Converging self-consistent field equations in quantum chemistry - recent achievements and remaining challenges
ESAIM: Mathematical Modelling and Numerical Analysis - 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.

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
     author = {Kudin, Konstantin N. and Scuseria, Gustavo E.},
     title = {Converging self-consistent field equations in quantum chemistry - recent achievements and remaining challenges},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     pages = {281--296},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {2},
     year = {2007},
     doi = {10.1051/m2an:2007022},
     zbl = {1135.81381},
     language = {en},
     url = {}
Kudin, Konstantin N.; Scuseria, Gustavo E. Converging self-consistent field equations in quantum chemistry - recent achievements and remaining challenges. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) no. 2, pp. 281-296. doi : 10.1051/m2an:2007022.

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