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Krawczuk A, Genoni A. Current developments and trends in quantum crystallography. ACTA CRYSTALLOGRAPHICA SECTION B, STRUCTURAL SCIENCE, CRYSTAL ENGINEERING AND MATERIALS 2024; 80:S2052520624003421. [PMID: 38888407 PMCID: PMC11301899 DOI: 10.1107/s2052520624003421] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2024] [Accepted: 04/17/2024] [Indexed: 06/20/2024]
Abstract
Quantum crystallography is an emerging research field of science that has its origin in the early days of quantum physics and modern crystallography when it was almost immediately envisaged that X-ray radiation could be somehow exploited to determine the electron distribution of atoms and molecules. Today it can be seen as a composite research area at the intersection of crystallography, quantum chemistry, solid-state physics, applied mathematics and computer science, with the goal of investigating quantum problems, phenomena and features of the crystalline state. In this article, the state-of-the-art of quantum crystallography will be described by presenting developments and applications of novel techniques that have been introduced in the last 15 years. The focus will be on advances in the framework of multipole model strategies, wavefunction-/density matrix-based approaches and quantum chemical topological techniques. Finally, possible future improvements and expansions in the field will be discussed, also considering new emerging experimental and computational technologies.
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Affiliation(s)
- Anna Krawczuk
- Institut für Anorganische Chemie, Georg-August-Universität, Tammannstraße 4, Göttingen, 37077, Germany
| | - Alessandro Genoni
- Université de Lorraine and CNRSLaboratoire de Physique et Chimie Théoriques1 Boulevard AragoMetz57078France
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2
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Kumar A, Jha KK, Olech B, Goral T, Malinska M, Woźniak K, Dominiak PM. TAAM refinement on high-resolution experimental and simulated 3D ED/MicroED data for organic molecules. Acta Crystallogr C Struct Chem 2024; 80:264-277. [PMID: 38934273 PMCID: PMC11225613 DOI: 10.1107/s2053229624005357] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2023] [Accepted: 06/05/2024] [Indexed: 06/28/2024] Open
Abstract
3D electron diffraction (3D ED), or microcrystal electron diffraction (MicroED), has become an alternative technique for determining the high-resolution crystal structures of compounds from sub-micron-sized crystals. Here, we considered L-alanine, α-glycine and urea, which are known to form good-quality crystals, and collected high-resolution 3D ED data on our in-house TEM instrument. In this study, we present a comparison of independent atom model (IAM) and transferable aspherical atom model (TAAM) kinematical refinement against experimental and simulated data. TAAM refinement on both experimental and simulated data clearly improves the model fitting statistics (R factors and residual electrostatic potential) compared to IAM refinement. This shows that TAAM better represents the experimental electrostatic potential of organic crystals than IAM. Furthermore, we compared the geometrical parameters and atomic displacement parameters (ADPs) resulting from the experimental refinements with the simulated refinements, with the periodic density functional theory (DFT) calculations and with published X-ray and neutron crystal structures. The TAAM refinements on the 3D ED data did not improve the accuracy of the bond lengths between the non-H atoms. The experimental 3D ED data provided more accurate H-atom positions than the IAM refinements on the X-ray diffraction data. The IAM refinements against 3D ED data had a tendency to lead to slightly longer X-H bond lengths than TAAM, but the difference was statistically insignificant. Atomic displacement parameters were too large by tens of percent for L-alanine and α-glycine. Most probably, other unmodelled effects were causing this behaviour, such as radiation damage or dynamical scattering.
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Affiliation(s)
- Anil Kumar
- Biological and Chemical Research Centre Faculty of Chemistry University of Warsaw, ul Żwirki i Wigury 101 02-089 Warszawa Poland
| | - Kunal Kumar Jha
- Biological and Chemical Research Centre Faculty of Chemistry University of Warsaw, ul Żwirki i Wigury 101 02-089 Warszawa Poland
- Centre of New Technologies University of Warsaw, ul S Banacha 2c 02-097 Warszawa Poland
| | - Barbara Olech
- Biological and Chemical Research Centre Faculty of Chemistry University of Warsaw, ul Żwirki i Wigury 101 02-089 Warszawa Poland
- Centre of New Technologies University of Warsaw, ul S Banacha 2c 02-097 Warszawa Poland
| | - Tomasz Goral
- Biological and Chemical Research Centre Faculty of Chemistry University of Warsaw, ul Żwirki i Wigury 101 02-089 Warszawa Poland
- Centre of New Technologies University of Warsaw, ul S Banacha 2c 02-097 Warszawa Poland
| | - Maura Malinska
- Faculty of Chemistry University of Warsaw, Pasteura 1 02-093 Warszawa Poland
| | - Krzysztof Woźniak
- Centre of New Technologies University of Warsaw, ul S Banacha 2c 02-097 Warszawa Poland
- Faculty of Chemistry University of Warsaw, Pasteura 1 02-093 Warszawa Poland
| | - Paulina Maria Dominiak
- Biological and Chemical Research Centre Faculty of Chemistry University of Warsaw, ul Żwirki i Wigury 101 02-089 Warszawa Poland
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Olech B, Brázda P, Palatinus L, Dominiak PM. Dynamical refinement with multipolar electron scattering factors. IUCRJ 2024; 11:309-324. [PMID: 38512772 PMCID: PMC11067749 DOI: 10.1107/s2052252524001763] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2023] [Accepted: 02/22/2024] [Indexed: 03/23/2024]
Abstract
Dynamical refinement is a well established method for refining crystal structures against 3D electron diffraction (ED) data and its benefits have been discussed in the literature [Palatinus, Petříček & Corrêa, (2015). Acta Cryst. A71, 235-244; Palatinus, Corrêa et al. (2015). Acta Cryst. B71, 740-751]. However, until now, dynamical refinements have only been conducted using the independent atom model (IAM). Recent research has shown that a more accurate description can be achieved by applying the transferable aspherical atom model (TAAM), but this has been limited only to kinematical refinements [Gruza et al. (2020). Acta Cryst. A76, 92-109; Jha et al. (2021). J. Appl. Cryst. 54, 1234-1243]. In this study, we combine dynamical refinement with TAAM for the crystal structure of 1-methyluracil, using data from precession ED. Our results show that this approach improves the residual Fourier electrostatic potential and refinement figures of merit. Furthermore, it leads to systematic changes in the atomic displacement parameters of all atoms and the positions of hydrogen atoms. We found that the refinement results are sensitive to the parameters used in the TAAM modelling process. Though our results show that TAAM offers superior performance compared with IAM in all cases, they also show that TAAM parameters obtained by periodic DFT calculations on the refined structure are superior to the TAAM parameters from the UBDB/MATTS database. It appears that multipolar parameters transferred from the database may not be sufficiently accurate to provide a satisfactory description of all details of the electrostatic potential probed by the 3D ED experiment.
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Affiliation(s)
- Barbara Olech
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Warsaw, Poland
| | - Petr Brázda
- Institute of Physics of the Czech Academy of Sciences, Na Slovance 1999/2, 182 00 Prague, Czechia
| | - Lukas Palatinus
- Institute of Physics of the Czech Academy of Sciences, Na Slovance 1999/2, 182 00 Prague, Czechia
| | - Paulina Maria Dominiak
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Warsaw, Poland
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4
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Chodkiewicz M, Patrikeev L, Pawlędzio S, Woźniak K. Transferable Hirshfeld atom model for rapid evaluation of aspherical atomic form factors. IUCRJ 2024; 11:249-259. [PMID: 38446457 PMCID: PMC10916294 DOI: 10.1107/s2052252524001507] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2023] [Accepted: 02/14/2024] [Indexed: 03/07/2024]
Abstract
Form factors based on aspherical models of atomic electron density have brought great improvement in the accuracies of hydrogen atom parameters derived from X-ray crystal structure refinement. Today, two main groups of such models are available, the banks of transferable atomic densities parametrized using the Hansen-Coppens multipole model which allows for rapid evaluation of atomic form factors and Hirshfeld atom refinement (HAR)-related methods which are usually more accurate but also slower. In this work, a model that combines the ideas utilized in the two approaches is tested. It uses atomic electron densities based on Hirshfeld partitions of electron densities, which are precalculated and stored in a databank. This model was also applied during the refinement of the structures of five small molecules. A comparison of the resulting hydrogen atom parameters with those derived from neutron diffraction data indicates that they are more accurate than those obtained with the Hansen-Coppens based databank, and only slightly less accurate than those obtained with a version of HAR that neglects the crystal environment. The advantage of using HAR becomes more noticeable when the effects of the environment are included. To speed up calculations, atomic densities were represented by multipole expansion with spherical harmonics up to l = 7, which used numerical radial functions (a different approach to that applied in the Hansen-Coppens model). Calculations of atomic form factors for the small protein crambin (at 0.73 Å resolution) took only 68 s using 12 CPU cores.
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Affiliation(s)
- Michał Chodkiewicz
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa 02-089, Poland
| | - Leonid Patrikeev
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa 02-089, Poland
| | - Sylwia Pawlędzio
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa 02-089, Poland
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA
| | - Krzysztof Woźniak
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa 02-089, Poland
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5
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Woińska M, Hoser AA, Chodkiewicz ML, Woźniak K. Enhancing hydrogen positions in X-ray structures of transition metal hydride complexes with dynamic quantum crystallography. IUCRJ 2024; 11:45-56. [PMID: 37990870 PMCID: PMC10833390 DOI: 10.1107/s205225252300951x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/25/2023] [Accepted: 10/31/2023] [Indexed: 11/23/2023]
Abstract
Hirshfeld atom refinement (HAR) is a method which enables the user to obtain more accurate positions of hydrogen atoms bonded to light chemical elements using X-ray data. When data quality permits, this method can be extended to hydrogen-bonded transition metals (TMs), as in hydride complexes. However, addressing hydrogen thermal motions with HAR, particularly in TM hydrides, presents a challenge. At the same time, proper description of thermal vibrations can be vital for determining hydrogen positions correctly. In this study, we employ tools such as SHADE3 and Normal Mode Refinement (NoMoRe) to estimate anisotropic displacement parameters (ADPs) for hydrogen atoms during HAR and IAM refinements performed for seven structures of TM (Fe, Ni, Cr, Nb, Rh and Os) and metalloid (Sb) hydride complexes for which both the neutron and the X-ray structures have been determined. A direct comparison between neutron and HAR/SHADE3/NoMoRe ADPs reveals that the similarity between neutron hydrogen ADPs and those estimated with NoMoRe or SHADE3 is significantly higher than when hydrogen ADPs are refined with HAR. Regarding TM-H bond lengths, traditional HAR exhibits a slight advantage over the other methods. However, combining NoMoRe/SHADE3 with HAR results in a minor decrease in agreement with neutron TM-H bond lengths. For the Cr complex, for which high-resolution X-ray data were collected, an investigation of resolution-related effects was possible.
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Affiliation(s)
- Magdalena Woińska
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Żwirki i Wigury 101, Warsaw 02-089, Poland
| | - Anna A. Hoser
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Żwirki i Wigury 101, Warsaw 02-089, Poland
| | - Michał L. Chodkiewicz
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Żwirki i Wigury 101, Warsaw 02-089, Poland
| | - Krzysztof Woźniak
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Żwirki i Wigury 101, Warsaw 02-089, Poland
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6
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Woińska M, Pawlędzio S, Chodkiewicz ML, Woźniak K. Hirshfeld Atom Refinement of Metal-Organic Complexes: Treatment of Hydrogen Atoms Bonded to Transition Metals. J Phys Chem A 2023; 127:3020-3035. [PMID: 36947670 PMCID: PMC10084459 DOI: 10.1021/acs.jpca.2c06998] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/24/2023]
Abstract
Hydrogen positions in hydrides play a key role in hydrogen storage materials and high-temperature superconductors. Our recently published study of five crystal structures of transition-metal-bound hydride complexes showed that using aspherical atomic scattering factors for Hirshfeld atom refinement (HAR) resulted in a systematic elongation of metal-hydrogen bonds compared to using spherical scattering factors with the Independent Atom Model (IAM). Even though only standard-resolution X-ray data was used, for the highest-quality data, we obtained excellent agreement between the X-ray and the neutron-derived bond lengths. We present an extended version of this study including 10 crystal structures of metal-organic complexes containing hydrogen atoms bonded to transition-metal atoms for which both X-ray and neutron data are available. The neutron structures were used as a benchmark, and the X-ray structures were refined by applying Hirshfeld atom refinement using various basis sets and DFT functionals in order to investigate the influence of the technical aspects on the length of metal-hydrogen bonds. The result of including relativistic effects in the Hamiltonian and using a cluster of multipoles simulating interactions with a crystal environment during wave function calculations was examined. The effect of the data quality on the final result was also evaluated. The study confirms that a high quality of experimental data is the key factor allowing us to obtain significant improvement in transition metal (TM)-hydrogen bond lengths from HAR in comparison with the IAM. Individual adjustments and better choices of the basis set can improve hydrogen positions. Average differences between TM-H bond lengths obtained with various DFT functionals upon including relativistic effects or between double-ζ and triple-ζ basis sets were not statistically significant. However, if all bonds formed by H atoms were considered, significant differences caused by different refinement strategies were observed. Finally, we examined the refinement of atomic thermal motions. Anisotropic refinement of hydrogen thermal motions with HAR was feasible only in some cases, and isotropically refined hydrogen thermal motions were in similar agreement with neutron values whether obtained with HAR or with the IAM.
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Affiliation(s)
- Magdalena Woińska
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Żwirki i Wigury 101, 02-089 Warszawa, Poland
| | - Sylwia Pawlędzio
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Żwirki i Wigury 101, 02-089 Warszawa, Poland
| | - Michał L Chodkiewicz
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Żwirki i Wigury 101, 02-089 Warszawa, Poland
| | - Krzysztof Woźniak
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Żwirki i Wigury 101, 02-089 Warszawa, Poland
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7
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Landeros-Rivera B, Ramírez-Palma D, Cortés-Guzmán F, Dominiak PM, Contreras-García J. How do density functionals affect the Hirshfeld atom refinement? Phys Chem Chem Phys 2023; 25:12702-12711. [PMID: 36644944 DOI: 10.1039/d2cp04098k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
In this work, the effect of mixing different amounts of Hartree-Fock (HF) exchange with hybrid density functionals applied to the Hirshfeld atom refinement (HAR) of urea and oxalic acid dihydrate is explored. Together, the influence of using different basis sets, methods (including MP2 and HF) and cluster sizes (to model bulk effects) is studied. The results show that changing the amount of HF exchange, no matter the level of theory, has an impact almost exclusively on the H atom refinement parameters. Contrary to pure quantum mechanical calculations where good geometries are obtained with intermediate HF exchange mixtures, in the HAR the best match with neutron diffraction reference values is not necessarily found for these admixtures. While the non-hydrogen covalent bond lengths are insensitive to the combination of method or basis set employed, the X-H bond lengths always increase proportionally to the HF exchange for the analysed systems. This outcome is opposite to what is normally observed from geometry optimisations, i.e., shorter bonds are obtained with greater HF exchange. Additionally, the thermal ellipsoids tend to shrink with larger HF exchange, especially for the H atoms involved in strong hydrogen bonding. Thus, it may be the case that the development of density functionals or basis sets suitable for quantum crystallography should take a different path than those fitted for quantum chemistry calculations.
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Affiliation(s)
| | - David Ramírez-Palma
- Departamento de Química, Centro de Investigación y de Estudios Avanzados del IPN (CINVESTAV), Avenida IPN 2508, Col. San Pedro Zacatenco, Ciudad de México, 07360, Mexico
| | - Fernando Cortés-Guzmán
- Universidad Nacional Autónoma de México, Instituto de Química, Ciudad Universitaria, Ciudad de México, 04510, Mexico
| | - Paulina M Dominiak
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Poland
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8
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Chodkiewicz ML, Gajda R, Lavina B, Tkachev S, Prakapenka VB, Dera P, Wozniak K. Accurate crystal structure of ice VI from X-ray diffraction with Hirshfeld atom refinement. IUCRJ 2022; 9:573-579. [PMID: 36071798 PMCID: PMC9438488 DOI: 10.1107/s2052252522006662] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 05/03/2022] [Accepted: 06/28/2022] [Indexed: 06/15/2023]
Abstract
Water is an essential chemical compound for living organisms, and twenty of its different crystal solid forms (ices) are known. Still, there are many fundamental problems with these structures such as establishing the correct positions and thermal motions of hydrogen atoms. The list of ice structures is not yet complete as DFT calculations have suggested the existence of additional and - to date - unknown phases. In many ice structures, neither neutron diffraction nor DFT calculations nor X-ray diffraction methods can easily solve the problem of hydrogen atom disorder or accurately determine their anisotropic displacement parameters (ADPs). Here, accurate crystal structures of H2O, D2O and mixed (50%H2O/50%D2O) ice VI obtained by Hirshfeld atom refinement (HAR) of high-pressure single-crystal synchrotron and laboratory X-ray diffraction data are presented. It was possible to obtain O-H/D bond lengths and ADPs for disordered hydrogen atoms which are in good agreement with the corresponding single-crystal neutron diffraction data. These results show that HAR combined with X-ray diffraction can compete with neutron diffraction in detailed studies of polymorphic forms of ice and crystals of other hydrogen-rich compounds. As neutron diffraction is relatively expensive, requires larger crystals which can be difficult to obtain and access to neutron facilities is restricted, cheaper and more accessible X-ray measurements combined with HAR can facilitate the verification of the existing ice polymorphs and the quest for new ones.
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Affiliation(s)
- Michal L. Chodkiewicz
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury, Warszawa 02-089, Poland
| | - Roman Gajda
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury, Warszawa 02-089, Poland
| | - Barbara Lavina
- Advanced Photon Source, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, IL 60439, USA
| | - Sergey Tkachev
- Advanced Photon Source, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, IL 60439, USA
| | - Vitali B. Prakapenka
- Hawai’i Institute of Geophysics and Planetology, Université d’hawaï à mānoa, 1680 East-West Road, Honolulu, HI 96822, USA
| | - Przemyslaw Dera
- Hawai’i Institute of Geophysics and Planetology, Université d’hawaï à mānoa, 1680 East-West Road, Honolulu, HI 96822, USA
| | - Krzysztof Wozniak
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury, Warszawa 02-089, Poland
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Pawlędzio S, Malinska M, Kleemiss F, Grabowsky S, Woźniak K. Influence of modelling disorder on Hirshfeld atom refinement results of an organo-gold(I) compound. IUCRJ 2022; 9:497-507. [PMID: 35844484 PMCID: PMC9252150 DOI: 10.1107/s2052252522005309] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/21/2022] [Accepted: 05/19/2022] [Indexed: 06/15/2023]
Abstract
Details of the validation of disorder modelling with Hirshfeld atom refinement (HAR) for a previously investigated organo-gold(I) compound are presented here. The impact of refining disorder on HAR results is discussed using an analysis of the differences of dynamic structure factors. These dynamic structure factor differences are calculated from thermally smeared quantum mechanical electron densities based on wavefunctions that include or exclude electron correlation and relativistic effects. When disorder is modelled, the electron densities stem from a weighted superposition of two (or more) different conformers. Here this is shown to impact the relative importance of electron correlation and relativistic effect estimates expressed by the structure factor magnitudes. The role of disorder modelling is also compared with the effect of the treatment of hydrogen anisotropic displacement parameter (ADP) values and atomic anharmonicity of the gold atom. The analysis of ADP values of gold and disordered carbon atoms showed that the effect of disorder significantly altered carbon ADP values and did not influence those of the gold atom.
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Affiliation(s)
- Sylwia Pawlędzio
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warsaw 02-089, Poland
| | - Maura Malinska
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warsaw 02-089, Poland
| | - Florian Kleemiss
- Faculty for Chemistry und Pharmacy, University of Regensburg, Universitätsstraße 31, 93053 Regensburg, Germany
| | - Simon Grabowsky
- Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern, Freiestrasse 3, 3012 Bern, Switzerland
| | - Krzysztof Woźniak
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warsaw 02-089, Poland
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10
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Bürgi HB. Crystal structures. ACTA CRYSTALLOGRAPHICA SECTION B, STRUCTURAL SCIENCE, CRYSTAL ENGINEERING AND MATERIALS 2022; 78:283-289. [PMID: 35695099 DOI: 10.1107/s205252062200292x] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2022] [Accepted: 03/16/2022] [Indexed: 06/15/2023]
Abstract
A personal view is offered on various solved and open problems related to crystal structures: the present state of reconstructing the crystal electron density from X-ray diffraction data; characterization of atomic and molecular motion from a combination of atomic displacement parameters and quantum chemical calculations; Bragg diffraction and diffuse scattering: twins, but different; models of real (as opposed to ideal) crystal structures from diffuse scattering; exploiting unexplored neighbourhoods of crystallography to mathematics, physics and chemistry.
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Affiliation(s)
- Hans Beat Bürgi
- Department of Chemistry, Biochemistry and Pharmacy, University of Berne, Freiestrasse 12, Bern, CH-3012, Switzerland
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11
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Davidson ML, Grabowsky S, Jayatilaka D. X-ray constrained wavefunctions based on Hirshfeld atoms. I. Method and review. ACTA CRYSTALLOGRAPHICA SECTION B, STRUCTURAL SCIENCE, CRYSTAL ENGINEERING AND MATERIALS 2022; 78:312-332. [PMID: 35695105 DOI: 10.1107/s2052520622004097] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/07/2022] [Accepted: 04/18/2022] [Indexed: 06/15/2023]
Abstract
The X-ray constrained wavefunction (XCW) procedure for obtaining an experimentally reconstructed wavefunction from X-ray diffraction data is reviewed. The two-center probability distribution model used to perform nuclear-position averaging in the original paper [Grimwood & Jayatilaka (2001). Acta Cryst. A57, 87-100] is carefully distinguished from the newer one-center probability distribution model. In the one-center model, Hirshfeld atoms are used, and the Hirshfeld atom based X-ray constrained wavefunction (HA-XCW) procedure is described for the first time, as well as its efficient implementation. In this context, the definition of the related X-ray wavefunction refinement (XWR) method is refined. The key halting problem for the XCW method - the procedure by which one determines when overfitting has occurred - is named and work on it reviewed.
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Affiliation(s)
- Max L Davidson
- School of Molecular Sciences, The University of Western Australia, 35 Stirling Highway, Crawley 6009, Western Australia, Australia
| | - Simon Grabowsky
- Departement für Chemie, Biochemie und Pharmazie, Universität Bern, Freiestrasse 3, 3012 Bern, Switzerland
| | - Dylan Jayatilaka
- School of Molecular Sciences, The University of Western Australia, 35 Stirling Highway, Crawley 6009, Western Australia, Australia
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12
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Chodkiewicz M, Pawlędzio S, Woińska M, Woźniak K. Fragmentation and transferability in Hirshfeld atom refinement. IUCRJ 2022; 9:298-315. [PMID: 35371499 PMCID: PMC8895009 DOI: 10.1107/s2052252522000690] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2021] [Accepted: 01/19/2022] [Indexed: 05/06/2023]
Abstract
Hirshfeld atom refinement (HAR) is one of the most effective methods for obtaining accurate structural parameters for hydrogen atoms from X-ray diffraction data. Unfortunately, it is also relatively computationally expensive, especially for larger molecules due to wavefunction calculations. Here, a fragmentation approach has been tested as a remedy for this problem. It gives an order of magnitude improvement in computation time for larger organic systems and is a few times faster for metal-organic systems at the cost of only minor differences in the calculated structural parameters when compared with the original HAR calculations. Fragmentation was also applied to polymeric and disordered systems where it provides a natural solution to problems that arise when HAR is applied. The concept of fragmentation is closely related to the transferable aspherical atom model (TAAM) and allows insight into possible ways to improve TAAM. Hybrid approaches combining fragmentation with the transfer of atomic densities between chemically similar atoms have been tested. An efficient handling of intermolecular interactions was also introduced for calculations involving fragmentation. When applied in fragHAR (a fragmentation approach for polypeptides) as a replacement for the original approach, it allowed for more efficient calculations. All of the calculations were performed with a locally modified version of Olex2 combined with a development version of discamb2tsc and ORCA. Care was taken to efficiently use the power of multicore processors by simple implementation of load-balancing, which was found to be very important for lowering computational time.
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Affiliation(s)
- Michał Chodkiewicz
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa 02-089, Poland
| | - Sylwia Pawlędzio
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa 02-089, Poland
| | - Magdalena Woińska
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa 02-089, Poland
| | - Krzysztof Woźniak
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa 02-089, Poland
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13
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Ruth PN, Herbst-Irmer R, Stalke D. Hirshfeld atom refinement based on projector augmented wave densities with periodic boundary conditions. IUCRJ 2022; 9:286-297. [PMID: 35371508 PMCID: PMC8895013 DOI: 10.1107/s2052252522001385] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/04/2021] [Accepted: 02/04/2022] [Indexed: 06/14/2023]
Abstract
Hirshfeld atom refinement (HAR) is an X-ray diffraction refinement method that, in numerous publications, has been shown to give H-atom bond lengths in close agreement with neutron diffraction derived values. Presented here is a first evaluation of an approach using densities derived from projector augmented wave (PAW) densities with three-dimensional periodic boundary conditions for HAR. The results show an improvement over refinements that neglect the crystal environment or treat it classically, while being on a par with non-periodic approximations for treating the solid-state environment quantum mechanically. A suite of functionals were evaluated for this purpose, showing that the SCAN and revSCAN functionals are most suited to these types of calculation.
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Affiliation(s)
- Paul Niklas Ruth
- Institut für Anorganische Chemie, Georg-August-Universität Göttingen, Tammannstraße 4, Göttingen, Lower Saxony 37077, Germany
| | - Regine Herbst-Irmer
- Institut für Anorganische Chemie, Georg-August-Universität Göttingen, Tammannstraße 4, Göttingen, Lower Saxony 37077, Germany
| | - Dietmar Stalke
- Institut für Anorganische Chemie, Georg-August-Universität Göttingen, Tammannstraße 4, Göttingen, Lower Saxony 37077, Germany
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14
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Wenger JS, Wang X, Johnstone TC. H-Atom Assignment and Sb-O Bonding of [Mes 3SbOH][O 3SPh] Confirmed by Neutron Diffraction, Multipole Modeling, and Hirshfeld Atom Refinement. Inorg Chem 2021; 60:16048-16052. [PMID: 34661394 DOI: 10.1021/acs.inorgchem.1c02229] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Neutron wavelength-resolved Laue diffraction experiments permit accurate refinement of the H-atom positions and anisotropic displacement parameters of [Mes3SbOH][O3SPh]. A multipole-based charge density refinement and a topological analysis of the refined electron density were also performed. Hirshfeld atom refinement (HAR) recovers the neutron-determined H-atom parameters, and the quantum-mechanical electron density used in HAR recovers the electron density topology from the refined multipole model. These results confirm that [Mes3SbOH][O3SPh] does indeed feature a hydroxystibonium cation with a nominal Sb-O single bond and not a stibine oxide with an Sb=O/Sb+-O- bond.
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Affiliation(s)
- John S Wenger
- Department of Chemistry and Biochemistry, University of California Santa Cruz, Santa Cruz, California 95064, United States
| | - Xiaoping Wang
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States
| | - Timothy C Johnstone
- Department of Chemistry and Biochemistry, University of California Santa Cruz, Santa Cruz, California 95064, United States
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15
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Midgley L, Bourhis LJ, Dolomanov OV, Grabowsky S, Kleemiss F, Puschmann H, Peyerimhoff N. 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 A-FOUNDATION AND ADVANCES 2021; 77:519-533. [PMID: 34726630 DOI: 10.1107/s2053273321009086] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2021] [Accepted: 09/02/2021] [Indexed: 11/10/2022]
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.
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Affiliation(s)
- Laura Midgley
- Department of Mathematical Sciences, Durham University, Upper Mountjoy Campus, Stockton Road, Durham, DH1 3LE, United Kingdom
| | - Luc J Bourhis
- Bruker, 4 Allée Lorentz, Champs-sur-Marne, 77447 Marne-la-Vallée cedex 2, France
| | - Oleg V Dolomanov
- OlexSys Ltd, Department of Chemistry, Durham University, South Road, Durham, DH1 3LE, United Kingdom
| | - Simon Grabowsky
- Departement für Chemie, Biochemie und Pharmazie, Universität Bern, Freiestrasse 3, 3012 Bern, Switzerland
| | - Florian Kleemiss
- Departement für Chemie, Biochemie und Pharmazie, Universität Bern, Freiestrasse 3, 3012 Bern, Switzerland
| | - Horst Puschmann
- OlexSys Ltd, Department of Chemistry, Durham University, South Road, Durham, DH1 3LE, United Kingdom
| | - Norbert Peyerimhoff
- Department of Mathematical Sciences, Durham University, Upper Mountjoy Campus, Stockton Road, Durham, DH1 3LE, United Kingdom
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16
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Pawlędzio S, Malinska M, Woińska M, Wojciechowski J, Andrade Malaspina L, Kleemiss F, Grabowsky S, Woźniak K. Relativistic Hirshfeld atom refinement of an organo-gold(I) compound. IUCRJ 2021; 8:608-620. [PMID: 34258009 PMCID: PMC8256711 DOI: 10.1107/s2052252521004541] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/02/2021] [Accepted: 04/28/2021] [Indexed: 06/13/2023]
Abstract
The main goal of this study is the validation of relativistic Hirshfeld atom refinement (HAR) as implemented in Tonto for high-resolution X-ray diffraction datasets of an organo-gold(I) compound. The influence of the relativistic effects on statistical parameters, geometries and electron density properties was analyzed and compared with the influence of electron correlation and anharmonic atomic motions. Recent work in this field has indicated the importance of relativistic effects in the static electron density distribution of organo-mercury compounds. This study confirms that differences in electron density due to relativistic effects are also of significant magnitude for organo-gold compounds. Relativistic effects dominate not only the core region of the gold atom, but also influence the electron density in the valence and bonding region, which has measurable consequences for the HAR refinement model parameters. To study the effects of anharmonic motion on the electron density distribution, dynamic electron density difference maps were constructed. Unlike relativistic and electron correlation effects, the effects of anharmonic nuclear motion are mostly observed in the core area of the gold atom.
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Affiliation(s)
- Sylwia Pawlędzio
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa 02-089, Poland
| | - Maura Malinska
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa 02-089, Poland
| | - Magdalena Woińska
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa 02-089, Poland
| | | | - Lorraine Andrade Malaspina
- Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern, Freiestrasse 3, Bern 3012, Switzerland
| | - Florian Kleemiss
- Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern, Freiestrasse 3, Bern 3012, Switzerland
| | - Simon Grabowsky
- Department of Chemistry, Biochemistry and Pharmaceutical Sciences, University of Bern, Freiestrasse 3, Bern 3012, Switzerland
| | - Krzysztof Woźniak
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, Żwirki i Wigury 101, Warszawa 02-089, Poland
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17
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Destro R, Roversi P, Barzaghi M, Lo Presti L. Anharmonic Thermal Motion Modelling in the Experimental XRD Charge Density Determination of 1-Methyluracil at T = 23 K. Molecules 2021; 26:3075. [PMID: 34063908 PMCID: PMC8196607 DOI: 10.3390/molecules26113075] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/22/2021] [Revised: 05/13/2021] [Accepted: 05/17/2021] [Indexed: 11/16/2022] Open
Abstract
The experimental electron density distribution (EDD) of 1-methyluracil (1-MUR) was obtained by single crystal X-ray diffraction (XRD) experiments at 23 K. Four different structural models fitting an extensive set of XRD data to a resolution of (sinθ/λ)max = 1.143 Å-1 are compared. Two of the models include anharmonic temperature factors, whose inclusion is supported by the Hamilton test at a 99.95% level of confidence. Positive Fourier residuals up to 0.5 eÅ-3 in magnitude were found close to the methyl group and in the region of hydrogen bonds. Residual density analysis (RDA) and molecular dynamics simulations in the solid-state demonstrate that these residuals can be likely attributed to unresolved disorder, possibly dynamical and long-range in nature. Atomic volumes and charges, molecular moments up to hexadecapoles, as well as maps of the molecular electrostatic potential were obtained from distributed multipole analysis of the EDD. The derived electrostatic properties neither depend on the details of the multipole model, nor are significantly affected by the explicit inclusion of anharmonicity in the least-squares model. The distribution of atomic charges in 1-MUR is not affected by the crystal environment in a significant way. The quality of experimental findings is discussed in light of in-crystal and gas-phase quantum simulations.
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Affiliation(s)
- Riccardo Destro
- Chemistry Department, Università degli Studi di Milano, Via Golgi 19, 20133 Milano, Italy;
| | - Pietro Roversi
- Department of Molecular and Cell Biology, Leicester Institute of Structural and Chemical Biology, University of Leicester, Lancaster Road, Leicester LE1 7HB, UK;
| | - Mario Barzaghi
- Consiglio Nazionale delle Ricerche (CNR), Piazzale Aldo Moro 7, 00185 Roma, Italy;
| | - Leonardo Lo Presti
- Chemistry Department, Università degli Studi di Milano, Via Golgi 19, 20133 Milano, Italy;
- Istituto Nazionale di Fisica Nucleare (INFN), Laboratori Nazionali di Frascati, 00044 Frascati, Italy
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18
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Woińska M, Chodkiewicz ML, Woźniak K. Towards accurate and precise positions of hydrogen atoms bonded to heavy metal atoms. Chem Commun (Camb) 2021; 57:3652-3655. [PMID: 33870351 DOI: 10.1039/d0cc07661a] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A comparison of five X-ray structures of transition-metal-bound hydride complexes, successfully refined using Hirshfeld Atom Refinement (HAR) against low resolution X-ray diffraction data (including the positions and ADPs of all hydrogen atoms), with neutron structures shows that using aspherical atomic scattering factors instead of spherical ones results in systematic elongation of metal-hydrogen bonds, which in the case of the highest-quality data leads to excellent agreement of the X-ray and the neutron-derived bond lengths.
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Affiliation(s)
- Magdalena Woińska
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Żwirki i Wigury 101, 02-089 Warszawa, Poland.
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19
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Macetti G, Wieduwilt EK, Genoni A. QM/ELMO: A Multi-Purpose Fully Quantum Mechanical Embedding Scheme Based on Extremely Localized Molecular Orbitals. J Phys Chem A 2021; 125:2709-2726. [DOI: 10.1021/acs.jpca.0c11450] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023]
Affiliation(s)
- Giovanni Macetti
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Erna K. Wieduwilt
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Alessandro Genoni
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
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20
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Desiraju GR. Crystal engineering in IUCrJ: from 'the' crystal structure to 'a' crystal structure. IUCRJ 2021; 8:148-149. [PMID: 33708389 PMCID: PMC7924231 DOI: 10.1107/s2052252521000993] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
What is 'structure' in the context of a molecular solid?
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Affiliation(s)
- Gautam R. Desiraju
- Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore, 560 012, India
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21
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Wieduwilt EK, Macetti G, Genoni A. Climbing Jacob's Ladder of Structural Refinement: Introduction of a Localized Molecular Orbital-Based Embedding for Accurate X-ray Determinations of Hydrogen Atom Positions. J Phys Chem Lett 2021; 12:463-471. [PMID: 33369421 DOI: 10.1021/acs.jpclett.0c03421] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The positions of hydrogen atoms in molecules are fundamental in many aspects of chemistry. Nevertheless, most molecular structures are obtained from refinements of X-ray data exploiting the independent atom model (IAM), which uses spherical atomic densities and provides bond lengths involving hydrogen atoms that are too short compared to the neutron reference values. To overcome the IAM shortcomings, the wave function-based Hirshfeld atom refinement (HAR) method has been recently proposed, emerging as a promising strategy able to give element-hydrogen bond distances in excellent agreement with the neutron ones in terms of accuracy and precision. In this Letter, we propose a significant improvement of HAR based on the idea of describing the crystal environment explicitly in the underlying wave function calculation through a quantum mechanical embedding strategy that exploits extremely localized molecular orbitals. Test-bed refinements on a crystal structure characterized by strong intermolecular interactions are also discussed.
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Affiliation(s)
- Erna K Wieduwilt
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Giovanni Macetti
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Alessandro Genoni
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
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