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

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ID: 101664
2020
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Abstract
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.
Reference Key
lehtola2020anmolecules Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Lehtola, Susi;Blockhuys, Frank;Van Alsenoy, Christian;
Journal molecules
Year 2020
DOI
E1218
URL
Keywords
Density functional theory hartree-fock self-consistent field theory

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