From molecule to solid: The prediction of organic crystal structures

A method for predicting the structure of a molecular crystal based on the systematic search for a global potential energy minimum is considered. The method takes into account unequal occurrences of the structural classes of organic crystals and symmetry of the multidimensional configuration space. The programs of global minimization PMC, comparison of crystal structures CRYCOM, and approximation to the distributions of the electrostatic potentials of molecules FitMEP are presented as tools for numerically solving the problem. Examples of predicted structures substantiated experimentally and the experience of author’s participation in international tests of crystal structure prediction organized by the Cambridge Crystallographic Data Center (Cambridge, UK) are considered.     

Prediction of possible crystal structures for C-, H-, N-, O-, and F-containing organic compounds

A procedure is reported for the prediction of dense crystal structures of C-, H-, N-, O-, and F-containing organic compounds in the primitive triclinic, monoclinic, and orthorhombic space groups with Z ≤ 4. The crystal environments of molecules in 242 crystal structures have been analyzed to determine the common coordination sphere pattens. This led to the development of the MOLPAK (MOLecular PAcKing) program, which uses a rigid-body molecular structure probe to build packing arrangements (possible crystal structures) in the various space groups. A MOLPAK search, which involves the investigation of all unique orientations of a central molecule and the construction of the appropriate coordination patterns about the central molecule, provides a 3-D map of minimum unit cell volume as a function of the orientation of the central molecule. MOLPAK uses a repulsion-only potential and a preset threshold to place molecules in contact with each other. The 5–10 smallest volume packing arrangements from a search are subjected to a lattice energy minimization refinement with the WMIN program to yield possible crystal structures. The results are described from the analyses of several known compounds starting with the crystal molecular structures as the MOLPAK search probes in the P1, P2₁, P2₁/c, and P2₁2₁2₁ space groups. In addition, several examples are given in which the search probes were created by AM1 geometry optimization of preliminary molecular models. More extensive data are given in supplementary tables. © 1993 John Wiley & Sons, Inc.     

Crystal packing of “strained” organic molecules

Comparison of the energy of nonbonding interactions in the molecules of a series of conformers and isomers showed that a looser molecular crystal packing corresponds to the conformer or isomer with greater U_nb. Analysis of the distribution of the packing coefficients (K_p) for 159 medium and high density organic crystalline structures indicates that the fraction of structures with low K_p is greater for the high density crystals. The minimal K_p (0.612) is close to the value predicted by Kitaigorodskii in the dense packing theory (0.60). A tendency was noted to decreasing K_p with increasing molecular density.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2866–2869, December, 1990.     

Predictability of the polymorphs of small organic compounds: crystal structure predictions of four benchmark blind test molecules

Predicting the crystal structure of an organic molecule from first principles has been a major challenge in physical chemistry. Recently, the application of Density Functional Theory including a dispersive energy correction (the DFT(d) method) has been shown to be a reliable method for predicting experimental structures based purely on their ranking according to lattice energy. Further validation results of the application of the DFT(d) method to four organic molecules are presented here. The compounds were targets (labelled molecule II, VI, VII and XI) in previous blind tests of crystal structure prediction, and their structures proved difficult to predict. However, this study shows that the DFT(d) approach is capable of predicting the solid state structures of these small molecules. For molecule VII, the most stable (rank 1) predicted crystal structure corresponds to the experimentally observed structure. For molecule VI, the rank 1, 2 and 3 predicted structures correspond to the three experimental polymorphs, forms I, III and II, respectively. For molecules II and XI, their rank 1 predicted structures are energetically more stable than those corresponding to the experimental crystal structures, and were not found amongst the structures submitted by the participants in the blind tests. The rank 1 structure of molecule II is predicted to exist under high pressure, whilst the rank 1 structure predicted for molecule XI has the same space group and hydrogen bonding pattern as observed in the crystal of 1-amino-1-methyl-cyclopropane, which is structurally related to molecule XI. The experimental crystal structure of molecule II corresponds to the rank 4 prediction, 0.8 kJ mol(-1) above the global minimum structure, and the experimental structure of molecule XI corresponds to the rank 2 prediction, 0.4 kJ mol(-1) above the global minimum.     

Molecular Recognition and Crystal Energy Landscapes: An X‐ray and Computational Study of Caffeine and Other Methylxanthines

We introduce a new approach to crystal‐packing analysis, based on the study of mutual recognition modes of entire molecules or of molecular moieties, rather than a search for selected atom–atom contacts, and on the study of crystal energy landscapes over many computer‐generated polymorphs, rather than a quest for the one most stable crystal structure. The computational tools for this task are a polymorph generator and the PIXEL density sums method for the calculation of intermolecular energies. From this perspective, the molecular recognition, crystal packing, and solid‐state phase behavior of caffeine and several methylxanthines (purine‐2,6‐diones) have been analyzed. Many possible crystal structures for anhydrous caffeine have been generated by computer simulation, and the most stable among them is a thermodynamic, ordered equivalent of the disordered phase, revealed by powder X‐ray crystallography. Molecular recognition energies between two caffeine molecules or between caffeine and water have been calculated, and the results reveal the largely predominant mode to be the stacking of parallel caffeine molecules, an intermediately favorable caffeine–water interaction, and many other equivalent energy minima for lateral interactions of much less stabilization power. This last indetermination helps to explain why caffeine does not crystallize easily into an ordered anhydrous structure. In contrast, the mono‐ and dimethylxanthines (theophylline, theobromine, and the 1,7‐isomer, for which we present a single‐crystal X‐ray study and a lattice energy landscape) do crystallize in anhydrous form thanks to the formation of lateral hydrogen bonds.     

Self-association and self-assembly of molecular clips in solution and in the solid state

Clip molecules based on diphenylglycoluril form well-defined dimeric structures in chloroform solution and in the solid state. In solution the dimerization process is based on favourable π-π interactions and cavity filling effects. A combination of favourable π-π interactions and crystal packing forces determine the self-assembly of clips in the solid state. The geometry that the clip molecules adopt in solution and in a series of X-ray crystal structures is compared with favourable geometries predicted by molecular modelling calculations.     

Molecular recognition and crystal energy landscapes: an X-ray and computational study of caffeine and other methylxanthines

We introduce a new approach to crystal-packing analysis, based on the study of mutual recognition modes of entire molecules or of molecular moieties, rather than a search for selected atom-atom contacts, and on the study of crystal energy landscapes over many computer-generated polymorphs, rather than a quest for the one most stable crystal structure. The computational tools for this task are a polymorph generator and the PIXEL density sums method for the calculation of intermolecular energies. From this perspective, the molecular recognition, crystal packing, and solid-state phase behavior of caffeine and several methylxanthines (purine-2,6-diones) have been analyzed. Many possible crystal structures for anhydrous caffeine have been generated by computer simulation, and the most stable among them is a thermodynamic, ordered equivalent of the disordered phase, revealed by powder X-ray crystallography. Molecular recognition energies between two caffeine molecules or between caffeine and water have been calculated, and the results reveal the largely predominant mode to be the stacking of parallel caffeine molecules, an intermediately favorable caffeine-water interaction, and many other equivalent energy minima for lateral interactions of much less stabilization power. This last indetermination helps to explain why caffeine does not crystallize easily into an ordered anhydrous structure. In contrast, the mono- and dimethylxanthines (theophylline, theobromine, and the 1,7-isomer, for which we present a single-crystal X-ray study and a lattice energy landscape) do crystallize in anhydrous form thanks to the formation of lateral hydrogen bonds.     

Crystallization Force—A Density Functional Theory Concept for Revealing Intermolecular Interactions and Molecular Packing in Organic Crystals

Organic molecules are prone to polymorphic formation in the solid state due to the rich diversity of functional groups that results in comparable intermolecular interactions, which can be greatly affected by the selection of solvent and other crystallization conditions. Intermolecular interactions are typically weak forces, such as van der Waals and stronger short‐range ones including hydrogen bonding, that are believed to determine the packing of organic molecules during the crystal‐growth process. A different packing of the same molecules leads to the formation of a new crystal structure. To disclose the underlying causes that drive the molecule to have various packing motifs in the solid state, an electronic concept or function within the framework of conceptual density functional theory has been developed, namely, crystallization force. The concept aims to describe the local change in electronic structure as a result of the self‐assembly process of crystallization and may likely quantify the locality of intermolecular interactions that directs the molecular packing in a crystal. To assess the applicability of the concept, 5‐methyl‐2‐[(2‐nitrophenyl)amino]‐3‐thiophenecarbonitrile, so‐called ROY, which is known to have the largest number of solved polymorphs, has been examined. Electronic calculations were conducted on the seven available crystal structures as well as on the single molecule. The electronic structures were analyzed and crystallization force values were obtained. The results indicate that the crystallization forces are able to reveal intermolecular interactions in the crystals, in particular, the close contacts that are formed between molecules. Strong correlations exist between the total crystallization force and lattice energy of a crystal structure, further suggesting the underlying connection between the crystallization force and molecular packing.     

Comparison of conformer distributions in the crystalline state with conformational energies calculated by ab initio techniques

Summary The conformational preferences of 12 molecular substructures in the crystalline state have been determined and compared with those predicted for relevant model compounds by ab initio molecular orbital calculations. Least-squares regression shows that there is a statistically significant correlation between the crystal-structure conformer distributions and the calculated potential-energy differences, even though the calculations relate to a gas-phase environment. Torsion angles associated with high strain energy (>1 kcal mol^-1) appear to be very unusual in crystal structures and, in general, high-energy conformers are underrepresented in crystal structures compared with a gas-phase, room-temperature Boltzmann distribution. It is concluded that crystal packing effects rarely have a strong systematic effect on molecular conformations. Therefore, the conformational distribution of a molecular substructure in a series of related crystal structures is likely to be a good guide to the corresponding gas-phase potential energy surface.     

几种极性有机晶体的生长习性与形成机理 2: 分子堆积、界面结构与晶体的习性

极性有机晶体在不同的溶剂中具有明显不同的生长习性, 主要有两个方面的原因: 一是极性有机晶体属非中心对称性晶类, 晶体具有极轴, 极轴的存在对分子堆积和晶体生长具有重要影响; 另一是极性有机晶体的界面结构不同, 溶剂与晶体界面的相互作用不同, 使得晶体同一面族的生长速率不同, 从而导致了晶体习性的改变。本文从几种典型极性有机晶体的分子排列和结构特征出发, 着重探讨了极性有机晶体的界面结构的差异对晶体习性的影响; 结合晶体生长界面与溶剂分子的相互作用进一步理解了晶体生长的溶剂效应; 通过理解极性有机晶体的习性机制, 探讨了晶体实际形态的控制。     

Coarse-grained modelling to predict the packing of porous organic cages

How molecules pack has vital ramifications for their applications as functional molecular materials. Small changes in a molecule''s functionality can lead to large, non-intuitive, changes in their global solid-state packing, resulting in difficulty in targeted design. Predicting the crystal structure of organic molecules from only their molecular structure is a well-known problem plaguing crystal engineering. Although relevant to the properties of many organic molecules, the packing behaviour of modular porous materials, such as porous organic cages (POCs), greatly impacts the properties of the material. We present a novel way of predicting the solid-state phase behaviour of POCs by using a simplistic model containing the dominant degrees of freedom driving crystalline phase formation. We employ coarse-grained simulations to systematically study how chemical functionality of pseudo-octahedral cages can be used to manipulate the solid-state phase formation of POCs. Our results support those of experimentally reported structures, showing that for cages which pack via their windows forming a porous network, only one phase is formed, whereas when cages pack via their windows and arenes, the phase behaviour is more complex. While presenting a lower computational cost route for predicting molecular crystal packing, coarse-grained models also allow for the development of design rules which we start to formulate through our results.

This work presents a novel method for predicting molecular crystal structure formation using coarse-grained modelling, enabling the development of design rules.     

Mechanoluminescence or Room‐Temperature Phosphorescence: Molecular Packing‐Dependent Emission Response

Mechanoluminescence (ML) and room‐temperature photophosphorescence (RTP) were achieved in polymorphisms of a triphenylamine derivative with ortho‐substitution. This molecular packing‐dependent emission afforded crucial information to deeply understand the intrinsic mechanism of different emission forms and the possible packing–function relationship. With the incorporation of solid‐state ¹³C NMR spectra of single crystals, as well as the analysis of crystal structures, the preferred packing modes for ML and/or RTP were investigated in detail, which can guide the reasonable design of organic molecules with special light‐emission properties.     

Ab initio crystal structure prediction-I. Rigid molecules

A new methodology for the prediction of molecular crystal structures using only the atomic connectivity of the molecule under consideration is presented. The approach is based on the global minimization of the lattice enthalpy of the crystal. The modeling of the electrostatic interactions is accomplished through a set of distributed charges that are optimally and automatically selected and positioned based on results of quantum mechanical calculations. A four-step global optimization algorithm is used for the identification of the local minima of the lattice enthalpy surface. A parallelized implementation of the algorithm permits a much more extensive search of the solution space than has hitherto been possible, allowing the identification of crystal structures in less frequently occurring space groups and with more than one molecule in the asymmetric unit. The algorithm has been applied successfully to the prediction of the crystal structures of 3-aza-bicyclo(3.3.1)nonane-2,4-dione (P2(1)/a, Z' = 1), allopurinol (P2(1)/c, Z' = 1), 1,3,4,6,7,9-hexa-azacycl(3.3.3)azine (Pbca, Z' = 2), and triethylenediamine (P6(3)/m, Z' = 1). In all cases, the experimentally known structure is among the most stable predicted structures, but not necessarily the global minimum.     

Computer simulations and analysis of structural and energetic features of some crystalline energetic materials

A database of 43 literature X-ray crystal structure determinations for compounds with known, or possible, energetic properties has been collected along with some sublimation enthalpies. A statistical study of these crystal structures, when compared to a sample of general organic crystals, reveals a population of anomalously short intermolecular oxygen-oxygen separations with an average crystal packing coefficient of 0.77 that differs significantly from 0.70 found for the general population. For the calculation of lattice energies, three atom-atom potential energy schemes and the semiempirical SCDS-PIXEL scheme are compared. The nature of the packing forces in these energetic materials is further analyzed by a study of the dispersive versus Coulombic contributions to overall lattice energies and to molecule-molecule energies in pairs of near neighbors in the crystals, a partitioning made possible by the unique features of the SCDS-PIXEL scheme. It is shown that dispersion forces are stronger than Coulombic forces, contrary to common belief. The low abundance of hydrogen atoms in these molecules, the close oxygen-oxygen contacts, and the high packing coefficients explain the observation that, for these energetic materials, crystal densities are anomalously high compared to those of most organic materials. However, an understanding, not to mention prediction or control, of the deeper mechanisms for the explosive power of these crystalline materials, such as the role of lattice defects, remains beyond present capabilities.     

物质材料的结构预测和光物理性能模拟

具有良好性能的非线性光学材料的成功设计,关键问题在于材料晶体结构和分子结构的可信和有效的预测结果,继而对获得结构信息的材料开展光物理性能计算模拟,这种结构预测与性能模拟结合的方法,为新材料的成功制备创出一条又省时又经济的路子。本文中,我们使用Oganov等发展的全局搜索进化算法的晶体结构预测工具(USPEX软件),成功地预测具有中远红外区透过的二阶非线性光学材料Ba2BiInS5的晶体结构;介绍应用DFT方法优化和预测内嵌富勒烯C2@Sc4@C80-Ih和Sc4C2@C80-Ih分子结构。在结构预测和优化基础上,应用基于态叠加原理(SOS)自行创建的BGP软件与计算激发态性质的软件结合,计算模拟分子晶体、纳米结构分子、生物蛋白分子等体系频率相关和态相关的非线性光学性质(包括不同光学过程的二阶、三阶极化率以及双光子、三光子吸收截面)。此外,还报道了利用固体能带理论与反谐振子模型结合,计算模拟部分离子晶体的二阶和三阶非线性光学性质。     

A systematic docking approach. Application to the α-cyclodextrin/phenyl-ethanol complex

A new approach for systematic docking is applied to the structure of the -cyclodextrin/phenyl-ethanol complex. This methodology includes systematic scanning of the possible guest positions, clustering of low energy structures into families and final refinement using molecular mechanics. The clustering was performed on internal parameters of the complex by a program named PROXIM based on a very simple proximity criterion. This program organized nearly 30 000 structures into about 100 families. Thirty conformations have been considered (10 and 20 for the complexation on the primary and secondary face respectively), the two forms of complexation encountered in the crystal packing yield the lowest energy combination.     

Packing of molecules of poly-<Emphasis Type="Italic">p</Emphasis>-phenylenebenzo-bis-oxazole in crystalline structures: Calculation by the molecular mechanics method

The mutual packing of trans- and cis-stereoisomeric molecules of poly-p-phenylenebenzo-bisoxazole is calculated by the molecular mechanics method. By varying all intramolecular and intermolecular parameters, energetically favorable structures are found. Calculation is performed both for molecules with uniform rotational isomeric composition (only TRANS or CIS mutual orientation of heterocycles along the polymer chain) and for molecules with random alternation of rotational isomers. In ordered structures, all molecules are shown to have a flat conformation and they are packed so that their planes are shifted along and perpendicular to the direction of molecular axes. The shifts can be similar [towards one (Δ) or another (?Δ) side] and alternating (±Δ). For trans-TRANS molecules with a homogeneous rotational isomeric composition, longitudinal shifts Δ and ?Δ are not equivalent because, in one case, similar heteroatoms of neighboring molecules appear to be the most closely positioned, whereas in the other case, this is true of different heteroatoms. As a result, different types of molecular packing develop: in the first case, structures with parallel mutual orientation of molecular planes form and, in the second case, the structures are characterized by parquet arrangement. When trans-TRANS molecules are packed with an alternating longitudinal shift, the mutual packing of molecules shows the parquet pattern. At the same time, for cis-stereoisomeric molecules with homogeneous or arbitrary rotational isomeric composition, only the parquet pattern in their mutual arrangement is observed. This conclusion disagrees with experimental evidence according to which, in crystalline structures, the planes of molecules are parallel to each other. For the above structures, the packing energy calculated with allowance for the experimental values of cell parameters appears higher than that for the structures under study. The difference in energy exceeds 80 kJ/mol (per one monomer unit). The experimentally observed type of crystalline structure is assumed to be conceived even at the stage of nucleation of crystal-solvate phases.     

Predicting Inclusion Behaviour and Framework Structures in Organic Crystals

We have used well‐established computational methods to generate and explore the crystal structure landscapes of four organic molecules of well‐known inclusion behaviour. Using these methods, we are able to generate both close‐packed crystal structures and high‐energy open frameworks containing voids of molecular dimensions. Some of these high‐energy open frameworks correspond to real structures observed experimentally when the appropriate guest molecules are present during crystallisation. We propose a combination of crystal structure prediction methodologies with structure rankings based on relative lattice energy and solvent‐accessible volume as a way of selecting likely inclusion frameworks completely ab initio. This methodology can be used as part of a rational strategy in the design of inclusion compounds, and also for the anticipation of inclusion behaviour in organic molecules.