Dynamic simulation of orientational disorder in organic crystals: methyl groups, trifluoromethyl groups and whole molecules.

Large amplitude librations of atomic groups or of entire molecules in their crystals are simulated using optimized intermolecular potentials and crystal structures deposited in the Cambridge Structural Database. The analysis proceeds by a simple static model in which reorientations take place in a fixed environment, or by Monte Carlo (MC) simulation of equilibria dotted by rotational defects, or eventually by full Molecular Dynamics (MD). The simplest approach provides a valuable qualitative preview, but MC and MD are becoming easily accessible to the general solid-state chemist thanks to the facilities of the newly developed Milano Chemistry Molecular Simulation (MiCMoS) platform. Their combined results offer a wealth of information on the behaviour of phenyl-methyl and phenyl-trifluoromethyl groups, almost invariably affected by rotational flipping, whose nature and consequences are discussed with respect to disorder modelling in the refinement of X-ray structures. Whole-body reorientation takes place in flat molecules, benzene being the well-known prototype, but also in a very large molecule like coronene. Molecular dynamics of rotations in the cyclohexa-1,4-diene crystal offer a spectacular picture of the energetic profiles with jumping times. The dynamic oscillations described here are seldom considered in the formulation of crystal `bonds' or of `synthon' stability.

A quantitative measure of halogen bond activation in cocrystallization.

A theoretical investigation of bond lengths and bond energies for several kinds of halogen bonding interactions is carried out using the PIXEL method. The effect of different kinds of activating agents, fluoro-, nitro-, ethynyl substitution and combinations thereof, is assessed quantitatively, and is found to be fully consistent with the results of literature screenings of the corresponding strengths, as judged by the ease of formation of cocrystals. In the best combination of activators the halogen bond is comparable or superior to a strong O-HO hydrogen bond in what concerns stabilization energies and stretching force constants. At least with iodine acceptors, in our picture the halogen-bonding effect is a localized interaction arising from the detail of the electron distribution at the halogen atom, mainly of a Coulombic-polarization nature but with dispersion energies contributing significantly. Binding energies correlate with the electrostatic potential at the tip of the halogen and even with Mulliken population analysis atomic charges, providing easily accessible guidelines for crystal engineers. For one typical cocrystal structure the analysis of separate molecule-molecule energies reveals the nature of the packing forces and rank halogen bonding as the main influence, closely followed by coplanar stacking of coformers.

Are racemic crystals favored over homochiral crystals by higher stability or by kinetics? Insights from comparative studies of crystalline stereoisomers.

The crystal and molecular structures of 134 pairs of diastereoisomers and of 279 racemic-homochiral pairs were retrieved from the Cambridge Structural Database. Lattice and intramolecular energies are calculated. Density differences between crystals of stereoisomers of all kind are mostly within 5%, as observed also for crystal polymorphs. Racemic crystals are predominantly, but not exclusively, more stable and more dense. Denser crystals are predominantly more stable, but there is no quantitative correlation between density and energy differences between partners in the chosen pairs. Second-order symmetry operators are neither ubiquitous in the racemic nor patently superior to first-order operators in promoting crystal cohesion. Thermodynamic, energetic factors in the final crystalline products are not enough to explain the (largely) predominant occurrence of racemic crystallization from racemic solution. At least for homogeneous nucleation, a probabilistic factor, from kinetics or from statistical predominance of mixed versus enantiopure aggregates, must be in action during the early separation of liquid-like particles, which are thought to be the precursors of crystal nucleation.

Computational studies of crystal structure and bonding.

The analysis, prediction, and control of crystal structures are frontier topics in present-day research in view of their importance for materials science, pharmaceutical sciences, and many other chemical processes. Computational crystallography is nowadays a branch of the chemical and physicals sciences dealing with the study of inner structure, intermolecular bonding, and cohesive energies in crystals. This chapter, mainly focused on organic compounds, first reviews the current methods for X-ray diffraction data treatment, and the new tools available both for quantitative statistical analysis of geometries of intermolecular contacts using crystallographic databases and for the comparison of crystal structures to detect similarities or differences. Quantum chemical methods for the evaluation of intermolecular energies are then reviewed in detail: atoms-in-molecules and other density-based methods, ab initio MO theory, perturbation theory methods, dispersion-supplemented DFT, semiempirical methods and, finally, entirely empirical atom-atom force fields. The superiority of analyses based on energy over analyses based on geometry is highlighted, with caveats on improvised definitions of some intermolecular chemical bonds that are in fact no more than fluxional approach preferences. A perspective is also given on the present status of computational methods for the prediction of crystal structures: in spite of great steps forward, some fundamental obstacles related to the kinetic-thermodynamic dilemma persist. Molecular dynamics and Monte Carlo methods for the simulation of crystal structures and of phase transitions are reviewed. These methods are still at a very speculative stage, but hold promise for substantial future developments.

Intermolecular interaction energies in molecular crystals: comparison and agreement of localized Møller-Plesset 2, dispersion-corrected density functional, and classical empirical two-body calculations.

A comparative analysis of the intermolecular energy for a data set including 60 molecular crystals with a large variety of functional groups has been carried out using three different computational approaches: (i) a method based on a physically meaningful empirical partition of the interaction energy (PIXEL), (ii) density functional methods with a posteriori empirical correction for the dispersion interactions (DFT-D), and (iii) a full periodic ab initio quantum mechanical method based on Møller-Plesset perturbation theory for the electron correlation using localized crystal orbitals (LMP2). Due to the large computational cost, LMP2 calculations have been restricted to a subset of seven molecular crystal comprising benzene, formic acid, formamide, succinic anhydride, urea, oxalic acid, and nitroguanidine, and the results compared with PIXEL and DFT-D data as well as with the experimental data show excellent agreement among all adopted methods. This shows that both DFT-D and PIXEL approaches are robust predictive tools for studying molecular crystals. A detailed analysis shows a very similar dispersion contribution of the two methods across the 60 considered molecular crystals. The study also confirms that pure DFT shows serious deficiencies in properly handling molecular crystals in which the dispersive contribution is large. Due to the negligible requested computational resources, PIXEL is the method of choice in screening of a large number of molecular crystals, an essential step to predict crystal polymorphism or to study crystal growth processes. DFT-D can then be used to refine the ranking emerged from PIXEL calculations due to its general applicability and robustness in properly handling short-range interactions.

The lines-of-force landscape of interactions between molecules in crystals; cohesive versus tolerant and 'collateral damage' contact.

A quantitative analysis of relative stabilities in organic crystal structures is possible by means of reliable calculations of interaction energies between pairs of molecules. Such calculations have been performed by the PIXEL method for 1108 non-ionic and 98 ionic organic crystals, yielding total energies and separate Coulombic polarization and dispersive contributions. A classification of molecule-molecule interactions emerges based on pair energy and its first derivative, the interaction force, which is estimated here explicitly along an approximate stretching path. When molecular separation is not at the minimum-energy value, as frequently happens, forces may be attractive or repulsive. This information provides a fine structural fingerprint and may be relevant to the mechanical properties of materials. The calculations show that the first coordination shell includes destabilizing contacts in approximately 9% of crystal structures for compounds with highly polar chemical groups (e.g. CN, NO(2), SO(2)). Calculations also show many pair contacts with weakly stabilizing (neutral) energies; such fine modulation is presumably what makes crystal structure prediction so difficult. Ionic organic salts or zwitterions, including small peptides, show a Madelung-mode pairing of opposite ions where the total lattice energy is stabilized from sums of strongly repulsive and strongly attractive interactions. No obvious relationships between atom-atom distances and interaction energies emerge, so analyses of crystal packing in terms of geometrical parameters alone should be conducted with due care.

A structural and spectroscopic investigation of the hydrochlorination of 4,4'-methylenedianiline.

The hydrochlorination of 4,4'-methylenedianiline, NH(2)C(6)H(4)CH(2)C(6)H(4)NH(2) (MDA), in chlorobenzene to produce 4,4'-methylenedianiline dihydrochloride, [H(3)NC(6)H(4)CH(2)C(6)H(4)NH(3)]Cl(2) (MDA x 2 HCl) is an important reaction for the production of isocyanates, which are used to manufacture polyurethanes. This reaction is examined here. MDA is moderately soluble in chlorobenzene, whereas MDA x 2 HCl is effectively insoluble. Controlled addition of anhydrous HCl to MDA in chlorobenzene led to the isolation of a solid whose stoichiometry is MDA x HCl. Crystals obtained from solutions of MDA x HCl in methanol were found by X-ray analysis to consist of the basic hydrochloride salt, [MDAH(2)][Cl](2)[MDA](2)H(2)O, which is stabilised by complex hydrogen-bonding. The starting material MDA has an H-bonded structure in which the molecules are linked in a one-dimensional chain. Hydrogen-bonding is extensive in MDA x 2 HCl which contains ladders of [H(3)NC(6)H(4)CH(2)C(6)H(4)NH(3)](2+) dications stabilised by N-H...Cl linkages. Energy calculations on the crystalline systems allow an identification of the main factors in intermolecular cohesion; these are related to melting temperature and solubility data. Such improvements in understanding of solute-solute interactions are prerequisites for improving the atom economy of this important stage within the polyurethane manufacture process chain. The solid phase IR spectrum of MDA x 2 HCl is diagnostic, principally as a result of a Fermi resonance process.

How molecules stick together in organic crystals: weak intermolecular interactions.

This tutorial review introduces the fundamentals of intermolecular interactions in terms of the underlying physics and goes on to illustrate the most popular methods for the computer simulation of intermolecular interactions, from atom-atom potentials to ab initio methods, including intermediate, hybrid methods, with an appreciation of their relative merits and costs. Typical results are critically presented, culminating in the most difficult exercise of all, the computer prediction of crystal structures. Perspectives on our present and future ability to understand and exploit intermolecular interactions are given.

A structural and spectroscopic investigation of the hydrochlorination of 4-benzylaniline: the interaction of anhydrous hydrogen chloride with chlorobenzene.

The hydrochlorination of 4-benzylaniline in chlorobenzene to produce 4-benzylaniline hydrochloride has been examined. This has required spectroscopic and computational analysis of the solvation of gaseous HCl in the process solvent. The characterisation of the reagent and product of the hydrochlorination reaction by various techniques, including FTIR and (1)H NMR spectroscopy and X-ray diffraction, is described. The infrared spectrum of the hydrochloride salt contains a strong Fermi resonance interaction, readily distinguishing it from that of the starting material. Using the structural results as a basis, the lattice energies of reagent and product have been evaluated by the recently developed PIXEL method. This method allows the contributions of specific intermolecular interactions to the total lattice energy to be assessed and, in this case, tentatively correlated with solubility measurements.

Coulombic and dispersive factors in the molecular recognition of peptides: PIXEL calculations on two NNQQ (Asn-Asn-Gln-Gln) crystal polymorphs.

The crystal-packing and cohesive energies in the structures of two polymorphs of the title tetrapeptide have been analyzed using molecule-molecule energies calculated using the PIXEL method. Coulombic energies are non-empirical and are much more accurate than those calculated using point-charge methods. The results explain and rationalize the cohesion and mutual recognition of these peptide molecules, with a clear distinction between polar and dispersive contributions, shedding light on subtle differences between polymorphic arrangements. For systems of the present size, the necessary calculations can be carried out on a personal computer and require quite acceptable computing times. Although an extension to larger peptides is problematic for obvious reasons, it is suggested that this type of analysis could be a valuable and practical tool in the understanding of the principles of peptide aggregation.

Hydrogen bond strength and bond geometry in cyclic dimers of crystalline carboxylic acids.

In a study of 101 crystal structures of carboxylic acids we have observed a clear trend in the difference between the formally single and formally double C-O bond distances, as observed by X-ray diffraction, with a clear-cut distinction between aromatic acids, where the two distances are similar, and non-aromatic acids, where the two distances distinctly differ by 0.06-0.12 A. A tentative energy classification - within the limits of the many assumptions - and a correlation with the O...O separation over the hydrogen bond indicate that the stability of the carboxylic acid dimer increases as the difference between the two apparent C-O distances becomes smaller, owing to an increasing Coulombic contribution to the dimerization energy. No simple hypothesis is adequate for a complete explanation of the origin, of the details and of the variations of this phenomenon. As often happens in crystal chemistry problems, one is presumably confronted with a balance of several subtle intra- and intermolecular factors.

A solid-state chemist's view of the crystal polymorphism of organic compounds.

In a survey of some structural and energetic aspects of crystal polymorphism, definitions are proposed, and a method for generating an unequivocal fingerprint of the cohesive pattern of an organic crystal structure is presented. The method identifies the electronic nature of molecule-molecule interactions in crystals, and its application requires a minimal training in basic crystallography and molecular modeling. The analysis suggests that thermodynamic and physical properties of polymorphs of organic crystals are quite often very similar, and sometimes depend on morphology as well as on crystal structure. It is also suggested that real polymorphism should be distinguished from the many defective or modulated structural variations often appearing in the crystallization of weakly bound molecular materials.

Synthesis, X-ray diffraction and computational study of the crystal packing of polycyclic hydrocarbons featuring aromatic and perfluoroaromatic rings condensed in the same molecule: 1,2,3,4-tetrafluoronaphthalene, -anthracene and -phenanthrene.

We have synthesised some planar polycyclic compounds, in which unsubstituted aromatic rings are condensed with perfluorinated aromatic rings, and have carried out a combined X-ray diffraction and computational study to analyse their self-recognition behaviour in crystalline phases. We compare our results with the parent hydrocarbons and with other compounds that have a variable degree of fluorination. Whereas the molecular planes in crystals of hydrocarbons with mono- or difluorinated aromatic rings or of perfluorinated compounds arrange themselves in V-shaped configurations, our present results show that perfluorinated rings tend to stack over unsubstituted rings even when these two moieties coexist in a condensed system, producing crystalline materials with parallel molecular layers with the arene-perfluoroarene recognition pattern. Our analysis shows that the packing energy of all these crystals is dispersion-dominated and that coulombic terms are selective rather than quantitatively predominant in crystals with arene-perfluoroarene interactions. No compelling proof of a special role of C-H...F interactions has been found.

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.

X-ray diffraction and theoretical studies for the quantitative assessment of intermolecular arene-perfluoroarene stacking interactions.

The arene-perfluoroarene stacking interaction was studied by experimental and theoretical methods. A series of compounds with different possibilities for formation of this recognition motif in the solid state were synthesized, and their crystal structures determined by single-crystal X-ray diffraction. The crystal packing of these compounds, as well as the packing of related compounds retrieved from crystallographic databases, were analyzed with quantitative crystal potentials: total lattice energies and the cohesive energies of closest molecular pairs in the crystals were calculated. The arene-perfluoroarene recognition motif emerges as a dominant interaction in the non-hydrogen-bonding compounds studied here, to the point that asymmetric dimers formed over the stacking motif carry over to asymmetric units made of two molecules in the crystal both for pure compounds and for molecular complexes; however, inter-ring distances and angles range from 3.70 to 4.85 A and from 5 to 21 degrees , respectively. Pixel energy partitioning reveals that whenever aromatic rings stack, the largest cohesive energy contribution comes from dispersion, which roughly amounts to 20 kJ mol(-1) per phenyl ring, while the coulombic term is minor but significant enough to make a difference between the arene-arene or perfluoroarene-perfluoroarene interactions on the one hand, and arene-perfluoroarene interactions on the other, whereby the latter are favored by about 10 kJ mol(-1) per phenyl ring. No evidence of special interaction which can be attributed to HF confrontation was recognizable.

Molecular recognition in organic crystals: directed intermolecular bonds or nonlocalized bonding?

Molecules are held together mainly by forces acting between individual atoms. Does the same apply to molecular clusters? Does intermolecular cohesion depend on weak bonds between individual atoms in different molecules or on less localized, more diffuse interactions between molecules? We discuss these questions from several viewpoints and in particular compare interpretations based on the extension of Bader's atoms in molecules (AIM) theory to cover closed-shell intermolecular interactions with interpretations based on the new pixel method for the calculation of coulombic, polarization, dispersion, and repulsion energies from the electron density of molecular clusters.

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.

X-ray diffraction and packing analysis on vintage crystals: Wilhelm Koerner's nitrobenzene derivatives from the School of Agricultural Sciences in Milano.

The crystal structures of six nitrotoluene derivatives, synthesized by Wilhelm Koerner about a century ago and retrieved from a depository at the University of Milano, were determined. The correct assignment of molecular structures is verified. The geometry of the nitro groups and factors affecting the orientation of nitro groups with respect to the benzene ring are discussed, also using an auxiliary set of crystal structures retrieved from the Cambridge Structural Database. The crystal packings have been analyzed, and lattice energies have been calculated by atom-atom potential methods and by the newly proposed Pixel method. This method allows a more complete description of intermolecular potentials in terms of the interaction between molecular electron densities and separate Coulombic, polarization, dispersion and overlap repulsion energies. Lattice vibrations and external entropies were calculated by lattice-dynamical procedures. The results of the Pixel energy calculations allow a reliable, quantitative assessment of the relative importance of stacking interactions and hydrogen bonding in the rationalization of the recognition modes of nitrobenzene derivatives, which is impossible to attain using only qualitative atom- atom geometry concepts.

Crystal structure prediction of small organic molecules: a second blind test.

The first collaborative workshop on crystal structure prediction (CSP1999) has been followed by a second workshop (CSP2001) held at the Cambridge Crystallographic Data Centre. The 17 participants were given only the chemical diagram for three organic molecules and were invited to test their prediction programs within a range of named common space groups. Several different computer programs were used, using the methodology wherein a molecular model is used to construct theoretical crystal structures in given space groups, and prediction is usually based on the minimum calculated lattice energy. A maximum of three predictions were allowed per molecule. The results showed two correct predictions for the first molecule, four for the second molecule and none for the third molecule (which had torsional flexibility). The correct structure was often present in the sorted low-energy lists from the participants but at a ranking position greater than three. The use of non-indexed powder diffraction data was investigated in a secondary test, after completion of the ab initio submissions. Although no one method can be said to be completely reliable, this workshop gives an objective measure of the success and failure of current methodologies.

X-ray diffraction and molecular simulation study of the crystalline and liquid states of succinic anhydride.

The crystal structure of succinic anhydride was studied at five temperatures between 100 K and the melting point by single-crystal X-ray diffraction. The temperature dependence of molecular libration tensors was determined. Intermolecular interactions, in particular through unusually close molecule-molecule contacts, are discussed, with a detailed calculation of electrostatic energies. A method for the adaptation of existing crystal force fields to molecular dynamics has been developed; the adapted force field was used to study molecular motion and rotational diffusion with increasing temperature. Equilibration of the crystalline system becomes impossible at a temperature very close to the experimental melting temperature, where a sudden transition to the liquid state occurs, and a partial kinetic picture of the melting process is obtained. After validation of the force field against experimental crystal data, the state equation of the liquid was predicted. Enthalpies of sublimation, melting, and vaporization were calculated. The dynamics of a solution of succinic anhydride in a nonpolar solvent was simulated, for a discussion of the aggregation process leading to demixing and to crystal nucleation.