Midgley, Laura; Bourhis, Luc J.; Dolomanov, Oleg V.; Grabowsky, Simon; Kleemiss, Florian; Puschmann, Horst; Peyerimhoff, Norbert
(2021).
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Vanishing of the atomic form factor derivatives in non-spherical structural refinement – a key approximation scrutinized in the case of Hirshfeld atom refinement.
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Acta Crystallographica Section A Foundations and Advances, 77(6), pp. 519-533.
International Union of Crystallography
10.1107/S2053273321009086

Text
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When calculating derivatives of structure factors, there is one particular term (the derivatives of the atomic form factors) that will always be zero in the case of tabulated spherical atomic form factors. What happens if the form factors are non-spherical? The assumption that this particular term is very close to zero is generally made in non-spherical refinements (for example, implementations of Hirshfeld atom refinement or transferable aspherical atom models), unless the

form factors are refinable parameters (for example multipole modelling). To evaluate this general approximation for one specific method, a numerical differentiation was implemented within the NoSpherA2 framework to calculate the derivatives of the structure factors in a Hirshfeld atom refinement directly as accurately as possible, thus bypassing the approximation altogether. Comparing wR2 factors and atomic parameters, along with their uncertainties from the approximate and numerically differentiating refinements, it turns out that the impact of this approximation on the final crystallographic model is indeed negligible.

## Item Type: |
Journal Article (Original Article) |
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## Division/Institute: |
08 Faculty of Science > Department of Chemistry, Biochemistry and Pharmaceutical Sciences (DCBP) |

## UniBE Contributor: |
Grabowsky, Simon, Kleemiss, Florian |

## Subjects: |
500 Science > 570 Life sciences; biology 500 Science > 540 Chemistry |

## ISSN: |
2053-2733 |

## Publisher: |
International Union of Crystallography |

## Language: |
English |

## Submitter: |
Simon Grabowsky |

## Date Deposited: |
01 Feb 2022 15:05 |

## Last Modified: |
05 Dec 2022 16:03 |

## Publisher DOI: |
10.1107/S2053273321009086 |

## PubMed ID: |
34726630 |

## BORIS DOI: |
10.48350/164388 |

## URI: |
https://boris.unibe.ch/id/eprint/164388 |