Simplified Multireference Coupled-Cluster Methods: Hybrid Approaches With Averaged Coupled Pair Theories.

We define an approximation to the internally contracted multireference coupled-cluster method with single and double excitations by a hybrid approach. The rationale is to treat the external pair energy contributions by the coupled-cluster method, which provides accurate results for a large part of the correlation energy while being tractable as the involved pair cluster operators commute. For the internal and semi-internal contributions, for which the coupled-cluster part becomes involved due to non-commuting operators, a linearized approach based on the coupled-electron pair approximation (CEPA) is used. For the latter, the CEPA(0) method, the averaged coupled pair functional (ACPF), the averaged quadratic coupled-cluster (AQCC) method, and the averaged CEPA method are tested. We test the methods concerning size consistency, potential energy curves for C(2), N(2), CN, and O(3) and for the singlet-triplet splitting of ortho-, meta-, and para-benzynes. Our results show that AQCC provides the most accurate results and stable performance. The main drawback of the method is that it shows small violations of size consistency.