On the connectivity criteria in the open-shell coupled-cluster theory for general model spaces

In this paper we study the following aspects of the open-shell coupled-cluster (CC) theories: (a) we examine the current theoretical status regarding the existence or non-existence of a linked-cluster theorem, ensuring the connectedness of the cluster amplitudes and the effective Hamiltonian; (b) we lay down the necessary and sufficient conditions for connectivity for a general (incomplete) model space, involving valence particles as well as valence holes; and (c) critically re-assess the earlier theoretical works from a comprehensive and unifying view point.