Affiliation:
1. Département de Chimie, Université de Montréal 1 , C.P. 6128 Succursale A, Montréal, Québec H3C 3J7, Canada
2. Department of Physics and Materials Science, University of Luxembourg 2 , L-1511 Luxembourg City, Luxembourg
Abstract
The Kohn-Sham theory addresses the challenge of representing the kinetic energy by re-quantizing density functional theory at a level of non-interacting electrons. It transforms the many-electron problem into a fictitious non-interacting electron problem, with the many-electron effects concealed within the exchange-correlation (XC) energy, which is expressed in terms of the electron density ρ(r). Unlike the wave function, ρ(r) can be viewed as a classical quantity, and expressing the XC energy in terms of it circumvents the need for correlated wave functions. In this work, we once again employ the re-quantization strategy and determine the XC energy using a local one-particle Schrödinger equation. The ground-state eigenfunction of the corresponding Hamiltonian is a reference point (r) dependent orbital φr,σ(u, σ′) which is subsequently used to generate the XC hole and the XC energy. The spin coordinate is denoted by σ and u is the electron-electron separation. The one-particle equation for φr,σ(u, σ′) includes a local potential vr,σ(u, σ′) that we approximate using two simple physical constraints. We assess the approximation by applying it to the helium iso-electronic series, the homogeneous electron gas, and the dissociation of the hydrogen molecule.
Funder
Natural Sciences and Engineering Research Council of Canada
Subject
Physical and Theoretical Chemistry,General Physics and Astronomy