Crystal Structure Prediction and Isostructurality of Three Small Molecules

A crystal structure prediction (CSP) study of three small, rigid and structurally related organic compounds (differing only in the position and number of methyl groups) is presented. A tailor‐made force field (TMFF; a non‐transferable force field specific for each molecule) was constructed with the aid of a dispersion‐corrected density functional theory method (the hybrid method). Parameters for all energy terms in each TMFF were fitted to reference data generated by the hybrid method. Each force field was then employed during structure generation. The experimentally observed crystal structures of two of the three molecules were found as the most stable crystal packings in the lists of their force‐field‐optimised structures. A number of the most stable crystal structures were re‐optimised with the hybrid method. One experimental crystal structure was still calculated to be the most stable structure, whereas for another compound the experimental structure became the third most stable structure according to the hybrid method. For the third molecule, the experimentally observed polymorph, which was found to be the fourth most stable form using its TMFF, became the second most stable form. Good geometrical agreements were observed between the experimental structures and those calculated by both methods. The average structural deviation achieved by the TMFFs was almost twice that obtained with the hybrid method. The TMFF approach was extended by exploring the accuracy of a more general TMFF (GTMFF), which involved fitting the force‐field parameters to the reference data for all three molecules simultaneously. This GTMFF was slightly less accurate than the individual TMFFs but still of sufficient accuracy to be used in CSP. A study of the isostructural relationships between these molecules and their crystal lattices revealed a potential polymorph of one of the compounds that has not been observed experimentally and that may be accessible in a thorough polymorph screen, through seeding, or through the use of a suitable tailor‐made additive.     

Crystal structure prediction of flexible molecules using parallel genetic algorithms with a standard force field

This article describes the application of our distributed computing framework for crystal structure prediction (CSP) the modified genetic algorithms for crystal and cluster prediction (MGAC), to predict the crystal structure of flexible molecules using the general Amber force field (GAFF) and the CHARMM program. The MGAC distributed computing framework includes a series of tightly integrated computer programs for generating the molecule's force field, sampling crystal structures using a distributed parallel genetic algorithm and local energy minimization of the structures followed by the classifying, sorting, and archiving of the most relevant structures. Our results indicate that the method can consistently find the experimentally known crystal structures of flexible molecules, but the number of missing structures and poor ranking observed in some crystals show the need for further improvement of the potential. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Progress in crystal structure prediction

The results of the application of a density functional theory method incorporating dispersive corrections in the 2010 crystal structure prediction blind test are reported. The method correctly predicted four out of the six experimental structures. Three of the four correct predictions were found to have the lowest lattice energy of any crystal structure for that molecule. The experimental crystal structures for all six compounds were found during the structure generation phase of the simulations, indicating that the tailor-made force fields used for screening structures were valid and that the structure generation engine, which combines a Monte Carlo parallel tempering algorithm with an efficient lattice energy minimiser, was working effectively. For the three compounds for which the experimental crystal structures did not correspond to the lowest energy structures found, the method for calculating the lattice energy needs to be further refined or there may be other polymorphs that have not yet been found experimentally.     

Molecular mechanics (MM2) calculations on peptides and on the protein Crambin using the CYBER 205

The MM2 potential functions for amides and peptides have been further extended by examining the experimental crystal structures for cyclo-(-Ala-Ala-Gly-Gly-Ala-Gly-), I, and cyclo-(-Ala-Ala-Gly-Ala-Gly-Gly-), II. The force field obtained was then applied to a study of the structure of the hydrophobic protein Crambin, for which a high resolution crystal structure is available. The energy minimization was carried out using a version of MM2 adapted to the CYBER 205.     

Potential polymorphs of aspirin

Aspirin is only found experimentally in one crystal structure. In this article, the method of Karfunkel and Gdanitz is used to predict potential polymorphs of aspirin. The known structure, containing a nonplanar conformer is found, along with a number of other low energy structures, many of which are based on a planar conformer. Semiempirical and ab initio calculations show that the planar conformer is less stable than the experimentally known one. Force field calculations suggest that the planar conformer is more stable. The lattice energy of the experimentally known crystal structure is 1.4 kcal/mol lower than any of the potential crystal structures, even though there are a number of structures with lower total (lattice+intramolecular) energies. Conformational maps indicate that another stable conformation occurs within a few kilocalories per mole of the known structure. Polymorphs are predicted for this conformer, but it is found to pack poorly. It is proposed that routes to producing polymorphs of aspirin might be found if consideration is given to promoting the stability of the planar conformer with appropriate solvents or additives. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 262–273, 1999     

Choosing GTO basis sets for periodic HF calculations

We investigate numerical linear dependencies of Gaussian-type orbital basis sets employed in the framework of the Hartree-Fock self-consistent field method for periodic structures, which so far have hampered the use of extended basis sets for non-ionic crystals. These linear dependencies occur when diffuse basis functions are included in a basis set in an uncontrolled manner. We use the condition number of the overlap matrix to lead us in the construction of extended basis sets for periodic structures which avoid numerical linear dependencies. Extended basis sets of high quality are optimized for a number of periodic structures (fcc He, α-Be, α-BN, and B1 NaF) with respect to the energy of the constituent atoms or ions. The results obtained with our basis sets, which do not require reoptimization in the crystal environment, compare favorably with those obtained with other extended basis sets reported in the literature. Received: 20 July 1998/Accepted: 21 August 1998 / Published online: 19 October 1998     

Ab initio crystal structure predictions for flexible hydrogen‐bonded molecules. Part III. Effect of lattice vibrations

In crystal structure predictions possible structures are usually ranked according to static energy. Here, this criterion has been replaced by the free energy at any temperature. The effects of harmonic lattice vibrations were found by standard lattice‐dynamical calculations, including a rough estimate of the effects of thermal expansion. The procedure was tested on glycol and glycerol, for which accurate static energies had been obtained previously (Part II of this series). It was found that entropy and zero‐point energy give the largest contribution to free energy differences between hypothetical crystal structures, adding up to about 3 kJ/mol for the structures with lowest energy. The temperature‐dependent contribution to the energy and the effects of thermal expansion showed less variation among the structures. The overall accuracy in relative energies was estimated to be a few kJ/mol. The experimental crystal structure for glycol corresponded to the global free energy minimum, whereas for glycerol it ranked second at 1 kJ/mol. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 816–826, 2001     

Theoretical investigation of histidine-tryptophan preferential interactions

Several histidine-tryptophan complexes (either stacked or T-shaped), derived from the crystal structures available in the Brookhaven Protein Data Bank, have been examined with molecular mechanics (MM), using the Tripos force field with Gasteiger-Hückel charges, whose trend was found to be analogous to the AMBER or CHARMM ones. The MM results were compared to the ab initio MP2 results, with and without counterpoise (CP) correction, previously obtained using extended basis sets on 5-methylimidazole and indole as model systems. MM seems to underestimate the interaction energy between the two monomers when compared to the uncorrected MP2 results, while the agreement is much better after including the CP correction at the MP2 level in all cases. MM was thus used to qualitatively analyse the dependence of the stacking energy on the ring rotation at a variable distance and ring centroid displacement for these systems, while keeping the rings in parallel planes. An analogous study was carried out for a T-shaped adduct. Received: 24 March 1998 / Accepted: 3 September 1998 / Published online: 1 February 1999     

Crystal structure of 5,6‐bis(9H‐carbazol‐9‐yl)benzo[c][1,2,5]thiadiazole: distortion from a hypothetical higher‐symmetry structure

Nucleophilic substitution of F atoms in 5,6‐difluorobenzo[c ][1,2,5]thiadiazole (DFBT) for carbazole could be potentially interesting as a novel way of synthesizing building blocks for new conjugated materials for applications in organic chemistry. The crystal structures of 5,6‐bis(9H‐carbazol‐9‐yl)benzo[c ][1,2,5]thiadiazole (DCBT), C₃₀H₁₈N₄S, and its hydrate, C₃₀H₁₈N₄S·0.125H₂O, were investigated using single‐crystal X‐ray analysis. The hydrate contains two symmetry‐independent DCBT molecules. The dihedral angles between the plane of the central benzothiadiazole fragment and that of the carbazole units vary between 50.8 and 69.9°, indicating conformational flexibility of the DCBT molecule in the crystals, which is consistent with quantum chemical calculations. The analysis of the crystal packing of DCBT revealed that the experimental triclinic structure could be described as a distortion from a hypothetical higher‐symmetry monoclinic structure. The quantum chemical calculations of two possible monoclinic structures, which are related to the experimental structure by a shifting of molecular layers, showed that the proposed structures are higher in energy by 5.4 and 10.1 kcal mol⁻¹. This energy increase is caused by less dense crystal packings of the symmetric structures, which results in a decrease of the number of intermolecular interactions.     

Mercury telluride crystals encapsulated within single walled carbon nanotubes: A density functional study

The structure and binding energies of mercury telluride crystals encapsulated within single walled carbon nanotubes (SWNTs) have been studied using density functional theory. The energies of three different pseudo one‐dimensional crystals of HgTe with 4:4, 3:3, and 2:2 coordination are compared. The initial structure for the 4:4 crystal was a 2 × 2 cubic motif derived from rock salt bulk structure, the 3:3 crystal corresponds to a novel structure found when HgTe was intercalated within SWNTs, and the 2:2 crystal is a chain motif derived from cinnabar (HgS) bulk structure. The isolated 3:3 crystal was found to be the most thermodynamically stable of the three structures. Calculations were performed on the 3:3 crystal inserted into three different SWNTs, (15, 0), (9, 9), and (17, 0), in order to investigate the perturbations on the molecular and electronic structure of the crystal and the SWNT, and the energy of formation of the HgTe@SWNT composites. The calculated structures are in good agreement with the experimental high resolution transmission electron microscopy images of the HgTe@SWNT composite. The calculated binding energies and density of states show that the interaction between nanotubes and the HgTe crystals is noncovalent. Since the energy difference of the “free” 4:4 and 3:3 structures is small and of the order of magnitude of the binding energies with the nanotubes, we carried out calculations on 4:4 HgTe structure inserted in to two different SWNTs, (15, 0) and (17, 0). The calculated binding energies show that, when the 4:4 structure is inserted into the smallest tube, the resultant composite has an energy comparable to the 3:3 structure, suggesting that this polymporph may also be found experimentally. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Force field studies of cholesterol and cholesteryl acetate crystals and cholesterol–cholesterol intermolecular interactions

To model the physical properties of sterols and related species, an all-atom Class II force field has been derived based on the recently reported CFF93 force field for hydrocarbons. It has been tested using both energy minimization and molecular dynamics (MD) simulations of the low-temperature neutron-diffraction structure of cholesteryl acetate crystals and the X-ray diffraction crystal structure of cholesterol. Thus these studies test the techniques and limitations of high-accuracy crystal simulations as well. Employing energy minimization, all cell vectors and volumes were reproduced to within 2.4% of experimental values. For cholesteryl acetate, the root mean square (rms) deviations between the calculated and experimental bond lengths, angles, and torsions of nonhydrogen atoms are 0.013 Å, 1.2°, and 2.4°, respectively. The corresponding maximum deviations are also very small: 0.027 Å for bond length, 3.2° for angle, and 7.6° for torsion. For cholesterol, good agreement between the calculated and experimental structures was found only when the comparison was limited to atoms with relatively small thermal factors (B_eq < 15 Ų). It was found that for both systems, the MD averaged structures were in better agreement with the experimental ones than the energy minimized structures, since the rms deviations in atom positions are smaller for the MD-averaged structures (0.064 Å for cholesteryl acetate and 0.152 Å for cholesterol) than those for the minimized structures (0.178 Å for cholesteryl acetate and 0.189 Å for cholesterol). The force field was then applied to isolated molecules focusing on the rigidity of the cholesteryl ring and cholesterol–cholesterol interaction energies. It is concluded that the cholesteryl ring is fairly rigid since no major conformational change was observed during an MD simulation of a single cholesterol molecule in vacuo at 500 K, in agreement with condensed phase experiments. Calculations of cholesterol–cholesterol pairs suggest that there are only four low-energy configurations and that it is more useful to describe each molecule as having a plane (flat face) and two grooves rather than as having two (one flat and one rough) faces. This provides some insight into the equilibrium crystal structures. Limited results from a modified Class I (CVFF) force field are presented for comparison. © 1995 by John Wiley & Sons, Inc.     

Evolutionary Algorithm-Based Crystal Structure Prediction for Copper(I) Fluoride

Despite numerous experimental studies since 1824, the binary copper(I) fluoride remains unknown. A crystal structure prediction has been carried out for CuF using the USPEX evolutionary algorithm and a dispersion-corrected hybrid density functional method. In total about 5000 hypothetical structures were investigated. The energetics of the predicted structures were also counter-checked with local second-order Møller–Plesset perturbation theory. Herein 39 new hypothetical copper(I) fluoride structures are reported that are lower in energy compared to the previously predicted cinnabar-type structure. Cuprophilic Cu−Cu interactions are present in all the low-energy structures, leading to ordered Cu substructures such as helical or zig-zag-type Cu−Cu motifs. The lowest-energy structure adopts a trigonal crystal structure with space group P3₁21. From an electronic point of view, the predicted CuF modification is a semiconductor with an indirect band gap of 2.3 eV.     

An Extension of the Consistent Valence Force Field (CVFF) with the Aim to Simulate the Structures of Vanadium Phosphorus Oxides and the Adsorption of n‐Butane and of 1‐Butene on their Crystal Planes

A specific force field of Consistent Valence Force Field type was developed with the aim to simulate the structures of catalysts of vanadium phosphorus oxide type and the reversible adsorption of organic compounds on specific crystallographic planes of such catalysts by molecular modeling. The appropriate parameters were derived for the bonded (stretching, bending, and torsional deformations) and nonbonded (attractive and repulsive van der Waals and Coulomb forces) atomic interactions for V—O and P—O bonds in typical fragments of these catalysts with the vanadium atom in the oxidation state IV. The parameters for bonded interactions were computed from Hessian matrices, supplied by the program DMol for performing Density Functional Theory, by means of a program for non‐linear regression. The DMol program was applied to energy minimize structures of known vanadium phosphorus oxides, which were compared with X‐ray structures, and to obtain their Hessian matrices as a basis for the force constants needed. Some hypothetical structural models had to be added. The van der Waals parameters were estimated by means of correlations between van der Waals radii and the repulsive parameters and between polarizabilities and the dispersive parameters from the literature. The force field obtained was applied to simulate the crystal structure of vanadyl pyrophosphate and to compute the heat of adsorption of n‐butane and of 1‐butene on its (100) plane (computer codes of company Biosym/MSI/Accelrys). The experimental crystal structure and the adsorption energies were fairly well reproduced, except that the a lattice constant proves somewhat too large.     

Study on mechanism of photocatalytic performance of La-doped TiO2/Ti photoelectrodes by theoretical and experimental methods

TiO₂ photoelectrodes with various nanostructures have been successfully prepared by the anodization method. The morphology, microstructure and optical properties of as-prepared photoelectrodes were studied by scanning electron microscopy (SEM), X-ray diffraction (XRD), ultraviolet/visible light diffuse reflectance spectra (UV/vis/DRS), surface photovoltage spectroscopy (SPS) and photocurrent. The electronic structure and optical properties of La doped/undoped TiO₂ photoelectrodes with different crystal structures were calculated by the density function theory. The photocatalytic and photoelectrocatalytic activities of as-prepared photoelectrodes were evaluated. The results showed that the anodization potentials played a crucial role in the surface morphology and microstructure. Both results of theoretical calculations and experimental tests demonstrated that La-doped photoelectrodes were more sensitive to light than undoped one. The difference of photoelectrodes performance was ascribed to the crystal configuration, impurity energy levels and long-range orientation moving of photogenerated carriers.     

Periodic DFT investigation on the structure and properties of TNAD crystal

Density function theory calculations were performed at the GGA/PW91, GGA/PBE, and LDA/CA‐PZ levels to study the structures and properties of the crystalline TNAD (trans‐1,4,5,8‐tetranitrotetraazadecalin). The relaxed crystal structure compares well with the experimental data. Analysis on the band structures shows that the frontier energy bands are generally quite flat, and the energy gap between the highest occupied crystal orbital and the lowest unoccupied crystal orbital is about 3.4 eV, indicating that the crystal is an electrical insulator. All the atoms of TNAD make up both the lower and the higher energy bands. The projection of density of state demonstrates that the N? NO₂ bond is the most reactive region of the material. The lattice energy is predicted to be ?155.13 kJ/mol at the LDA/CA‐PZ level, consistent with the previous studies, whereas it is underestimated by the GGA/PW91 (?70.41 kJ/mol) and GGA/PBE (?74.33 kJ/mol). The optical properties under ambient condition were investigated, including dielectric function, absorption coefficient, and reflectivity. The calculated absorption spectra show a number of absorption peaks in the fundamental absorption region, which are believed to be associated with different exciton states. And the reflectivity spectra are mainly composed of four peak structures, where the magnitude changes in the order of GGA/PBE < GGA/PW91 < LDA/CA‐PZ on the whole. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Improved intermolecular force field for molecules containing H,C, N,and O atoms,with application to nucleoside and peptide crystals

A new intermolecular force field for nitrogen atoms in organic molecules was derived from a training dataset of 76 observed azahydrocarbon crystal structures and 11 observed heats of sublimation. The previously published W99 force field for hydrogen, carbon, and oxygen was thus extended to include nitrogen atoms. Nitrogen atoms were divided into four classes: N(1) for triply bonded nitrogen, N(2) for nitrogen with no bonded hydrogen (except the triple bonded case), N(3) for nitrogen with one bonded hydrogen, and N(4) for nitrogen with two or more bonded hydrogens. H(4) designated hydrogen bonded to nitrogen. Wavefunctions of 6‐31g** quality were calculated for each molecule and the molecular electric potential (MEP) was modeled with net atomic and supplementary site charges. Lone pair electron charge sites were included for nitrogen atoms where appropriate, and methylene bisector charges were used for CH₂ and CH₃ groups when fitting the MEP. X? H bond distances were set to standard values for the wave function calculation and then foreshortened by 0.1 Å for the MEP and force field fitting. Using the force field optimized to the training dataset, each azahydrocarbon crystal structure was relaxed by intermolecular energy minimization. Predicted maximum changes in unit cell edge lengths for each crystal were 3% or less. The complete force field for H, C, N, and O atoms was tested by intermolecular energy relaxation of nucleoside and peptide molecular crystals. Even though these molecules were not included in any of the training datasets for the force field, agreement with their observed crystal structures was very good, with predicted unit cell edge shifts usually less than 2%. These tests included crystal structures of representatives of all eight common nucleosides found in DNA and RNA, 15 dipeptides, four tripeptides, two tetrapeptides, and a pentapeptide with two molecules in the asymmetric unit. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1154–1166, 2001     

Derivation of class II force fields: V. Quantum force field for amides,peptides, and related compounds

As the field of biomolecular structure advances, there is an ever-growing need for accurate modeling of molecular energy surfaces to simulate and predict the properties of these important systems. To address this need, a second generation amide force field for use in simulations of small organics as well as proteins and peptides has been derived. The critical question of what accuracy can be expected from calculations in general, and with this class II force field in particular, is addressed for structural, dynamic, and energetic properties. The force field is derived from a recent methodology we have developed that involves the systematic use of quantum mechanical observables. Systematic ab initio calculations were carried out for numerous configurations of 17 amide and related compounds. Relative energies and first and second derivatives of the energy of 638 structures of these compounds resulted in 140,970 ab initio quantum mechanical observables. The class II peptide quantum mechanical force field (QMFF), containing 732 force constants and reference values, was parameterized against these observables. A major objective of this work is to help establish the role of anharmonicity and coupling in improving the accuracy of molecular force fields, as these terms have not yet become an agreed upon standard in the ever more extensive simulations being used to probe biomolecular properties. This has been addressed by deriving a class I harmonic diagonal force field (HDFF), which was fit to the same energy surface as the QMFF, thus providing an opportunity to quantify the effects of these coupling and anharmonic contributions. Both force field representations are assessed in terms of their ability to fit the observables. They have also been tested by calculating the properties of 11 stationary states of these amide molecules. Optimized structures, vibrational frequencies, and conformational energies obtained from the quantum calculations and from both the QMFF and the HDFF are compared. Several strained and derivatized compounds including urea, formylformamide, and butyrolactam are included in these tests to assess the range of applicability (transferability) of the force fields. It was found that the class II coupled anharmonic force field reproduced the structures, energies, and vibrational frequencies significantly more faithfully than the class I harmonic diagonal force field. An important measure, rms energy deviation, was found to be 1.06 kcal/mol with the class II force field, and 2.30 kcal/mol with the harmonic diagonal force field. These deviations represent the error in relative configurational energy differences for strained and distorted structures calculated with the force fields compared with quantum mechanics. This provides a measure of the accuracy that might be expected in applications where strain may be important such as calculating the energy of a system as it approaches a (rotational) barrier, in ligand binding to a protein, or effects of introducing substituents into a molecule that may induce strain. Similar results were found for structural properties. Protein dynamics is becoming of ever-increasing interest, and, to simulate dynamic properties accurately, the dynamic behavior of model compounds needs to be well accounted for. To this end, the ability of the class I and class II force fields to reproduce the vibrational frequencies obtained from the quantum energy surface was assessed. An rms deviation of 43 cm⁻¹ was achieved with the coupled anharmonic force field, as compared to 105 cm⁻¹ with the harmonic diagonal force field. Thus, the analysis presented here of the class II force field for the amide functional group demonstrates that the incorporation of anharmonicity and coupling terms in the force field significantly improves the accuracy and transferability with regard to the simulation of structural, energetic, and dynamic properties of amides. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 430–458, 1998     

A new molecular mechanics force field for the oxidized form of blue copper proteins

A molecular mechanics force field for blue copper proteins has been developed, based on a rigid potential energy surface scan of the Cu(II)/His/His/Cys/Met chromophore, using DFT (B3LYP) calculations and the AMBER force field for the protein backbone. The strain-energy-minimized structures of the model chromophore alone are in excellent agreement with the DFT-optimized structure, and those of the entire set of cupredoxins (five structures are considered) are, within the experimental error limits, in good agreement with the single crystal structural data. However, the structural variation in the computed structures is much smaller than those in the experimental structures. It is shown that, due to the large error limits in the experimental data, a validation of the force field with experimental structural data is impossible because, within the error limits, all experimental structures considered are virtually identical. A validation on the basis of spectroscopic data and their correlation with experimental and computed structural data is proposed, and, as a first example, the correlation of intensity ratios of the charge transfer transitions with a specific distortion mode is presented. The quality of the correlation, using the computed structures, is higher than that with the X-ray structures, and this indicates that the computed structures are meaningful.