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 linearized 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 to three orders of magnitude faster and comparable to those of the 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
