Applicability of Almost Strongly Orthogonal Geminals in Many-Electron Wavefunctions

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Abstract
Assuming that truncated strongly orthogonal geminals for a system are already known, the possibility of using rij-dependent correction functions in the geminals is discussed with an emphasis on the violation of the strong orthogonality conditions. It is shown that for given truncated geminals there always exists at least one optimally decomposed complete set of one-electron functions, which makes it possible to pick out the configurations giving rise to strong orthogonality condition violating terms in the energy expression. The latter can be neglected, as compared with others which are of second order in the correction functions, when the system consists of spatially separated pairs in the sense that the one-electron functions contributing appreciably to one pair do not have significant differential overlap with the starting basis functions of other pairs. In this case interorbital effects are also small. For systems consisting of weakly localizable pairs, when the strong orthogonality condition violating terms are all omitted, the energy expression is correct only up to first order in the correction functions. It is shown that the same difficulties arise in the many-electron theory of Sinanoğlu.

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