Localization in exchange perturbation theory

A new formalism is developed for exchange perturbation theory by applying a localization criterion to remove much of the arbitrariness associated with the definition of the primitive wavefunction. In contrast to Adams’ method, which is based on a certain energy-related localization, our prescription is based on a direct spatial localization of the primitive function by maximizing its overlap with a given reference function. If our primitive function is constrained only by requiring that one of its symmetry projections yield an exact eigenfunction, then the wavefunction and energy coincide through first order with that of the Eisenschitz–London (EL), and Hirschfelder–van der Avoird (HAV) methods, and through the second order with the Murrell–Shaw–Musher–Amos (MSMA) method, while differing in the third and higher orders. If, instead, the primitive function is constrained by requiring that all of its symmetry projections yield exact eigenfunctions, then it coincides in first order with that of the Distinguishable Electron Method (DEM) developed by Kirtman and co-workers. Our analysis then provides a new justification of the first order terms in the EL–HAV, MSMA, and the DEM expansions, and of the second order terms in the MSMA expansion, and also provides soundly based extensions to higher orders.