Orbital-invariant formulation and second-order gradient evaluation in MOller-Plesset perturbation theory

TLDR: In this article, the second and third orders of Moller-Plesset perturbation theory are reformulated in terms of arbitrary (e.g., localized) internal orbitals, and atomic orbitals in the virtual space.

Abstract: Based on the Hylleraas functional form, the second and third orders of Moller-Plesset perturbation theory are reformulated in terms of arbitrary (e.g., localized) internal orbitals, and atomic orbitals in the virtual space. The results are strictly equivalent to the canonical formulation if no further approximations are introduced. The new formalism permits the extension of the local correlation method to Moller-Plesset theory. It also facilitates the treatment of weak pairs at a lower (e.g., second order) level of theory in CI and coupled cluster methods. Based on our formalism, an MP2 gradient algorithm is outlined which does not require the storage of derivative integrals, integrals with three external MO indices, and, using the method of Handy and Schaefer, the repeated solution of the coupled-perturbed SCF equations.