Block correlated coupled cluster method with the complete active-space self-consistent-field reference function: Applications for low-lying electronic excited states

Block correlated coupled cluster (BCCC) method with the complete active-space (CAS) self-consistent-field reference function (CAS-BCCC) has been applied to investigate the vertical excitation energies of low-lying valence excited states in a number of medium-sized organic molecules, including unsaturated aliphatic hydrocarbons (ethene, E-butadiene, cyclopropene, and cyclopentadiene), aromatic heterocycles (furan and pyrrole), and carbonyl compounds (formaldehyde, acetone, and formamide). An approximate CAS-BCCC with the cluster operator truncated up to the four-block correlation level, CAS-BCCC4, is employed in the calculations. The results are compared with those from the multireference configuration interaction with singles and doubles (MR-CISD and its corrected version, MR-CISD+Q), the complete active space with second-order perturbation theory (CASPT2), and CC3. Our results show that the overall performance of CAS-BCCC4 is competitive with that of the multistate CASPT2 (slightly inferior to MR-CISD+Q), better than that of the single-state CASPT2 and MR-CISD approaches. For triplet excited states, various methods tend to give relatively consistent predictions. However, for singlet excited states, various methods lead to quite different excitation energies in some cases.