  Predicting charge transport in organic molecular crystals is notoriously
challenging. Carrier mobility calculations in organic semiconductors are
dominated by quantum chemistry methods based on charge hopping, which are
laborious and only moderately accurate. We compute from first principles the
electron-phonon scattering and the phonon-limited hole mobility of naphthalene
crystal in the framework of ab initio band theory. Our calculations combine GW
electronic bandstructures, ab initio electron-phonon scattering, and the
Boltzmann transport equation. The calculated hole mobility is in very good
agreement with experiment between 100$-$300 K, and we can predict its
temperature dependence with high accuracy. We show that scattering between
inter-molecular phonons and holes regulates the mobility, though
intra-molecular phonons possess the strongest coupling with holes. We revisit
the common belief that only rigid molecular motions affect carrier dynamics in
organic molecular crystals. Our work provides a quantitative and rigorous
framework to compute charge transport in organic crystals, and is a first step
toward reconciling band theory and carrier hopping computational methods.
