New implementation of the configuration-based multi-reference second order perturbation theory.

We present an improved version of the configuration-based multi-reference second-order perturbation approach (CB-MRPT2) according to the formulation of Lindgren on perturbation theory of a degenerate model space. This version involves a reclassification of the perturbation functions and new algorithms to calculate matrix elements in the perturber energy expressions utilizing the graphical unitary group approach and the hole-particle symmetry. The diagonalize-then-perturb (DP), including Rayleigh-Schrödinger and Brillouin-Wigner, and diagonalize-then-perturb-then-diagonalize (DPD) modes have been implemented. The new CB-MRPT2 method is applied to several typical and interesting systems: (1) the vertical excitation energies for several states of CO and N(2), (2) energy comparison and timing of the ground state of C(4)H(6), (3) the quasi-degeneracy of states in LiF, (4) the intruder state problems of AgH, and (5) the relative energies of di-copper-oxygen-ammonia complex isomers. The results indicate that the computational accuracy and efficiency of the presented methods are competitive and intruder-free. It should be emphasized that the DPD method rectifies naturally the shortcomings of LiF potential energy curves constructed by the original second order complete active space perturbation theory (CASPT2), without having to recourse to the so-called state mixture. Unlike CASPT2, the new methods give the same energy ordering for the two di-copper-oxygen-ammonia isomers as the previous multi-reference configuration interaction with single and double excitations methods. The new CB-MRPT2 method is shown to be a useful tool to study small to medium-sized systems.