Angelo Gavezzotti

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.

Non-conventional bonding between organic molecules. The "halogen bond" in crystalline systems

The intermolecular interaction in organic crystals, when close contact between a halogen atom and an oxygen or nitrogen atom is present, is investigated by surveys of existing crystal structure determinations in the Cambridge Structural Database and by theoretical methods. Short halogen–oxygen and–nitrogen contacts are restricted to systems with peculiar electronic and steric properties. Energy well depths for sample systems range from almost nil to about 20 kJ mol−1, considerably less than for hydrogen bonding, with which halogen bonding can hardly compete. The width of the energy wells suggests that some short contacts may correspond to just permissive (i.e. energetically neutral) approach, or even to compressed bonding. The strongest bond is attainable only by aromatic iodine, highly activated by electron-attracting substituents, in molecular complexes with strong and sterically unhindered Lewis bases; only in such special cases is the halogen bond the most relevant cohesive factor in the crystal structure. In the PIXEL energy dissection scheme, the largest contribution to halogen bonding comes from Coulombic plus first-order polarization terms. Dispersive interactions between parallel aromatic systems are often more stabilizing and should not be neglected in assessing the tendency of halogen compounds to form linear aggregates in polar crystal structures.

Efficient computer modeling of organic materials. The atom–atom, Coulomb–London–Pauli (AA-CLP) model for intermolecular electrostatic-polarization, dispersion and repulsion energies

An atom–atom intermolecular force field with subdivision of interaction energies into Coulombic-polarization, dispersion (London) and repulsion (Pauli) terms is presented. Instead of using fixed interaction functions for atomic species, atom–atom potential functions are calculated for each different molecule on the basis of a few standard atomic parameters like atomic numbers, atomic polarizability and ionization potentials, and of local atomic point charges from Mulliken population analysis. The energy partitioning is conducted under guidance from the more accurate evaluation of the same terms by the PIXEL method, also highlighting some intrinsic deficiencies of all atom–atom schemes due to the neglect of penetration energies in Coulombic terms on localized charges. The potential energy scheme is optimized for H, C, N, O, Cl atoms in all chemical connectivities and can be extended to F, S, P, Br, I atoms with minor modifications. The scheme is shown to reproduce the sublimation heats of 154 organic crystal structures, to reproduce about 400 observed crystal structures without distortion, and to reproduce heats of evaporation and specific gravities of 12 common organic liquids. It is therefore suitable for both static and evolutionary (Monte Carlo) molecular simulation. Fine tuning of the four terms for specific systems can be easily performed on the basis of chemical intuition, by the introduction of one overall damping factor for each of them. The scheme is embedded in a suite of Fortran computer programs portable on any platform. For reproducibility and general use, source codes are available for distribution.

Structure and energy in organic crystals with two molecules in the asymmetric unit: causality or chance?

The structures of 5547 organic crystals with two molecules in the asymmetric unit (Z′ = 2) are collected from the Cambridge Structural Database, and compared with a sample of 45182 crystal structures with one molecule in the asymmetric unit (Z′ = 1). A new method for standardizing H-atom positions is described. Approximate symmetry in Z′ = 2 crystals is analyzed using real-space information only. Lattice energies are calculated by the PIXEL method and partitioned into contributions from the two different sites in Z′ = 2 crystals and into molecule–molecule contributions, with special attention paid to the most energetic molecular pair. There are no obvious differences between the Z′ = 1 and Z′ = 2 sets in chemical composition, except for a slightly smaller average size of Z′ = 2 molecules. The frequency of space groupsP1, P21 and P increases in Z′ = 2 crystals, while the frequency of space groupsP21/c and P212121 decreases. 83% of the Z′ = 2 crystals show some form of pseudosymmetry with a tolerance of 0.5 A atom−1. The most energetic pair is on average more tightly bound in Z′ = 2 crystals than in Z′ = 1 crystals, and in Z′ = 2 crystals the asymmetric pair ranks first in the list of molecule–molecule energies in 55–60% of the cases. However, even in crystals where the asymmetric pair is the most energetic, its contribution to the total lattice energy can be as high as 70% or as low as 10%: in many cases, the asymmetry is between weakly interacting molecules. Structural molecular features leading to Z′ = 2 crystals are tentatively analyzed. On the whole, there appears to be a continuum of situations from asymmetric pairs formed between clearly different molecules that pack in clearly different environments (hinting at causality of Z′ = 2) and pairs formed by nearly identical molecules packing in nearly identical environments (hinting at casual, local conditions), but even in the latter case, there is no proof that a fully symmetric structure would be more stable.

Towards a realistic model for the quantitative evaluation of intermolecular potentials and for the rationalization of organic crystal structures. Part I. Philosophy

Calculations on prototypical dimer structures and representative crystal structures of organic compounds have been carried out by SCDS-Pixel, a new method for the evaluation of intermolecular potentials. Systems not included in the set originally employed in calibration of the method are considered, and a significant improvement in performance is obtained by adjustment of the disposable parameters over a wider collection of experimental and computational evidence. The results cast some new light on the organization of molecular crystals, and suggest that the density sums method is an advantageous alternative to atom–atom potential techniques, as concerns both detailed quantitative results and general ways of thinking about crystal packing. While the SCDS-Pixel method, as it is now, is general and applicable to a wide range of chemical systems, further development and improvements are possible and a few sensitive points in this respect are examined.

Ten years of experience in polymorph prediction: what next?

Several issues in the computational prediction of polymorphic crystal structures are examined: the enthalpy–force field issue, the intra–intermolecular energy issue, the entropy issue, the temperature issue, the kinetic energy issue, and the kinetic–dynamic issue. Perspectives in the derivation of an absolute force field, based solely on molecular electron densities, are examined, together with its possible application to static and dynamic calculations, with an estimate of the investment and computational costs.

A Statistical Study of Density and Packing Variations among Crystalline Isomers

Abstract Crystal structures of groups of isomeric hydrocarbons, oxahydrocarbons and azahydrocarbons have been retrieved from the Cambridge Structural Database. Correlations among crystal and molecular descriptors were sought, with particular attention to factors affecting crystal density. Packing coefficients do not differ much from 0.74, so organic molecules have roughly the same packing efficiency as a close packed assembly of spheres. Molecular shape factors associated with high crystal density are difficult to identify. However, crystal density is higher for compact polycyclic molecules, since they have smaller molecular volumes. Also, flat, rigid molecules pack better than flexible, twisted ones. On the other hand, substituents such as alkyl or nitrile groups tend to lower the packing efficiency. High crystal density does not necessarily lead to high lattice energy, and, in particular, hydrogen bonding seems to have no immediate effect on crystal density. Results of bivariate statistics were confirmed by principal component analysis. These results may be of interest for practical applications in crystal chemistry and crystal physics.

The Crystal Packing of Organic Molecules: Challenge and Fascination Below 1000 Da

Abstract Studies and insights on the crystal packing of organic molecules are reviewed, beginning with the first investigations of intermolecular effects in the sixties, the early database studies in the seventies, and proceeding to the structure correlation principle and the Kitaigorodski approach to intermolecular analysis. Present-day instrumentation allows a new attitude towards organic small-molecule X-ray crystallography: connections with solid-state thermodynamics and kinetics are envisaged. Recent Cambridge Database studies, new intermolecular “bonds”, optimizations of crystal potentials, and crystal structure generation and prediction software, are critically analyzed, together with crystal engineering which, as it appears now, is a branch of synthetic organic chemistry. The future of theoretical studies of crystals, and more generally of all physical chemistry, is molecular dynamics; its use in simulating and describing solids, liquids and solutions is outlined, with special attention to crystal...

Solid-State Behaviour of the Dichlorobenzenes: Actual, Semi-Virtual and Virtual Crystallography

The crystal structures of the low-melting 1,2- and 1,3-dichlorobenzene isomers in monoclinic space group P21/n and monoclinic space group P21/c, resp., were detd. by x-ray anal. and in situ crystn. techniques. Attempts to predict these structures in advance by force-field calcns. were not successful, although the known crystal structures of two of the three polymorphs of the 1,4-isomer were successfully a posteriori predicted. Calcd. lattice energies were supplemented with estd. lattice-vibrational entropies obtained in the rigid-body approxn. Energy calcns. for actual and virtual crystal structures indicate that the higher m.p. of the 1,4-isomer can be largely attributed to more efficient crystal packing.

Towards a realistic model for the quantitative evaluation of intermolecular potentials and for the rationalization of organic crystal structures. Part II. Crystal energy landscapes

Many crystal structures were generated by a computer predictor for naphthalene, naphthoquinone, 1,2-dichlorobenzene, 2,3-dimethylbenzoic acid, parabanic acid and pyridine, and the lattice energies were then calculated by standard atom–atom potentials, by point-charge models, and by the SCDS-Pixel method. Using results from the latter approach, the relative importance of coulombic, polarization, dispersion and repulsion energies in crystals is discussed in relationship with the chemical characteristics of the constituent molecule, with crystal density, and with some key crystal structural factors like interplanar angles and some intermolecular distances believed to be indicators of crystal stabilization. In general, intermolecular interactions are better discussed when considering the electron density of large molecular moieties or of entire molecules, than when considering atom–atom distances. Significant comparisons between atom–atom energies and the more accurate Pixel energies are presented. The performance of the Pixel-SCDS method in ranking crystal energies against experimental structures, in the so-called crystal structure prediction exercise, is comparable to, and sometimes better than that of atom–atom force fields.