  We report on the structural, electronic and vibrational properties of the
Ga$_{1-x}$In$_x$N alloy using virtual crystal approximation (VCA) from
first-principles. A band gap bowing parameter of 3.85 eV is obtained with the
TB09 functional. Phonon density of states shifts to lower frequency as the In
content is increased. However, VCA ignores disorder effect and is therefore
unable to describe the broadening of the phonon spectra upon alloying. The role
of electron-phonon interaction in the temperature dependence of the band gap is
also studied for GaN, InN and their alloy Ga$_{1-x}$In$_x$N. The calculated
zero-point motion renormalization and the fitted Varshni parameter over the
entire composition range are discussed.
