The Al₂SiO₅ polymorphs have been examined to provide new insights into their chemical bonding, their crystal chemistry, their equations of state, and the incorporation of water in the form of hydroxyl in their structures. The Al₂SiO₅ polymorphs provide a unique structural assemblage for a crystal chemical examination due to the variation in Al coordination in the structures where Al is in 4-fold, 5-fold, and 6-fold in sillimanite, andalusite, and kyanite, respectively. Consequently, the Al₂SiO₅ polymorphs have been examined with a combination of experimental (high pressure X-ray diffraction and Polarized FTIR spectroscopy) and theoretical (VASP and Crystal 98) methods. An experimental high pressure X-ray diffraction study on andalusite and sillimanite has constrained their equation of state and the pressure derivatives of their bulk modulus with pressure. Additionally, the effect of pressure on the crystal structures has been examined, where the main structural response is compression of the AlO₆ octahedra. Comparatively, compression of the AlO₆ octahedra in andalusite is more anisotropic, while the major direction of axial compressibility in both structures is dependent on the orientation of the AlO6 octahedra. In order to better understand the crystal chemistry of the Al-O and Si-O bonds in the polymorphs, ELF isosurfaces were examined. ELF isosurfaces represent a graphical representation of the localized electron probability density. Six distinct types of ELF isosurfaces were observed in the Al₂SiO₅ polymorphs resulting from differences in the geometry, coordination, and coordinated cation atomic number surrounding the oxygens within the crystal structures. The ELF was also shown to be isostructurally related to electron density difference maps. In a combined experimental and theoretical investigation of the Al₂SiO₅ polymorphs, potential protonation sites within the crystal structures were determined at an atomic level with polarized FTIR spectroscopy and analysis of (3,-3) critical points of the negative Laplacian. The polarized FTIR spectra indicate the orientation of the OH dipole in the three polymorphs and the (3,-3) critical points indicate regions of locally concentrated electron density. Potential protonation sites were determined based on the value of the negative Laplacian, the underbonded nature of the oxygens, and the number of surrounding cations. / Ph. D.

The Electron Localization Function (ELF) measures electron localization within matter and provides insights into the nature of bonds in materials and molecules. This thesis examines the relationship between ELF and binding energy in bimolecular systems, focusing on van der Waals interactions—specifically Keesom forces, Debye forces, and London dispersion forces—which play significant roles in molecular and crystalline materials. This research addresses the challenge of accurately calculating binding energies in crystalline materials by exploring their correlation with ELF. Using Density Functional Theory (DFT) with two exchange-correlation functionals, rev-vdW-DF2 and PBE-D3(BJ), this study proposes a method for calculating binding energies in crystalline materials with promising accuracy. By analysing the ELF and its correlation with binding energies in 75 bimolecular systems, the research demonstrates a strong linear correlation, with a coefficient of determination (R2) reaching up to 0.956. The findings suggest that ELF can effectively differentiate between weak and strong van der Waals interactions, providing a reliable metric for evaluating interaction strengths. The results indicate that ELF is a valuable tool for understanding the strength of molecular interactions, with potential applications in materials science and electronic structure theory. The study highlights the importance of refining the accuracy of the ELF-based method and expanding its scope to include other types of non-covalent interactions, such as halogen bonds. The main contribution of this thesis is the exploration of methodologies for analysing and predicting molecular interaction strengths within crystalline materials, which may improve computational approaches in the field. Deriving binding energies within the unit cell directly from the ELF has the potential to simplify practical calculations.