Volume 77, Number 5, March 2007
|Number of page(s)||5|
|Published online||23 February 2007|
Solving Hartree-Fock systems with global optimization methods
Department of Applied Mathematics (IMECC-UNICAMP), State University of Campinas - CP 6065, 13081-970, Campinas-SP, Brazil
2 LIX, École Polytechnique - F-91128 Palaiseau, France
3 COPPE, Universidade Federal do Rio de Janeiro, UFRJ - CP 68511, Rio de Janeiro - RJ, 21945-970, Brazil
4 Departamento de Físico-Química, Instituto de Química, Universidade Federal do Rio de Janeiro, UFRJ, Rio de Janeiro - RJ, 21949-970, Brazil
Accepted: 11 January 2007
The Hartree-Fock equations describe atomic and molecular eletronic wave functions, based on the minimization of a functional of the energy. This can be formulated as a constrained global optimization problem involving nonconvex polynomials exhibiting many local minima. The traditional method of solving the Hartree-Fock problem does not provide a guarantee of global optimality and is very sensitive to the initial starting point. In this paper we show how to use a deterministic global optimization method to solve Hartree-Fock systems. The validity of the proposed approach was established by successfully computing the ground-state of the He and Be atoms.
PACS: 02.60.Pn – Numerical optimization / 31.15.Ar – Ab initio calculations / 71.15.Dx – Computational methodology (Brillouin zone sampling, iterative diagonalization, pseudopotential construction)
© Europhysics Letters Association, 2007
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