The Hartree-Fock method is well known in quantum chemistry, and widely used to obtain atomic and molecular eletronic wave functions, based on the minimization of a functional of the energy. This gives rise to a multi-extremal, nonconvex, polynomial optimization problem. We give a novel mathematical programming formulation of the problem, which we solve by using a spatial branch-and-Bound algorithm. Lower bounds are obtained by solving a tight linear relaxation of the problem derived prom an exact reformulation based on reduction constraints (a subset of RLT constraints). The proposed approach was successfully applied to the ground-state of the He and Be atoms.
Internal report 2004.31, DEI Politecnico di Milano, Oct. 2004.