  We present a unified and nonperturbative method for calculating spectral and
transport properties of Hamiltonians with simultaneous Holstein (diagonal) and
Peierls (off-diagonal) electron-phonon coupling. Our approach is motivated by
the separation of energy scales in semiconducting organic molecular cystals, in
which electrons couple to high-frequency intramolecular Holstein modes and to
low-frequency intermolecular Peierls modes. We treat Peierls modes as
quasi-classical dynamic disorder, while Holstein modes are included with a
Lang-Firsov polaron transformation and no narrow-band approximation. Our method
reduces to the popular polaron picture due to Holstein coupling and the dynamic
disorder picture due to Peierls coupling. We derive an expression for efficient
numerical evaluation of the frequency-resolved optical conductivity based on
the Kubo formula and obtain the DC mobility from its zero-frequency component.
We also use our method to calculate the electron-addition Green's function
corresponding to the inverse photoemission spectrum. For realistic parameters,
temperature-dependent DC mobility is largely determined by the Peierls-induced
dynamic disorder with minor quantitative corrections due to polaronic
band-narrowing, and an activated regime is not observed at relevant
temperatures. In contrast, for frequency-resolved observables, a quantum
mechanical treatment of the Holstein coupling is qualitatively important for
capturing the phonon replica satellite structure.
