Numerical methods for solving the Hartree-Fock equations of diatomic molecules I.
Journal article, 2009

The theory of domain decomposition is described and used to divide the variable domain of a diatomic molecule into separate regions which are solved independently. This approach makes it possible to use fast Krylov methods in the broad interior of the region while using explicit methods such as Gaussian elimination on the boundaries. As is demonstrated by solving a number of model problems, these methods enable one to obtain solutions of the relevant partial differential equations and eigenvalue equations accurate to six significant figures with a small amount of computational time. Since the numerical approach described in this article decomposes the variable space into separate regions where the equations are solved independently, our approach is very well-suited to parallel computing and offers the long term possibility of studying complex molecules by dividing them into smaller fragments that are calculated separately.


eigenvalue problem.

diatomic molecules

Hartree-Fock equations

Fast Krylov methods


John C. Morrison

University of Louisville

Scott Boyd

University of Louisville

Luis Marsano

University of Louisville

Bernard Bialecki

Colorado School of Mines

Thomas Ericsson

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Jose Paulo Santos

Nova University of Lisbon

Communications in Computational Physics

1815-2406 (ISSN) 1991-7120 (eISSN)

Vol. 5 5 959-985

Subject Categories

Computational Mathematics

Atom and Molecular Physics and Optics

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