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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

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

Abstract

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:Article
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1107/S2053273321009086
Date accepted:02 September 2021
Date deposited:22 November 2021
Date of first online publication:29 October 2021
Date first made open access:22 November 2021

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