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Kleemiss F, Peyerimhoff N, Bodensteiner M. Refinement of X-ray and electron diffraction crystal structures using analytical Fourier transforms of Slater-type atomic wavefunctions in Olex2. J Appl Crystallogr 2024; 57:161-174. [PMID: 38322726 PMCID: PMC10840308 DOI: 10.1107/s1600576723010981] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2023] [Accepted: 12/21/2023] [Indexed: 02/08/2024] Open
Abstract
An implementation of Slater-type spherical scattering factors for X-ray and electron diffraction for elements in the range Z = 1-103 is presented within the software Olex2. Both high- and low-angle Fourier behaviour of atomic electron density and electrostatic potential can thus be addressed, in contrast to the limited flexibility of the four Gaussian plus constant descriptions which are currently the most widely used method for calculating atomic scattering factors during refinement. The implementation presented here accommodates the increasing complexity of the electronic structure of heavier elements by using complete atomic wavefunctions without any interpolation between precalculated tables or intermediate fitting functions. Atomic wavefunctions for singly charged ions are implemented and made accessible, and these show drastic changes in electron diffraction scattering factors compared with the neutral atom. A comparison between the two different spherical models of neutral atoms is presented as an example for four different kinds of X-ray and two electron diffraction structures, and comparisons of refinement results using the existing diffraction data are discussed. A systematic but slight improvement in R values and residual densities can be observed when using the new scattering factors, and this is discussed relative to effects on the atomic displacement parameters and atomic positions, which are prominent near the heavier elements in a structure.
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Affiliation(s)
- Florian Kleemiss
- Institut für Anorganische Chemie, RWTH Aachen University, Landoltweg 1a, 52074 Aachen, Germany
- Universität Regensburg, Universitätsstraße 31, 93053 Regensburg, Germany
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Kibalin I, Voufack AB, Souhassou M, Gillon B, Gillet JM, Claiser N, Gukasov A, Porcher F, Lecomte C. Spin-resolved atomic orbital model refinement for combined charge and spin density analysis: application to the YTiO 3 perovskite. Acta Crystallogr A Found Adv 2021; 77:96-104. [PMID: 33646195 DOI: 10.1107/s205327332001637x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2020] [Accepted: 12/17/2020] [Indexed: 11/10/2022] Open
Abstract
A new crystallographic method is proposed in order to refine a spin-resolved atomic orbital model against X-ray and polarized neutron diffraction data. This atomic orbital model is applied to the YTiO3 perovskite crystal, where orbital ordering has previously been observed by several techniques: X-ray diffraction, polarized neutron diffraction and nuclear magnetic resonance. This method gives the radial extension, orientation and population of outer atomic orbitals for each atom. The interaction term between Ti3+, Y3+ cations and O2- ligands has been estimated. The refinement statistics obtained by means of the orbital method are compared with those obtained by the multipole model previously published.
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Affiliation(s)
- Iurii Kibalin
- Laboratoire Léon Brillouin, CEA-CNRS, CE-Saclay, Gif-sur-Yvette, 91191, France
| | - Ariste Bolivard Voufack
- CRM2, Institut Jean Barriol, Lorraine University and CNRS, BP239, Vandoeuvre-les-Nancy, F54506, France
| | - Mohamed Souhassou
- CRM2, Institut Jean Barriol, Lorraine University and CNRS, BP239, Vandoeuvre-les-Nancy, F54506, France
| | - Béatrice Gillon
- Laboratoire Léon Brillouin, CEA-CNRS, CE-Saclay, Gif-sur-Yvette, 91191, France
| | - Jean Michel Gillet
- Laboratoire SPMS, UMR 8580, CentraleSupélec, Paris-Saclay University, Gif-sur-Yvette, 91191, France
| | - Nicolas Claiser
- CRM2, Institut Jean Barriol, Lorraine University and CNRS, BP239, Vandoeuvre-les-Nancy, F54506, France
| | - Arsen Gukasov
- Laboratoire Léon Brillouin, CEA-CNRS, CE-Saclay, Gif-sur-Yvette, 91191, France
| | - Florence Porcher
- Laboratoire Léon Brillouin, CEA-CNRS, CE-Saclay, Gif-sur-Yvette, 91191, France
| | - Claude Lecomte
- CRM2, Institut Jean Barriol, Lorraine University and CNRS, BP239, Vandoeuvre-les-Nancy, F54506, France
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Chodkiewicz ML, Migacz S, Rudnicki W, Makal A, Kalinowski JA, Moriarty NW, Grosse-Kunstleve RW, Afonine PV, Adams PD, Dominiak PM. DiSCaMB: a software library for aspherical atom model X-ray scattering factor calculations with CPUs and GPUs. J Appl Crystallogr 2018; 51:193-199. [PMID: 29507550 PMCID: PMC5822993 DOI: 10.1107/s1600576717015825] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/04/2017] [Accepted: 10/30/2017] [Indexed: 11/10/2022] Open
Abstract
It has been recently established that the accuracy of structural parameters from X-ray refinement of crystal structures can be improved by using a bank of aspherical pseudoatoms instead of the classical spherical model of atomic form factors. This comes, however, at the cost of increased complexity of the underlying calculations. In order to facilitate the adoption of this more advanced electron density model by the broader community of crystallographers, a new software implementation called DiSCaMB, 'densities in structural chemistry and molecular biology', has been developed. It addresses the challenge of providing for high performance on modern computing architectures. With parallelization options for both multi-core processors and graphics processing units (using CUDA), the library features calculation of X-ray scattering factors and their derivatives with respect to structural parameters, gives access to intermediate steps of the scattering factor calculations (thus allowing for experimentation with modifications of the underlying electron density model), and provides tools for basic structural crystallographic operations. Permissively (MIT) licensed, DiSCaMB is an open-source C++ library that can be embedded in both academic and commercial tools for X-ray structure refinement.
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Affiliation(s)
- Michał L. Chodkiewicz
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, ulica Żwirki i Wigury 101, Warszawa, 02-089, Poland
| | - Szymon Migacz
- Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw, Warsaw, Poland
| | - Witold Rudnicki
- Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw, Warsaw, Poland
- Institute of Informatics, University of Białystok, Białystok, Poland
| | - Anna Makal
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, ulica Żwirki i Wigury 101, Warszawa, 02-089, Poland
| | - Jarosław A. Kalinowski
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA
| | - Nigel W. Moriarty
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA
| | - Ralf W. Grosse-Kunstleve
- Physical Biosciences Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA
| | - Pavel V. Afonine
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA
| | - Paul D. Adams
- Molecular Biophysics and Integrated Bioimaging Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA
- Department of Bioengineering, University of California at Berkeley, Berkeley, CA 94720, USA
| | - Paulina Maria Dominiak
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, ulica Żwirki i Wigury 101, Warszawa, 02-089, Poland
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