  We study the impact of phonon anharmonicity on the electronic dynamics of
soft materials using a nonperturbative quantum-classical approach. The method
is applied to a one-dimensional model of doped organic semiconductors with
low-frequency intermolecular lattice phonons. We find that anharmonicity that
leads to phonon hardening increases the mobility and anharmonicity that leads
to phonon softening decreases the mobility. We also test various
approximations, including the use of adiabatic phonon disorder, an effective
harmonic model with temperature-dependent frequencies, and the Boltzmann
transport equation with second-order perturbation theory scattering rates.
Overall, we find surprisingly good agreement between all methods but that
accounting for phonon anharmonicity is important for accurate prediction of
electronic transport including both quantitative mobility values and their
qualitative temperature dependence. For the model studied, phonon lifetime
effects have relatively little impact on carrier transport, but the effective
frequency shift due to anharmonicity is essential. In cases with highly
asymmetric, non-Gaussian disorder, an effective harmonic model cannot
quantitatively reproduce mobilities or finite-frequency conductivity, and this
is especially true for acoustic phonons.
