A state-specific approach to multireference coupled electron-pair approximation like methods: development and applications

Abstract

The traditional multireference (MR) coupled-cluster (CC) methods based on the effective Hamiltonian are often beset by the problem of intruder states, and are not suitable for studying potential energy surface (PES) involving real or avoided curve crossing. State-specific MR-based approaches obviate this limitation. The state-specific MRCC (SS-MRCC) method developed some years ago [Mahapatra et al., J. Chem. Phys. 110, 6171 (1999)] can handle quasidegeneracy of varying degrees over a wide range of PES, including regions of real or avoided curve-crossing. Motivated by its success, we have suggested and explored in this paper a suite of physically motivated coupled electron-pair approximations (SS-MRCEPA) like methods, which are designed to capture the essential strength of the parent SS-MRCC method without significant sacrificing its accuracy. These SS-MRCEPA theories, like their CC counterparts, are based on complete active space, treat all the reference functions on the same footing and provide a description of potentially uniform precision of PES of states with varying MR character. The combining coefficients of the reference functions are self-consistently determined along with the cluster amplitudes themselves. The newly developed SS-MRCEPA methods are size-extensive, and are also size-consistent with localized orbitals. Among the various versions, there are two which are invariant with respect to the restricted rotations among doubly occupied and active orbitals separately. Similarity of performance of this latter and the noninvariant versions at the crossing points of the degenerate orbitals imply that the all the methods presented are rather robust with respect to the rotations among degenerate orbitals. Illustrative numerical applications are presented for PES of the ground state of a number of difficult test cases such as the model H4, H₈ problems, the insertion of Be into H₂, and Li₂, where intruders exist and for a state of a molecule such as CH₂, with pronounced MR character. Results obtained with SS-MRCEPA methods are found to be comparable in accuracy to the parent SS-MRCC and FCI/large scale CI results throughout the PES, which indicates the efficacy of our SS-MRCEPA methods over a wide range of geometries, despite their neglect of a host of complicated nonlinear terms, even when the traditional MR-based methods based on effective Hamiltonians fail due to intruders.