Quantum-mechanical calculation of the solid-state equilibrium MgO+α-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Al</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>⇄<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">MgAl</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>(spinel) versus pressure

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.