Solving Hartree-Fock systems with global optimization methods
نویسندگان
چکیده
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. Copyright c © EPLA, 2007 Introduction. – The quantum behaviour of atoms and molecules, in the absence of relativistic effects, is determined by the time-independent Schrödinger equation:
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