A canonical transformation theory from extended normal ordering

TL;DR

This paper introduces a new formulation of the Canonical Transformation theory using extended normal ordering, achieving high accuracy and significantly reduced computational cost for multireference problems.

Contribution

It presents a novel formulation of the Canonical Transformation theory based on extended normal ordering, improving accuracy and efficiency over previous methods.

Findings

Competitive accuracy with advanced multireference methods

Two to three orders of magnitude faster computational timings

Significant improvements over previous formulations

Abstract

The Canonical Transformation theory of Yanai and Chan [J. Chem. Phys. 124, 194106 (2006)] provides a rigorously size-extensive description of dynamical correlation in multireference problems. Here we describe a new formulation of the theory based on the extended normal ordering procedure of Mukherjee and Kutzelnigg [J. Chem. Phys. 107, 432 (1997)]. On studies of the water, nitrogen, and iron-oxide potential energy curves, the Linearised Canonical Transformation Singles and Doubles theory is competitive in accuracy with some of the best multireference methods, such as the Multireference Averaged Coupled Pair Functional, while computational timings (in the case of the iron-oxide molecule) are two-three orders of magnitude faster and comparable to those of Complete Active Space Second-Order Perturbation Theory. The results presented here are greatly improved both in accuracy and in cost over our earlier study as the result of a new numerical algorithm for solving the amplitude equations.