Calculation of the free energy of crystalline solids
Creators: name: Vasileiadis, Manolis
Publisher: name: Imperial College London
Year: 2013

description: The prediction of the packing of molecules into crystalline phases is a key step in understanding the properties of solids. Of particular interest is the phenomenon of polymorphism, which refers to the ability of one compound to form crystals with different structures, which have identical chemical properties, but whose physical properties may vary tremendously. Consequently the control of the polymorphic behavior of a compound is of scientific interest and also of immense industrial importance. Over the last decades there has been growing interest in the development of crystal structure prediction algorithms as a complement and guide to experimental screenings for polymorphs. The majority of existing crystal structure prediction methodologies is based on the minimization of the static lattice energy. Building on recent advances, such approaches have proved increasingly successful in identifying experimentally observed crystals of organic compounds. However, they do not always predict satisfactorily the relative stability among the many predicted structures they generate. This can partly be attributed to the fact that temperature effects are not accounted for in static calculations. Furthermore, existing approaches are not applicable to enantiotropic crystals, in which relative stability is a function of temperature. In this thesis, a method for the calculation of the free energy of crystals is developed with the aim to address these issues. To ensure reliable predictions, it is essential to adopt highly accurate molecular models and to carry out an exhaustive search for putative structures. In view of these requirements, the harmonic approximation in lattice dynamics offers a good balance between accuracy and efficiency. In the models adopted, the intra-molecular interactions are calculated using quantum mechanical techniques; the electrostatic inter-molecular interactions are modeled using an ab-initio derived multipole expansion; a semi-empirical potential is used for the repulsion/dispersion interactions. Rapidly convergent expressions for the calculation of the conditionally and poorly convergent series that arise in the electrostatic model are derived based on the Ewald summation method. Using the proposed approach, the phonon frequencies of argon are predicted successfully using a simple model. With a more detailed model, the effects of temperature on the predicted lattice energy landscapes of imidazole and tetracyanoethylene are investigated. The experimental structure of imidazole is Abstract | ii correctly predicted to be the most stable structure up to the melting point. The phase transition that has been reported between the two known polymorphs of tetracyanoethylene is also observed computationally. Furthermore, the predicted phonon frequencies of the monoclinic form of tetracyanoethylene are in good agreement with experimental data. The potential to extend the approach to predict the effect of temperature on crystal structure by minimizing the free energy is also investigated in the case of argon, with very encouraging results.