Benchmarking the completely renormalised equation-of-motion coupled-cluster approaches for vertical excitation energies

Abstract

The vertical excitation energies for a comprehensive test set of about 150 singlet excited states of 28 medium-sized organic molecules computed using two variants of the completely renormalised (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as δ-CR-EOMCCSD(T), and the analogous two variants of the newer, left-eigenstate δ-CR-EOMCC(2,3) approach are benchmarked against the previously published CASPT2, CC3, and EOMCCSDT-3 results, as well as the suggested theoretical best estimate (TBE) values. The δ-CR-EOMCC approaches are also used to identify and characterise about 50 additional excited states, including several states having substantial two-electron excitation components, which have not been found in the previous work and which can be used in future benchmark studies. It is demonstrated that the non-iterative triples corrections to the EOMCCSD excitation energies defining the relatively inexpensive, single-reference, black-box δ-CR-EOMCC approaches provide significant improvements in the EOMCCSD data, while closely matching the results of the iterative and considerably more expensive CC3 and EOMCCSDT-3 calculations and their CASPT2 and TBE counterparts. It is also shown that the δ-CR-EOMCC methods, especially δ-CR-EOMCC(2,3), are capable of bringing the results of the CC3 and EOMCCSDT-3 calculations to a closer agreement with the CASPT2 and TBE data, demonstrating the utility of the cost-effective δ-CR-EOMCC methods in applications involving molecular electronic spectra. We show that there may exist a relationship between the magnitude of the triples corrections defining δ-CR-EOMCC approaches and the reduced excitation level diagnostic resulting from EOMCCSD.

Keywords:

• equation-of-motion coupled-cluster methods
• completely renormalised approaches
• non-iterative triples corrections
• electronically excited states
• benchmarking quantum chemistry methods

Acknowledgements

We dedicate this paper to Professor Sourav Pal. One of us (P. Piecuch) would like to thank Professors Nayana Vaval, G. Narhari Sastry, and Ajit Thakkar for inviting him to submit an article for the Special Issue of Molecular Physics in honour of Professor Sourav Pal. We thank Mr. J. Emiliano Deustua for useful discussions. This work has been supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy through a Grant No. DE-FG02-01ER15228 awarded to P. Piecuch.

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental data

Supplemental data for this article containing symmetry unique Cartesian coordinates for the ground-state geometries of the 28 molecules comprising the benchmark set of Schreiber et al. [17] resulting from the MP2/6-31G* and CR-CC(2,3),D/TZVP optimisations can be accessed here http://dx.doi.org/10.1080/00268976.2015.1076901.

Additional information

Funding

This work has been supported by the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy [grant number DE-FG02-01ER15228] awarded to P. Piecuch.