Multiscale Modeling of Charge Transport in Organic Semiconductors: Assessing the Validity of the Harmonic Approximation for Low-Frequency Vibrations

In recent years, the importance of intrinsic disorder in organic semiconductors has gained increasing attention as a factor limiting transport properties in these substrates. In particular, the presence of low-frequency phonon modes modulating transport questions the adoption of the harmonic approximation in theoretical descriptions of such modes, since large displacements from equilibrium positions are expected. Herein, we have analyzed the transport process in several organic semiconductors using a combination of molecular dynamics simulations based on quantum mechanically derived force fields, together with transferable and differentiable deep learning models, trained on density functional theory calculations, able to predict transfer integrals and their gradients for different substrates, providing the ingredients to be used within a kinetic Monte Carlo prediction of charge mobility. In particular, we obtained the fluctuations of transfer integrals for several molecular species in their crystals with the harmonic approximation, both adopting DFT and a differentiable deep learning model, which was also used within anharmonic strategies exploiting molecular dynamics. Although the comparison among the different approaches used to evaluate transfer integral fluctuations was difficult to interpret, we incorporated fluctuations as disorder in a kinetic Monte Carlo calculation of charge mobility, to compare with experiments. Mobilities computed with disorder described with different theoretical foundations were consistent and in agreement with experimental and literature data, highlighting that, although low-frequency modes are involved in the modulation of transport properties, the harmonic approximation is still appropriate.