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Solving a Quantum Chemistry problem with Deterministic Global Optimization

Carlile Lavor (clavor***at***ime.unicamp.br)
Leo Liberti (liberti***at***elet.polimi.it)
Nelson Maculan (maculan***at***cos.ufrj.br)
Marco Antonio Chaer Nascimento (chaer***at***iq.ufrj.br)

Abstract: 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.

Keywords: Hartree-Fock method, global optimization, branch and bound, reduction constraints

Category 1: Applications -- Science and Engineering (Basic Sciences Applications )

Category 2: Applications -- Science and Engineering (Biomedical Applications )

Category 3: Global Optimization (Applications )

Citation: Internal report 2004.31, DEI Politecnico di Milano, Oct. 2004.

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Entry Submitted: 07/12/2005
Entry Accepted: 07/12/2005
Entry Last Modified: 07/12/2005

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