The linked-cluster theorem in the open-shell coupled-cluster theory for incomplete model spaces

Abstract

The linked-cluster theorem (LCT) holds good in open-shell coupled-cluster theory for incomplete model spaces provided the intermediate normalization condition (IN) for the eigenfunctions is abandoned. The crucial requirement for proving the LCT is the valence universality of the wave operator Ω. Thus Ω contains not only m-valence operators S¯^(m) for an m-valence problem but also all the lower-valence S¯ S^(k) operators to correlate k < m valence problems. LCT is proved using a particular scheme for choosing the S¯ S^(k) operators for which IN does not hold good.