A Classic Optimisation Problem Predicting Crystal Structures

16 A Classic Optimisation Problem Predicting Crystal Structures 

Many molecules are obtained and used in a crystalline form, the nature of which can have a significant impact on their properties and behaviour. Moreover, it is sometimes possible for a given material to exist in more than one crystalline form, depending upon the conditions under which it was prepared. This is the phenomenon of polymorphism. This can be important because the various polymorphs may themselves have different properties. It is therefore of interest to be able to predict the three-dimensional atomic structure(s) that a given molecule may adopt, for those cases where it is difficult to obtain experimental data and also where one might wish to prioritise molecules not yet synthesised. 

Many different approaches have been suggested as possible approaches to this problem, from the 1960s onwards [Verwer and Leusen 1998]. What is obvious from aU of these efforts is that this is an extremely difficult problem Both thermodynamics and kinetics can be important in determining which crystalline form is obtained under a certain set of experimental conditions. Kinetic effects are particularly difficult to take into account and so are usually ignored. A proper treatment of the thermodynamic factors would require one to deal with the relative free energies of the different possible polymorphs. 

These relative free energies are dependent upon internal energies, crystal densities and entropies  

Probably the main difference between the different variants lies in the way in which the molecules move in the first step. One approach is to use Monte Carlo simulated annealing 

---