Derivation of an extended geminal model

Abstract

An extended geminal model is derived by applying perturbation theory to a matrix representation of the electronic Hamiltonian. The matrix representation is formed by a complete set of orthogonal configuration functions generated from a given finite orbital basis set. By construction, the function defined by the APSG approximation (antisymmetric product of strongly orthogonal geminals) is an element of this set of configuration functions. Considering the nondiagonal part of the Hamiltonian matrix as the perturbation, our model is obtained by a partitioning and reordering of the infinite order Rayleigh–Schrödinger perturbation expansion. The model has a hierarchical structure, is size extensive, and has favorable properties with respect to interpretation. In a test calculation on the water molecule, it is demonstrated that the extended geminal model truncated at the double pair correction level, recovers 100.8% of the correlation energy defined by the corresponding full CI calculation.