New classes of non-iterative energy corrections to multi-reference coupled-cluster energies

Two new classes of non-iterative corrections to the ground- and excited-state energies obtained in the state-universal multi-reference coupled-cluster (SUMRCC) calculations have been developed using the multi-reference extension of the method of moments of coupled-cluster equations (MMCC) [Kowalski, K., and Piecuch, P., 2001, J. molec. Struct. (THEOCHEM), 547, 191]. In the first class of the configuration interaction (CI) corrected multi-reference MMCC (MRMMCC) approximations, the non-iterative corrections due to triply or triply and quadruply excited clusters are constructed with the help of multi-reference CI (MRCI) calculations employing the same active space as used in the SUMRCC calculations. In the second class of the completely renormalized (CR) SUMRCC methods, which can be viewed as the multi-reference extensions of the single-reference CR-CCSD(T) theory [Kowalski, K., and Piecuch, P., 2000, J. chem. Phys., 113, 18], the non-iterative corrections due to triply excited clusters are constructed with the help of the multi-reference many-body perturbation theory. In both cases, the non-iterative corrections due to higher-order clusters are added to the energies obtained with the SUMRCC method with singles and doubles. It is demonstrated that the newly developed corrections, including the CR-SUMRCC methods, offer considerable improvements in the SUMRCCSD results, reducing, in particular, the large errors in the SUMRCCSD results due to intruders.