The Fourier transforms of some exponential-type basis functions and their relevance to multicenter problems

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Abstract
We analyze the properties of Slater-type functions (STFs) and B functions with respect to the Fourier transformation which is one of the most important methods for the evaluation of multicenter integrals. Although B functions have a much more complicated structure than STFs, their Fourier transform is probably the simplest of all expontential-type basis functions. Accordingly, in multicenter integrals, B functions seem to have much more attractive properties than STFs. We demonstrate this by analyzing shifting operators which make it possible to increase quantum numbers of the orbitals. Again we find that the shifting operators of B functions can be applied much more easily and yield much more compact results than the corresponding operators for STFs. We also show that the extremely compact convolution and Coulomb integrals of B functions are direct consequences of the simple Fourier transform of B functions.