Structural, vibrational, elastic, and dielectric properties of ZnO single-walled nanotubes are investigated theoretically. Calculations are carried out by using a Gaussian basis set and the B3LYP hybrid functional as implemented in the periodic ab initio CRYSTAL code. Nanotubes with increasing radius display asymptotic limits to the infinite monolayer. One soft phonon mode is recognized, whose vibration frequency is shown to be connected to the elastic constant C11 of the monolayer as the 1D → 2D transition is approached. The value of Young's elastic modulus of the nanotubes denotes a remarkable flexibility. Electronic and ionic contributions to the polarizability turn out to be comparable in magnitude. In particular, geometry relaxations at increasing radii show large influence on the transverse vibrational polarizability.

Andradite-uvarovite (Ca3Fe2Si3O12-Ca3CrSi3O12) solid solutions have been investigated at an ab initio quantum-mechanical level by using an all-electron Gaussian-type basis set and the hybrid B3LYP functional in its unrestricted formulation. Only ferromagnetic phases have been considered. All possible nonequivalent geometrical configurations resulting from the substitution of Cr atoms for x = 1-8 Fe atoms in the 16a site in the garnet primitive cell have been fully optimized (cell parameters and fractional coordinates of 80 atoms). As the lattice parameters of the two end-members are very similar (11.99 and 12.05 angstrom for uvarovite and andradite, respectively), geometry rearrangements at the various x are extremely small, the largest excess volume being 0.15 angstrom(3) and the largest excess energy 3.68 kJ/mol. Thermodynamic functions are calculated from the configurational contribution to entropy and disregarding the vibrational contribution, which is expected to be negligible. Almost ideal miscibility is predicted.

The vibrational spectrum of Mg2SiO4 olivine was calculated at the Γ point by using the periodic ab initio CRYSTAL program. An all electron localized Gaussian-type basis set and the B3LYP Hamiltonian were employed. The full set of frequencies (35 IR active, 36 Raman active, 10 “silent” modes) was computed and compared to experimental data from different sources (four for IR and four for Raman). A generally good agreement is observed with experiment (the mean absolute difference ranging from 7 to 10 cm−1 for the various sets), when some of the experimental frequencies, whose attribution is uncertain or appears to be affected by large errors, are not taken into account. A small number of observed peaks are not consistent with calculated frequencies, and a few theoretical peaks do not correspond to measured values. The implications are discussed in detail. The full set of modes are characterized using different tools, namely isotopic substitution, direct inspection of the eigenvectors and graphical representation, so as to obtain a consistent mode assignment.

The relative stability of MgSiO3-ilmenite, MgSiO3-perovskite and (periclase+stishovite) assemblage phases as a function of the pressure is investigated with the periodic quantum mechanical ab initio HartreeFock program CRYSTAL. For the first time, the structure of MgSiO3-ilmenite is fully optimized. Basis set effects are explored. It turns out that relatively small basis sets reproduce correctly experimental geometries. However, larger basis sets (“triple zeta” quality, plus polarization d functions) are needed to yield significant thermochemical results. All contributions to the 0 K enthalpy are discussed. On the basis of the present highest level calculations, it appears that in the explored range of pressure (0<P< 60 GPa) the mineralogical assemblage periclase+stishovite has higher enthalpy than MgSiO3-ilmenite or perovskite, and that ilmenite transforms to orthorhombic perovskite around to 29.4 GPa in good agreement with experimental data extrapolated down to 0 K.

Pseudopotential periodic Hartree-Fock calculations have been performed on the three polymorphs of Mg2SiO4 with a polarized split valence basis set. The energy differences between polymorphs at their experimental geometries are correctly predicted. The olivine to modified spinel and olivine to spinel phase transition pressures have been estimated and agree within a few GPa with their experimental values. The bonding in Mg2SiO4 is discussed from the point of view of the, band structures, projected density of states, electron density and electron localization function (ELF) curves. It is concluded that both Mg-O and Si-O bonds are highly ionic.

The periodic ab-initio Hartree-Fock Self Consistent Field program CRYSTAL has been used to study the electronic structure and equation of state of MgSiO3 perovskite. Three space groups were considered: Pm3m (cubic; ideal untilted SiO6 octahedra), P4/mbm (tetragonal; the octahedra are allowed to deform along and rotate about the crystallographic c cell edge) and Pbnm (orthorhombic; octahedra are allowed to deform along and rotate about the three cell edges).

Silicon is tetracoordinated in most silica polymorphs except stishovite, in which it is hexacoordinated. Pseudopotential periodic Hartree-Fock calculations have been performed to study a possible reaction pathway between cristobalite and stishovite. The calculated transition pressure (6 GPa) is consistent with the stishovite synthesis pressure range, whereas the activation enthalpy at 0 K is predicted to be of the order of 125 kJ per SiO2 mole under that pressure. Electron density has been plotted for different geometries intermediate between low-cristobalite and stishovite equilibrium structures. The ionicity increases and the electron density around oxygen and silicon atoms becomes more spherical as the system becomes hexacoordinated.

Periodic Hartree-Fock STO-3G calculations have been performed on several tetracoordinated silica polymorphs: low and high quartz, low and idealized high cristobalite and prototype tridymite. The optimized structural parameters are in overall good agreement with experimental data. In the particular case of α-quartz, the SiO4 tetrahedra are found to be irregular. The optimized values of the two different SiO bond lengths are respectively 1.608 Å and 1.613 Å. The potential energy versus tilt angle curves suggest a picture of the high temperature phases in terms of delocalized oxygen atoms which is consistent with a disordered structure. Finally, the bonding in silica polymorphs is discussed from electron density maps and Mulliken population analysis.