Similarity transformed equation of motion coupled cluster theory revisited: a benchmark study of valence excited states

Abstract

The similarity transformed equation of motion coupled cluster (STEOM-CC) method is benchmarked against CC3 and EOM-CCSDT-3 for a large test set of valence excited states of organic molecules studied by Schreiber et al. [M. Schreiber, M.R. Silva-Junior, S.P. Sauer, and W. Thiel, J. Chem. Phys. 128, 134110 (2008)]. STEOM-CC is found to behave quite satisfactorily and provides significant improvement over EOM-CCSD, CASPT2 and NEVPT2 for singlet excited states, lowering standard deviations of these methods by almost a factor of 2. Triplet excited states are found to be described less accurately, however. Besides the parent version of STEOM-CC, additional variations are considered. STEOM-D includes a perturbative correction from doubly excited determinants. The novel STEOM-H (ω) approach presents a sophisticated technique to render the STEOM-CC transformed Hamiltonian hermitian. In STEOM-PT, the expensive CCSD step is replaced by many-body second-order perturbation theory (MBPT(2)), while extended STEOM (EXT-STEOM) provides access to doubly excited states. To study orbital invariance in STEOM, we investigate orbital rotation in the STEOM-ORB approach. Comparison of theses variations of STEOM for the large test set provides a comprehensive statistical basis to gauge the usefulness of these approaches.

Keywords:

• electronically excited states
• coupled cluster
• equation of motion coupled cluster

Acknowledgements

The original work on STEOM-CC was done in the group of Rodney J. Bartlett, and the library of ACES II subroutines developed then is still in active use today (see, e.g. Refs. [71,72]). M. Nooijen is grateful to Rodney J. Bartlett for providing such a stimulating environment when he was a postdoctoral associate in his group (1993–1997). It is a pleasure to contribute this paper in this festschrift on the occasion of Rodney's 70th birthday and to revisit methodologies conceived in those days of fruitful collaboration. This work was financially supported by a discovery grant from the Natural Sciences and Engineering Research Council of Canada (NSERC).