An Overview of Self-Consistent Field Calculations Within Finite Basis Sets

Molecules

Christian Van Alsenoy¹  Frank Blockhuys¹  Susi Lehtola² 

[1] Department of Chemistry, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerpen, Belgium;Department of Chemistry, University of Helsinki, P.O. Box 55 (A. I. Virtasen aukio 1) Helsinki, Finland;

关键词: self-consistent field theory;    hartree-fock;    density functional theory;   

DOI  :  10.3390/molecules25051218

来源: DOAJ

【 摘 要 】

A uniform derivation of the self-consistent field equations in a finite basis set is presented. Both restricted and unrestricted Hartree−Fock (HF) theory as well as various density functional approximations are considered. The unitary invariance of the HF and density functional models is discussed, paving the way for the use of localized molecular orbitals. The self-consistent field equations are derived in a non-orthogonal basis set, and their solution is discussed also in the presence of linear dependencies in the basis. It is argued why iterative diagonalization of the Kohn−Sham−Fock matrix leads to the minimization of the total energy. Alternative methods for the solution of the self-consistent field equations via direct minimization as well as stability analysis are briefly discussed. Explicit expressions are given for the contributions to the Kohn−Sham−Fock matrix up to meta-GGA functionals. Range-separated hybrids and non-local correlation functionals are summarily reviewed.

【 授权许可】

Unknown