Multi-reference state-universal coupled-cluster approaches to electronically excited states

The multi-reference (MR), general model space (GMS), state-universal (SU), coupled-cluster (CC) method with singles and doubles (GMS-SU-CCSD), as well as its triple-corrected versions GMS-SU-CCSD(T), are employed to assess their ability to describe low-lying excited states of various molecules, with an emphasis on a simultaneous handling of several states of the same symmetry species. A special attention is given to the role of the so-called C-conditions that account for non-vanishing internal cluster amplitudes when relying on an incomplete GMS, as well as to the choice of suitable model spaces and a perturbative account of secondary triples. The ambiguities arising when using large basis sets are also pointed out. To achieve a general assessment of the potential of the GMS-type SU-CC approaches, the vertical excitation energies of several species, including the challenging BN diatomic as well as larger systems, namely formaldehyde, trans -butadiene, formamide, and benzene are considered. These results are compared with those provided by the equation-of-motion EOM-CCSD method and, whenever available, the density functional theory results and experimental data. These comparisons clearly demonstrate the usefulness of GMS-type MR-CC approaches.