CONSISTENT PROPAGATOR THEORY-BASED ON THE EXTENDED COUPLED-CLUSTER PARAMETRIZATION OF THE GROUND-STATE

We develop in this paper a consistent superoperator-resolvent-based pr opagator theory using the extended coupled-cluster (CC) parametrizatio n [Phys. Rev. A 36, 2519 (1987); Ann. Phys. 151, 311 (1983)] of the gr ound state. The method exploits the underlying non-Hermitian nature of the transformed Hamiltonian appearing in the extended coupled-cluster method. In this method, we obtain finite expressions in powers of clu ster coefficients for both the transition amplitudes as the residues a nd the elements of the effective matrix contributing to the poles of t he propagator. There is a natural ''resolution of identity'' involving consistent basis constructed by us, which leads to the biorthogonal s ets of ket and bra functions used in the representation of the interme diate states in the inner projection of the propagator. The manifold o f operators generating these states satisfies the ''vacuum-annihilatio n condition'' on the ground state and is thus consistent. There is a n atural decoupling of the forward and backward components of the propag ator even under the uneven truncation of the CC expansion of the groun d state and the operator basis, which should be convenient for practic al applications. We have discussed in detail the realization of the co nsistent representation of the ionized or excited states by taking as illustrative examples the case of one-electron and polarization propag ators and have suggested practical truncation schemes for their implem entation. An order-by-order perturbative analysis has been made to ind icate the relation of our formalism to some of the more recent theorie s. We have also shown that the now established coupled-cluster-based l inear-response theory can be viewed as an approximate version of the c onsistent propagator theory, which furnishes the same poles as the lat ter but nonconsistent residues.