Use of a size-consistent energy functional in many electron theory for closed shells

Abstract

If the ground state wave-function Ψ_gr is written as Ψ_gr = Φ_o+X, with X as the correlation part satisfying (Φ_o|x) = 0, and x expressed as an expansion in terms of pair, pair-pair etc. cluster functions, then the expectation value of the energy E = (Ψ_gr|H|Ψ_gr)/(Ψ_gr|Ψ_gr) has the property that the normalization term in the denominator completely cancels the unlinked part of the numerator, as noted by Sinanoglu. We use Cizek's coupled-pair ansatz Ψ_gr = exp(T₂) Φ₀ for transcribing Sinanoglu's expansion in a many-body language to study the behaviour of the size-consistent (linked) energy functional thus generated. For calculating the matrix-elements of the cluster components of T, we use two recipes: (1) a variational determination of the cluster components using Euler's principle for the energy functional akin in spirit to the Varied Portion Approach (VPA) of Sinanoglu and (ii) a nonvariational determination of the cluster components using the conventional coupled-cluster theory. Results are presented for model test systems and are compared with variational CI and nonvariational coupled-cluster values. It has been observed that the values obtained from the size-consistent energy functional from the cluster components obtained from methods (i) and (ii) are quite close and both compare well with the nonvariational coupled-cluster results. Some useful simplifications afforded by the VPA are also indicated. A brief perspective of the method vis-a-vis other related theories is also given.