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

Overview

Journal Molecules

Publisher MDPI

Specialty Biology

Date 2020 Mar 19

PMID 32182727

Citations 7

Authors

Susi Lehtola

Frank Blockhuys

Christian Van Alsenoy

Affiliations

Soon will be listed here.

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.

Citing Articles

Ensemble Generalization of the Perdew-Zunger Self-Interaction Correction: A Way Out of Multiple Minima and Symmetry Breaking.

Schwalbe S, Schulze W, Trepte K, Lehtola S J Chem Theory Comput. 2024; 20(16):7144-7154.

PMID: 39140402 PMC: 11360130. DOI: 10.1021/acs.jctc.4c00694.

A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures.

Sethio D, Azzopardi E, Fdez Galvan I, Lindh R J Phys Chem A. 2024; 128(12):2472-2486.

PMID: 38483190 PMC: 10983011. DOI: 10.1021/acs.jpca.3c07647.

Atomic Electronic Structure Calculations with Hermite Interpolating Polynomials.

Lehtola S J Phys Chem A. 2023; 127(18):4180-4193.

PMID: 37129275 PMC: 10184118. DOI: 10.1021/acs.jpca.3c00729.

Meta-GGA Density Functional Calculations on Atoms with Spherically Symmetric Densities in the Finite Element Formalism.

Lehtola S J Chem Theory Comput. 2023; 19(9):2502-2517.

PMID: 37084260 PMC: 10173457. DOI: 10.1021/acs.jctc.3c00183.

Toward Pair Atomic Density Fitting for Correlation Energies with Benchmark Accuracy.

Spadetto E, Philipsen P, Forster A, Visscher L J Chem Theory Comput. 2023; 19(5):1499-1516.

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