Abstract
The general two-center Dalitz integral of the form:
is calculated analytically and numerically for an arbitrary set {i,f} of indices associated with the Fourier transforms\(\tilde \varphi _i (q + \beta )\) and\(\tilde \varphi _f (q - \alpha )\) of exponential-type orbitals. The analytical results for hydrogenic, Sturmian and other related functions, as well as for Slater-type orbitals with an arbitrary quantization axis, are presented as concise, closed expressions. These contain only a few finite summations of easily available quantities, such as Gaunt coefficients, Clausen hypergeometric polynomials of unit argument, spherical harmonics, etc. .... The present closed formulae are also valid for all scaling parameters of the orbitals involved. Furthermore, an additional angular momentum decomposition of the final result can readily be accomplished.
Finally, an algorithm based upon the present theory has been devised and proven to be both extremely efficient and numerically stable. High precision computation of the general two-center Dalitz integral is thus possible to any prescribed degree of accuracy, hence obviating cumbersome triple numerical quadratures with sharply peaking and highly oscillating functions.
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