Linked-cluster theorem in open shell coupled-cluster theory for mp-mh model space determinants

Abstract

In this paper we have demonstrated the following aspects of the open-shell coupled cluster (CC) theory when the model space consists ofmp-mh determinants: (I) If no other subsidiary conditions (besides the ‘minimality’ requirementPSP=0) on the normalization of the wave functions are imposed, then the demand that the wave operator admits of the corevalence separation of energy is inconsistent with the assumption of intermediate normalization. Thus all the discussions on the appearance of unlinked diagrams based on the implicit use of intermediate normalization are invalid. (ii) The open-shell CC developments of Mukherjeeet al are independent: of the normalization of the wavefunctions and the linked cluster theorems and the core-valence separation derived by them are valid formp-mh model space functions. In particular it has been shown that there are two different cluster ansatz for which the aspect (iii) above is valid. For a valence-universal wave operator ω admitting of a corevalence separation, it has been proved that the CC equations are linked as a consequence of the multicommutator nature of the expressions. There is a choice between two alternative schemes: one in whichS operators connecting all thekp-kh determinants withk m are retained, and another in which transitions fork<m are ignored. For a normal ordered cluster ansatz for ω, one has a linked expression if the subsystem embedding condition (sec) is adhered to. Here coupling of all thekp-kh determinants to the model space has to be retained if we wish to decouple the various valence sectors of the Hilbert space.