Compact model potentials for ab initio embedded cluster calculations. Part I. Basic formulation

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Abstract
In light of the theory of separability of many-electron systems, a methodology to perform embedded cluster calculations in order to study localized phenomena in a large electronic system is reported. A general equation for the cluster spin orbitals under the assumptions of frozen environment and cluster-environment strong orthogonality requirements is presented. The interactions between active and frozen electrons are adequately introduced through computationally convenient ab initio compact model potentials (CMPs) built up as a sum of long- and short-range terms. The short-range term, Coulomb and exchange interactions, are developed as a spectral representation in a nonorthogonal basis set. Cluster wave function, energy, and analytic geometrical derivatives calculations with CMPs have been implemented for several kinds of cluster wave functions. In order to evaluate the accuracy of the results obtained using this methodology, some simple test calculations for different hydrogen molecule-cation complexes have been performed both at the Hartree–Fock and multiconfigurational self-consistent-field levels of theory. As shown by an analysis based on the constrained space orbitals variations method, the main deviations are due to the lack of charge transfer contributions in the CMP calculations.