General-model-space state-universal coupled-cluster theory: Connectivity conditions and explicit equations

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Abstract
We present a new version of the state-universal (SU), multireference, coupled-cluster (CC) theory that is capable of handling completely general, incomplete model spaces. This is achieved by exploiting the concept of “locality” for the active molecular spin orbitals and by introducing the constraining conditions (C conditions) on cluster amplitudes that are associated with the internal excitations transforming one reference configuration into another one. These C conditions make it possible to represent the exact (i.e., full configuration interaction) wave function via the SU CC cluster ansatz based on an arbitrary model space. The C conditions are then taken into account together with the standard SU CC equations for the external amplitudes, thus enabling us to reach the exact result in the limit, while preserving the connectivity property and thus the size extensivity. We also present compact expressions for the matrix elements of the effective Hamiltonian as well as the explicit expressions for the most important coupling coefficients that are required at the single and double excitation level. All other expressions are the same as in the single reference CC formalism.