Combining active-space coupled-cluster approaches with moment energy corrections via the CC(P;Q) methodology: connected quadruple excitations

ABSTRACT

We have recently proposed the CC(P;Q) methodology that provides a systematic approach to correcting the energies obtained in active-space coupled-cluster (CC) calculations for the remaining, mostly dynamical, correlations. We report the development of the CC(t,q;3) and CC(t,q;3,4) methods, which use the CC(P;Q) formalism to correct the energies obtained with the CC approach with singles, doubles and active-space triples and quadruples, termed CCSDtq, for the remaining triples [CC(t,q;3)] or the remaining triples and quadruples [CC(t,q;3,4)] missing in CCSDtq. By examining the double dissociation of water, the Be + H₂ → HBeH insertion, and the singlet–triplet gap in the (HFH)⁻ system, we demonstrate that the CC(t,q;3) and CC(t,q;3,4) methods, particularly the latter one, offer significant improvements in the CCSDtq results, reproducing the total and relative energies obtained with the CC approach with singles, doubles, triples and quadruples (CCSDTQ) to within fractions of a millihartree, at the tiny fraction of the computational effort involved in the CCSDTQ calculations, even when electronic quasi-degeneracies become substantial. We also show that the previously examined CC(t;3) approach, which corrects the active-space CCSDt energies for the triples missing in CCSDt, accurately reproduces the CCSDT energetics.

KEYWORDS:

• Coupled-cluster theory
• biorthogonal moment expansions
• completely renormalised approaches
• active-space approaches
• benchmarking quantum chemistry methods

Acknowledgements

We dedicate this paper to Professor Debashis Mukherjee. One of us (Piotr Piecuch) would like to thank Professors Sourav Pal, Andreas Savin and Trygve Helgaker for inviting him to submit an article for the Special Issue of Molecular Physics in honor of Professor Debashis Mukhejree. 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 Piotr Piecuch.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

U.S. Department of Energy [grant number DE-FG02-01ER15228].