A hierarchy of local electron correlation models based on atomic truncations

Abstract

While wavefunction-based treatments of electron correlation have been very successful for the study of small molecules, they cannot be readily applied to large molecules because their computational cost rises too steeply with molecular size. For example, second order Møller-Plesset perturbation theory (MP2), the simplest such method, involves computational costs that asymptotically increase with the 5th power of molecular size. In this article we discuss the development of new local electron correlation models that ameliorate this problem, by truncating the number of substituted determinants that are included in the correlation treatment. Using atom-centered functions to span the occupied and virtual subspaces permits the truncations to be made by an atomic criterion, that satisfies all of the requirements of a well-defined theoretical model chemistry. The double substitutions that arise in MP2 theory generally involve promoting electrons from occupied orbitals on two atoms to unoccupied (virtual) orbitals on two other atoms, or tetra-atomics in molecules. The simplest restriction is to require one occupied and one virtual orbital to be on a common atom, leading to a triatomics in molecules (TRIM) model. A stronger approximation is to model double substitutions by the direct product of two such atomic excitations, which is a diatomics in molecules (DIM) model of electron correlation. The still more drastic approximation of forcing all double substitutions to be centered on single atoms, cannot describe dispersion interactions, and is not considered here. The theory of the DIM and TRIM models is outlined, and methods for obtaining the atom-centered functions spanning the occupied and virtual subspaces are discussed. Some numerical results are provided to compare the performance of the DIM and TRIM models against untruncated MP2 theory. Finally the outlook for the application of these methods to large molecules is discussed.