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Band structure and ground-state total energy calculations were performed on layered ${\mathrm{LiCoO}}_{2}$ (rhombohedral $R3\ifmmode\bar\else\textasciimacron\fi{}m)$ and ${\mathrm{Li}}_{0.5}{\mathrm{CoO}}_{2}$ (monoclinic $P2/m)$ by periodic Hartree-Fock methods, using effective core pseudopotential basis sets. Insulating and conducting behaviors are correctly predicted for the former and latter compound, respectively, on the basis of nonmagnetic closed-shell wave functions. Lithium diffusion was simulated in ${\mathrm{Li}}_{0.5}{\mathrm{CoO}}_{2}$ along the [100] and [110] directions, by relaxing all atomic positions in Pm and $P1\ifmmode\bar\else\textasciimacron\fi{}$ space groups and obtaining the corresponding energy profiles as a function of the ${\mathrm{Li}}^{+}$ position. An a posteriori density-functional theory-based correction for the correlation energy was included. The two-step diffusion mechanism $(\mathrm{octahedra}\stackrel{\ensuremath{\rightarrow}}{l}\mathrm{tetrahedra}\stackrel{\ensuremath{\rightarrow}}{l}\mathrm{octahedral}\mathrm{ }\mathrm{site})$ is predicted to be favoured with respect to the direct jump between octahedral sites, with an activation energy of 0.13 against 0.27 eV. A significant cobalt-oxygen charge transfer is observed during the diffusion process, and its meaning is analyzed.

The ground-state electronic and magnetic properties of rhombohedral ${\mathrm{Ti}}_{2}$${\mathrm{O}}_{3}$ and ${\mathrm{V}}_{2}$${\mathrm{O}}_{3}$ have been investigated by ab initio all-electron periodic Hartree-Fock calculations. Both unrestricted open-shell and restricted closed-shell methods have been employed, with basis sets of atomic orbitals represented by contracted Gaussian-type functions. The ${\mathrm{t}}_{2\mathrm{g}}$ degeneracy of d electrons is removed by the rhombohedral field, giving rise to orbital ordering between ${\mathrm{a}}_{1\mathrm{g}}$ and ${\mathrm{e}}_{\mathrm{g}}^{\mathrm{\ensuremath{\pi}}}$ levels. The self-consistent-field variational solutions are spin-polarized insulating states with single (${\mathrm{a}}_{1\mathrm{g}}$) and double (${\mathrm{e}}_{\mathrm{g}}^{\mathrm{\ensuremath{\pi}}}$) electron occupations for ${\mathrm{Ti}}_{2}$${\mathrm{O}}_{3}$ and ${\mathrm{V}}_{2}$${\mathrm{O}}_{3}$, respectively. Conducting or semiconducting states, with different relative energies of ${\mathrm{a}}_{1\mathrm{g}}$ and ${\mathrm{e}}_{\mathrm{g}}^{\mathrm{\ensuremath{\pi}}}$ bands, have also been obtained by changing the c/a ratio of the hexagonal unit cell. The charge transfer into ${\mathrm{e}}_{\mathrm{g}}^{\mathrm{\ensuremath{\sigma}}}$ levels is discussed and compared to the ${\mathrm{Cr}}_{2}$${\mathrm{O}}_{3}$ and ${\mathrm{Fe}}_{2}$${\mathrm{O}}_{3}$ behavior.

Antiferromagnetic rhombohedral \ensuremath{\alpha}-${\mathrm{Fe}}_{2}$${\mathrm{O}}_{3}$ has been studied by calculations of the ground-state spin-polarized wave function and total energy, using the ab initio periodic unrestricted Hartree-Fock approach. All-electron basis sets of contracted Gaussian-type functions are employed to represent the O and Fe atoms (18 and 27 orbitals, respectively); Fe is alternatively described by a large-core pseudopotential plus 18 valence-shell orbitals. Computations have been performed for both the antiferromagnetic (AF) and ferromagnetic (FM) structures; the correct relative stability is reproduced, with \ensuremath{\Delta}E(AF-FM)=-0.0027 hartree per formula unit (including a correction for correlation energy). The dependence of \ensuremath{\Delta}E(AF-FM) on variations of the Fe-O bond lengths and Fe-O-Fe' angles involved in superexchange is analyzed, finding that for some configurations the FM structure becomes more stable than the AF one. The athermal equation of state, equilibrium crystal structure, elastic bulk modulus, and binding energy have been computed and compared to experimental quantities. An analysis of the density of electronic states show that the band gap is of p-d rather than d-d type, confirming the charge-transfer-insulator nature of hematite as inferred from photoelectron spectra. The overall shape of the valence band is also fully consistent with spectroscopic results. Mulliken electron population data indicate a charge back transfer of 0.29\ensuremath{\Vert}e\ensuremath{\Vert} from ${\mathrm{O}}^{2\mathrm{\ensuremath{-}}}$ to the d shell of ${\mathrm{Fe}}^{3+}$, causing a partial spin pairing with a magnetic moment of 4.7${\mathrm{\ensuremath{\mu}}}_{\mathit{B}}$.

The ground-state crystal energies of cubic ${\mathrm{MgAl}}_{2}$${\mathrm{O}}_{4}$ (spinel) and MgO (periclase) and of rhombohedral \ensuremath{\alpha}-${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ (corundum) have been calculated at different volumes, relaxing the corresponding structures, by all-electron periodic Hartree-Fock methods (crystal program). Basis sets of contracted Gaussian-type functions are employed for the 18 atomic (including d) orbitals representing each of the Mg, Al, and O atoms. Mulliken net atomic charges ${\mathit{z}}_{\mathrm{Mg}}$=1.86\ensuremath{\Vert}e\ensuremath{\Vert} (MgO), ${\mathit{z}}_{\mathrm{Al}}$=2.30\ensuremath{\Vert}e\ensuremath{\Vert} (\ensuremath{\alpha}-${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$), ${\mathit{z}}_{\mathrm{Mg}}$=1.74\ensuremath{\Vert}e\ensuremath{\Vert}, and ${\mathit{z}}_{\mathrm{Al}}$=2.24\ensuremath{\Vert}e\ensuremath{\Vert} (spinel) are obtained. The elastic bulk modulus, the Murnaghan equation of state p(V) at the athermal limit, the Mg-O and Al-O bond compressibilities, and the binding energy have been derived for each phase (and the elastic constants ${\mathit{C}}_{11}$ and ${\mathit{C}}_{12}$ for spinel only). Comparison with existing experimental data is discussed. The enthalpy change for spinel decomposition into the simple oxides has been computed as a function of pressure, including a correction for the electron correlation energy based on local-density-functional theory. A decomposition pressure of 11 GPa at T=0 K is predicted, against values of 8 and 13 GPa derived from experimental thermodynamic data and from direct compression experiments, respectively.

Calculations of the Hartree-Fock ground-state wave function and total energy of crystalline ${\mathrm{MgCO}}_{3}$ have been performed using the ab initio crystal program. Contracted Gaussian-type functions have been used to represent 18, 18, and 14 (including d) atomic orbitals for Mg, O, and C, respectively. The rhombohedral calcite-type structure has been fully relaxed, determining the equilibrium lattice constants and coordinate of the O atom as a function of volume. The bulk elastic modulus and the ${\mathit{C}}_{33}$ and ${\mathit{C}}_{11}$+${\mathit{C}}_{12}$ elastic constants have been calculated. Deviations from experimental data are within 1% for the structural parameters and amount to +6.8% for the bulk modulus. The computed binding energy (including a correction for the electron correlation based on local-density-functional theory) is smaller by 6% than the measured value. Mulliken electron charges are +1.750, -0.986, and +1.207 \ensuremath{\Vert}e\ensuremath{\Vert} for Mg, O, and C. Energy bands, density of states, and electron-density maps permit the characterization of chemical bonding within the ${\mathrm{CO}}_{3}$ molecular unit and between ${\mathrm{CO}}_{3}$ groups and Mg atoms.

A periodic ab initio Hartree-Fock method (the program crystal) has been used to evaluate the total-electron-energy surface of ${\mathrm{MgF}}_{2}$ (rutile-type tetragonal structure) as a function of crystal strain. Mg and F atoms are represented by 13 atomic orbitals in the form of contracted Gaussian-type functions. The equilibrium unit-cell edges and fluorine coordinates, the binding energy, and the six elastic constants ${\mathit{C}}_{11}$,${\mathit{C}}_{12}$, ${\mathrm{C}}_{13}$,${\mathit{C}}_{33}$,${\mathit{C}}_{44}$, and ${\mathit{C}}_{66}$ have been calculated. Inner strain was accounted for by relaxing the F-atom position for each lattice deformation applied, and contributed significantly to the ${\mathit{C}}_{44}$,${\mathit{C}}_{66}$, and ${\mathit{C}}_{33}$ components. An average deviation of 8.0% is observed with respect to experimental elastic data. Classical two-body empirical calculations have been performed for the purpose of comparison. Energy bands, Mulliken electron populations, and charge-density maps are analyzed, and the chemical bonding is discussed, showing significant deviations from ionicity (${\mathit{z}}_{\mathrm{Mg}}$=1.80\ensuremath{\Vert}e\ensuremath{\Vert}).

Two high-pressure displacive phase transformations of AgI (from cubic $Fm\overline{3}m$ to monoclinic $P{2}_{1}∕m$ to orthorhombic $Cmcm$ symmetry) were studied by periodic ab initio calculations, employing a B3LYP hybrid density functional theory--Hartree-Fock functional (CRYSTAL code). The order parameter was represented as a distortion of the monoclinic lattice, $\ensuremath{\eta}=\ensuremath{-}(2c\phantom{\rule{0.2em}{0ex}}\mathrm{cos}\phantom{\rule{0.2em}{0ex}}\ensuremath{\beta})∕a$, and enthalpy $H=E+pV$ was the appropriate Landau potential at the athermal limit. Constant-pressure structural optimizations were performed at different $\ensuremath{\eta}$ and $p$ values, obtaining a set of $H(\ensuremath{\eta},p)$ curves. A study of their behavior in the neighborhood of $\ensuremath{\eta}=0$ (rocksalt type) and $\ensuremath{\eta}=1$ (TlI-type phase) allowed us to establish unambiguously the weak first-order character of the cubic-monoclinic transition, with an enthalpy barrier of $0.010\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ at the equilibrium pressure of $19.3\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. For the monoclinic-orthorhombic transformation, not observed experimentally yet, an activation barrier of only $0.001\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ was determined at ${p}_{t}=41.7\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, so as to indicate an effective second-order behavior at nonvanishing temperatures. Expansions of the Landau potential around $\ensuremath{\eta}=1$ showed that the numerical curves obtained can be fitted by eighth-order even polynomials, with a consistent pressure dependence of the coefficients.

Ab initio periodic DFT-GGA-LCAO calculations at the athermal limit have shown that AgI transforms from the zinc blende to the tetragonal antilitharge structure at $1.2\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$, and then to rock salt at $1.6\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. A monoclinic $Pm$ pathway is proposed for both reconstructive phase transitions, which leads to a ``bifurcate'' three-step mechanism. One step relates the antilitharge structure to a metastable $Bmm2$ orthorhombic phase (with Ag and I in five-fold coordination), and is followed by two alternative steps transforming the metastable structure into either zinc blende or rock salt. The enthalpy curve along the $Pm$ pathway shows two bottleneck states bracketing the orthorhombic phase, with a predicted maximum activation enthalpy of $0.088\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Changes of the Ag crystal-chemical environment account for the mechanism. The kinetics of direct zinc blende/rock salt conversion is also considered, within an orthorhombic $Imm2$ pathway, and it is compared to the previous mechanism.

Three different pathways have been analyzed, by periodic DFT-GGA-LCAO calculations, for the rocksalt-(B 1) to CsCl-type (B2) phase transformation of calcium oxide at the equilibrium pressure of 64.7 GPa. The monoclinic P2 1 /m mechanism shows a lower enthalpy barrier (0.13 eV) with respect to the other ones (R3m and Pmmn), and a secondary minimum in its enthalpy profile gives evidence of a metastable intermediate phase with TII-like structure and coordination number 7 for both Ca and 0. The changes of chemical bonding along the transition path are analyzed.

Ab initio periodic DFT-LCAO methods $(B3\mathrm{LYP}$ and LDA functionals), at the all-electron level, were employed to study the atomic pathway of the zinc blende to rocksalt phase transition of ZnS. By the technique of constant pressure enthalpy minimization, the transformation mechanism based on a $\mathrm{Pmm}2$ orthorhombic intermediate structure, recently proposed for SiC, was examined and compared to the traditional $R3m$ rhombohedral pathway. At the equilibrium pressure of 19 GPa, an activation enthalpy of 0.15 $(\mathrm{Pmm}2)$ against 0.50 $(R3m)$ eV was obtained, confirming the orthorhombic mechanism to be definitely most favored also for a more ionic solid such as ZnS. The band gap is predicted to narrow progressively from zinc blende to rocksalt, with a parallel increase of the Zn to S charge transfer. Some structural and electronic features indicate a jumplike character of the transformation mechanism at about one third of the path.