Energy Calculations and Crystal Structure Predictions

To determine the deepest minimum on the multidimensional energy surface as a function of many structural parameters is a formidable mathematical task. Usually, simplifications and assumptions are introduced concerning, for example, the space-group symmetry. Accordingly, the conclusions from these theoretical calculations cannot be considered to be entirely a priori. 

The considerations of the intermolecular interactions can be conveniently reduced to considerations of atom-atom nonbonded interactions. Although these interactions can be treated by nonempirical quantum-mechanical calculations, empirical and semiempirical approaches have also proved successful in dealing with them. In the description of the atom-atom nonbonded interactions, it is supposed that the van der Waals forces originate from a variety of sources. 

In addition to the intermolecular interactions, the intramolecular interactions may also be taken into account in a similar way. This rather limited approach may nevertheless be useful for calculating molecular conformation and even molecular symmetry. Deviations from the ideal conformations and symmetries may also be estimated in this way, provided they are due to steric effects. 

By summation over the interaction energies of the molecular pairs, the total potential energy of the molecular crystal may be obtained in an atom-atom potential approximation. The result is expected to be approximately the same as the heat of sublimation extrapolated to 0 K provided that no changes take place in the molecular conformation and vibrational interactions during evaporation. 

In many of the molecular packing studies, the crystal classes are taken from experimental X-ray diffraction determinations. The optimal packing is then determined for the assumed crystal class. In other cases, the crystal classes have also been established in the optimization calculations. 

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