Diagram technique for nonorthogonal electron group functions. II. Reduced density matrices and total energy

In part I, both the arrow diagram (AD) and expanded AD decompositions of the antisymmetrization operator A for an N-electron system with wave function represented by the product of mutually nonorthogonal group functions have been considered. Based on them, new diagrams for decompositions of normalization and overlap integrals, reduced density matrices, as well as for total electronic energy of the system are proposed and discussed in detail in the present part. The rules for evaluation of the contribution of each diagram in the form of an analytical expression are obtained. Both the strong and p-orthogonality approximations are discussed.