By employing density-functional theory coupled with Holstein-Peierls model, we investigate the pressure and temperature dependence of the hole and electron mobilities in naphthalene single crystal from atmospheric pressure up to 2.1 GPa (at room temperature) and from 5 to 296 K (at ambient pressure). It is found that the pressure reduces the electron-phonon coupling strength and enhances the mobilities. Importantly, we point out that only when temperature-dependent structure modifications are taken into account can one better describe the temperature-dependent transport behavior. Especially, the band to hopping crossover transition temperature for the electron transport in the c'-axis is calculated to be around 153 K, which is close to the experimental result of between 100 and 150 K. If this temperature-dependent structure modifications were neglected, the transition temperature would be only about 23 K, as previously obtained [L. J. Wang et al., J. Chem. Phys. 127, 044506 (2007)].
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