A set of star-shaped molecules (SSMs) with benzothiadiazole and benzoxadiazole groups in the arms were designed and synthesized as a low band gap material for use in organic photovoltaic devices. Benzene and silicon atoms were exploited as core moieties to yield three-arm and four-arm SSMs, respectively. Absorption spectra of all SSMs show two major bands around 370 and 530 nm with the latter having significant charge transfer character. The band gaps of SSMs vary between 1.83 and 2.05 eV. Nevertheless, benzoxadiazole containing structures display the lowest band gaps and the deepest highest-occupied molecular orbital levels, suggesting benzoxadiazole is a stronger electron-withdrawing group than benzothiadiazole. Meta-substitution inhibits excitonic delocalization over the three-arm SSMs. Thus, both four-arm and three-arm structures display very similar photophysical properties as verified by experiment as well as theory. The films of SSMs are amorphous in nature; however, hole mobilities of four-arm structures are larger than those of three-arm analogs which has been attributed to isotropic transport of carriers in condensed phase. Atomic force microscopy images reveal similar SSM/[6,6]-phenyl C61-butyric acid methyl ester blend morphology for all SSMs studied in this work. Yet, benzothiadiazole-containing SSMs exhibit better photovoltaic performance than the SSMs with benzoxadiazole groups. One remarkable observation is that the hole reorganization energies determine the magnitude of hole mobilities in an Arrhenius-like law with essentially negligible energetic disorder. The results highlight the importance of minimization of internal reorganization energies for improving carrier mobilities in disordered materials.