Comparison of the completely renormalized equation-of-motion coupled-cluster and Quantum Monte Carlo results for the low-lying electronic states of methylene

Abstract

The left-eigenstate completely renormalized (CR) equation-of-motion (EOM) coupled-cluster (CC) method with singles, doubles, and non-iterative triples, abbreviated as CR-EOMCC(2,3) [M. Włoch et al., Mol. Phys. 104, 2149 (2006); P. Piecuch et al., Int. J. Quantum Chem. 109, 3268 (2009)], and the companion ground-state CR-CC(2,3) methodology [P. Piecuch and M. Włoch, J. Chem. Phys. 123, 224105 (2005); P. Piecuch et al., Chem. Phys. Lett. 418, 467 (2006)] are used to determine the total electronic and adiabatic excitation energies corresponding to the ground and lowest three excited states of methylene. The emphasis is on comparing the CR-CC(2,3)/CR-EOMCC(2,3) results obtained with the large correlation-consistent basis sets of the aug-cc-pCV xZ (x = T, Q, 5) quality and the corresponding complete basis set (CBS) limits with the recently published variational and diffusion Quantum Monte Carlo (QMC) data [P. Zimmerman et al., J. Chem. Phys. 131, 124103 (2009)]. It is demonstrated that the CBS CR-CC(2,3)/CR-EOMCC(2,3) results are in very good agreement with the best QMC, i.e. diffusion MC (DMC) data, with errors in the total and adiabatic excitation energies of all calculated states on the order of a few millihartree and less than 0.1 eV, respectively, even for the challenging, strongly multi-reference C ¹ A ₁ state for which the basic EOMCC approach with singles and doubles completely fails. The agreement between the CBS CR-CC(2,3)/CR-EOMCC(2,3) and variational MC (VMC) results for the total energies is not as good as in the DMC case, but the excitation energies resulting from the CBS CR-CC(2,3)/CR-EOMCC(2,3) and VMC calculations agree very well.

Keywords:

• equation-of-motion coupled-cluster method
• completely renormalized coupled-cluster approaches
• Quantum Monte Carlo
• methylene
• excited states

Acknowledgements

We dedicate this paper to Professor Henry F. Schaefer III. One of us (P.P.) would like to thank Professors Rodney J. Bartlett, T. Daniel Crawford, Martin Head-Gordon, and C. David Sherrill for inviting him to speak at the Molecular Quantum Mechanics 2010 (MQM 2010) conference, and for encouraging us to submit an article for the MQM 2010 Special Issue of Molecular Physics in honour of Professor Henry F. Schaefer III. We would also like to thank Professor Cyrus J. Umrigar for useful discussions, interest in this work, and for providing us with the QMC results reported in 94 prior to their publication. 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 No. DEFG02-01ER15228, P.P.) and the Dissertation Completion Fellowship provided by Michigan State University (J.R.G.). The calculations were performed on the computer systems provided by the High Performance Computing Center at Michigan State University.