Parallel Calculation of Electron-Transfer and Resonance Matrix Elements of Hartree-Fock and Generalized Valence Bond Wave Functions

Abstract

We review the theory for the computation of the Hamiltonian matrix element between two distinct electronic wave functions ψ_A and ψ_B sharing the same nuclear configuration but differing electronic density distributions. For example, ψ_A and ψ_B might describe two endpoints in an electron transfer reaction or two configurations in a resonance description of a molecule. In such cases the calculation of the rate of electron transfer or resonance energy requires evaluation of <ψ_A\Ĥ\ψ_B> = H_(AB) matrix elements. Because the orbitals of ψ_A and ψ_B have complicated (non-orthogonal) relationships, the calculation of H_(AB) had been computationally intensive. In this paper we consider ψ_A, ψ_B having the form of closed or open-shell Hartree-Fock or Generalized Valence Bond wave functions and show the parallel structure of the theory. Using this parallel structure we present an efficient computational implementation for shared memory multiprocessors.

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