Multireference general-model-space state-universal and state-specific coupled-cluster approaches to excited states

The concept of C-conditions, originally introduced in the framework of the multireference (MR), general-model-space (GMS), state-universal (SU), coupled-cluster (CC) approach with singles and doubles (GMS-SU-CCSD) to account for the internal amplitudes that vanish in the case of a complete model space, is applied to a state-selective or state-specific Mukherjee MR-CC method (MkCCSD). In contrast to the existing applications, the emphasis is on the description of excited states, particularly those belonging to the same symmetry species. The applicability of the C-conditions in all MR-SU-CC approaches is emphasized. Convergence problems encountered in the MkCCSD method when handling higher-lying states are pointed out. The performance of the GMS-SU-CCSD and MkCCSD methods is illustrated by considering low-lying vertical excitation energies of the ethylene molecule and para -benzyne diradical. A comparison with the equation-of-motion CCSD results, as well as with the available experimental data and recent multireference configuration interaction theoretical results, is also provided.