  We study the effect of quantum vibronic coupling on the electronic properties
of carbon allotropes, including molecules and solids, by combining path
integral first principles molecular dynamics (FPMD) with a colored noise
thermostat. In addition to avoiding several approximations commonly adopted in
calculations of electron-phonon coupling, our approach only adds a moderate
computational cost to FPMD simulations and hence it is applicable to large
supercells, such as those required to describe amorphous solids. We predict the
effect of electron-phonon coupling on the fundamental gap of amorphous carbon,
and we show that in diamond the zero-phonon renormalization of the band gap is
larger than previously reported.
