(180r) Consideration of the Entropy in the Prediction of Stable Crystalline Polymorphs

In order to predict the stable crystalline polymorph, we can compare the free energy of each polymorph and select the one with the lowest free energy. Most of the current prediction techniques only take into account the energetic contribution to the free energy and have ignored the entropic contribution. This is mainly because determining the entropic contribution is another degree of complication. In order to improve the accuracy of these approximation methods, we have included the neglected entropic term into our free-energy calculation by using methods that build on the lattice-dynamics approach. This idea is motivated by many previous studies, which have reported that in many cases, the difference between the energies of the most stable polymorphs is relatively small and the stability is believed in some cases to be influenced by entropy.

Calculation of true free energy is performed by computing the difference with respect to a known reference. In this work, we use a harmonic reference system with spring constants given to match the configurational correlations measured in the target system. We consider various perturbation techniques that compute the free energy difference between the target and reference systems while avoiding lengthy thermodynamic integration procedures. The basic methods we look at are free-energy perturbation approaches involving a single intermediate stage, which include overlap sampling and umbrella sampling. Such methods require only one or two simulations (of the target and/or reference system) to yield a result, and for small enough systems we show that these methods can be effective. In larger or more difficult systems we consider a process of switching on various harmonic modes in groups, and evaluate the free-energy change for each before summing to determine the total difference. We consider whether and how this process may be abbreviated in a way that does not require transformation of all harmonic modes. Different prototype systems are studied and discussed in the context of these methods.