Method of Moments for the Continuous Transition Between the Brillouin-Wigner-Type and Rayleigh-Schrodinger-Type Multireference Coupled Cluster Theories

We apply the method of moments to the multireference (MR) coupled cluster (CC) formalism representing the continuous transition between the Brillouin-Wigner-type and Rayleigh-Schr\"{o}dinger-type theories based on the Jeziorski-Monkhorst wave function ansatz and derive the formula for the noniterative energy corrections to the corresponding MRCC energies that recover the exact, full configuration interaction energies in the general model space case, including complete and incomplete model spaces. We also extend the relationship between the generalized moments of the state-universal (SU) MRCC equations within the Jeziorski-Monkhorst and Kucharski-Bartlett formulations of the SUMRCC theory to the general model space case. Finally, we argue that in the complete model space case, the relationship between moments of the SUMRCC equations corresponding to the Jeziorski-Monkhorst and Kucharski-Bartlett formulations of the SUMRCC theory, derived in this work, implies an equivalence of these two formulations of the SUMRCC approach, provided that the disconnected linked terms are included in the Kucharski-Bartlett formulation, and verify this statement numerically.