The fourier transform of a two-center product of exponential-type functions and its efficient evaluation

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Abstract

We analyze the analytical and numerical properties of the hitherto known formulas of the Fourier transform of a two-center product of exponentially declining functions (exponential-type functions, ETFs) which are derived with the help of the Fourier convolution theorem and Feynman's identity. In detail, we consider B functions which are a special class of ETFs having advantageous properties under Fourier transformation. Other ETFs (orbitals) can be expressed in terms of B functions by linear combinations. In our derivations we use the properties of the differential operator Ylm(▽) specifying a solid harmonic whose argument is the nabla operator ∂/∂r instead of the vector r in order to generate multicenter integrals over nonscalar functions from integrals over scalar functions. Applying the generating differential operator Ylm(Λ) we obtain a recently derived new formula for the Fourier transform of a two-center product of B functions in a much more straightforward manner. Furthermore, we present an efficient procedure to compute this new formula which is valid for arbitrary quantum numbers and exponential parameters and report various numerical test values. © 1985.

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Grotendorst, J., & Otto Steinborn, E. (1985). The fourier transform of a two-center product of exponential-type functions and its efficient evaluation. Journal of Computational Physics, 61(2), 195–217. https://doi.org/10.1016/0021-9991(85)90082-8

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