Partial delocalisation enhances the transport of charges and excitons.

Charge transport is well understood in both highly ordered materials (band conduction) or highly disordered ones (hopping conduction). In moderately disordered materials---including many organic semiconductors---the approximations valid in either extreme break down, making it difficult to accurately model the conduction. In particular, describing wavefunction delocalisation requires a quantum treatment, which is difficult in disordered materials that lack periodicity. Here, we present the first three-dimensional model of partially delocalised charge and exciton transport in materials in the intermediate disorder regime. Our approach is based on polaron-transformed Redfield theory, but overcomes several computational roadblocks by mapping the quantum-mechanical techniques onto kinetic Monte Carlo. Our theory, delocalised kinetic Monte Carlo (dKMC), shows that the fundamental physics of transport in moderately disordered materials is that of charges hopping between partially delocalised electronic states. Our results reveal why traditional kinetic Monte Carlo can dramatically underestimate organic-semiconductor mobilities and show that higher-dimensional calculations capture important delocalisation effects neglected in lower-dimensional approximations.