We explore the dependence of the dark current Of C-60-based organic photovoltaic (OPV) cells on molecular composition and the degree of intermolecular interaction of several molecular donor materials. The saturation dark current density, J(S) is an important factor in determining the open circuit voltage, V-oc. The V-oc values of OPVs show a strong inverse correlation with J(S). Donor materials that show evidence for aggregation in their thin-film absorption spectra and polycrystallinity in thin film X-ray diffraction result in a high dark current, and thus a low V-oc. In contrast, donor materials with structures that hinder intermolecular pi-interaction give amorphous thin films and reduced values of J(S), relative to donors with strong intermolecular pi-interactions, leading to a high V-oc. This work provides guidance for the design of materials and device architectures that maximize OPV cell power conversion efficiency.