1
|
Nash HW, Shaw RA, Hill JG. Correlation consistent auxiliary basis sets in density fitting Hartree-Fock: The atoms sodium through argon revisited. J Comput Chem 2023; 44:1119-1128. [PMID: 36636897 PMCID: PMC10947126 DOI: 10.1002/jcc.27069] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2022] [Revised: 11/29/2022] [Accepted: 12/14/2022] [Indexed: 01/14/2023]
Abstract
We present a series of auxiliary basis sets, for the elements Na to Ar, for use in density-fitted Hartree-Fock calculations with the correlation consistent cc-pV(n + d)Z orbital basis sets. Benchmarking on total molecular energies, reaction energies and the spectroscopic constants of the SO molecule demonstrate that the new sets address the deficiencies of using existing auxiliary sets in combination with these orbital basis sets. We also report auxiliary basis sets for Na and Mg matched to cc-pVnZ, along with recommendations for pairing auxiliary basis sets to the cc-pVnZ-F12 basis sets for Hartree-Fock calculations.
Collapse
Affiliation(s)
- Harry W. Nash
- Department of ChemistryUniversity of SheffieldSheffieldUK
| | - Robert A. Shaw
- Department of ChemistryUniversity of SheffieldSheffieldUK
| | | |
Collapse
|
2
|
Zhang Y, Zhao J. A density fitting scheme for the fast evaluation of molecular electrostatic potential. J Comput Chem 2023; 44:806-813. [PMID: 36411980 DOI: 10.1002/jcc.27042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2022] [Revised: 11/01/2022] [Accepted: 11/03/2022] [Indexed: 11/23/2022]
Abstract
Molecular electrostatic potential (MEP) is a significant and crucial physical quantity that can be applied to a large number of scenarios, such as the prediction of nucleophilic or electrophilic attacks, fitting atomic charges, σ-hole, and so forth. The computational cost for the MEP has an O(N2 ) scaling with the increase of atoms, which is intractable and laborious for macromolecules. Herein, a density fitting molecular electrostatic potential (DF-MEP) is used to reduce the computational costs for the macromolecular MEP. It is found that the accuracy of DF-MEP is almost identical to the conventional molecular electrostatic potential (Conv-MEP), while the computational costs can be reduced to an O(N) scaling, for example, the computational time of 699,200 grids for the Trp-cage molecule (304 atoms) only takes 16.6 s at the B3LYP-D3(BJ)/def2-SVP level of theory with 16 CPU cores compared with 3060.2 s for the Conv-MEP method.
Collapse
Affiliation(s)
- Yingfeng Zhang
- Key Laboratory of Magnetic Resonance in Biological Systems, State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Innovation Academy of Precision Measurement Science and Technology, Chinese Academy of Sciences, Wuhan, China.,University of Chinese Academy of Sciences, Beijing, China
| | - Jian Zhao
- State Key Laboratory of Catalysis, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, China
| |
Collapse
|
3
|
Medves M, Fronzoni G, Stener M. Optimization of density fitting auxiliary Slater-type basis functions for time-dependent density functional theory. J Comput Chem 2022; 43:1923-1935. [PMID: 36069663 PMCID: PMC9825902 DOI: 10.1002/jcc.26992] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2022] [Revised: 08/02/2022] [Accepted: 08/02/2022] [Indexed: 01/11/2023]
Abstract
A new set of auxiliary basis function suitable to fit the induced electron density is presented. Such set has been optimized in order to furnish accurate absorption spectra using the complex polarizability algorithm of time-dependent density functional theory (TDDFT). An automatic procedure has been set up, able, thanks to the definition of suitable descriptors, to evaluate the resemblance of the auxiliary basis-dependent calculated spectra with respect to a reference. In this way, it has been possible to reduce the size of the basis set maximizing the basis set accuracy. Thanks to the choice to employ a collection of molecules for each element, such basis has proven transferable to molecules outside the collection. The final sets are therefore much more accurate and smaller than the previously optimized ones and have been already included in the database of the last release of the AMS suite of programs. The availability of the present new set will allow to improve drastically the applicability range of the polTDDFT method with higher accuracy and less computational effort.
Collapse
Affiliation(s)
- Marco Medves
- Dipartimento di Scienze Chimiche e FarmaceuticheUniversità di TriesteTriesteItaly
| | - Giovanna Fronzoni
- Dipartimento di Scienze Chimiche e FarmaceuticheUniversità di TriesteTriesteItaly
| | - Mauro Stener
- Dipartimento di Scienze Chimiche e FarmaceuticheUniversità di TriesteTriesteItaly
| |
Collapse
|
4
|
Müller C, Sharma M, Sierka M. Real-time time-dependent density functional theory using density fitting and the continuous fast multipole method. J Comput Chem 2020; 41:2573-2582. [PMID: 33464600 DOI: 10.1002/jcc.26412] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/26/2020] [Revised: 08/17/2020] [Accepted: 08/18/2020] [Indexed: 11/07/2022]
Abstract
An implementation of real-time time-dependent density functional theory (RT-TDDFT) within the TURBOMOLE program package is reported using Gaussian-type orbitals as basis functions, second and fourth order Magnus propagator, and the self-consistent field as well as the predictor-corrector time integration schemes. The Coulomb contribution to the Kohn-Sham matrix is calculated combining density fitting approximation and the continuous fast multipole method. Performance of the implementation is benchmarked for molecular systems with different sizes and dimensionalities. For linear alkane chains, the wall time for density matrix time propagation step is comparable to the Kohn-Sham (KS) matrix construction. However, for larger two- and three-dimensional molecules, with up to about 5,000 basis functions, the computational effort of RT-TDDFT calculations is dominated by the KS matrix evaluation. In addition, the maximum time step is evaluated using a set of small molecules of different polarities. The photoabsorption spectra of several molecular systems calculated using RT-TDDFT are compared to those obtained using linear response time-dependent density functional theory and coupled cluster methods.
Collapse
Affiliation(s)
- Carolin Müller
- Otto Schott Institute of Materials Research, Friedrich Schiller University of Jena, Jena, Germany
| | - Manas Sharma
- Otto Schott Institute of Materials Research, Friedrich Schiller University of Jena, Jena, Germany
| | - Marek Sierka
- Otto Schott Institute of Materials Research, Friedrich Schiller University of Jena, Jena, Germany
| |
Collapse
|
5
|
Chen X, Qu Z, Suo B, Gao J. A self-consistent coulomb bath model using density fitting. J Comput Chem 2020; 41:1698-1708. [PMID: 32369627 DOI: 10.1002/jcc.26211] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2019] [Revised: 03/02/2020] [Accepted: 04/05/2020] [Indexed: 12/24/2022]
Abstract
A self-consistent Coulomb bath model is presented to provide an accurate and efficient way of performing calculations for interfragment electrostatic and polarization interactions. In this method, a condensed-phase system is partitioned into molecular fragment blocks. Each fragment is embedded in the Coulomb bath due to other fragments. Importantly, the present Coulomb bath is represented using a density fitting method in which the electron densities of molecular fragments are fitted using an atom-centered auxiliary basis set of Gaussian type. The Coulomb bath is incorporated into an effective Hamiltonian for each fragment, with which the electron density is optimized through an iterative double self-consistent field (DSCF) procedure to realize the mutual many-body polarization effects. In this work, the accuracy of interfragment interaction energies enumerated using the Coulomb bath is tested, showing a good agreement with the exact results from an energy decomposition analysis. The qualitative features of many-body polarization effects are visualized by electron density difference plots. It is also shown that the present DSCF method can yield fast and robust convergence with near-linear scaling in performance with increase in system size.
Collapse
Affiliation(s)
- Xin Chen
- Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, China.,Shenzhen Bay Laboratory, Shenzhen, China
| | - Zexing Qu
- Laboratory of Theoretical and Computational Chemistry, Institute of Theoretical Chemistry, Jilin University, Changchun, China
| | - Bingbing Suo
- Shaanxi Key Laboratory for Theoretical Physics Frontiers, Institute of Modern Physics, Northwest University, Xi'an, Shaanxi, China
| | - Jiali Gao
- Shenzhen Bay Laboratory, Shenzhen, China.,Laboratory of Computational Chemistry and Drug Design, Peking University Shenzhen Graduate School, Shenzhen, China.,Department of Chemistry and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota, USA
| |
Collapse
|
6
|
Becker M, Sierka M. Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Stress tensor. J Comput Chem 2019; 40:2563-2570. [PMID: 31322769 DOI: 10.1002/jcc.26033] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2019] [Revised: 06/24/2019] [Accepted: 06/27/2019] [Indexed: 11/06/2022]
Abstract
A full implementation of the analytical stress tensor for periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. It is the extension of the implementation of analytical energy gradients (Lazarski et al., Journal of Computational Chemistry 2016, 37, 2518-2526) to the stress tensor for the purpose of optimization of lattice vectors. Its key component is the efficient calculation of the Coulomb contribution by combining density fitting approximation and continuous fast multipole method. For the exchange-correlation (XC) part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097-3104) is extended to XC weight derivatives and stress tensor. The computational efficiency and favorable scaling behavior of the stress tensor implementation are demonstrated for various model systems. The overall computational effort for energy gradient and stress tensor for the largest systems investigated is shown to be at most two and a half times the computational effort for the Kohn-Sham matrix formation. © 2019 Wiley Periodicals, Inc.
Collapse
Affiliation(s)
- Martin Becker
- Otto-Schott-Institut für Materialforschung, Friedrich-Schiller-Universität Jena, Löbdergraben 32, Jena, D-07743, Germany
| | - Marek Sierka
- Otto-Schott-Institut für Materialforschung, Friedrich-Schiller-Universität Jena, Löbdergraben 32, Jena, D-07743, Germany
| |
Collapse
|
7
|
Isbill SB, Chandrachud PP, Kern JL, Jenkins DM, Roy S. Elucidation of the Reaction Mechanism of C 2 + N 1 Aziridination from Tetracarbene Iron Catalysts. ACS Catal 2019; 9:6223-6233. [PMID: 31534826 DOI: 10.1021/acscatal.9b01306] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/07/2023]
Abstract
A combined computational and experimental study was undertaken to elucidate the mechanism of catalytic C2 + N1 aziridination supported by tetracarbene iron complexes. Three specific aspects of the catalytic cycle were addressed. First, how do organic azides react with different iron catalysts and why are alkyl azides ineffective for some catalysts? Computation of the catalytic pathway using density functional theory (DFT) revealed that an alkyl azide needs to overcome a higher activation barrier than an aryl azide to form an iron imide, and the activation barrier with the first-generation catalyst is higher than the activation barrier with the second-generation variant. Second, does the aziridination from the imide complex proceed through an open-chain radical intermediate that can change stereochemistry or, instead, via an azametallacyclobutane intermediate that retains stereochemistry? DFT calculations show that the formation of aziridine proceeds via the open-chain radical intermediate, which qualitatively explains the formation of both aziridine diastereomers as seen in experiments. Third, how can the formation of the side product, a metallotetrazene, be prevented, which would improve the yield of aziridine at lower alkene loading? DFT and experimental results demonstrate that sterically bulky organic azides prohibit formation of the metallotetrazene and, thus, allow lower alkene loading for effective catalysis. These multiple insights of different aspects of the catalytic cycle are critical for developing improved catalysts for C2 + N1 aziridination.
Collapse
Affiliation(s)
- Sara B. Isbill
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Preeti P. Chandrachud
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Jesse L. Kern
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - David M. Jenkins
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Sharani Roy
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
| |
Collapse
|
8
|
Heuser J, Höfener S. Analytical nuclear excited-state gradients for the Tamm-Dancoff approximation using uncoupled frozen-density embedding. J Comput Chem 2017; 38:2316-2325. [PMID: 28766728 DOI: 10.1002/jcc.24885] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2017] [Revised: 06/24/2017] [Accepted: 06/27/2017] [Indexed: 11/11/2022]
Abstract
We report the derivation and implementation of analytical nuclear gradients for excited states using time-dependent density functional theory using the Tamm-Dancoff approximation combined with uncoupled frozen-density embedding using density fitting. Explicit equations are presented and discussed. The implementation is able to treat singlet as well as triplet states and functionals using the local density approximation, the generalized gradient approximation, combinations with Hartree-Fock exchange (hybrids), and range-separated functionals such as CAM-B3LYP. The new method is benchmarked against supermolecule calculations in two case studies: The solvatochromic shift of the (vertical) fluorescence energy of 4-aminophthalimide on solvation, and the first local excitation of the benzonitrile dimer. Whereas for the 4-aminophthalimide-water complex deviations of about 0.2 eV are obtained to supermolecular calculations, for the benzonitrile dimer the maximum error for adiabatic excitation energies is below 0.01 eV due to a weak coupling of the subsystems. © 2017 Wiley Periodicals, Inc.
Collapse
Affiliation(s)
- Johannes Heuser
- Institut für Physikalische Chemie, Fakultät für Chemie und Biowissenschaften, Karlsruher Institut für Technologie (KIT), D-76131, Karlsruhe
| | - Sebastian Höfener
- Institut für Physikalische Chemie, Fakultät für Chemie und Biowissenschaften, Karlsruher Institut für Technologie (KIT), D-76131, Karlsruhe
| |
Collapse
|
9
|
Łazarski R, Burow AM, Grajciar L, Sierka M. Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Analytical gradients. J Comput Chem 2016; 37:2518-26. [PMID: 27555218 DOI: 10.1002/jcc.24477] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2016] [Revised: 08/02/2016] [Accepted: 08/04/2016] [Indexed: 11/10/2022]
Abstract
A full implementation of analytical energy gradients for molecular and periodic systems is reported in the TURBOMOLE program package within the framework of Kohn-Sham density functional theory using Gaussian-type orbitals as basis functions. Its key component is a combination of density fitting (DF) approximation and continuous fast multipole method (CFMM) that allows for an efficient calculation of the Coulomb energy gradient. For exchange-correlation part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097) is extended to energy gradients. Computational efficiency and asymptotic O(N) scaling behavior of the implementation is demonstrated for various molecular and periodic model systems, with the largest unit cell of hematite containing 640 atoms and 19,072 basis functions. The overall computational effort of energy gradient is comparable to that of the Kohn-Sham matrix formation. © 2016 Wiley Periodicals, Inc.
Collapse
Affiliation(s)
- Roman Łazarski
- Otto-Schott-Institut für Materialforschung (OSIM), Friedrich-Schiller-Universität Jena, Löbdergraben 32, Jena, D-07743, Germany
| | - Asbjörn Manfred Burow
- Department of Chemistry, Chair of Theoretical Chemistry, University of Munich (LMU), Butenandtstrasse 7, Munich, D-81377, Germany
| | - Lukáš Grajciar
- Otto-Schott-Institut für Materialforschung (OSIM), Friedrich-Schiller-Universität Jena, Löbdergraben 32, Jena, D-07743, Germany
| | - Marek Sierka
- Otto-Schott-Institut für Materialforschung (OSIM), Friedrich-Schiller-Universität Jena, Löbdergraben 32, Jena, D-07743, Germany.
| |
Collapse
|
10
|
Derevyanko G, Grudinin S. HermiteFit: fast-fitting atomic structures into a low-resolution density map using three-dimensional orthogonal Hermite functions. ACTA ACUST UNITED AC 2014; 70:2069-84. [PMID: 25084327 DOI: 10.1107/s1399004714011493] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2013] [Accepted: 05/19/2014] [Indexed: 08/30/2023]
Abstract
HermiteFit, a novel algorithm for fitting a protein structure into a low-resolution electron-density map, is presented. The algorithm accelerates the rotation of the Fourier image of the electron density by using three-dimensional orthogonal Hermite functions. As part of the new method, an algorithm for the rotation of the density in the Hermite basis and an algorithm for the conversion of the expansion coefficients into the Fourier basis are presented. HermiteFit was implemented using the cross-correlation or the Laplacian-filtered cross-correlation as the fitting criterion. It is demonstrated that in the Hermite basis the Laplacian filter has a particularly simple form. To assess the quality of density encoding in the Hermite basis, an analytical way of computing the crystallographic R factor is presented. Finally, the algorithm is validated using two examples and its efficiency is compared with two widely used fitting methods, ADP_EM and colores from the Situs package. HermiteFit will be made available at http://nano-d.inrialpes.fr/software/HermiteFit or upon request from the authors.
Collapse
Affiliation(s)
- Georgy Derevyanko
- Institute of Complex Systems (ICS-6), Forschungszentrum Jülich, Jülich, Germany
| | | |
Collapse
|
11
|
Beck M, Topf M, Frazier Z, Tjong H, Xu M, Zhang S, Alber F. Exploring the spatial and temporal organization of a cell's proteome. J Struct Biol 2011; 173:483-96. [PMID: 21094684 PMCID: PMC3784337 DOI: 10.1016/j.jsb.2010.11.011] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2010] [Revised: 11/05/2010] [Accepted: 11/08/2010] [Indexed: 10/18/2022]
Abstract
To increase our current understanding of cellular processes, such as cell signaling and division, knowledge is needed about the spatial and temporal organization of the proteome at different organizational levels. These levels cover a wide range of length and time scales: from the atomic structures of macromolecules for inferring their molecular function, to the quantitative description of their abundance, and spatial distribution in the cell. Emerging new experimental technologies are greatly increasing the availability of such spatial information on the molecular organization in living cells. This review addresses three fields that have significantly contributed to our understanding of the proteome's spatial and temporal organization: first, methods for the structure determination of individual macromolecular assemblies, specifically the fitting of atomic structures into density maps generated from electron microscopy techniques; second, research that visualizes the spatial distributions of these complexes within the cellular context using cryo electron tomography techniques combined with computational image processing; and third, methods for the spatial modeling of the dynamic organization of the proteome, specifically those methods for simulating reaction and diffusion of proteins and complexes in crowded intracellular fluids. The long-term goal is to integrate the varied data about a proteome's organization into a spatially explicit, predictive model of cellular processes.
Collapse
Affiliation(s)
- Martin Beck
- European Molecular Biology Laboratory, Meyerhofstr. 1, 69117 Heidelberg, Germany
| | - Maya Topf
- Molecular Biology, Crystallography, Department of Biological Sciences, Birkbeck College, University of London, London, UK
| | - Zachary Frazier
- Program in Molecular and Computational Biology, University of Southern California, 1050 Childs Way, RRI 413E, Los Angeles, CA 90068, USA
| | - Harianto Tjong
- Program in Molecular and Computational Biology, University of Southern California, 1050 Childs Way, RRI 413E, Los Angeles, CA 90068, USA
| | - Min Xu
- Program in Molecular and Computational Biology, University of Southern California, 1050 Childs Way, RRI 413E, Los Angeles, CA 90068, USA
| | - Shihua Zhang
- Program in Molecular and Computational Biology, University of Southern California, 1050 Childs Way, RRI 413E, Los Angeles, CA 90068, USA
| | - Frank Alber
- Program in Molecular and Computational Biology, University of Southern California, 1050 Childs Way, RRI 413E, Los Angeles, CA 90068, USA
| |
Collapse
|
12
|
Topf M, Lasker K, Webb B, Wolfson H, Chiu W, Sali A. Protein structure fitting and refinement guided by cryo-EM density. Structure 2008; 16:295-307. [PMID: 18275820 PMCID: PMC2409374 DOI: 10.1016/j.str.2007.11.016] [Citation(s) in RCA: 263] [Impact Index Per Article: 16.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2007] [Revised: 11/20/2007] [Accepted: 11/26/2007] [Indexed: 11/23/2022]
Abstract
For many macromolecular assemblies, both a cryo-electron microscopy map and atomic structures of its component proteins are available. Here we describe a method for fitting and refining a component structure within its map at intermediate resolution (<15 A). The atomic positions are optimized with respect to a scoring function that includes the crosscorrelation coefficient between the structure and the map as well as stereochemical and nonbonded interaction terms. A heuristic optimization that relies on a Monte Carlo search, a conjugate-gradients minimization, and simulated annealing molecular dynamics is applied to a series of subdivisions of the structure into progressively smaller rigid bodies. The method was tested on 15 proteins of known structure with 13 simulated maps and 3 experimentally determined maps. At approximately 10 A resolution, Calpha rmsd between the initial and final structures was reduced on average by approximately 53%. The method is automated and can refine both experimental and predicted atomic structures.
Collapse
Affiliation(s)
- Maya Topf
- School of Crystallography, Birkbeck College, University of London, Malet Street, London WC1E 7HX, United Kingdom.
| | | | | | | | | | | |
Collapse
|