The integral formulae for the variational solution of the molecular many-electron wave equation in terms of Gaussian functions with direct electronic correlation

Abstract
Some years ago the author proved that explicit formulae could be obtained for all the many-dimensional integrals occurring in variational solutions of Schrödinger’s many-electron equation for molecules if the expansion functions are constructed from factors of polynomials and radial Gaussian functions about any centres. These have been applied both directly and indirectly in calculations on molecular structure. An extension to this analysis is now reported and it is shown that if any factors of the form exp (–crij) are included in the expansion functions there are explicit formulas for all the necessary many-dimensional integrals. This will make possible both direct and indirect calculations with a more powerful class of expansion functions which appear as if they may give faster convergence for the hitherto very troublesome electronic correlation aspects of many-dimensional wave functions.

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