International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 9.7, p. 906

Section 9.7.8. A priori predictions of molecular crystal structures

A. J. C. Wilson,a V. L. Karenb and A. Mighellb

aSt John's College, Cambridge CB2 1TP, England, and bNIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA

9.7.8. A priori predictions of molecular crystal structures

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As physical properties of a molecular compound are a function of the spatial arrangement of molecules, an important goal of the structural chemist is to predict the space group and crystal structure from the molecular shape. On the basis of the observation that many structures of organic compounds are formed on the principle of periodic close packing of variously shaped molecules, it seems that such prediction would be a more or less straightforward computational task. However, the task of predicting the crystal structure of a specific molecular solid is complicated owing to the occurrence of hydrogen bonding (Subsection 9.7.7.2[link]) and the widespread phenomenon of polymorphism (Gavezzotti, 1994[link]). With only subtle differences in their Gibbs free energies, the occurrence of the structural modifications can be influenced by various non-equilibrium factors during crystallization.

In spite of the above problems, experience has shown that prediction algorithms can often be used to generate several reasonable structures for any given molecule and that in many cases the correct structure is among them. There are two general strategies that have been adapted for structure prediction. In the first one, developed by Kitajgorodskij (1955[link], 1973[link]), the molecular shape is physically constructed from models of atoms having van der Waals radii, resulting in the calot model. The physical calot model is then used for an analogue calculation of the space filling using a mechanical instrument that relates the molecules in three-dimensional space so that the projection of one molecule fits into the voids of other molecules. When the unit-cell dimensions are known, the entire crystal structure can be derived in this way. In the second approach, the same yet abstract `fused sphere model' is analysed for its symmetry by what can be called a `morphic' (as opposed to metric) transformation by the methods of molecular topology (Mezey, 1993[link]). The abstract topological molecular shapes can in principle be treated more rigorously and are computable into probable crystal structures.

Such a priori predictions of molecular structures are still in a relatively early stage of development. Several recent studies are indicative of the current progress in the field. For layered structures, good predictions can be obtained using construction techniques, symmetry probabilities, and potential energy functions (Scaringe, 1991[link]). An algorithm for the generation of crystal structures by the optimization of packing potential energy over several possible space groups has been devised by Gavezzotti (1991[link], 1994[link]). In a third approach, energy minimization without symmetry constraints is used for determining molecular crystal structures (Gibson & Scheraga, 1995[link]).

In spite of recent progress, the conceptual link between the molecular and crystal structures still relies to a large extent on the chemical intuition of scientists. The space-group statistics have played a critical role, as they provide the researcher with a summary of what happens in nature. It is likely that the prediction process can be enhanced by calculating statistics of the space-group frequencies and symmetry for molecules that are the most closely related to the shape or chemistry of the molecule under study. As such statistical subsets are often significantly different from the overall statistics, they may prove more valuable in the a priori prediction of the crystal structure for a specific molecule. The space-group frequencies and symmetry statistics remain one of the important strings in this link.

References

Gavezzotti, A. (1991). Generation of possible crystal structures from the molecular structure for low-polarity organic compounds. J. Am. Chem. Soc. 113, 4622–4629.
Gavezzotti, A. (1994). Molecular packing and correlations between molecular and crystal properties. Structure correlation, Vol. 2, edited by H.-B. Bürgi & J. D. Dunitz, Chap. 12, pp. 509–542. Weinheim/New York/Basel/Cambridge/Tokyo: VCH Publishers.
Gibson, K. D. & Scheraga, H. A. (1995). Crystal packings without symmetry constraints. 1. Test of a new algorithm for determining crystal structures by energy minimization. J. Phys. Chem. 99, 3752–3764.
Kitaigorodsky, A. I. (1973). Molecular crystals and molecules. New York: Academic Press.
Kitajgorodskij, A. I. (1955). Organicheskaya Kristallokhimiya. Moscow: Academy of Science.
Mezey, P. G. (1993). Shape in chemistry, an introduction into molecular shape and topology. New York/Weinheim/Cambridge: VCH Publishers.
Scaringe, R. P. (1991). A theoretical technique for layer structure prediction. Electron crystallography of organic molecules, edited by J. R. Fryer & D. L. Dorset, pp. 85–113. Dordrecht: Kluwer Academic Publishers.








































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