Solving Hartree-Fock systems with global optimization methodsC. Lavor1, L. Liberti2, N. Maculan3 and M. A. C. Nascimento4
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
received 21 September 2006; accepted in final form 11 January 2007; published March 2007
published online 23 February 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.
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