Lattice Energy Minimization Research Articles

FIDEL: A new method for SDPD of nanocrystalline organic compounds

Rietveld refinements generally fail, if the lattice parameters of the structural model differ more than slightly from the correct lattice parameters and the simulated reflections do not overlap with the experimental ones. For molecular crystals, we have developed a more robust fitting algorithm, which uses the cross-correlation function of calculated and experimental powder patterns, and allows a FIt with DEviating Lattice parameters (FIDEL). The method is also successful for nanocrystalline organic compounds showing only 10-20 peaks in their powder diagrams. The FIDEL method has proven to be useful for various applications, including refinements starting from (1) structure data of an isostructural chemical derivative; (2) structure data of an isostructural hydrate or solvate; (3) structure data from measurements at another temperature (e.g. for fitting a room-temperature powder diagram starting with a structure determined from a single-crystal measurement at 100K). FIDEL is also used for determining crystal structures from non-indexed powder diagrams of nanocrystalline organic compounds. Three steps are performed: (1) Prediction of possible crystal structures in various space groups using global lattice-energy minimizations by force-field methods. (2) FIDEL fit of 100 to 600 low-energy structures to the experimental powder pattern. The structure candidate leading to the correct structure results in a significantly better fit than all other structures. (3) Rietveld refinement. The FIDEL method was used to determine the hitherto unknown crystal structure of the nanocrystalline alpha-phase of 2,9-dichloroquinacridone (C20H10Cl2N2O2). The upper part of the figure shows the experimental powder pattern and the simulated powder diagram of one of the predicted low-energy structures before any fitting. The lower part displays the result of the FIDEL fit, before the Rietveld refinement.

Explanation of the stacking disorder in the β-phase of Pigment Red 170

The β-phase of Pigment Red 170, C26H22N4O4, which is used industrially for the colouration of plastics, crystallizes in a layer structure with stacking disorder. The disorder is characterized by a lateral translational shift between the layers with a component ty of either +0.421 or -0.421. Order-disorder (OD) theory is used to derive the possible stacking sequences. Extensive lattice-energy minimizations were carried out on a large set of structural models with different stacking sequences, containing up to 2688 atoms. These calculations were used to determine the actual local structures and to derive the stacking probabilities. It is shown that local structures and energies depend not only on the arrangement of neighbouring layers, but also next-neighbouring layers. Large models with 100 layers were constructed according to the derived stacking probabilities. The diffraction patterns simulated from those models are in good agreement with the experimental single-crystal and powder diffraction patterns. Electron diffraction investigation on a nanocrystalline industrial sample revealed the same disorder. Hence the lattice-energy minimizations are able to explain the disorder and the diffuse scattering.

A Computational Study of Magnesium Incorporation in the Bulk and Surfaces of Hydroxyapatite

We have used a combination of static lattice energy minimization and molecular dynamics simulations to investigate the thermodynamics of Mg incorporation into the bulk and hydrated surfaces of hydroxyapatite (HA). In agreement with recent experimental and theoretical work, our simulations show that the incorporation of low levels of Mg in the Ca (II) site is preferred with respect to incorporation in Ca (I) sites. However, we predict that Mg in the HA bulk material is metastable both with respect to the Mg/Ca exchange with aqueous solution and with respect to separation into bulk phases of magnesium phosphate [Mg3(PO4)2] and magnesium hydroxide [Mg(OH)2]. This finding suggests that Mg siting in the HA bulk is at least partially controlled by kinetics rather than by thermodynamics during crystal growth, which can explain the discrepancies found in the literature about the preferential substitution site. Finally, we found that Mg incorporation from solution into the hydrated surfaces, rather than the bulk material, is energetically favorable, in particular in the (011̅0) plane where cation sites are exposed to solution, thereby enabling the favorable interaction of Mg with water.

Determination of the Crystal Structure of a New Polymorph of Theophylline

A new approach to crystal structure determination, combining crystal structure prediction and transmission electron microscopy, was used to identify a potential new crystal phase of the pharmaceutical compound theophylline. The crystal structure was determined despite the new polymorph occurring as a minor component in a mixture with Form II of theophylline, at a concentration below the limits of detection of analytical methods routinely used for pharmaceutical characterisation. Detection and characterisation of crystallites of this new form were achieved with transmission electron microscopy, exploiting the combination of high magnification imaging and electron diffraction measurements. A plausible crystal structure was identified by indexing experimental electron-diffraction patterns from a single crystallite of the new polymorph against a reference set of putative crystal structures of theophylline generated by global lattice energy minimisation calculations.

Stacking disorder in Pigment Red 170 explained by lattice-energy minimizations

Stacking disorder in Pigment Red 170 explained by lattice-energy minimizations

Lattice energy minimization and lattice dynamics calculations on pharmaceutical hydrates

Lattice energy minimization and lattice dynamics calculations on pharmaceutical hydrates

Efficient Handling of Molecular Flexibility in Lattice Energy Minimization of Organic Crystals.

This paper presents a novel algorithm, CrystalOptimizer, for the minimization of the lattice energy of crystals formed by flexible molecules. The algorithm employs isolated-molecule quantum mechanical (QM) calculations of the intramolecular energy and conformation-dependent atomic multipoles in the course of the lattice energy minimization. The algorithm eliminates the need to perform QM calculations at each iteration of the minimization by using Local Approximate Models (LAMs), with a minimal impact on accuracy. Additional computational efficiencies are achieved by storing QM-derived components of the lattice energy model in a database and reusing them in subsequent calculations whenever possible. This makes the approach particularly well suited to applications that involve a sequence of lattice energy evaluations, such as crystal structure prediction. The algorithm is capable of handling efficiently complex systems with considerable conformational flexibility. The paper presents examples of the algorithm's application ranging from single-component crystals to cocrystals and salts of flexible molecules with tens of intramolecular degrees of freedom whose optimal values are determined by the interplay of conformational strain and packing forces. For any given molecule, the degree of flexibility to be considered can vary from a few torsional angles to relaxation of the entire set of torsion angles, bond angles, and bond lengths present in the molecule.

Predicted and experimental crystal structures of ethyl-tert-butyl ether

Possible crystal structures of ethyl-tert-butyl ether (ETBE) were predicted by global lattice-energy minimizations using the force-field approach. 33 structures were found within an energy range of 2 kJmol(-1) above the global minimum. Low-temperature crystallization experiments were carried out at 80-160 K. The crystal structure was determined from X-ray powder data. ETBE crystallizes in C2/m, Z = 4, with molecules on mirror planes. The ETBE molecule adopts a trans conformation with a (CH(3))(3)C-O-C-C torsion angle of 180°. The experimental structure corresponds with high accuracy to the predicted structure with energy rank 2, which has an energy of 0.54 kJmol(-1) above the global minimum and is the most dense low-energy structure. In some crystallization experiments a second polymorph was observed, but the quality of the powder data did not allow the determination of the crystal structure. Possibilities and limitations are discussed for solving crystal structures from powder diffraction data by real-space methods and lattice-energy minimizations.

Current approaches to predicting molecular organic crystal structures

Considerable effort has been invested in developing methods for predicting the crystalline structure(s) of a given compound, ideally starting from no more than a structural formula of the molecule. Reliable computational predictions would be of great value in many areas of materials chemistry, from the design of materials with novel properties to the avoidance of an undesirable change of form in the late stages of development of an industrially important molecule. Methods used in crystal structure prediction are reviewed, with particular focus on the most common approach – global lattice energy minimization. Progress and current limitations are highlighted, with reference to examples from the literature and the results of blind tests organized to objectively monitor developments in the field.

Adsorption sites, adsorption enthalpies and potential removal of terpenoids by atmospheric ice

Abstract Ice crystal formation and its effect on atmospheric trace gases are currently an important area of research because of its radiation and climate effects. However, the processes of adsorption of trace gases on ice surfaces and absorption into ice crystals are poorly understood. Both processes are investigated by lattice-energy minimisation for a selected number of atmospherically relevant volatile organic compounds, i.e. isoprene, methacrolein, acetone, methylbutenol, perillyl alcohol and 2,10-pinanediol, which can be considered as exemplary substances for similar structured compounds. Adsorption and absorption geometries and enthalpies are computed and the potential uptake strength is approximated. According to our calculations non-polar terpenes like isoprene are not significantly adsorbed by ice crystals. Oxidized terpenoids have stronger interactions with the ice surface (at least two hydrogen bonds) leading to larger adsorption enthalpies. Absorption into the ice crystal plays only a minor role. Correspondingly, in the atmosphere terpenoid compounds are increasingly adsorbed to ice surfaces with increasing oxygen numbers. Subsequently this process can contribute to the wet removal of terpenoids by ice, which is so far ignored in global transport models.

Experimental and predicted crystal structures of Pigment Red 168 and other dihalogenated anthanthrones

The crystal structures of 4,10-dibromo-anthanthrone (Pigment Red 168; 4,10-dibromo-dibenzo[def,mno]chrysene-6,12-dione), 4,10-dichloro- and 4,10-diiodo-anthanthrone have been determined by single-crystal X-ray analyses. The dibromo and diiodo derivatives crystallize in P2(1)/c, Z = 2, the dichloro derivative in P1, Z = 1. The molecular structures are almost identical and the unit-cell parameters show some similarities for all three compounds, but the crystal structures are neither isotypic to another nor to the unsubstituted anthanthrone, which crystallizes in P2(1)/c, Z = 8. In order to explain why the four anthanthrone derivatives have four different crystal structures, lattice-energy minimizations were performed using anisotropic atom-atom model potentials as well as using the semi-classical density sums (SCDS-Pixel) approach. The calculations showed the crystal structures of the dichloro and the diiodo derivatives to be the most stable ones for the corresponding compound; whereas for dibromo-anthanthrone the calculations suggest that the dichloro and diiodo structure types should be more stable than the experimentally observed structure. An experimental search for new polymorphs of dibromo-anthanthrone was carried out, but the experiments were hampered by the remarkable insolubility of the compound. A metastable nanocrystalline second polymorph of the dibromo derivative does exist, but it is not isostructural to the dichloro or diiodo compound. In order to determine the crystal structure of this phase, crystal structure predictions were performed in various space groups, using anisotropic atom-atom potentials. For all low-energy structures, X-ray powder patterns were calculated and compared with the experimental diagram, which consisted of a few broad lines only. It turned out that the crystallinity of this phase was not sufficient to determine which of the calculated structures corresponds to the actual structure of this nanocrystalline polymorph.

Structural and energetic aspects of the differences between real and predicted polymorphs

AbstractIn crystal structure prediction simulations based on lattice energy minimization, usually hundreds of structures within a reasonable range of lattice energy and density are found, whereas in practice, it is very rare to find more than a few polymorphs of the same compound. In the work presented here, this discrepancy is investigated from a structural and energetic point of view. 56 crystal structures of 26 polymorphic mono‐ and disubstituted aromatic compounds, extracted from the Cambridge Structural Database, have been analysed with respect to inter‐polymorphic structural similarity. For comparison, potential crystal packing arrangements of the substances have been predicted with molecular mechanics simulations using a generic force field. The predicted structures are analysed with respect to structural features and similarity, and with respect to the number of structures and their lattice energy. It is found that the real polymorphs studied in this work tend to be structurally quite dissimilar with regard to hydrogen bonding and spatial packing of structural motifs, while many of the predicted structures of a given compound are very similar to each other. The results suggest that structure and lattice energy alone cannot explain why so few polymorphs are found in practice compared to the very large numbers predicted in simulations. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Predicted crystal structures of tetramethylsilane and tetramethylgermane and an experimental low-temperature structure of tetramethylsilane

No crystal structure at ambient pressure is known for tetramethylsilane, Si(CH(3))(4), which is used as a standard in NMR spectroscopy. Possible crystal structures were predicted by global lattice-energy minimizations using force-field methods. The lowest-energy structure corresponds to the high-pressure room-temperature phase (Pa3, Z = 8). Low-temperature crystallization at 100 K resulted in a single crystal, and its crystal structure has been determined. The structure corresponds to the predicted structure with the second lowest energy rank. In X-ray powder analyses this is the only observed phase between 80 and 159 K. For tetramethylgermane, Ge(CH(3))(4), no experimental crystal structure is known. Global lattice-energy minimizations resulted in 47 possible crystal structures within an energy range of 5 kJ mol(-1). The lowest-energy structure was found in Pa3, Z = 8.

Locating Extra-Framework Cations in Low-Silica Zeolites by a Combinatorial Approach of the Direct Space Method and Rietveld Refinement: Application to Ni2+ and Co2+ Enriched Clinoptilolite

The location of extra-framework cations in low-silica zeolites is determined from in-house X-ray powder diffraction pattern by a successful implementation of a newly developed methodology. The method combines reciprocal and direct space methods plus a cost function that accounts for simultaneous fit of the chemical composition and the X-ray diffractogram. We demonstrated that the iterative combination of relaxation methods (Monte Carlo exploration and lattice energy minimization) helps to improve the structural refinement. The methodology is successfully applied to the study of natural clinoptilolite samples enriched with Ni and Co; in both cases, two different cation sites were found octahedrally coordinated to water molecules. The most populated site is located in the center of the A channel, while the second one is found in the window of the B channel. This result was validated using XANES and EXAFS spectroscopies.

Spontaneous Resolution of Enantiomers by Crystallization: Insights from Computed Crystal Energy Landscapes

We used crystal structure prediction methods to generate racemic and homochiral crystal structures of benzo(c)phenanthrene, 3,4-dehydroproline anhydride, and 2,6-dimethylglycoluril, which are all known to spontaneously resolve. The known homochiral crystal structures were found at or near the global minimum in lattice energy; however, in all three cases there were hypothetical racemic crystal structures within a few kJ mol−1 in energy. The comparison of hypothetical racemic structures with the known homochiral crystal structures showed structural similarities, despite the symmetry differences, suggesting that most molecules are very unlikely to crystallize in a chiral crystal structure that is markedly more stable than any racemic crystal. Thus the experimentally observed asymmetry in the thermodynamic favorability of racemic and homochiral crystal structures is not due to experimental bias; that is, any thermodynamic drive for spontaneous resolution is genuinely small. Hence, whereas the formation of a r...

The Structural Directing Role of Water and Hydroxyl Groups in the Synthesis of Beta Zeolite Polymorphs

The investigation of stability of as-made Beta zeolite polymorphs A, B, and C (BEA, BEB, and BEC) was carried out on the basis of lattice energy minimization and molecular dynamic atomistic simulations. The force field employed provided an excellent agreement between calculated and experimental enthalpies of formation of zeolites with respect to quartz. BEA and BEB are obtained at low water and KOH concentration in the initial mixture, while BEC forms at higher concentrations of both water and KOH. The four-component systems of unit cell composition (C12NH20+)6/zeolite/F−6/(H2O)l for BEA and BEB polymorphs and five-component systems (C12NH20+)3/BEC/F−2/OH−/(H2O)l, (C18N2H302+)2/BEC/F−2/(OH−)2/(H2O)l were simulated for different water content, l. It was shown that the presence of water molecules stabilized the systems but to a different extent, in a way such that BEC is favored at higher water contents. Water amounts are rationalized in terms of the free volume available in the micropore, not totally filled by the organic. Defects have been found to form in BEC through interaction of hydroxyl anions with Si−O−Si linkages. The number and location of defects (silanol and siloxy groups) are in agreement with 29Si MAS NMR signals due to Q3 (Si) atoms.

Electron diffraction, X-ray powder diffraction, lattice energy minimisation, and pair distribution function analysis to determine the crystal structures of Pigment Yellow 213, C23H21O9N5

Electron diffraction, X-ray powder diffraction, lattice energy minimisation, and pair distribution function analysis to determine the crystal structures of Pigment Yellow 213, C₂₃H₂₁O₉N₅

SiBr4 – prediction and determination of crystal structures

For SiBr4 no crystal structures have been reported yet. In this work the crystal structures of SiBr4 were predicted by global lattice-energy minimizations using force-field methods. Over an energy range of 5 kJ mol(-1) above the global minimum ten possible structures were found. Two of these structures were experimentally determined from X-ray synchrotron powder diffraction data: The low-temperature beta phase crystallizes in P2(1)/c, the high-temperature alpha phase in Pa3. Temperature-dependant X-ray powder diffraction shows that the phase transition occurs at 168 K.

Can the Formation of Pharmaceutical Cocrystals Be Computationally Predicted? 2. Crystal Structure Prediction.

We report a multistage lattice energy minimization methodology for generating stable packing arrangements of cocrystals containing flexible molecules. In the first approximation, the intermolecular electrostatic interactions are modeled with atomic charges and the molecular deformation energy is interpolated over a set of precomputed quantum mechanical values. At subsequent stages, the accuracy is improved by first using analytically rotated and then conformation-dependent multipole moments, computed from the isolated-molecule charge density, and "on-the-fly" quantum mechanical calculations to compute the intramolecular deformation energy. This multistage approach increases the efficiency of the search and establishes the molecule-dependent error due to the atomic charge representation of the charge density and the neglect of the conformational dependence of atomic multipole moments. The methodology is used to study the lattice energy landscapes of the cocrystals of 4-aminobenzoic acid with 2,2'-bipyridine and 4-nitrophenylacetic acid, as well as the single-component crystals. All single-component, experimentally determined crystal structures within the scope of the search were found at, or very close to, the global minimum. The experimental cocrystal with 2,2'-bipyridine is also predicted to be among the most stable packing arrangements. On the contrary, the lattice energy landscape of the cocrystal with 4-nitrophenylacetic acid contains several low energy structures that are more stable than the experimentally observed form and have different hydrogen bonding motifs. Overall, the methodology can provide worthwhile crystal energy landscapes for multicomponent organic solids and thereby contribute to understanding cocrystal formation.

The crystal structure of the API Montelukast

The sodium salt of the title compound (1-{[(R)-m-(E)-2-(7-chloroquinol-2-yl)vinyl)]-a-[2-(1-hydroxy-1-methylethyl)phenylethyl]-benzylthio}-methyl)cyclopropane acetic acid (1), known as Montelukast (a free acid), is a potent and selective leukotriene D-4 receptor antagonist. With an annual turnover of over 3 billion US dollars, it still attracts considerable interest in current pharmaceutical research, however, up until now no structural information has been available. The unit cell contains two symmetry independent molecules, which are connected to long ribbons along the c-axis viahydrogen bonds. Lattice energy minimizations reveal that the main part of the lattice energy may be attributed to multipole–multipole interactions between highly polarized Montelukast moieties. However, it seems that the comparable small contributions of the above mentioned hydrogen bonds are essential structure directing ingredients for crystallization.