Cluster perturbation theory. I. Theoretical foundation for a coupled cluster target state and ground-state energies

We introduce a new class of perturbation models-the cluster perturbation (CP) models-where the major drawbacks of Møller-Plesset perturbation theory and coupled cluster perturbation theory have been eliminated. In CP theory, we consider a target excitation space relative to the Hartree-Fock state and partition the target excitation space into a parent and an auxiliary excitation space. The zeroth-order state is a coupled cluster (CC) state in the parent excitation space, and the target state is either a cluster linear or a CC state in the target excitation space. In CP theory, perturbation series are determined in orders of the CC parent state similarity-transformed fluctuation potential for the energy and for a molecular property, where the zeroth-order term in the series is the energy or a molecular property for the CC parent state and where the series formally converge to the energy or a molecular property for the target state. In CP theory, we use a generalized order concept, where the zeroth-order component of the extended parent-state Jacobian contains a fluctuation potential contribution, and use this new generalized order to treat internal relaxation in the parent excitation space at zeroth order and hence remove it from the perturbation calculation. Even more importantly, using this new generalized order concept, CP series can be determined for molecular properties of ground and excited states and for transition properties between these states, including excitation energies and energies of the excited states. The applicability of CP theory to both the energy and molecular properties and numerical results for the CP energy and molecular property series demonstrate the superiority of CP theory compared to previous perturbation models. Low-order corrections in the CP perturbation series can be expected soon to become state-of-the-art electronic structure models for the determination of energies and molecular properties of target-state quality for single-configuration dominated molecular systems.