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Transition metal nanoparticle catalysts show great promise as the key enabling breakthrough for the realization of efficient and economical fuel cells. These, in turn, will provide a sustainable source of clean energy with applications in transportation and portable power generation. In order to better understand the reactivity of nanoparticles, we have been studying a number of pure and core-shell transition metal nanoparticles involving 12 different transition metals. One of our primary tools for gaining insight into chemical reactivity in the condensed Fukui function which has been widely applied in organic chemistry. The condensed Fukui function, which is readily obtained from quantum chemistry calculations, give a numerical value indicating the likelihood of reaction at a given atomic center. We have shown that the predictions made using the Fukui function agree well with the well-established d-band center method of Norskov and coworkers. Recently, we have considered the effect of a molecule adsorbed on the surface of a nanoparticle on the reactivity of other atoms on the nanoparticle surface. We are also studying the interactions of a number of molecules with transition metal surfaces, with the goal of gaining deeper insight into the chemistry of processes occurring on nanoparticle catalysts. Our work is done in collaboration with the experimental research group of Prof. YuYe Tong at Georgetown University.