Science, 2009Co-Authors: Lucian A Constantin, Adrienn Ruzsinszky, John P PerdewAbstract:In recent work, generalized gradient approximations (GGA's) have been constructed from the Energy density of the Airy gas for Exchange but not for Correlation. We report the random phase approximation (RPA) conventional Correlation Energy density of the Airy gas, the simplest edge electron gas, in which the auxiliary noninteracting electrons experience a linear potential. By fitting the Airy-gas RPA Exchange-Correlation Energy density and making an accurate short-range correction to RPA, we propose a simple beyond-RPA GGA density functional ("ARPA+") for the Exchange-Correlation Energy. Our functional, tested for jellium surfaces, atoms, molecules and solids, improves mildly over the local spin density approximation for atomization energies and lattice constants without much worsening the already-good surface Exchange-Correlation energies.
-
workhorse semilocal density functional for condensed matter physics and quantum chemistry
arXiv: Materials Science, 2009Co-Authors: John P Perdew, Adrienn Ruzsinszky, Gabor I Csonka, Lucian A ConstantinAbstract:Semilocal density functionals for the Exchange-Correlation Energy are needed for large electronic systems. The Tao-Perdew-Staroverov-Scuseria (TPSS) meta-generalized gradient approximation (meta-GGA) is semilocal and usefully accurate, but predicts too-long lattice constants. Recent "GGA's for solids" yield good lattice constants but poor atomization energies of molecules. We show that the construction principle for one of them (restoring the density gradient expansion for Exchange over a wide range of densities) can be used to construct a "revised TPSS" meta-GGA with accurate lattice constants, surface energies, and atomization energies for ordinary matter.
-
one parameter optimization of a nonempirical meta generalized gradient approximation for the Exchange Correlation Energy
Physical Review A, 2007Co-Authors: John P Perdew, Adrienn Ruzsinszky, Jianmin Tao, Gabor I Csonka, Gustavo E ScuseriaAbstract:The meta-generalized-gradient-approximation (meta-GGA) for the Exchange-Correlation Energy, as constructed by Tao, Perdew, Staroverov, and Scuseria (TPSS) [Phys. Rev. Lett. 91, 146401 (2003)], has achieved usefully consistent accuracy for diverse systems and is the most reliable nonempirical density functional (and the most reliable nonhybrid) in common use. We present here an optimized version of this TPSS functional obtained by empirically fitting a single free parameter that controls the approach of the Exchange enhancement factor to its rapidly-varying-density limit, while preserving all the exact constraints that the original TPSS functional satisfies. We find that molecular atomization energies are significantly improved with the optimized version and are even better than those obtained with the best hybrid functionals employing a fraction of exact Exchange (e.g., the TPSS hybrid), while Energy barrier heights are slightly improved; jellium surface energies remain accurate and almost unchanged. The one-parameter freedom of the TPSS functional may be useful even beyond the meta-GGA level, since the TPSS approximation is a natural starting point for the higher-level hyper-GGA.
-
laplacian level density functionals for the kinetic Energy density and Exchange Correlation Energy
Physical Review B, 2007Co-Authors: John P Perdew, Lucian A ConstantinAbstract:We construct a Laplacian-level meta-generalized-gradient-approximation (meta-GGA) for the noninteracting (Kohn-Sham orbital) positive kinetic Energy density $\ensuremath{\tau}$ of an electronic ground state of density $n$. This meta-GGA is designed to recover the fourth-order gradient expansion ${\ensuremath{\tau}}^{\mathit{GE}4}$ in the appropriate slowly varying limit and the von Weizs\"acker expression ${\ensuremath{\tau}}^{W}={\ensuremath{\mid}\ensuremath{\nabla}n\ensuremath{\mid}}^{2}∕(8n)$ in the rapidly varying limit. It is constrained to satisfy the rigorous lower bound ${\ensuremath{\tau}}^{W}(\mathbf{r})\ensuremath{\leqslant}\ensuremath{\tau}(\mathbf{r})$. Our meta-GGA is typically a strong improvement over the gradient expansion of $\ensuremath{\tau}$ for atoms, spherical jellium clusters, jellium surfaces, the Airy gas, Hooke's atom, one-electron Gaussian density, quasi-two-dimensional electron gas, and nonuniformly scaled hydrogen atom. We also construct a Laplacian-level meta-GGA for Exchange and Correlation by employing our approximate $\ensuremath{\tau}$ in the Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA density functional. The Laplacian-level TPSS gives almost the same Exchange-Correlation enhancement factors and energies as the full TPSS, suggesting that $\ensuremath{\tau}$ and ${\ensuremath{\nabla}}^{2}n$ carry about the same information beyond that carried by $n$ and $\ensuremath{\nabla}n$. Our kinetic Energy density integrates to an orbital-free kinetic Energy functional that is about as accurate as the fourth-order gradient expansion for many real densities (with noticeable improvement in molecular atomization energies), but considerably more accurate for rapidly varying ones.
Katsuhiko Higuchi - One of the best experts on this subject based on the ideXlab platform.
-
sum rules for the Exchange Correlation Energy functional of the extended constrained search theory application to checking the validity of the vorticity expansion approximation of the current density functional theory
Physical Review A, 2010Co-Authors: Masahiko Higuchi, Katsuhiko HiguchiAbstract:We present four kinds of sum rules for the Exchange-Correlation Energy functional of the extended constrained-search theory. They are applicable even to the conventional density functional theory. As an application of these sum rules, we utilize them to check the validity of the vorticity expansion approximation (VEA) of the current-density functional theory (CDFT). The VEA formula fulfils three of them, though the local density approximation formula of the CDFT fulfills only one. The validity of the VEA formula is thus confirmed successfully from the viewpoint of the sum rules.
-
kinetic Energy contribution to the Exchange Correlation Energy functional of the extended constrained search theory
Physical Review A, 2009Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:We present the kinetic Energy contribution to the Exchange-Correlation Energy functional of the extended constrained-search (ECS) theory by means of the generalized Bauer's relation. Due to the nature of the Exchange-Correlation Energy functional being a function of the Bohr radius and ${e}^{2}$, three kinds of expressions for the kinetic Energy contribution are obtained. These can be utilized as constraints in developing and/or evaluating the approximate form of the Exchange-Correlation Energy functional of the ECS theory. Furthermore, by combining three expressions with the virial relation, we derive other useful relations that include not the kinetic Energy contribution but only the Exchange-Correlation Energy functional.
-
vorticity expansion approximation of the Exchange Correlation Energy functional in current density functional theory
Physical Review B, 2006Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:We propose the vorticity expansion approximation VEA formulas of the Exchange and Correlation Energy functionals of the current density functional theory CDFT. They have a form of the second-order expansion with respect to the vorticity. Expansion coefficients are determined by requiring them to satisfy exact relations that have been derived from scaling properties of Exchange and Correlation Energy functionals. Resultant VEA formulas satisfy a larger number of exact relations than those of the local-density approximation of the CDFT. Due to the well-behaved forms, the VEA formulas can be in quite good agreement with the Exchange and Correlation energies of the homogeneous electron liquid under a uniform magnetic field.
-
Exchange Correlation Energy functional and virial theorem in the extended constrained search theory
Physical Review B, 2005Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:The coupling-constant expression and virial relation for the Exchange-Correlation Energy functional of the extended-constrained search theory [M. Higuchi and K. Higuchi, Phys. Rev. B 69, 035113 (2004)] are derived. These provide the guideline for developing and testing the approximate form of the Exchange-Correlation Energy functional.
-
Exchange and Correlation Energy functional in the current density functional theory
Physica B-condensed Matter, 2002Co-Authors: Katsuhiko Higuchi, Masahiko HiguchiAbstract:Abstract The exact conditions fulfilled by the Exchange–Correlation Energy functional E xc [ρ, j p ] of the current-density functional theory (CDFT) are investigated for the purpose of developing the approximate form of E xc [ρ, j p ] . A set of new exact conditions is obtained by considering the behavior of the Correlation Energy functional under a nonuniform coordinate scaling of electrons. We also compile certain known exact conditions for E xc [ρ, j p ] of the CDFT. By using some of the exact conditions as the constraint, we newly derive the approximation of the Exchange Energy functional in the form of the second-order vorticity expansion.
Lucian A Constantin - One of the best experts on this subject based on the ideXlab platform.
-
gradient dependent upper bound for the Exchange Correlation Energy and application to density functional theory
Physical Review B, 2015Co-Authors: Lucian A Constantin, Aleksandrs Terentjevs, Fabio Della Sala, Eduardo FabianoAbstract:We propose a simple gradient-dependent bound for the Exchange-Correlation Energy (sLL), based on the recent nonlocal bound derived by Lewin and Lieb. We show that sLL is equivalent to the original Lieb-Oxford bound in rapidly varying density cases, but it is tighter for slowly varying density systems. To show the utility of the sLL bound we apply it to the construction of simple semilocal and nonlocal Exchange and Correlation functionals. In both cases improved results, with respect to the use of Lieb-Oxford bound, are obtained, showing the power of the sLL bound.
-
adiabatic connection fluctuation dissipation approach to long range behavior of Exchange Correlation Energy at metal surfaces a numerical study for jellium slabs
Physical Review B, 2011Co-Authors: Lucian A Constantin, J. M. PitarkeAbstract:A still open issue in many-body theory is the asymptotic behavior of the Exchange-Correlation Energy and potential in the vacuum region of a metal surface. Here we report a numerical study of the position-dependent Exchange-Correlation Energy for jellium slabs, as obtained by combining the formally exact adiabatic-connection-fluctuation-dissipation theorem with either time-dependent density-functional theory or an inhomogeneous Singwi-Tosi-Land-Sj\"olander approach. We find that the inclusion of Correlation allows to obtain well-converged semi-infinite-jellium results (independent of the slab thickness) that exhibit an image-like asymptotic behavior close to the classical image potential $V_{im}(z)=-e^2/4z$.
-
Exchange Correlation Energy functional based on the airy gas reference system
Physical Review B, 2009Co-Authors: Lucian A Constantin, Adrienn Ruzsinszky, John P PerdewAbstract:In recent work, generalized gradient approximations (GGAs) have been constructed from the Energy density of the Airy gas for Exchange but not for Correlation. We report the random-phase approximation (RPA) conventional Correlation Energy density of the Airy gas, the simplest edge electron gas, in which the auxiliary noninteracting electrons experience a linear potential. By fitting the Airy-gas RPA Exchange-Correlation Energy density and making an accurate short-range correction to RPA, we propose a simple beyond RPA GGA density functional (``$\text{ARPA}+$'') for the Exchange-Correlation Energy. Our functional, tested for jellium surfaces, atoms, molecules, and solids, improves mildly over the local spin-density approximation for atomization energies and lattice constants without much worsening the already good surface Exchange-Correlation energies.
-
Exchange Correlation Energy functional based on the airy gas reference system
arXiv: Materials Science, 2009Co-Authors: Lucian A Constantin, Adrienn Ruzsinszky, John P PerdewAbstract:In recent work, generalized gradient approximations (GGA's) have been constructed from the Energy density of the Airy gas for Exchange but not for Correlation. We report the random phase approximation (RPA) conventional Correlation Energy density of the Airy gas, the simplest edge electron gas, in which the auxiliary noninteracting electrons experience a linear potential. By fitting the Airy-gas RPA Exchange-Correlation Energy density and making an accurate short-range correction to RPA, we propose a simple beyond-RPA GGA density functional ("ARPA+") for the Exchange-Correlation Energy. Our functional, tested for jellium surfaces, atoms, molecules and solids, improves mildly over the local spin density approximation for atomization energies and lattice constants without much worsening the already-good surface Exchange-Correlation energies.
-
workhorse semilocal density functional for condensed matter physics and quantum chemistry
arXiv: Materials Science, 2009Co-Authors: John P Perdew, Adrienn Ruzsinszky, Gabor I Csonka, Lucian A ConstantinAbstract:Semilocal density functionals for the Exchange-Correlation Energy are needed for large electronic systems. The Tao-Perdew-Staroverov-Scuseria (TPSS) meta-generalized gradient approximation (meta-GGA) is semilocal and usefully accurate, but predicts too-long lattice constants. Recent "GGA's for solids" yield good lattice constants but poor atomization energies of molecules. We show that the construction principle for one of them (restoring the density gradient expansion for Exchange over a wide range of densities) can be used to construct a "revised TPSS" meta-GGA with accurate lattice constants, surface energies, and atomization energies for ordinary matter.
