First-principles study of the structural, electronic, and optical properties of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi mathvariant="normal">Ga</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math>in its monoclinic and hexagonal phases

We report the results of a comprehensive study on the structural, electronic, and optical properties of ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ in its ambient, monoclinic $(\ensuremath{\beta})$ and high-pressure, hexagonal $(\ensuremath{\alpha})$ phases in the framework of all-electron density functional theory. In both phases, the conduction band minimum is at the zone center while the valance band maximum is rather flat in the $k$ space. The calculated electron effective mass ${m}_{e}^{*}∕{m}_{0}$ comes out to be 0.342 and 0.276 for $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ and $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$, respectively. The dynamic dielectric function, reflectance, and energy-loss function for both phases are reported for a wide energy range of $0--50\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The subtle differences in electronic and optical properties can be attributed to the higher symmetry, coordination number of Ga atoms, and packing density in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ relative to that in $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$.