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Description
Crystalline caged hydrocarbons serve as suitable candidates for the study of the effect of local disorder on solid phase thermodynamic properties. The carbon skeleton of these compounds is often compact and experiences a considerable amount of strain. This puts caged hydrocarbons in a unique position as molecules of interest in the fields of explosive materials, energy conservation, and drug design. Unfortunately, the available thermodynamic data are in most cases scarce, contradictory, or outright missing.
The quasi-harmonic approximation (QHA) provides a satisfactory estimation of important thermodynamic functions such as the solid phase entropy and isobaric heat capacity, and subsequently the sublimation properties, when paired up with predicted properties for the gaseous phase. This work aims at expanding the QHA prediction by including the possibility of local disorder in the crystal structure. Large-amplitude anharmonic degrees of freedom can lead to dynamic disorder in the solid phase, contributing to the crystal entropy as a result. In the case of the highly symmetrical molecules of caged hydrocarbons, the possibility of hindered molecular rotations (or librations) within the crystal lattice is postulated. Rotational energy profiles are obtained by simply rotating a molecule within a periodic crystalline structure using the principle rotational axes belonging to their respective point groups of the molecules as a guide. The resulting profile is further refined by means of optimizing the crystalline structure corresponding to the local minima of the energy curve and the improved dimer method for the maxima. Using these profiles as the external potential in the one-dimensional hindered rotor approximation, anharmonic corrections to the crystal entropy and heat capacity are evaluated. This simplified model gives an upper bound for the resulting correction.
In an attempt to capture the point-defect nature of the molecular rotations, a fragment-based additive scheme is utilized, dividing the many-body region around the rotated molecule within the crystal into a series of dimers. The sum of the dimer energies within a narrow range around the point defect constitutes the local change in energy associated with the rotation. This fragmentation is performed for several crystal structures of interest along the rotational energy curve, further refining it in the process. Such point-defect-refined energy curves are again used to compute the anharmonic contributions to the crystalline thermodynamic properties.
