Theory of electronic transport in molecular crystals. II. Zeroth order states incorporating nonlocal linear electron-phonon coupling

A generalized transformation is applied to a model Hamiltonian incorporating both local and nonlocal exciton-phonon coupling. For the application of the usual transport theory, the difference between the transformed coupling and its thermal average over the free phonon ensemble must be small. This is achieved by a temperature-dependent set of transformation coefficients defined by a transcendental equation which is soluble numerically after some approximation. Nonlocal coupling increases both the exciton binding energy and the usual band narrowing, but it also changes the band shape in a way which may introduce new minima and band broadening. The exciton velocities are then no longer related to the exciton hopping and scattering rates in the same way as in local coupling.