ALGEBRAIC PROPAGATOR APPROACHES AND INTERMEDIATE-STATE REPRESENTATIONS .1. THE BIORTHOGONAL AND UNITARY COUPLED-CLUSTER METHODS

As a general common concept, underlying diverse methods used to comput e generalized electronic excitations in atoms and molecules, intermedi ate-state representations (ISR's), are considered and analyzed. Essent ially, an ISR results by representing the excitation energy operator i n terms of so-called correlated excited states (CES's) or states deriv ed thereof. Three different ISR schemes are compared, namely the biort hogonal coupled-cluster (BCC) representation used in both the coupled- cluster linear response and equation-of-motion coupled-cluster methods , a unitary coupled-cluster (UCC) representation, and the excitation c lass orthogonalized (EGO) representation resulting from a Gram-Schmidt orthogonalization procedure for the CES. Moreover, the relationship b etween the BCC scheme and the symmetry-adapted-cluster-configuration-i nteraction method is discussed. The relevance of the ISR schemes, as o pposed to the much simpler configuration-interaction (CI) expansions, arises from two basic properties referred to as separability and compa ctness. The former property is a sufficient condition for size-consist ent results, while the latter allows one to use smaller explicit confi guration spaces than in comparable CI treatments. We show that the ECO and UCC representations are both separable and compact, whereas a som ewhat restricted compactness property applies in the BCC case.