Fourth-order Mo/ller–Plessett perturbation theory in the local correlation treatment. I. Method

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Abstract
Fourth‐order Mo/ller–Plesset perturbation theory (MP4) is formulated for localized internal orbitals of closed‐shell systems. Unlike previous localized perturbation theories, our formulation is strictly identical with canonical MP4 theory if no further approximations are made. In the local treatment, large savings can be achieved by two techniques: (1) neglecting or treating at a lower (second order) level pair correlation between distant pairs, and (2) restricting the correlation basis to the atomic orbitals in the spatial vicinity of the correlated pair. These techniques have been used in our previous local correlation treatment for variational CI, coupled electron pair (CEPA), and approximate coupled cluster (ACCD) wave functions. The MP4 method is more economical than these techniques because of the absence of iterative cycles. Implementation with single, double, and quadruple substitutions is discussed.