Analysis and application of density functional theory to intermolecular forces, crystal structures, and pressure-induced phase transitions

The accuracy of density functionals in regions of large density gradients is assessed by examining the accuracy of the interaction energies of rare gas atom pairs. A new exchange functional is proposed, which is comparable in accuracy to the previously proposed functionals for the total exchange energies, but more accurate for the exchange contributions to the interaction energy.; The approximations in the electron gas model of intermolecular forces were examined. The errors in the additive density approximation are large and render the electron gas model invalid at large interatomic separations, such as those in van der Waals molecules, but can allow semi-quantitative results at small interatomic separations, such as those in ion-ion interactions. The modified electron gas scaling factors actually decrease the accuracy of the kinetic energy calculation by further overestimating its value, but this error tends to cancel the error in the additive density approximation more fully, leading to better results for intermolecular forces.; The polarization-included electron gas (PEG) model for the calculation of crystal structures is presented. The PEG model is an extension of the modified electron gas (MEG) model of crystal structures, in which the ions are able to distort or polarize from spherical shapes, allowing partial covalency. The PEG model gives improved results over the MEG model for crystal structures and energies where the nonspherical distortions are important. The relative magnitudes of the distortions are in agreement with the extents of covalency expected from electronegativity differences.; The PEG model is used to examine pressure induced phase transitions which are relevant to geophysics. Two phase transitions in silica are examined: the transition from the quartz structure to the stishovite structure, and the transition from the stishovite structure to the CaCl{dollar}sb2{dollar} structure. The results are significantly improved over those of the MEG model and are in reasonable agreement with experiment. The compression of quartz is more accurately reproduced with the PEG model than with the MEG model. The spinel to perovskite phase transitions in magnesiosilicates are examined. Reasonable agreement with experiment for the transition pressures is obtained, and the results are improved over those of the MEG model.