Insights into the orbital invariance problem in state-specific multireference coupled cluster theory

In this communication we report the results of our studies on the orbital invariance properties of the state-specific multireference coupled cluster approach suggested by Mukherjee and co-workers (Mk-MRCC). In particular, we have gathered numerical evidence to show that even when the linear excitation manifold is modified in order to span the same space for each reference, the resulting method is not orbital invariant. In order to test this conjecture we have proposed a new truncation scheme (Mk-MRCCSDtq) which, in addition to full single and double excitations, contains partial triple and quadruple excitations. For a reference space generated by all possible combinations of two electrons in two orbitals, the linear excitation manifold of Mk-MRCCSDtq spans the same set for each reference determinant. Mk-MRCCSDtq is found to lack energy invariance for rotations among active molecular orbitals but it is less sensitive to orbital rotations than the conventional scheme which includes only singles and doubles (Mk-MRCCSD). Nevertheless, Mk-MRCCSDtq is a very accurate method, superior with respect to multireference configuration interaction approaches, and competitive with the active-space coupled cluster method and the MRexpT ansatz. (C) 2010 American Institute of Physics. [doi:10.1063/1.3456546]