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Recursive calculation of closed‐form scattering factors for atomic orbitals
Author(s) -
Deutsch M.
Publication year - 1993
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s0021889893004091
Subject(s) - linear combination of atomic orbitals , legendre function , atomic orbital , bessel function , fourier transform , gaussian , sto ng basis sets , slater type orbital , hypergeometric function , cubic harmonic , hypergeometric distribution , physics , quantum mechanics , legendre polynomials , mathematical analysis , mathematics , pure mathematics , electron
Recurrence relations are derived for calculating closed‐form expressions for the Fourier–Bessel transform of electronic charge densities represented by Gaussian‐ and Slater‐type atomic orbitals. The derivation is based on hypergeometric and Legendre function representations of the transform and the use of their recurrence properties. The scattering‐factor calculations are discussed in detail. A table of closed‐form expressions for Gaussian‐type orbitals, not hitherto available, has been calculated using the new method and is available on request.