On certain correspondences among various coupled-cluster theories for closed-shell systems

Abstract

In this paper certain correspondences have been shown among various formulations of coupled-cluster theories for many electron closed-shell systems. Specifically it is shown that (i) the energy functional using unitary ansatz of the form exp (T-T⁺) is exactly sameorder by order in T with the size-consistent energy functional <ψ|H|ψ>/<ψ|ψ> recently obtained by us in coupled-cluster framework; (ii) in the framework of unitary ansatz of the form exp (T-T ⁺), both non-variational and variational approaches lead to identical equations upto any given order in T and T⁺ in T~T₂ approximation; (iii) variational procedure using our size-consistent energy functional or using the functional obtained in the framework of unitary ansatz (as envisaged by Kutzelnigg) leads to energy in both cases, in T~T₂ approximation, for a total of quadratic powers in T and T⁺, same as Cizek's linearised coupled pair many electron theory energy; (iv) in case of practical calculation of the energy through the variational procedures using our size-consistent energy functional and the functional in unitary ansatz framework, there is a loss of upper bound.