Analysis of a b i n i t i o effective valence shell Hamiltonian calculations using third order quasidegenerate many-body perturbation theory

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Abstract
A generalization of quasidegenerate many‐body perturbation theory is provided which enables the calculation of the Hermitian effective valence shell Hamiltonian Hv along with the individual one‐ , two‐ , three‐ , and the never‐before‐calculated four‐electron effective integrals of Hv. Emphasis is placed upon the problems encountered by the use of large valence spaces and the desire to use the same Hv for all valence states of a given system and all its ions. These stringent requirements, motivated by a desire to investigate the theoretical foundations of semiempirical quantum chemistry, introduce severe difficulties with the quasidegeneracy constraints of the theory. A detailed analysis is presented of methods to handle these problems within a third order formulation which in its simplest form reduces to a symmetrized version of Brandow’s diagrammatic linked‐cluster (size consistent) perturbation expansion. An outline of practical ab initio third order Hv calculations is discussed here and systematically tested in the following paper.