CRYSTAL-STRUCTURE CALCULATIONS WITH DISTORTED IONS

We present the polarization-included electron-gas (PEG) model for crys tal structures, which is similar to the modified-electron-gas (ME(i) m odel for crystal structures, but in which the anions can distort from spherical symmetry. This nonspherical distortion is important when the anions occupy low-symmetry positions. For SiO2 quartz, SiO2 cristobal ite, BeF2 quartz, and the zeolite sodalite, which have open crystal st ructures, the structures and energies calculated with the PEG model ar e in much better agreement with experiment than those calculated with the MEG model. The improved structural results are due mainly to small er and more accurate cation-anion-cation bond angles. For SiO2 stishov ite, TiO2 rutile, and Mg2SiO4 spinel, which have more closely packed c rystal structures, the structures are modeled well with both the PEG a nd MEG models, but the energies are more accurately calculated with th e PEG model. The improved results for the energies are due to the stro nger bonds formed when charge density moves into the bonding regions. Electron-distribution plots are in good agreement with those from accu rate band-structure calculations for the cristobalite and stishovite p hases of silica. The electron-distribution plots show that the nonsphe rical distortions increase from BeF2 to TiO2 to SiO2, demonstrating th at the extent of covalent bonding increases from BeF2 to TiO2 to SiO2, in agreement with electronegativity differences. We find that covalen t effects are not as important in MgSiO3 perovskite as they are in the silica polymorphs quartz, cristobalite and stishovite, and Mg2SiO4 sp inel.