Quantum-classical study of charge transport in organic semiconductors with multiple low-frequency vibrational modes

Building on the recent success of a quantum-classical method for computing transport properties in the Holstein model with a single phonon mode [P. Mitri\'c et al., Phys. Rev. B ${\bf 111}$, L161105 (2025)], we now assess its reliability in more realistic scenarios involving multiple phonon modes in the Holstein model, as well as single- and multi-mode Peierls models. For parameters relevant to the prototypical organic semiconductor rubrene, we compute the frequency-dependent charge mobility and find excellent agreement with results from the state-of-the-art hierarchical equations of motion method. These results show that the method, previously validated only for the single-mode Holstein model, preserves quantitative accuracy in substantially more complex and material-relevant regimes. Our microscopic approach complements the phenomenological transient-localization theory and is readily applicable to realistic electron-phonon Hamiltonians.