Charge transport in organic molecular semiconductors from first principles: The bandlike hole mobility in a naphthalene crystal

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 $100--300\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, and we can predict its temperature dependence with high accuracy. We show that scattering between intermolecular phonons and holes regulates the mobility, though intramolecular 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 paper 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.