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Genoni A, Martín Pendás Á. Critical assessment of the x-ray restrained wave function approach: Advantages, drawbacks, and perspectives for density functional theory and periodic ab initio calculations. J Chem Phys 2024; 160:234108. [PMID: 38899684 DOI: 10.1063/5.0213247] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2024] [Accepted: 06/03/2024] [Indexed: 06/21/2024] Open
Abstract
The x-ray restrained wave function (XRW) method is a quantum crystallographic technique to extract wave functions compatible with experimental x-ray diffraction data. The approach looks for wave functions that minimize the energies of the investigated systems and also reproduce sets of x-ray structure factors. Given the strict relationship between x-ray structure factors and electron distributions, the strategy practically allows determining wave functions that correspond to given (usually experimental) electron densities. In this work, the capabilities of the XRW approach were further tested. The aim was to evaluate whether the XRW technique could serve as a tool for suggesting new exchange-correlation functionals for density functional theory or refining existing ones. Additionally, the ability of the method to address the influences of the crystalline environment was also assessed. The outcomes of XRW computations were thus compared to those of traditional gas-phase, embedding quantum mechanics/molecular mechanics, and fully periodic calculations. The results revealed that, irrespective of the initial conditions, the XRW computations practically yield a consensus electron density, in contrast to the currently employed density functional approximations (DFAs), which tend to give a too large range of electron distributions. This is encouraging in view of exploiting the XRW technique to develop improved functionals. Conversely, the calculations also emphasized that the XRW method is limited in its ability to effectively address the influences of the crystalline environment. This underscores the need for a periodic XRW technique, which would allow further untangling the shortcomings of DFAs from those inherent to the XRW approach.
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Affiliation(s)
- Alessandro Genoni
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, 1 Boulevard Arago, 57078 Metz, France
| | - Ángel Martín Pendás
- Departamento de Química Física y Analítica, Facultad de Química, Universidad de Oviedo, Avenida Julian Clavería 8, 33006 Oviedo, Spain
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2
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Macetti G, Genoni A. Introduction of a weighting scheme for the X-ray restrained wavefunction approach: advantages and drawbacks. Acta Crystallogr A Found Adv 2023; 79:25-40. [PMID: 36601761 DOI: 10.1107/s2053273322010221] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Accepted: 10/23/2022] [Indexed: 11/22/2022] Open
Abstract
In a quite recent study [Genoni et al. (2017). IUCrJ, 4, 136-146], it was observed that the X-ray restrained wavefunction (XRW) approach allows a more efficient and larger capture of electron correlation effects on the electron density if high-angle reflections are not considered in the calculations. This is due to the occurrence of two concomitant effects when one uses theoretical X-ray diffraction data corresponding to a single-molecule electron density in a large unit cell: (i) the high-angle reflections are generally much more numerous than the low- and medium-angle ones, and (ii) they are already very well described at unrestrained level. Nevertheless, since high-angle data also contain important information that should not be disregarded, it is not advisable to neglect them completely. For this reason, based on the results of the previous investigation, this work introduces a weighting scheme for XRW calculations to up-weight the contribution of low- and medium-angle reflections, and, at the same time, to reasonably down-weight the importance of the high-angle data. The proposed strategy was tested through XRW computations with both theoretical and experimental structure-factor amplitudes. The tests have shown that the new weighting scheme works optimally if it is applied with theoretically generated X-ray diffraction data, while it is not advantageous when traditional experimental X-ray diffraction data (even of very high resolution) are employed. This also led to the conclusion that the use of a specific external parameter λJ for each resolution range might not be a suitable strategy to adopt in XRW calculations exploiting experimental X-ray data as restraints.
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Affiliation(s)
- Giovanni Macetti
- Université de Lorraine and CNRS, Laboratoire de Physique et Chimie Théoriques, 1 Boulevard Arago, Metz, F-57078, France
| | - Alessandro Genoni
- Université de Lorraine and CNRS, Laboratoire de Physique et Chimie Théoriques, 1 Boulevard Arago, Metz, F-57078, France
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3
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Genoni A. On the termination of the X-ray constrained wavefunction procedure: reformulation of the method for an unequivocal determination of λ. Acta Crystallogr A Found Adv 2022; 78:302-308. [DOI: 10.1107/s2053273322003746] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Accepted: 04/05/2022] [Indexed: 11/10/2022] Open
Abstract
The X-ray constrained/restrained wavefunction (XCW/XRW) approach of quantum crystallography is revisited by introducing the stationary condition of the Jayatilaka functional with respect to the Lagrange multiplier λ. The theoretical derivation has unequivocally shown that the right value of λ is a maximum stationary point of the functional to optimize, thus enabling the solution of the longstanding problem of establishing the point at which to halt the XCW/XRW procedure. Based on the new finding, a reformulation of the X-ray constrained wavefunction algorithm is proposed and its implementation is envisaged. In addition to relying on more solid mathematical grounds, the new variant of the method will be intrinsically more physically meaningful, allowing a straightforward evaluation of the highest level of confidence with which the experimental X-ray diffraction data can be possibly reproduced.
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Davidson ML, Grabowsky S, Jayatilaka D. X-ray constrained wavefunctions based on Hirshfeld atoms. II. Reproducibility of electron densities in crystals of α-oxalic acid dihydrate. ACTA CRYSTALLOGRAPHICA SECTION B, STRUCTURAL SCIENCE, CRYSTAL ENGINEERING AND MATERIALS 2022; 78:397-415. [PMID: 35695114 DOI: 10.1107/s2052520622004103] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Accepted: 04/18/2022] [Indexed: 06/15/2023]
Abstract
The Hirshfeld atom-based X-ray constrained wavefunction fitting (HA-XCW) procedure is tested for its reproducibility, and the information content of the fitted wavefunction is critically assessed. Fourteen different α-oxalic acid dihydrate data sets are used for this purpose, and the first joint fitting to 12 of these data sets is reported. There are systematic features in the electron density obtained from all data sets which agree with higher level benchmark calculations, but there are also many other strong systematic features which disagree with the reference calculations, most notably those associated with the electron density near the nuclei. To enhance reproducibility, three new protocols are described and tested to address the halting problem of XCW fitting, namely: an empirical power-function method, which is useful for estimating the accuracy of the structure factor uncertainties; an asymptotic extrapolation method based on ideas from density functional theory; and a `conservative method' whereby the smallest value of the regularization parameter is chosen from a series of data sets, or subsets.
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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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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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Podhorský M, Bučinský L, Jayatilaka D, Grabowsky S. HgH 2 meets relativistic quantum crystallography. How to teach relativity to a non-relativistic wavefunction. ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2021; 77:54-66. [PMID: 33399131 DOI: 10.1107/s2053273320014837] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2020] [Accepted: 11/09/2020] [Indexed: 11/10/2022]
Abstract
The capability of X-ray constrained wavefunction (XCW) fitting to introduce relativistic effects into a non-relativistic wavefunction is tested. It is quantified how much of the reference relativistic effects can be absorbed in the non-relativistic XCW calculation when fitted against relativistic structure factors of a model HgH2 molecule. Scaling of the structure-factor sets to improve the agreement statistics is found to introduce a significant systematic error into the XCW fitting of relativistic effects.
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Affiliation(s)
- Michal Podhorský
- Institute of Physical Chemistry and Chemical Physics FCHPT, Slovak University of Technology, Radlinskeho 9, Bratislava SK-812 37, Slovakia
| | - Lukáš Bučinský
- Institute of Physical Chemistry and Chemical Physics FCHPT, Slovak University of Technology, Radlinskeho 9, Bratislava SK-812 37, Slovakia
| | - Dylan Jayatilaka
- School of Molecular Sciences, The University of Western Australia, 35 Stirling Hwy, Perth WA 6009, Australia
| | - Simon Grabowsky
- Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, 3012 Bern, Switzerland
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Affiliation(s)
- Piero Macchi
- Department, Chemistry, Materials and Chemical Engineering, Politecnico di Milano, Milano, Italy
- Center for Nano Science and Technology CNST@polimi, Italian Institute of Technology, Milano, Italy
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Abstract
In this review article, we report on the recent progresses in the field of quantum crystallography that has witnessed a massive increase of production coupled with a broadening of the scope in the last decade. It is shown that the early thoughts about extracting quantum mechanical information from crystallographic experiments are becoming reality, although a century after prediction. While in the past the focus was mainly on electron density and related quantities, the attention is now shifting toward determination of wavefunction from experiments, which enables an exhaustive determination of the quantum mechanical functions and properties of a system. Nonetheless, methods based on electron density modelling have evolved and are nowadays able to reconstruct tiny polarizations of core electrons, coupling charge and spin models, or determining the quantum behaviour at extreme conditions. Far from being routine, these experimental and computational results should be regarded with special attention by scientists for the wealth of information on a system that they actually contain.
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Post-Hartree-Fock methods for Hirshfeld atom refinement: are they necessary? Investigation of a strongly hydrogen-bonded molecular crystal. J Mol Struct 2020. [DOI: 10.1016/j.molstruc.2020.127934] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Ernst M, Genoni A, Macchi P. Analysis of crystal field effects and interactions using X-ray restrained ELMOs. J Mol Struct 2020. [DOI: 10.1016/j.molstruc.2020.127975] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Macetti G, Wieduwilt EK, Assfeld X, Genoni A. Localized Molecular Orbital-Based Embedding Scheme for Correlated Methods. J Chem Theory Comput 2020; 16:3578-3596. [PMID: 32369363 DOI: 10.1021/acs.jctc.0c00084] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Embedding strategies currently provide the best compromise between accuracy and computational cost in modeling chemical properties and processes of large and complex systems. In this framework, different methods have been proposed all over the years, from the very popular QM/MM approaches to the more recent and very promising density matrix and density functional embedding techniques. Here, we present a further development of the quantum mechanics/extremely localized molecular orbital technique (QM/ELMO) method, a recently proposed multiscale embedding strategy in which the chemically active region of the investigated system is treated at a fully quantum mechanical level, while the rest is described by frozen extremely localized molecular orbitals previously transferred from proper libraries or tailor-made model molecules. In particular, in this work we discuss and assess in detail the extension of the QM/ELMO approach to density functional theory and post-Hartree-Fock techniques by evaluating its performances when it is used to describe chemical reactions, bond dissociations, and intermolecular interactions. The preliminary test calculations have shown that, in the investigated cases, the new embedding strategy enables the results of the corresponding fully quantum mechanical computations to be reproduced within chemical accuracy in almost all the cases but with a significantly reduced computational cost, especially when correlated post-Hartree-Fock strategies are used to describe the quantum mechanical subsystem. In light of the obtained results, we already envisage the future application of the new correlated QM/ELMO techniques to the investigation of more challenging problems, such as the modeling of enzyme catalysis, the study of excited states of biomolecules, and the refinement of macromolecular X-ray crystal structures.
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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
| | - Xavier Assfeld
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019, Boulevard des Aiguilletes, BP 70239, F-54506 Vandoeuvre-lès-Nancy, 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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12
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Genoni A. On the use of the Obara–Saika recurrence relations for the calculation of structure factors in quantum crystallography. ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2020; 76:172-179. [DOI: 10.1107/s205327332000042x] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/07/2019] [Accepted: 01/14/2020] [Indexed: 11/10/2022]
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.
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Grabowsky S, Genoni A, Thomas SP, Jayatilaka D. The Advent of Quantum Crystallography: Form and Structure Factors from Quantum Mechanics for Advanced Structure Refinement and Wavefunction Fitting. 21ST CENTURY CHALLENGES IN CHEMICAL CRYSTALLOGRAPHY II 2020. [DOI: 10.1007/430_2020_62] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
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14
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Observation of the asphericity of 4f-electron density and its relation to the magnetic anisotropy axis in single-molecule magnets. Nat Chem 2019; 12:213-219. [PMID: 31844195 DOI: 10.1038/s41557-019-0387-6] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2018] [Accepted: 11/05/2019] [Indexed: 11/08/2022]
Abstract
The distribution of electrons in the 4f orbitals of lanthanide ions is often assigned a crucial role in the design of single-molecule magnets, which maintain magnetization in zero external field. Optimal spatial complementarity between the 4f-electron density and the ligand field is key to maximizing magnetic anisotropy, which is an important factor in the ability of lanthanide complexes to display single-molecule magnet behaviour. Here we have experimentally determined the electron density distribution in two dysprosium molecular complexes by interpreting high-resolution synchrotron X-ray diffraction with a multipole model. The ground-state 4f-electron density is found to be an oblate ellipsoid, as is often deduced from a simplified Sievers model that assumes a pure |±15/2> ground-state doublet for the lanthanide ion. The large equatorial asymmetry-determined by a model wavefunction-was found to contain considerable MJ mixing of |±11/2> and only 81% of |±15/2>. The experimental molecular magnetic easy axes were recovered, and found to deviate by 13.1° and 8.7° from those obtained by ab initio calculations.
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Arias-Olivares D, Wieduwilt EK, Contreras-García J, Genoni A. NCI-ELMO: A New Method To Quickly and Accurately Detect Noncovalent Interactions in Biosystems. J Chem Theory Comput 2019; 15:6456-6470. [DOI: 10.1021/acs.jctc.9b00658] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Affiliation(s)
- David Arias-Olivares
- Doctorado en Fisicoquímica Molecular, Facultad de Ciencias Exactas, Universidad Andrés Bello, Ave. Republica 275, Santiago, Chile
- Sorbonne Université & CNRS, Laboratoire de Chimie Théorique, UMR CNRS 7616, 4 Place Jussieu, F-75005 Paris, France
| | - Erna K. Wieduwilt
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques, UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
| | - Julia Contreras-García
- Sorbonne Université & CNRS, Laboratoire de Chimie Théorique, UMR CNRS 7616, 4 Place Jussieu, F-75005 Paris, France
| | - Alessandro Genoni
- Université de Lorraine & CNRS, Laboratoire de Physique et Chimie Théoriques, UMR CNRS 7019, 1 Boulevard Arago, F-57078 Metz, France
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16
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Genoni A, Macetti G, Franchini D, Pieraccini S, Sironi M. X-ray constrained spin-coupled technique: theoretical details and further assessment of the method. ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2019; 75:778-797. [PMID: 31692454 DOI: 10.1107/s2053273319011021] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2019] [Accepted: 08/07/2019] [Indexed: 11/11/2022]
Abstract
One of the well-established methods of modern quantum crystallography is undoubtedly the X-ray constrained wavefunction (XCW) approach, a technique that enables the determination of wavefunctions which not only minimize the energy of the system under examination, but also reproduce experimental X-ray diffraction data within the limit of the experimental errors. Initially proposed in the framework of the Hartree–Fock method, the strategy has been gradually extended to other techniques of quantum chemistry, but always remaining limited to a single-determinant ansatz for the wavefunction to extract. This limitation has been recently overcome through the development of the novel X-ray constrained spin-coupled (XCSC) approach [Genoni et al. (2018). Chem. Eur. J.
24, 15507–15511] which merges the XCW philosophy with the traditional spin-coupled strategy of valence bond theory. The main advantage of this new technique is the possibility of extracting traditional chemical descriptors (e.g. resonance structure weights) compatible with the experimental diffraction measurements, without the need to introduce information a priori or perform analyses a posteriori. This paper provides a detailed theoretical derivation of the fundamental equations at the basis of the XCSC method and also introduces a further advancement of its original version, mainly consisting in the use of molecular orbitals resulting from XCW calculations at the Hartree–Fock level to describe the inactive electrons in the XCSC computations. Furthermore, extensive test calculations, which have been performed by exploiting high-resolution X-ray diffraction data for salicylic acid and by adopting different basis sets, are presented and discussed. The computational tests have shown that the new technique does not suffer from particular convergence problems. Moreover, all the XCSC calculations provided resonance structure weights, spin-coupled orbitals and global electron densities slightly different from those resulting from the corresponding unconstrained computations. These discrepancies can be ascribed to the capability of the novel strategy to capture the information intrinsically contained in the experimental data used as external constraints.
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Staub R, Iannuzzi M, Khaliullin RZ, Steinmann SN. Energy Decomposition Analysis for Metal Surface-Adsorbate Interactions by Block Localized Wave Functions. J Chem Theory Comput 2018; 15:265-275. [PMID: 30462497 DOI: 10.1021/acs.jctc.8b00957] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The energy decomposition analysis based on block localized wave functions (BLW-EDA) allows one to gain physical insight into the nature of chemical bonding, decomposing the interaction energy in (1) a "frozen" term, accounting for the attraction due to electrostatic and dispersion interactions, modulated by Pauli repulsion, (2) the variationally assessed polarization energy, and (3) the charge transfer. This method has so far been applied to gas- and condensed-phase molecular systems. However, its standard version is not compatible with fractionally occupied orbitals (i.e., electronic smearing) and, as a consequence, cannot be applied to metallic surfaces. In this work, we propose a simple and practical extension of BLW-EDA to fractionally occupied orbitals, termed Ensemble BLW-EDA. As illustrative examples, we have applied the developed method to analyze the nature of the interaction of various adsorbates on Pt(111), ranging from physisorbed water to strongly chemisorbed ethylene. Our results show that polarization and charge transfer both contribute significantly at the adsorption minimum for all studied systems. The energy decomposition analysis provides details with respect to competing adsorption sites (e.g., CO on atop vs hollow sites) and elucidates the respective importance of polarization and charge transfer for the increased adsorption energy of H2S compared to H2O. Our development will enable a deeper understanding of the impact of charge transfer on catalytic processes in general.
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Affiliation(s)
- Ruben Staub
- Univ Lyon, Ecole Normale Supérieure de Lyon, CNRS Université Lyon 1 , Laboratoire de Chimie UMR 5182 , 46 allée d'Italie , Lyon , F-69364 , France
| | - Marcella Iannuzzi
- Institut für Chemie , University of Zurich , Winterthurerstrasse 190 , Zurich , CH-8057 , Switzerland
| | - Rustam Z Khaliullin
- Department of Chemistry , McGill University , 801 Sherbrooke Street West , Montreal , Québec H3A 0B8 , Canada
| | - Stephan N Steinmann
- Univ Lyon, Ecole Normale Supérieure de Lyon, CNRS Université Lyon 1 , Laboratoire de Chimie UMR 5182 , 46 allée d'Italie , Lyon , F-69364 , France
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Meyer B, Genoni A. Libraries of Extremely Localized Molecular Orbitals. 3. Construction and Preliminary Assessment of the New Databanks. J Phys Chem A 2018; 122:8965-8981. [PMID: 30339393 DOI: 10.1021/acs.jpca.8b09056] [Citation(s) in RCA: 40] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The fast and reliable determination of wave functions and electron densities of macromolecules has been one of the goals of theoretical chemistry for a long time, and in this context, several linear scaling techniques have been successfully devised over the years. Different approaches have been adopted to tackle this problem, and one of them exploits the fact that, according to the traditional chemical perception, molecules can be seen as constituted of recurring units (e.g., functional groups) with well-defined chemical features. This has led to the development of methods in which the global wave functions or electron densities of macromolecules are obtained by simply transferring density matrices or fuzzy electron densities associated with molecular fragments. In this context, we propose an alternative strategy that aims at quickly reconstructing wave functions and electron densities of proteins through the transfer of extremely localized molecular orbitals (ELMOs), which are orbitals strictly localized on small molecular units and, for this reason, easily transferable from molecule to molecule. To accomplish this task we have constructed original libraries of ELMOs that cover all the possible elementary fragments of the 20 natural amino acids in all their possible protonation states and forms. Our preliminary test calculations have shown that, compared to more traditional methods of quantum chemistry, the transfers from the novel ELMO databanks allow to obtain wave function and electron densities of large polypeptides and proteins at a significantly reduced computational cost. Furthermore, notwithstanding expected discrepancies, the obtained electron distributions and electrostatic potentials are in very good agreement with those obtained at Hartree-Fock and density functional theory (DFT) levels. Therefore, the results encourage to use the new libraries as alternatives to the popular pseudoatom-databases of crystallography in the refinement of crystallographic structures of macromolecules. In particular, in this context, we have already envisaged the coupling of the ELMO databanks with the promising Hirshfeld atom refinement technique to extend the applicability of the latter to very large systems.
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Affiliation(s)
- Benjamin Meyer
- Université de Lorraine and CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019 , 1 Boulevard Arago , F-57078 Metz , France
| | - Alessandro Genoni
- Université de Lorraine and CNRS, Laboratoire de Physique et Chimie Théoriques (LPCT), UMR CNRS 7019 , 1 Boulevard Arago , F-57078 Metz , France
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Genoni A, Franchini D, Pieraccini S, Sironi M. X‐ray Constrained Spin‐Coupled Wavefunction: a New Tool to Extract Chemical Information from X‐ray Diffraction Data. Chemistry 2018; 24:15507-15511. [DOI: 10.1002/chem.201803988] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2018] [Indexed: 11/08/2022]
Affiliation(s)
- Alessandro Genoni
- Université de Lorraine CNRS, Laboratoire LPCT 1 Boulevard Arago 57078 Metz France
| | - Davide Franchini
- Dipartimento di Chimica Università degli Studi di Milano Via Golgi 19 20133 Milano Italy
| | - Stefano Pieraccini
- Dipartimento di Chimica Università degli Studi di Milano Via Golgi 19 20133 Milano Italy
- Istituto di Scienze e Tecnologie Molecolari (ISTM), CNR Via Golgi 19 20133 Milano Italy
- Consorzio Interuniversitario Nazionale per la, Scienza e Tecnologia dei Materiali (INSTM), UdR Milano Via Golgi 19 20133 Milano Italy
| | - Maurizio Sironi
- Dipartimento di Chimica Università degli Studi di Milano Via Golgi 19 20133 Milano Italy
- Istituto di Scienze e Tecnologie Molecolari (ISTM), CNR Via Golgi 19 20133 Milano Italy
- Consorzio Interuniversitario Nazionale per la, Scienza e Tecnologia dei Materiali (INSTM), UdR Milano Via Golgi 19 20133 Milano Italy
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Genoni A, Bučinský L, Claiser N, Contreras-García J, Dittrich B, Dominiak PM, Espinosa E, Gatti C, Giannozzi P, Gillet JM, Jayatilaka D, Macchi P, Madsen AØ, Massa L, Matta CF, Merz KM, Nakashima PNH, Ott H, Ryde U, Schwarz K, Sierka M, Grabowsky S. Quantum Crystallography: Current Developments and Future Perspectives. Chemistry 2018; 24:10881-10905. [PMID: 29488652 DOI: 10.1002/chem.201705952] [Citation(s) in RCA: 85] [Impact Index Per Article: 14.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2017] [Revised: 02/27/2018] [Indexed: 11/09/2022]
Abstract
Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.
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Affiliation(s)
- Alessandro Genoni
- Université de Lorraine, CNRS, Laboratoire LPCT, 1 Boulevard Arago, F-57078, Metz, France
| | - Lukas Bučinský
- Institute of Physical Chemistry and Chemical Physics, Slovak University of Technology, FCHPT SUT, Radlinského 9, SK-812 37, Bratislava, Slovakia
| | - Nicolas Claiser
- Université de Lorraine, CNRS, Laboratoire CRM2, Boulevard des Aiguillettes, BP 70239, F-54506, Vandoeuvre-lès-Nancy, France
| | - Julia Contreras-García
- Sorbonne Universités, UPMC Université Paris 06, CNRS, Laboratoire de Chimie Théorique (LCT), 4 Place Jussieu, F-75252, Paris Cedex 05, France
| | - Birger Dittrich
- Anorganische und Strukturchemie II, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany
| | - Paulina M Dominiak
- Biological and Chemical Research Centre, Department of Chemistry, University of Warsaw, ul. Żwirki i Wigury 101, 02-089, Warszawa, Poland
| | - Enrique Espinosa
- Université de Lorraine, CNRS, Laboratoire CRM2, Boulevard des Aiguillettes, BP 70239, F-54506, Vandoeuvre-lès-Nancy, France
| | - Carlo Gatti
- CNR-ISTM Istituto di Scienze e Tecnologie Molecolari, via Golgi 19, Milano, I-20133, Italy.,Istituto Lombardo Accademia di Scienze e Lettere, via Brera 28, 20121, Milano, Italy
| | - Paolo Giannozzi
- Department of Mathematics, Computer Science and Physics, University of Udine, Via delle Scienze 208, I-33100, Udine, Italy
| | - Jean-Michel Gillet
- Structure, Properties and Modeling of Solids Laboratory, CentraleSupelec, Paris-Saclay University, 3 rue Joliot-Curie, 91191, Gif-sur-Yvette, France
| | - Dylan Jayatilaka
- School of Molecular Sciences, University of Western Australia, 35 Stirling Highway, Perth, WA, 6009, Australia
| | - Piero Macchi
- Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012, Bern, Switzerland
| | - Anders Ø Madsen
- Department of Pharmacy, University of Copenhagen, Universitetsparken 2, 2100, Copenhagen, Denmark
| | - Lou Massa
- Hunter College & the Ph.D. Program of the Graduate Center, City University of New York, New York, USA
| | - Chérif F Matta
- Department of Chemistry and Physics, Mount Saint Vincent University, Halifax, Nova Scotia, B3M 2J6, Canada.,Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, B3H 4J3, Canada.,Department of Chemistry, Saint Mary's University, Halifax, Nova Scotia, B3H 3C3, Canada.,Département de Chimie, Université Laval, Québec, QC G1V 0A6, Canada
| | - Kenneth M Merz
- Department of Chemistry and Department of Biochemistry and Molecular Biology, Michigan State University, 578 South Shaw Lane, East Lansing, Michigan, 48824, USA.,Institute for Cyber Enabled Research, Michigan State University, 567 Wilson Road, Room 1440, East Lansing, Michigan, 48824, USA
| | - Philip N H Nakashima
- Department of Materials Science and Engineering, Monash University, Victoria, 3800, Australia
| | - Holger Ott
- Bruker AXS GmbH, Östliche Rheinbrückenstraße 49, 76187, Karlsruhe, Germany
| | - Ulf Ryde
- Department of Theoretical Chemistry, Lund University, Chemical Centre, P.O. Box 124, SE-22100, Lund, Sweden
| | - Karlheinz Schwarz
- Technische Universität Wien, Institut für Materialwissenschaften, Getreidemarkt 9, A-1060, Vienna, Austria
| | - Marek Sierka
- Otto Schott Institute of Materials Research, Friedrich Schiller University Jena, Löbdergraben 32, 07743, Jena, Germany
| | - Simon Grabowsky
- Fachbereich 2-Biologie/Chemie, Institut für Anorganische Chemie und Kristallographie, Universität Bremen, Leobener Str. 3, 28359, Bremen, Germany
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21
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Woińska M, Jayatilaka D, Dittrich B, Flaig R, Luger P, Woźniak K, Dominiak PM, Grabowsky S. Validation of X-ray Wavefunction Refinement. Chemphyschem 2017; 18:3334-3351. [PMID: 29168318 DOI: 10.1002/cphc.201700810] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2017] [Revised: 09/22/2017] [Indexed: 11/10/2022]
Abstract
In this work, the quality of the electron density in crystals reconstructed by the multipolar model (MM) and by X-ray wavefunction refinement (XWR) is tested on a set of high-resolution X-ray diffraction data sets of four amino acids and six tripeptides. It results in the first thorough validation of XWR. Agreement statistics, figures of merit, residual- and deformation-density maps, as well as atomic displacement parameters are used to measure the quality of the reconstruction relative to the measured structure factors. Topological analysis of the reconstructed density is carried out to obtain atomic and bond-topological properties, which are subsequently compared to the values derived from benchmarking periodic DFT geometry optimizations. XWR is simultaneously in better agreement than the MM with both benchmarking theory and the measured diffraction pattern. In particular, the obvious problems with the description of polar bonds in the MM are significantly reduced by using XWR. Similarly, modeling of electron density in the vicinity of hydrogen atoms with XWR is visibly improved.
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Affiliation(s)
- Magdalena Woińska
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Zwirki i Wigury 101, 02-089, Warsaw, Poland
| | - Dylan Jayatilaka
- School of Molecular Sciences, The University of Western Australia, 35 Stirling Highway, Perth, WA, 6009, Australia
| | - Birger Dittrich
- Heinrich-Heine-Universität Düsseldorf, Anorganische Chemie und Strukturchemie, Gebäude 26.42.01.21, Universitätsstraße 1, 40225, Düsseldorf, Germany
| | - Ralf Flaig
- Diamond Light Source, Harwell Science and Innovation Campus, Didcot, Oxon, OX11 0DE, UK
| | - Peter Luger
- Freie Universität Berlin, Institut für Chemie und Biochemie, Fabeckstraße 36a, 14195, Berlin, Germany
| | - Krzysztof Woźniak
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Zwirki i Wigury 101, 02-089, Warsaw, Poland
| | - Paulina M Dominiak
- Biological and Chemical Research Centre, Chemistry Department, University of Warsaw, Zwirki i Wigury 101, 02-089, Warsaw, Poland
| | - Simon Grabowsky
- Institut für Anorganische Chemie und Kristallographie, Fachbereich 2-Biologie/Chemie, Universität Bremen, Leobener Straße NW2, 28359, Bremen, Germany
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22
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Tsirelson V. Early days of quantum crystallography: A personal account. J Comput Chem 2017; 39:1029-1037. [DOI: 10.1002/jcc.24893] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2017] [Revised: 06/16/2017] [Accepted: 06/29/2017] [Indexed: 11/09/2022]
Affiliation(s)
- Vladimir Tsirelson
- Quantum Chemistry Department; D.I. Mendeleev University of Chemical Technology; Miusskaya Square, 9, Moscow 125047 Russian Federation
- Chemistry Department; South Ural State University; Lenin Prospect, 76, Chelyabinsk 454080 Russian Federation
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23
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Casati N, Genoni A, Meyer B, Krawczuk A, Macchi P. Exploring charge density analysis in crystals at high pressure: data collection, data analysis and advanced modelling. ACTA CRYSTALLOGRAPHICA SECTION B-STRUCTURAL SCIENCE CRYSTAL ENGINEERING AND MATERIALS 2017; 73:584-597. [DOI: 10.1107/s2052520617008356] [Citation(s) in RCA: 38] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2017] [Accepted: 06/06/2017] [Indexed: 11/10/2022]
Abstract
The possibility to determine electron-density distribution in crystals has been an enormous breakthrough, stimulated by a favourable combination of equipment for X-ray and neutron diffraction at low temperature, by the development of simplified, though accurate, electron-density models refined from the experimental data and by the progress in charge density analysis often in combination with theoretical work. Many years after the first successful charge density determination and analysis, scientists face new challenges, for example: (i) determination of the finer details of the electron-density distribution in the atomic cores, (ii) simultaneous refinement of electron charge and spin density or (iii) measuring crystals under perturbation. In this context, the possibility of obtaining experimental charge density at high pressure has recently been demonstrated [Casatiet al.(2016).Nat. Commun.7, 10901]. This paper reports on the necessities and pitfalls of this new challenge, focusing on the speciessyn-1,6:8,13-biscarbonyl[14]annulene. The experimental requirements, the expected data quality and data corrections are discussed in detail, including warnings about possible shortcomings. At the same time, new modelling techniques are proposed, which could enable specific information to be extracted, from the limited and less accurate observations, like the degree of localization of double bonds, which is fundamental to the scientific case under examination.
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24
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Macchi P. The future of topological analysis in experimental charge-density research. ACTA CRYSTALLOGRAPHICA SECTION B, STRUCTURAL SCIENCE, CRYSTAL ENGINEERING AND MATERIALS 2017; 73:330-336. [PMID: 28572543 DOI: 10.1107/s2052520617006989] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2017] [Accepted: 05/10/2017] [Indexed: 06/07/2023]
Abstract
In a recent paper, Dittrich (2017) critically discussed the benefits of analysing experimental electron density within the framework of the quantum theory of atoms in molecules, often called simply the topological analysis of the charge density. The point he raised is important because it challenges the scientific production of a very active community. The question whether this kind of investigation is still sensible is intriguing and it fosters a multifaceted answer. Granted that none can predict the future of any field of science, but an alternative point of view emerges after answering three questions: Why should we investigate the electron charge (and spin) density? Is the interpretative scheme proposed by the quantum theory of atoms in molecules useful? Is an experimental charge density necessary?
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Affiliation(s)
- Piero Macchi
- Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, Bern 3012, Switzerland
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25
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Grabowsky S, Genoni A, Bürgi HB. Quantum crystallography. Chem Sci 2017; 8:4159-4176. [PMID: 28878872 PMCID: PMC5576428 DOI: 10.1039/c6sc05504d] [Citation(s) in RCA: 97] [Impact Index Per Article: 13.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2016] [Accepted: 03/03/2017] [Indexed: 12/12/2022] Open
Abstract
Approximate wavefunctions can be improved by constraining them to reproduce observations derived from diffraction and scattering experiments. Conversely, charge density models, incorporating electron-density distributions, atomic positions and atomic motion, can be improved by supplementing diffraction experiments with quantum chemically calculated, tailor-made electron densities (form factors). In both cases quantum chemistry and diffraction/scattering experiments are combined into a single, integrated tool. The development of quantum crystallographic research is reviewed. Some results obtained by quantum crystallography illustrate the potential and limitations of this field.
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Affiliation(s)
- Simon Grabowsky
- Universität Bremen , Fachbereich 2 - Biologie/Chemie , Institut für Anorganische Chemie und Kristallographie , Leobener Str. NW2 , 28359 Bremen , Germany .
| | - Alessandro Genoni
- CNRS , Laboratoire SRSMC , UMR 7565 , Vandoeuvre-lès-Nancy , F-54506 , France
- Université de Lorraine , Laboratoire SRSMC , UMR 7565 , Vandoeuvre-lès-Nancy , F-54506 , France .
| | - Hans-Beat Bürgi
- Universität Bern , Departement für Chemie und Biochemie , Freiestr. 3 , CH-3012 Bern , Switzerland .
- Universität Zürich , Institut für Chemie , Winterthurerstrasse 190 , CH-8057 Zürich , Switzerland
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26
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Genoni A. A first-prototype multi-determinant X-ray constrained wavefunction approach: the X-ray constrained extremely localized molecular orbital–valence bond method. ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2017; 73:312-316. [DOI: 10.1107/s2053273317005903] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2017] [Accepted: 04/19/2017] [Indexed: 11/10/2022]
Abstract
All the current variants of Jayatilaka's X-ray constrained wavefunction (XCW) approach work within the framework of the single-determinant wavefunctionansatz. In this paper, a first-prototype multi-determinant XCW technique is proposed. The strategy assumes that the desired XCW is written as a valence-bond-like expansion in terms of pre-determined single Slater determinants constructed with extremely localized molecular orbitals. The method, which can be particularly suitable to investigate systems with a multi-reference character, has been applied to determine the weights of the resonance structures of naphthalene at different temperatures by exploiting experimental high-resolution X-ray diffraction data. The results obtained have shown that the explicit consideration of experimental structure factors in the determination of the resonance structure weights may lead to results significantly different compared with those resulting only from the simple energy minimization.
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27
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Dittrich B, Lübben J, Mebs S, Wagner A, Luger P, Flaig R. Accurate Bond Lengths to Hydrogen Atoms from Single-Crystal X-ray Diffraction by Including Estimated Hydrogen ADPs and Comparison to Neutron and QM/MM Benchmarks. Chemistry 2017; 23:4605-4614. [PMID: 28295691 PMCID: PMC5434951 DOI: 10.1002/chem.201604705] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2016] [Revised: 11/21/2016] [Indexed: 11/21/2022]
Abstract
Amino acid structures are an ideal test set for method-development studies in crystallography. High-resolution X-ray diffraction data for eight previously studied genetically encoding amino acids are provided, complemented by a non-standard amino acid. Structures were re-investigated to study a widely applicable treatment that permits accurate X-H bond lengths to hydrogen atoms to be obtained: this treatment combines refinement of positional hydrogen-atom parameters with aspherical scattering factors with constrained "TLS+INV" estimated hydrogen anisotropic displacement parameters (H-ADPs). Tabulated invariom scattering factors allow rapid modeling without further computations, and unconstrained Hirshfeld atom refinement provides a computationally demanding alternative when database entries are missing. Both should incorporate estimated H-ADPs, as free refinement frequently leads to over-parameterization and non-positive definite H-ADPs irrespective of the aspherical scattering model used. Using estimated H-ADPs, both methods yield accurate and precise X-H distances in best quantitative agreement with neutron diffraction data (available for five of the test-set molecules). This work thus solves the last remaining problem to obtain such results more frequently. Density functional theoretical QM/MM computations are able to play the role of an alternative benchmark to neutron diffraction.
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Affiliation(s)
- Birger Dittrich
- Heinrich-Heine Universität DüsseldorfInstitut für Anorganische Chemie und Strukturchemie, Material- und Strukturforschung, Gebäude: 26.42Universitätsstraße 140225DüsseldorfGermany
| | - Jens Lübben
- Heinrich-Heine Universität DüsseldorfInstitut für Anorganische Chemie und Strukturchemie, Material- und Strukturforschung, Gebäude: 26.42Universitätsstraße 140225DüsseldorfGermany
| | - Stefan Mebs
- Institut für Chemie und Biochemie–Anorganische Chemie derFreien Universität Berlin14195BerlinGermany
| | - Armin Wagner
- Diamond Light SourceHarwell Science and Innovation CampusDidcotOX11 0DEUK
| | - Peter Luger
- Institut für Chemie und Biochemie–Anorganische Chemie derFreien Universität Berlin14195BerlinGermany
| | - Ralf Flaig
- Diamond Light SourceHarwell Science and Innovation CampusDidcotOX11 0DEUK
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28
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Genoni A, Dos Santos LHR, Meyer B, Macchi P. Can X-ray constrained Hartree-Fock wavefunctions retrieve electron correlation? IUCRJ 2017; 4:136-146. [PMID: 28250952 PMCID: PMC5330524 DOI: 10.1107/s2052252516019217] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2016] [Accepted: 12/02/2016] [Indexed: 05/29/2023]
Abstract
The X-ray constrained wavefunction (XC-WF) method proposed by Jayatilaka [Jayatilaka & Grimwood (2001) ▸, Acta Cryst. A57, 76-86] has attracted much attention because it represents a possible third way of theoretically studying the electronic structure of atoms and molecules, combining features of the more popular wavefunction- and DFT-based approaches. In its original formulation, the XC-WF technique extracts statistically plausible wavefunctions from experimental X-ray diffraction data of molecular crystals. A weight is used to constrain the pure Hartree-Fock solution to the observed X-ray structure factors. Despite the wavefunction being a single Slater determinant, it is generally assumed that its flexibility could guarantee the capture, better than any other experimental model, of electron correlation effects, absent in the Hartree-Fock Hamiltonian but present in the structure factors measured experimentally. However, although the approach has been known for long time, careful testing of this fundamental hypothesis is still missing. Since a formal demonstration is impossible, the validation can only be done heuristically and, to accomplish this task, X-ray constrained Hartree-Fock calculations have been performed using structure factor amplitudes computed at a very high correlation level (coupled cluster) for selected molecules in isolation, in order to avoid the perturbations due to intermolecular interactions. The results show that a single-determinant XC-WF is able to capture the electron correlation effects only partially. The largest amount of electron correlation is extracted when: (i) a large external weight is used (much larger than what has normally been used in XC-WF calculations using experimental data); and (ii) the high-order reflections, which carry less information on the electron correlation, are down-weighted (or even excluded), otherwise they would bias the fitting towards the unconstrained Hartree-Fock wavefunction.
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Affiliation(s)
- Alessandro Genoni
- CNRS, Laboratoire SRSMC, UMR 7565, Boulevard des Aiguillettes, BP 70239, Vandoeuvre-lès-Nancy, F-54506, France
- Université de Lorraine, Laboratoire SRSMC, UMR 7565, Boulevard des Aiguillettes, BP 70239, Vandoeuvre-lès-Nancy, F-54506, France
| | - Leonardo H. R. Dos Santos
- Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, Bern 3012, Switzerland
| | - Benjamin Meyer
- CNRS, Laboratoire SRSMC, UMR 7565, Boulevard des Aiguillettes, BP 70239, Vandoeuvre-lès-Nancy, F-54506, France
- Université de Lorraine, Laboratoire SRSMC, UMR 7565, Boulevard des Aiguillettes, BP 70239, Vandoeuvre-lès-Nancy, F-54506, France
| | - Piero Macchi
- Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, Bern 3012, Switzerland
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29
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Bučinský L, Jayatilaka D, Grabowsky S. Importance of Relativistic Effects and Electron Correlation in Structure Factors and Electron Density of Diphenyl Mercury and Triphenyl Bismuth. J Phys Chem A 2016; 120:6650-69. [PMID: 27434184 DOI: 10.1021/acs.jpca.6b05769] [Citation(s) in RCA: 48] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
This study investigates the possibility of detecting relativistic effects and electron correlation in single-crystal X-ray diffraction experiments using the examples of diphenyl mercury (HgPh2) and triphenyl bismuth (BiPh3). In detail, the importance of electron correlation (ECORR), relativistic effects (REL) [distinguishing between total, scalar and spin-orbit (SO) coupling relativistic effects] and picture change error (PCE) on the theoretical electron density, its topology and its Laplacian using infinite order two component (IOTC) wave functions is discussed. This is to develop an understanding of the order of magnitude and shape of these different effects as they manifest in the electron density. Subsequently, the same effects are considered for the theoretical structure factors. It becomes clear that SO and PCE are negligible, but ECORR and scalar REL are important in low- and medium-order reflections on absolute and relative scales-not in the high-order region. As a further step, Hirshfeld atom refinement (HAR) and subsequent X-ray constrained wavefunction (XCW) fitting have been performed for the compound HgPh2 with various relativistic and nonrelativistic wave functions against the experimental structure factors. IOTC calculations of theoretical structure factors and relativistic HAR as well as relativistic XCW fitting are presented for the first time, accounting for both scalar and spin-orbit relativistic effects.
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Affiliation(s)
- Lukáš Bučinský
- Institute of Physical Chemistry and Chemical Physics FCHPT, Slovak University of Technology , Radlinskeho 9, Bratislava SK-812 37, Slovakia
| | - Dylan Jayatilaka
- School of Chemistry and Biochemistry, The University of Western Australia , 35 Stirling Highway, Perth WA 6009, Australia
| | - Simon Grabowsky
- Fachbereich 2 - Biologie/Chemie, Universität Bremen , Leobener Straβe NW2, 28359 Bremen, Germany
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30
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Meyer B, Guillot B, Ruiz-Lopez MF, Genoni A. Libraries of Extremely Localized Molecular Orbitals. 1. Model Molecules Approximation and Molecular Orbitals Transferability. J Chem Theory Comput 2016; 12:1052-67. [PMID: 26799516 DOI: 10.1021/acs.jctc.5b01007] [Citation(s) in RCA: 51] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Despite more and more remarkable computational ab initio results are nowadays continuously obtained for large macromolecular systems, the development of new linear-scaling techniques is still an open and stimulating field of research in theoretical chemistry. In this family of methods, an important role is occupied by those strategies based on the observation that molecules are generally constituted by recurrent functional units with well-defined intrinsic features. In this context, we propose to exploit the notion of extremely localized molecular orbitals (ELMOs) that, due to their strict localization on small molecular fragments (e.g., atoms, bonds, or functional groups), are in principle transferable from one molecule to another. Accordingly, the construction of orbital libraries to almost instantaneously build up approximate wave functions and electron densities of very large systems becomes conceivable. In this work, the ELMOs transferability is further investigated in detail and, furthermore, suitable rules to construct model molecules for the computation of ELMOs to be stored in future databanks are also defined. The obtained results confirm the reliable transferability of the ELMOs and show that electron densities obtained from the transfer of extremely localized molecular orbitals are very close to the corresponding Hartree-Fock ones. These observations prompt us to construct new ELMOs databases that could represent an alternative/complement to the already popular pseudoatoms databanks both for determining electron densities and for refining crystallographic structures of very large molecules.
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Affiliation(s)
- Benjamin Meyer
- CNRS , Laboratoire SRSMC, UMR 7565, Vandoeuvre-lès-Nancy F-54506, France.,Université de Lorraine , Laboratoire SRSMC, UMR 7565, Vandoeuvre-lès-Nancy F-54506, France
| | - Benoît Guillot
- CNRS , Laboratoire CRM2, UMR 7036, Vandoeuvre-lès-Nancy F-54506, France.,Université de Lorraine , Laboratoire CRM2, UMR 7036, Vandoeuvre-lès-Nancy F-54506, France
| | - Manuel F Ruiz-Lopez
- CNRS , Laboratoire SRSMC, UMR 7565, Vandoeuvre-lès-Nancy F-54506, France.,Université de Lorraine , Laboratoire SRSMC, UMR 7565, Vandoeuvre-lès-Nancy F-54506, France
| | - Alessandro Genoni
- CNRS , Laboratoire SRSMC, UMR 7565, Vandoeuvre-lès-Nancy F-54506, France.,Université de Lorraine , Laboratoire SRSMC, UMR 7565, Vandoeuvre-lès-Nancy F-54506, France
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31
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Meyer B, Guillot B, Ruiz-Lopez MF, Jelsch C, Genoni A. Libraries of Extremely Localized Molecular Orbitals. 2. Comparison with the Pseudoatoms Transferability. J Chem Theory Comput 2016; 12:1068-81. [PMID: 26799595 DOI: 10.1021/acs.jctc.5b01008] [Citation(s) in RCA: 39] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Due to both technical and methodological difficulties, determining and analyzing charge densities of very large molecular systems represents a serious challenge that, in the crystallographers community, has been mainly tackled by observing that the so-called pseudoatoms of the electron density multipole expansions are reliably transferable from molecule to molecule. This has led to the construction of pseudoatoms databanks that have allowed successful refinements of crystallographic structures of macromolecules, while taking into account their corresponding reconstructed electron distributions. A recent alternative/complement to the previous approach is represented by techniques based on extremely localized molecular orbitals (ELMOs) that, due to their strict localization on small molecular fragments (e.g., atoms, bonds, and functional groups), are also in principle exportable from system to system. The ELMOs transferability has been already tested in detail, and, in this work, it has been compared to the one of the pseudoatoms. To accomplish this task, electron distributions obtained both through the transfer of pseudoatoms and through the transfer of extremely localized molecular orbitals have been analyzed, especially taking into account topological properties and similarity indexes. The obtained results indicate that all the considered reconstruction methods give completely reasonable and similar charge densities, and, consequently, the new ELMOs libraries will probably represent new useful tools not only for refining crystal structures but also for computing approximate electronic properties of very large molecules.
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Affiliation(s)
- Benjamin Meyer
- CNRS , Laboratoire SRSMC, UMR 7565, Vandoeuvre-lès-Nancy F-54506, France.,Université de Lorraine , Laboratoire SRSMC, UMR 7565, Vandoeuvre-lès-Nancy F-54506, France
| | - Benoît Guillot
- CNRS , Laboratoire CRM2, UMR 7036, Vandoeuvre-lès-Nancy F-54506, France.,Université de Lorraine , Laboratoire CRM2, UMR 7036, Vandoeuvre-lès-Nancy F-54506, France
| | - Manuel F Ruiz-Lopez
- CNRS , Laboratoire SRSMC, UMR 7565, Vandoeuvre-lès-Nancy F-54506, France.,Université de Lorraine , Laboratoire SRSMC, UMR 7565, Vandoeuvre-lès-Nancy F-54506, France
| | - Christian Jelsch
- CNRS , Laboratoire CRM2, UMR 7036, Vandoeuvre-lès-Nancy F-54506, France.,Université de Lorraine , Laboratoire CRM2, UMR 7036, Vandoeuvre-lès-Nancy F-54506, France
| | - Alessandro Genoni
- CNRS , Laboratoire SRSMC, UMR 7565, Vandoeuvre-lès-Nancy F-54506, France.,Université de Lorraine , Laboratoire SRSMC, UMR 7565, Vandoeuvre-lès-Nancy F-54506, France
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Macchi P, Gillet JM, Taulelle F, Campo J, Claiser N, Lecomte C. Modelling the experimental electron density: only the synergy of various approaches can tackle the new challenges. IUCRJ 2015; 2:441-51. [PMID: 26175903 PMCID: PMC4491316 DOI: 10.1107/s2052252515007538] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2015] [Accepted: 04/16/2015] [Indexed: 06/01/2023]
Abstract
Electron density is a fundamental quantity that enables understanding of the chemical bonding in a molecule or in a solid and the chemical/physical property of a material. Because electrons have a charge and a spin, two kinds of electron densities are available. Moreover, because electron distribution can be described in momentum or in position space, charge and spin density have two definitions and they can be observed through Bragg (for the position space) or Compton (for the momentum space) diffraction experiments, using X-rays (charge density) or polarized neutrons (spin density). In recent years, we have witnessed many advances in this field, stimulated by the increased power of experimental techniques. However, an accurate modelling is still necessary to determine the desired functions from the acquired data. The improved accuracy of measurements and the possibility to combine information from different experimental techniques require even more flexibility of the models. In this short review, we analyse some of the most important topics that have emerged in the recent literature, especially the most thought-provoking at the recent IUCr general meeting in Montreal.
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Affiliation(s)
- Piero Macchi
- Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland
| | - Jean-Michel Gillet
- Laboratoire Structures Propriétés et Modélisation des Solides, UMR 8580, Université Paris Saclay CentraleSupélec, CNRS, Grande Voie des Vignes, 92295 Chatenay-Malabry, France
| | - Francis Taulelle
- Institut Lavoisier de Versailles, Université de Versailles Saint Quentin en Yvelines, 45 Avenue des Etats-Unis, Versailles, 78035, France
| | - Javier Campo
- Materials Science Institute of Aragón, CSIC-University of Zaragoza, Zaragoza, 50009, Spain
| | - Nicolas Claiser
- Cristallographie, Résonance Magnetique et Modélisations, CRM2, UMR 7036, Institut Jean Barriol, Université de Lorraine, Vandoeuvre-les-Nancy, BP239, F54506, France
| | - Claude Lecomte
- Cristallographie, Résonance Magnetique et Modélisations, CRM2, UMR 7036, Institut Jean Barriol, Université de Lorraine, Vandoeuvre-les-Nancy, BP239, F54506, France
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