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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
Author(s) -
Kristyan Sandor
Publication year - 2012
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.24345
Subject(s) - lagrange multiplier , density functional theory , electron , gaussian , physics , quantum mechanics , atomic orbital , scaling , orbital free density functional theory , ground state , statistical physics , mathematics , local density approximation , geometry
The reduction of the electronic Schrodinger equation or its calculating algorithm from 4 N ‐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 (∫ g i ( r 1 ) g k ( r 2 )r 12 −1 d r 1 d r 2 , etc.) to estimate electron‐electron interactions with cheaper numerical integration. The KS method needs the numerical integration anyway for correlation estimation. © 2012 Wiley Periodicals, Inc.