An empirical molecular model of crystals of p-terphenyl doped with terrylene is developed and compared with recent experiments on single guest molecules. The model provides an assignment of the experimental electronic origins to the substitution sites and an interpretation of the photo-induced frequency jumps of single terrylene molecules. The Stark shifts of terrylene in the different sites are estimated by a coupled Hartree-Fock semi-empirical calculation. The topology of the many-dimensional energy surface of the X-1 electronic origin is explored with simulated annealing.