Charge transport in organic semiconductors (OSCs) depends on a number of molecular properties, one of which is the electronic coupling matrix element for charge transfer between the molecules forming the material. They are the off-diagonal elements of the electronic Hamiltonian in the charge-localised (or diabatic) basis. The focus of this work is on the development of a method for a fast calculation of these matrix elements for OSCs. After addressing the different methods of their calculation, I present a program to estimate the off-diagonal elements of the Hamiltonian with a fast yet accurate semi-empirical method. This model approximates the off-diagonal elements of the Hamiltonian to be proportional to the overlap between the orbitals of the molecules, which are projected onto a very small basis set. The analytical results are in a reasonable agreement with accurate ab initio and fragment orbital DFT calculations and the speed-up is up to six orders of magnitude compared to DFT calculations. Following on from this, the analytic overlap method was implemented in two programs for charge carrier propagation, one based on Kinetic Monte Carlo simulation of charge carrier hopping (presented here), the other on surface hopping non-adiabatic molecular dynamics. I also show that the analytic overlap method can be used to estimate non-adiabatic coupling vectors very efficiently, which is an important quantity in surface hopping simulations
