Unified analytical treatment of overlap, two-center nuclear attraction, and Coulomb integrals of B functions via the Fourier-transform method.

Abstract

In this paper a unified analytical treatment of overlap, two-center nuclear attraction, and Coulomb integrals of B functions [E. Filter and E. O. Steinborn, Phys. Rev. A 18, 1 (1978)] via the Fourier-transform method is presented. B functions, which are a special class of exponentially decreasing functions (for large arguments), have a relatively complicated analytical structure. However, the Fourier transform of a B function is of exceptional simplicity. Consequently, it is relatively easy to express the Fourier integral representations of the two-center integrals mentioned above as finite sums or infinite series of Fourier integral representations for B functions and irregular solid harmonics which may be considered to be limiting cases of special B functions. The only advanced mathematical concepts which we need are the connection between B functions, classically divergent Fourier integrals, and derivatives of the three-dimensional \ensuremath{\delta} functions. The other mathematical tools---partial-fraction decompositions and Taylor expansions of rational functions---are fairly elementary. Our approach leads not only to a considerable simplification of the derivation of the previously known analytical representations for the two-center integrals but also to a large number of hitherto unknown representations.