Consistent propagator theory based on the extended coupled-cluster parametrization of the ground state

We develop in this paper a consistent superoperator-resolvent-based propagator theory using the extended coupled-cluster (CC) parametrization [Phys. Rev. A 36, 2519 (1987); Ann. Phys. 151, 311 (1983)] of the ground 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 cluster coefficients for both the transition amplitudes as the residues and the elements of the effective matrix contributing to the poles of the propagator. There is a natural "resolution of identity" involving consistent basis constructed by us, which leads to the biorthogonal sets of ket and bra functions used in the representation of the intermediate states in the inner projection of the propagator. The manifold of operators generating these states satisfies the "vacuum-annihilation condition" on the ground state and is thus consistent. There is a natural decoupling of the forward and backward components of the propagator even under the uneven truncation of the CC expansion of the ground state and the operator basis, which should be convenient for practical applications. We have discussed in detail the realization of the consistent representation of the ionized or excited states by taking as illustrative examples the case of one-electron and polarization propagators and have suggested practical truncation schemes for their implementation. An order-by-order perturbative analysis has been made to indicate the relation of our formalism to some of the more recent theories. We have also shown that the now established coupled-cluster-based linear-response theory can be viewed as an approximate version of the consistent propagator theory, which furnishes the same poles as the latter but nonconsistent residues