Converging self-consistent field equations in quantum chemistry - recent achievements and remaining challenges
ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 2, pp. 281-296.

This paper reviews popular acceleration techniques to converge the non-linear self-consistent field equations appearing in quantum chemistry calculations with localized basis sets. The different methodologies, as well as their advantages and limitations are discussed within the same framework. Several illustrative examples of calculations are presented. This paper attempts to describe recent achievements and remaining challenges in this field.

DOI : 10.1051/m2an:2007022
Classification : 35P30, 65B99, 65K10, 81-08
Mots clés : Hartree-Fock equations, self-consistent field, convergence acceleration algorithms, level shift, direct inversion of the iterative subspace, DIIS, generalized minimum residue, GMRES, relaxed constraints algorithm, RCA, energy DIIS, EDIIS, density functional theory, DFT
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     author = {Kudin, Konstantin N. and Scuseria, Gustavo E.},
     title = {Converging self-consistent field equations in quantum chemistry - recent achievements and remaining challenges},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
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Kudin, Konstantin N.; Scuseria, Gustavo E. Converging self-consistent field equations in quantum chemistry - recent achievements and remaining challenges. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 2, pp. 281-296. doi : 10.1051/m2an:2007022. http://www.numdam.org/articles/10.1051/m2an:2007022/

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