Theory of variational calculation with a scaling correct moment functional to solve the electronic schrödinger equation directly for ground state one-electron density and electronic energy

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N-dimensions to a nonlinear, approximate density functional of a three spatial dimension one-electron density for an N electron system which is tractable in practice, is a long-desired goal in electronic structure calculation. In a seminal work, Parr et al. (Phys. Rev. A 1997, 55, 1792) suggested a well behaving density functional in power series with respect to density scaling within the orbital-free framework for kinetic and repulsion energy of electrons. The updated literature on this subject is listed, reviewed, and summarized. Using this series with some modifications, a good density functional approximation is analyzed and solved via the Lagrange multiplier device. (We call the attention that the introduction of a Lagrangian multiplier to ensure normalization is a new element in this part of the related, general theory.) Its relation to Hartree-Fock (HF) and Kohn-Sham (KS) formalism is also analyzed for the goal to replace all the analytical Gaussian based two and four center integrals (∫gi(r1)gk(r2)r 12-1dr1dr2, etc.) to estimate electron-electron interactions with cheaper numerical integration. The KS method needs the numerical integration anyway for correlation estimation.

Original languageEnglish
Pages (from-to)1479-1492
Number of pages14
JournalInternational Journal of Quantum Chemistry
Volume113
Issue number10
DOIs
Publication statusPublished - May 15 2013

Fingerprint

Ground state
Carrier concentration
Schrodinger equation
moments
Electron-electron interactions
scaling
ground state
Electrons
Lagrange multipliers
numerical integration
electronics
Electronic structure
N electrons
Kinetics
energy
power series
multipliers
electron scattering
electrons
kinetic energy

Keywords

  • density functional theory
  • ground state total electronic energy
  • one-electron density
  • power series with correct density scaling

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Atomic and Molecular Physics, and Optics
  • Physical and Theoretical Chemistry

Cite this

@article{0f81a66bc13f4d40abca99290b7f4a5f,
title = "Theory of variational calculation with a scaling correct moment functional to solve the electronic schr{\"o}dinger equation directly for ground state one-electron density and electronic energy",
abstract = "The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N-dimensions to a nonlinear, approximate density functional of a three spatial dimension one-electron density for an N electron system which is tractable in practice, is a long-desired goal in electronic structure calculation. In a seminal work, Parr et al. (Phys. Rev. A 1997, 55, 1792) suggested a well behaving density functional in power series with respect to density scaling within the orbital-free framework for kinetic and repulsion energy of electrons. The updated literature on this subject is listed, reviewed, and summarized. Using this series with some modifications, a good density functional approximation is analyzed and solved via the Lagrange multiplier device. (We call the attention that the introduction of a Lagrangian multiplier to ensure normalization is a new element in this part of the related, general theory.) Its relation to Hartree-Fock (HF) and Kohn-Sham (KS) formalism is also analyzed for the goal to replace all the analytical Gaussian based two and four center integrals (∫gi(r1)gk(r2)r 12-1dr1dr2, etc.) to estimate electron-electron interactions with cheaper numerical integration. The KS method needs the numerical integration anyway for correlation estimation.",
keywords = "density functional theory, ground state total electronic energy, one-electron density, power series with correct density scaling",
author = "S. Kristy{\'a}n",
year = "2013",
month = "5",
day = "15",
doi = "10.1002/qua.24345",
language = "English",
volume = "113",
pages = "1479--1492",
journal = "International Journal of Quantum Chemistry",
issn = "0020-7608",
publisher = "John Wiley and Sons Inc.",
number = "10",

}

TY - JOUR

T1 - Theory of variational calculation with a scaling correct moment functional to solve the electronic schrödinger equation directly for ground state one-electron density and electronic energy

AU - Kristyán, S.

PY - 2013/5/15

Y1 - 2013/5/15

N2 - The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N-dimensions to a nonlinear, approximate density functional of a three spatial dimension one-electron density for an N electron system which is tractable in practice, is a long-desired goal in electronic structure calculation. In a seminal work, Parr et al. (Phys. Rev. A 1997, 55, 1792) suggested a well behaving density functional in power series with respect to density scaling within the orbital-free framework for kinetic and repulsion energy of electrons. The updated literature on this subject is listed, reviewed, and summarized. Using this series with some modifications, a good density functional approximation is analyzed and solved via the Lagrange multiplier device. (We call the attention that the introduction of a Lagrangian multiplier to ensure normalization is a new element in this part of the related, general theory.) Its relation to Hartree-Fock (HF) and Kohn-Sham (KS) formalism is also analyzed for the goal to replace all the analytical Gaussian based two and four center integrals (∫gi(r1)gk(r2)r 12-1dr1dr2, etc.) to estimate electron-electron interactions with cheaper numerical integration. The KS method needs the numerical integration anyway for correlation estimation.

AB - The reduction of the electronic Schrodinger equation or its calculating algorithm from 4N-dimensions to a nonlinear, approximate density functional of a three spatial dimension one-electron density for an N electron system which is tractable in practice, is a long-desired goal in electronic structure calculation. In a seminal work, Parr et al. (Phys. Rev. A 1997, 55, 1792) suggested a well behaving density functional in power series with respect to density scaling within the orbital-free framework for kinetic and repulsion energy of electrons. The updated literature on this subject is listed, reviewed, and summarized. Using this series with some modifications, a good density functional approximation is analyzed and solved via the Lagrange multiplier device. (We call the attention that the introduction of a Lagrangian multiplier to ensure normalization is a new element in this part of the related, general theory.) Its relation to Hartree-Fock (HF) and Kohn-Sham (KS) formalism is also analyzed for the goal to replace all the analytical Gaussian based two and four center integrals (∫gi(r1)gk(r2)r 12-1dr1dr2, etc.) to estimate electron-electron interactions with cheaper numerical integration. The KS method needs the numerical integration anyway for correlation estimation.

KW - density functional theory

KW - ground state total electronic energy

KW - one-electron density

KW - power series with correct density scaling

UR - http://www.scopus.com/inward/record.url?scp=84875857016&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84875857016&partnerID=8YFLogxK

U2 - 10.1002/qua.24345

DO - 10.1002/qua.24345

M3 - Article

AN - SCOPUS:84875857016

VL - 113

SP - 1479

EP - 1492

JO - International Journal of Quantum Chemistry

JF - International Journal of Quantum Chemistry

SN - 0020-7608

IS - 10

ER -