The first structure-reactivity relationships for electron-transfer reactions of graphene nanoribbons (GNR) have been derived. These relationships are represented as relative reaction rate constants calculated by considering different electronic structure approximations of GNR and the Gerischer-Marcus (GM) or Marcus theories of electron transfer. The reactivity of GNR is observed to directly depend oil the ribbon width and the orientations of carbon atoms at their edges. A comparison of relative rate constants for the more accurate GM electron-transfer theory and tight-binding approximation,, predicts that armchair and zigzag GNR have opposite trends in reactivity with the former increasing with width and the latter decreasing. For zigzag ribbons, the major reactivity contribution comes from their edge states. and hence, ribbons of small widths are predicted to be the most reactive among all ribbons including armchair ribbons. The reactivity trend for zigzag GNR is reversed, however, when recent first-principles calculations are utilized with Marcus theory (fiat predict the presence of large semiconducting gaps for narrow ribbons with correspondingly low reactivities, The results should provide an aid to developing selective electron-transfer chemistries for GNR, methods to separate and sort ribbons by electronic structure, or methods to preferentially modify GNR of different ribbon widths and orientations of carbon atoms.
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