On the use of the Obara–Saika recurrence relations for the calculation of structure factors in quantum crystallography. Issue 2 (11th February 2020)

• Record Type: Journal Article
• Authors: Genoni, Alessandro
• Is Part Of: Acta crystallographica. Volume 76:Issue 2(2020:Mar.)
• Page Start: 172
• Page End: 179
• Publication Date: 2020-02-11
• Subjects: quantum crystallography -- structure factors -- Fourier transform integrals -- Obara–Saika recurrence relations; Crystallography -- Periodicals; Condensed matter -- Periodicals; 548
• DOI: 10.1107/S205327332000042X
• Languages: English
• ISSNs: 2053-2733

Abstract

Abstract : In modern methods of quantum crystallography, electron densities are usually expressed in the form of two‐centre expansions involving Cartesian Gaussian‐type functions centred on atomic nuclei. Therefore, for the efficient evaluation of structure factors, it is possible to exploit the Obara–Saika method used in quantum chemistry for the evaluation of molecular integrals. Abstract : 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.