General theory of electronic transport in molecular crystals. I. Local linear electron–phonon coupling

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Abstract
An improved general theory of electronic transport in molecular crystals with local linear electron–phonon coupling is presented. It is valid for arbitrary electronic and phonon bandwidths and for arbitrary electron–phonon coupling strength, yielding small‐polaron theory for narrow electronic bands and strong coupling, and semiconductor theory for wide electronic bands and weak coupling. Detailed results are derived for electronic excitations fully clothed with phonons and having a bandwidth no larger than the phonon frequency; the electronic and phonon densities of states are taken as Gaussian for simplicity. The dependence of the diffusion coefficient on temperature and on the other parameters is analyzed thoroughly. The calculated behavior provides a rational interpretation of observed trends in the magnitude and temperature dependence of charge‐carrier drift mobilities in molecular crystals.