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On the use of the Obara–Saika recurrence relations for the calculation of structure factors in quantum crystallography
Author(s) -
Gei Alessandro
Publication year - 2020
Publication title -
acta crystallographica section a
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.742
H-Index - 83
ISSN - 2053-2733
DOI - 10.1107/s205327332000042x
Subject(s) - fourier transform , computation , basis (linear algebra) , quantum , quantum chemistry , cartesian coordinate system , extension (predicate logic) , quantum chemical , quantum mechanics , physics , pure mathematics , statistical physics , mathematics , molecule , computer science , algorithm , geometry , supramolecular chemistry , programming language
Modern methods of quantum crystallography are techniques firmly rooted in quantum chemistry and, as in many quantum chemical strategies, electron densities are expressed as two‐centre expansions that involve basis functions centred on atomic nuclei. Therefore, the computation of the necessary structure factors requires the evaluation of Fourier transform integrals of basis function products. Since these functions are usually Cartesian Gaussians, in this communication it is shown that the Fourier integrals can be efficiently calculated by exploiting an extension of the Obara–Saika recurrence formulas, which are successfully used by quantum chemists in the computation of molecular integrals. Implementation and future perspectives of the technique are also discussed.