Variational localized-site cluster expansions. II. Trees and near trees

Abstract

Cluster expanded wavefunctions involving localized‐site states and only pair excitations between nearest neighbor sites are considered. In the case that the bonds connecting these nearest neighbor sites form a tree graph (without rings), exact matrix element formulas are obtained in terms of the inverse of a modified type of topological matrix associated with this tree graph. The treatment of some near‐tree cases, without any touching rings, is also discussed.