Solving Hartree-Fock systems with global optimization methods

¹  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

Corresponding authors: clavor@ime.unicamp.br liberti@lix.polytechnique.fr maculan@cos.ufrj.br chaer@iq.ufrj.br

Received: 21 September 2006
Accepted: 11 January 2007

Abstract

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.