A review of canonical transformation theory

Abstract

Canonical transformation (CT) theory targets the description of dynamic correlation in multireference quantum chemistry problems. When combined with a static correlation quantum chemistry method, it enables the quantitative description of chemical processes involving electronic structure not described by a single electronic configuration. We argue that many multireference dynamic correlation methods display unsatisfactory characteristics, including lack of size-consistency, a low-order treatment of correlation, and a poor computational scaling. By contrast, CT theory is based on an exponential ansatz that is rigorously size-consistent, reduces in a single-reference limit to a coupled cluster theory, and has an n ⁶ computational scaling with system and active space size. The efficient formulation of CT theory has allowed it to be applied to difficult systems in conjunction with active spaces with more than 30 orbitals, beyond the reach of traditional methods, with an accuracy that far exceeds multireference perturbation theories. Here we review the basic motivation, formulation, and implementation of CT theory, as well as survey some of our recent applications and possible future directions.

Keywords:

• correlation methods
• canonical transformation theory
• density matrix renormalization group
• coupled cluster theory
• configuration interaction
• perturbation theory

Acknowledgements

This work was supported by the National Science Foundation CAREER program CHE-0645380, the David and Lucile Packard Foundation, the Alfred P. Sloan Foundation, and the Camille and Henry Dreyfus Foundation. E.N. would like to acknowledge the support of the National Science Foundation Graduate Research Fellowship Program.