Validation of experimental molecular crystal structures with dispersion-corrected density functional theory calculations
01 Oct 2010-Acta Crystallographica Section B-structural Science (International Union of Crystallography)-Vol. 66, Iss: 5, pp 544-558
TL;DR: The accuracy of a dispersion-corrected density functional theory method is validated against 241 experimental organic crystal structures from Acta Cryst.
Abstract: This paper describes the validation of a dispersion-corrected density functional theory (d-DFT) method for the purpose of assessing the correctness of experimental organic crystal structures and enhancing the information content of purely experimental data. 241 experimental organic crystal structures from the August 2008 issue of Acta Cryst. Section E were energy-minimized in full, including unit-cell parameters. The differences between the experimental and the minimized crystal structures were subjected to statistical analysis. The r.m.s. Cartesian displacement excluding H atoms upon energy minimization with flexible unit-cell parameters is selected as a pertinent indicator of the correctness of a crystal structure. All 241 experimental crystal structures are reproduced very well: the average r.m.s. Cartesian displacement for the 241 crystal structures, including 16 disordered structures, is only 0.095 A (0.084 A for the 225 ordered structures). R.m.s. Cartesian displacements above 0.25 A either indicate incorrect experimental crystal structures or reveal interesting structural features such as exceptionally large temperature effects, incorrectly modelled disorder or symmetry breaking H atoms. After validation, the method is applied to nine examples that are known to be ambiguous or subtly incorrect.
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TL;DR: It is found that molecular flexibility or size has no correlation with the ability of a compound to be polymorphic and one in three compounds in the CSD are polymorphic whilst at least one in two compounds from the Roche and Lilly set display polymorphism with a higher estimate when compounds are screened intensively.
Abstract: We present new facts about polymorphism based on (i) crystallographic data from the Cambridge Structural Database (CSD, a database built over 50 years of community effort), (ii) 229 solid form screens conducted at Hoffmann-La Roche and Eli Lilly and Company over the course of 8+ and 15+ years respectively and (iii) a dataset of 446 polymorphic crystals with energies and properties computed with modern DFT-d methods. We found that molecular flexibility or size has no correlation with the ability of a compound to be polymorphic. Chiral molecules, however, were found to be less prone to polymorphism than their achiral counterparts and compounds able to hydrogen bond exhibit only a slightly higher propensity to polymorphism than those which do not. Whilst the energy difference between polymorphs is usually less than 1 kcal mol(-1), conformational polymorphs are capable of differing by larger values (up to 2.5 kcal mol(-1) in our dataset). As overall statistics, we found that one in three compounds in the CSD are polymorphic whilst at least one in two compounds from the Roche and Lilly set display polymorphism with a higher estimate of up to three in four when compounds are screened intensively. Whilst the statistics provide some guidance of expectations, each compound constitutes a new challenge and prediction and realization of targeted polymorphism still remains a holy grail of materials sciences.
451 citations
TL;DR: In this article, an atom-atom intermolecular force field with subdivision of interaction energies into Coulombic-polarization, dispersion (London) and repulsion (Pauli) terms is presented.
Abstract: An atom–atom intermolecular force field with subdivision of interaction energies into Coulombic-polarization, dispersion (London) and repulsion (Pauli) terms is presented. Instead of using fixed interaction functions for atomic species, atom–atom potential functions are calculated for each different molecule on the basis of a few standard atomic parameters like atomic numbers, atomic polarizability and ionization potentials, and of local atomic point charges from Mulliken population analysis. The energy partitioning is conducted under guidance from the more accurate evaluation of the same terms by the PIXEL method, also highlighting some intrinsic deficiencies of all atom–atom schemes due to the neglect of penetration energies in Coulombic terms on localized charges. The potential energy scheme is optimized for H, C, N, O, Cl atoms in all chemical connectivities and can be extended to F, S, P, Br, I atoms with minor modifications. The scheme is shown to reproduce the sublimation heats of 154 organic crystal structures, to reproduce about 400 observed crystal structures without distortion, and to reproduce heats of evaporation and specific gravities of 12 common organic liquids. It is therefore suitable for both static and evolutionary (Monte Carlo) molecular simulation. Fine tuning of the four terms for specific systems can be easily performed on the basis of chemical intuition, by the introduction of one overall damping factor for each of them. The scheme is embedded in a suite of Fortran computer programs portable on any platform. For reproducibility and general use, source codes are available for distribution.
311 citations
TL;DR: Electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo are reviewed.
Abstract: Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Moller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.
302 citations
TL;DR: The accuracy of 215 experimental organic crystal structures from powder diffraction data is validated against a dispersion-corrected density functional theory method.
Abstract: In 2010 we energy-minimized 225 high-quality single-crystal (SX) structures with dispersion-corrected density functional theory (DFT-D) to establish a quantitative benchmark. For the current paper, 215 organic crystal structures determined from X-ray powder diffraction (XRPD) data and published in an IUCr journal were energy-minimized with DFT-D and compared to the SX benchmark. The on average slightly less accurate atomic coordinates of XRPD structures do lead to systematically higher root mean square Cartesian displacement (RMSCD) values upon energy minimization than for SX structures, but the RMSCD value is still a good indicator for the detection of structures that deserve a closer look. The upper RMSCD limit for a correct structure must be increased from 0.25 A for SX structures to 0.35 A for XRPD structures; the grey area must be extended from 0.30 to 0.40 A. Based on the energy minimizations, three structures are re-refined to give more precise atomic coordinates. For six structures our calculations provide the missing positions for the H atoms, for five structures they provide corrected positions for some H atoms. Seven crystal structures showed a minor error for a non-H atom. For five structures the energy minimizations suggest a higher space-group symmetry. For the 225 SX structures, the only deviations observed upon energy minimization were three minor H-atom related issues. Preferred orientation is the most important cause of problems. A preferred-orientation correction is the only correction where the experimental data are modified to fit the model. We conclude that molecular crystal structures determined from powder diffraction data that are published in IUCr journals are of high quality, with less than 4% containing an error in a non-H atom.
232 citations
Cites methods from "Validation of experimental molecula..."
...Introduction In 2010, we published the validation of a dispersion-corrected density functional theory (DFT-D) method for the reproduction of molecular crystal structures against 225 high-quality single-crystal (SX) structures (Van de Streek & Neumann, 2010)....
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...Details of the DFT-D energy minimizations are given elsewhere (Van de Streek & Neumann, 2010)....
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References
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TL;DR: An efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set is presented and the application of Pulay's DIIS method to the iterative diagonalization of large matrices will be discussed.
Abstract: We present an efficient scheme for calculating the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrices will be discussed. Our approach is stable, reliable, and minimizes the number of order ${\mathit{N}}_{\mathrm{atoms}}^{3}$ operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special ``metric'' and a special ``preconditioning'' optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calculations. It will be shown that the number of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order ${\mathit{N}}_{\mathrm{atoms}}^{2}$ scaling is found for systems containing up to 1000 electrons. If we take into account that the number of k points can be decreased linearly with the system size, the overall scaling can approach ${\mathit{N}}_{\mathrm{atoms}}$. We have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large number of different systems (liquid and amorphous semiconductors, liquid simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable. \textcopyright{} 1996 The American Physical Society.
81,985 citations
"Validation of experimental molecula..." refers methods in this paper
...In 2005 Neumann & Perrin published a paper in which they combined the planewave DFT code VASP (Kresse & Furthmüller, 1996; Kresse & Hafner, 1993; Kresse & Joubert, 1999) with an in-house parameterized dispersion correction....
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...The d-DFT energy minimizations were carried out with the computer program GRACE, which uses the computer program VASP for single-point pure DFT calculations....
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TL;DR: In this paper, the formal relationship between US Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived and the Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional.
Abstract: The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Bl\"ochl's projector augmented wave (PAW) method is derived. It is shown that the total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addition, critical tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed core all electron methods. These tests include small molecules $({\mathrm{H}}_{2}{,\mathrm{}\mathrm{H}}_{2}{\mathrm{O},\mathrm{}\mathrm{Li}}_{2}{,\mathrm{}\mathrm{N}}_{2}{,\mathrm{}\mathrm{F}}_{2}{,\mathrm{}\mathrm{BF}}_{3}{,\mathrm{}\mathrm{SiF}}_{4})$ and several bulk systems (diamond, Si, V, Li, Ca, ${\mathrm{CaF}}_{2},$ Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
57,691 citations
"Validation of experimental molecula..." refers methods in this paper
...In 2005 Neumann & Perrin published a paper in which they combined the planewave DFT code VASP (Kresse & Furthmüller, 1996; Kresse & Hafner, 1993; Kresse & Joubert, 1999) with an in-house parameterized dispersion correction....
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TL;DR: In this paper, the authors present an ab initio quantum-mechanical molecular-dynamics calculations based on the calculation of the electronic ground state and of the Hellmann-Feynman forces in the local density approximation.
Abstract: We present ab initio quantum-mechanical molecular-dynamics calculations based on the calculation of the electronic ground state and of the Hellmann-Feynman forces in the local-density approximation at each molecular-dynamics step. This is possible using conjugate-gradient techniques for energy minimization, and predicting the wave functions for new ionic positions using subspace alignment. This approach avoids the instabilities inherent in quantum-mechanical molecular-dynamics calculations for metals based on the use of a fictitious Newtonian dynamics for the electronic degrees of freedom. This method gives perfect control of the adiabaticity and allows us to perform simulations over several picoseconds.
32,798 citations
"Validation of experimental molecula..." refers methods in this paper
...In 2005 Neumann & Perrin published a paper in which they combined the planewave DFT code VASP (Kresse & Furthmüller, 1996; Kresse & Hafner, 1993; Kresse & Joubert, 1999) with an in-house parameterized dispersion correction....
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10 Mar 1970
8,159 citations
"Validation of experimental molecula..." refers background or methods in this paper
...This idea is certainly not new and there are ample examples in the literature (for examples using quantum-mechanical calculations to supplement X-ray powder diffraction data see e.g. Smrčok et al., 2008; Ávila et al., 2009; Florence et al., 2009)....
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...…crystal structures with dispersion-corrected density functional theory calculations Jacco van de Streek* and Marcus A. Neumann Avant-garde Materials Simulation, Merzhauser Str. 177, D-79100 Freiburg im Breisgau, Germany Correspondence e-mail: vandestreek@avmatsim.de This paper describes the…...
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...For completeness, and to avoid confusion, we would like to mention explicitly that using energy calculations to complement powder diffraction data to validate crystal structures is fundamentally different from using energy calculations to solve crystal structures from powder diffraction data: the…...
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...B66, 544–558 Acta Crystallographica Section B Structural Science ISSN 0108-7681 Validation of experimental molecular crystal structures with dispersion-corrected density functional theory calculations Jacco van de Streek* and Marcus A. Neumann Avant-garde Materials Simulation, Merzhauser Str. 177, D-79100 Freiburg im Breisgau, Germany Correspondence e-mail: vandestreek@avmatsim.de This paper describes the validation of a dispersion-corrected density functional theory (d-DFT) method for the purpose of assessing the correctness of experimental organic crystal structures and enhancing the information content of purely experimental data....
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...…have been limited to calculations on isolated molecules, dimers or clusters (to keep the systems sizes small) or on ionic compounds (see e.g. Smrčok et al., 2008), or required the experimental unit cell to be kept fixed to avoid the crystal from expanding due to a lack of dispersion forces…...
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University of Cambridge1, University of Maryland, College Park2, Purdue University3, University of Bologna4, Savitribai Phule Pune University5, University of Hyderabad6, Utrecht University7, University of Utah8, University of Buenos Aires9, University of Bradford10, University College London11, Cornell University12, Goethe University Frankfurt13, ETH Zurich14
TL;DR: The results reflect important improvements in modelling methods and suggest that, at least for the small and fairly rigid types of molecules included in this blind test, such calculations can be constructively applied to help understand crystallization and polymorphism of organic molecules.
Abstract: We report on the organization and outcome of the fourth blind test of crystal structure prediction, an international collaborative project organized to evaluate the present state in computational methods of predicting the crystal structures of small organic molecules. There were 14 research groups which took part, using a variety of methods to generate and rank the most likely crystal structures for four target systems: three single-component crystal structures and a 1:1 cocrystal. Participants were challenged to predict the crystal structures of the four systems, given only their molecular diagrams, while the recently determined but as-yet unpublished crystal structures were withheld by an independent referee. Three predictions were allowed for each system. The results demonstrate a dramatic improvement in rates of success over previous blind tests; in total, there were 13 successful predictions and, for each of the four targets, at least two groups correctly predicted the observed crystal structure. The successes include one participating group who correctly predicted all four crystal structures as their first ranked choice, albeit at a considerable computational expense. The results reflect important improvements in modelling methods and suggest that, at least for the small and fairly rigid types of molecules included in this blind test, such calculations can be constructively applied to help understand crystallization and polymorphism of organic molecules.
380 citations
"Validation of experimental molecula..." refers methods in this paper
...The best validation of the accuracy of the energies from this dispersioncorrected DFT (d-DFT) method came in 2007, when it predicted all four crystal structures in the Crystal Structure Prediction Blind Test correctly (Day et al., 2009)....
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...In the four successful crystal structure predictions mentioned in x1 (Day et al., 2009), the relative energies computed with the d-DFT method successfully reproduced energy differences of the order of 1 kJ mol 1, proving beyond reasonable doubt that the correct orientation was published....
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