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Converging self-consistent field equations in quantum chemistry – recent achievements and remaining challenges

Konstantin N. Kudin;  Gustavo E. Scuseria — 2007

ESAIM: Mathematical Modelling and Numerical Analysis

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.

Local Exchange Potentials for Electronic Structure Calculations

Eric Cancès;  Gabriel Stoltz;  Gustavo E. Scuseria;  Viktor N. Staroverov;  Ernest R. Davidson — 2009

MathematicS In Action

The Hartree-Fock exchange operator is an integral operator arising in the Hartree-Fock model as well as in some instances of the density functional theory. In a number of applications, it is convenient to approximate this integral operator by a multiplication operator, i.e. by a local potential. This article presents a detailed analysis of the mathematical properties of various local approximations to the nonlocal Hartree-Fock exchange operator including the Slater potential, the optimized effective...

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