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

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http://hdl.handle.net/10138/315226

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Lehtola , S , Blockhuys , F & Van Alsenoy , C 2020 , ' An Overview of Self-Consistent Field Calculations Within Finite Basis Sets ' , Molecules , vol. 25 , no. 5 . https://doi.org/10.3390/molecules25051218

Title: An Overview of Self-Consistent Field Calculations Within Finite Basis Sets
Author: Lehtola, Susi; Blockhuys, Frank; Van Alsenoy, Christian
Contributor: University of Helsinki, Department of Chemistry
Date: 2020-03-01
Language: eng
Number of pages: 23
Belongs to series: Molecules
ISSN: 1420-3049
URI: http://hdl.handle.net/10138/315226
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.
Subject: self-consistent field theory
hartree-fock
density functional theory
DENSITY-FUNCTIONAL THEORY
HARTREE-FOCK
AB-INITIO
ORBITAL OPTIMIZATION
EXCHANGE-ENERGY
EXCITED-STATES
WAVE-FUNCTION
CONVERGENCE
ACCURATE
APPROXIMATIONS
116 Chemical sciences
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