Crystal structure prediction polymorphism

Pa)me RS, Roberts RJ, Rowe RC, Docherty R. Examples of successful crystal structure prediction polymorphs of primidone and progesterone. Int J Pharm 1999 177 231-245. 

Abraham, N.L. and Probert, N.J., A periodic genetic algorithm with real space representation for crystal structure and polymorph prediction, Phys. Rev. B., 73, 224106,2006. 

Both thermodynamic and kinetic factors need to be considered. Take, for instance, acetic acid. The liquid contains mostly dimer but the crystal contains the catemer and no (polymorphic) dimer crystal has ever been obtained. Various computations (R. S. Payne, R. J. Roberts, R. C. Rowe, R. Docherty, Generation of crystal structures of acetic acid and its halogenated analogs , J. Comput. Chem, 1998, 19,1-20 W. T. M. Mooij, B. P. van Eijck, S. L. Price, P. Verwer, J. Kroon, Crystal structure predictions for acetic acid , J. Comput. Chem., 1998, 19, 459-474) show the relative stability of the dimer. Perhaps the dimer is not formed in the crystal because it is 0-dimensional and as such, not able to propagate so easily to the bulk crystal as say, the 1-dimensional catemer. 

Algorithm with Real-Space Representation for Crystal Structure and Polymorph Prediction. 

It is consequential from these considerations that polymorphism occupies an extraordinarily relevant place in the solid-state sciences. Even the smallest step ahead in understanding the reasons for polymorphism, and of how to bend it to our wishes/needs, might represent a quantum leap in structural sciences with enormous conceptual, practical and economic consequences. One way to tackle this problem is the computational generation of theoretical crystal structures [11], which often goes under the epithet of crystal structure prediction. Even though this is a very important area of research, it will be touched upon only marginally in this chapter and mainly in connection with experimental results. 

In spite of these caveats, there is intense activity in the application of these methods to polymorphic systems and considerable progress has been made. Two general approaches to the use of these methods in the study of polymorphism may be distinguished. In the first, the methods are utilized to compute the energies of the known crystal structures of polymorphs to evaluate lattice energies and determine the relative stabilities of different modifications. By comparison with experimental thermodynamic data, this approach can be used to evaluate the methods and force fields employed. The ofher principal application has been in fhe generation of possible crystal structures for a substance whose crystal structure is not known, or which for experimental reasons has resisted determination. Such a process implies a certain ability to predict the crystal structure of a system. However, the intrinsically approximate energies of different polymorphs, the nature of force fields, and the inherent imprecision and inaccuracy of the computational method still limit the efificacy of such an approach (Lommerse et al. 2000). Nevertheless, in combination with other physical data, in particular the experimental X-ray powder diffraction pattern, these computational methods provide a potentially powerful approach to structure determination. The first approach is the one applicable to the study of conformational polymorphs. The second is discussed in more detail at the end of this chapter. 

C.M. Freeman, Inorganic Crystal-Structure Prediction Using Simplified Potentials and Experimental Unit Cells - Application to the Polymorphs of Titanium-Dioxide. J. Mater. Chem., 1993, 3, 531-535. 

Cross WI, Blagden N, Davey ly, Pritchard RG, Neumann MA, Roberts ly, and Rowe RC. A Whole Output Strategy for Polymorph Screening Combining Crystal Structure Prediction, Graph Set Analysis, and Targeted Crystallization Experiments in the Case of Diflunisal. Cryst Growth Des 2003 3 151-158. 

Price, S. L., The computational prediction of pharmaceutical crystal structures and polymorphism , Adv. Drug Deliv. Rev. 2004, 56, 301-319. 

There have been significant recent advances in both the model potentials that can be used in molecular crystal structure prediction and new methods of searching for hypothetical structures. We may expect that these will come together over the next decade, so that the prediction of a molecular crystal structure from first principles becomes possible. This should lead to an understanding of polymorphism. 

Quantum mechanical methods have also been applied to crystal structure prediction. A recent example involved the use of ab initio crystal field methods with the SM (supermolecule) model and the PC (point charge) model applied to the three known polymorphs of glycine [77]. Comparison of the optimised structures with published X-ray structures for these forms indicated that the quantum-mechanically based SM model employing a 15-molecule cluster produced results in better agreement with experiment than the PC model which describes the crystal environment purely electrostatically. 

Crystal structure determinations either from the powder x-ray diffraction pattern or from the molecular structure are not yet routine procedures. Currently, crystal structure prediction from the molecular structure is feasible only for relatively rigid and nonionic compounds. More sophisticated criteria need to be developed to select the likely polymorphs from the predicted crystal structures. In addition, in order to estimate accurately the stability of a crystal structure, the lattice entropy needs to be taken into account as well as the lattice energy. However, no accurate method is yet available to estimate the lattice entropy. These limitations may be overcome by advances in computational chemistry and computing power. 

Leusen, F. Engel, G. Computational approaches to crystal structure and polymorph prediction. J. Pharm. Pharmacol. 1999, 51 (S), 1. 

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