EXACT VERSUS TRUNCATED SPECTRALLY RESOLVED EXCHANGE IN ABINITIO CALCULATIONS

The truncated spectral resolution of the exact exchange operator for closed-shells systems, first proposed by Andzelm et al. [J. Chem. Phys. 83, 4565 (1985) ], and currently used in atomic, molecular, and solid-state ab initio calculations is revisited. We show how stating the exchange matrix elements in terms of projected functions over the subspace subtended by the exact exchange operator provides a means to extract valuable information about the quality of the approximation. Special interest is paid on two-center exchange interactions with truncated monocentric spectral resolution (TMSR) of the operator. We have undertaken numerical studies of the exact and TMSR exchange for the Li+-Li+, Li+-Cl-, Cl--Li+, Cl--Cl-, and He-He closed-shell pairs with an special attention to the fictitious asymmetry introduced by the approximation. Our main conclusions are: (a) the TMSR approximation for two-center exchange interactions deviates monotonically from the exact exchange with increasing internuclear distance; (b) the TMSR matrix elements are more accurate as more diffuse the primitive functions are; (c) for a particular pair of dislike ions, the approximation works better when the expansion center contains the most contracted primitive functions.