Method of moments for the continuous transition between the Brillouin–Wigner-type and Rayleigh–Schrödinger-type multireference coupled cluster theories

Abstract

We apply the method of moments to the multireference (MR) coupled cluster (CC) formalism representing the continuous transition between the Brillouin–Wigner-type and Rayleigh–Schrödinger-type theories based on the Jeziorski–Monkhorst wave function ansatz and derive the formula for the noniterative energy corrections to the corresponding MRCC energies that recover the exact, full configuration interaction energies in the general model space case, including complete and incomplete model spaces. We also extend the relationship between the generalised moments of the state-universal (SU) MRCC equations within the Jeziorski–Monkhorst and Kucharski–Bartlett formulations of the SUMRCC theory to the general model space case. Finally, we argue that in the complete model space case, the relationship between moments of the SUMRCC equations corresponding to the Jeziorski–Monkhorst and Kucharski–Bartlett formulations of the SUMRCC theory, derived in this work, implies an equivalence of these two formulations of the SUMRCC approach, provided that the disconnected linked terms are included in the Kucharski–Bartlett formulation, and verify this statement numerically.

Keywords:

• multireference coupled cluster theory
• method of moments of coupled cluster equations
• state-universal multireference coupled cluster approach
• Brillouin–Wigner multireference coupled cluster approach
• generalised Bloch equation
• effective Hamiltonian
• size extensivity
• size consistency
• C-conditions
• complete and incomplete model spaces

Acknowledgements

We dedicate this paper to Professor Henry F. Schaefer III in celebration of his 65th birthday and thank Professors T. Daniel Crawford and C. David Sherrill for inviting us to write a contribution for a special issue of Molecular Physics in honor of Professor Henry F. Schaefer III. We would like to thank Professor Debashis Mukherjee for enlightening discussions and Professor Rodney J. Bartlett for providing us with the source code of ACES II. This work has been supported by the Grant Agency of the Czech Republic (Grant No. 203/07/0070; JP), the Grant Agency of the Academy of Sciences of the Czech Republic (Grant No. 1ET400400413; JP), and the Chemical Sciences, Geosciences and Biosciences Division, Office of Basic Energy Sciences, Office of Science, US Department of Energy (Grant No. DE-FG02-01ER15228; PP). We acknowledge also the institutional support by the Academy of Sciences of the Czech Republic (Project No. K4040110) and Michigan State University, where part of the present study has been carried out.

Notes

†We dedicate this paper to Professor Henry F. Schaefer III on the occasion of his 65th birthday.

Additional information

Notes on contributors

Piotr Piecuch†

†We dedicate this paper to Professor Henry F. Schaefer III on the occasion of his 65th birthday.