Our calculations show linear scaling between NRR intermediates, which is consistent with previous studies that identified linear scaling between intermediates and the binding energy of an N* adatom (ΦN*). Linear scaling of intermediates with ΦN* results in linear scaling of the sequence of steps that comprise the energetic span with ΦN*. Consequently, Φmax scales with ΦN* for each energetic span. same but Φmax changes (seen as moving along a scaling line), or the steps that make up the energetic span change along with Φmax (seen as shifting to a different scaling line). Thus, as ΦN* changes, materials can move along the scaling lines or switch to new ones, but they cannot move significantly above the scaling line at any ΦN*. The lines that comprise the volcano therefore define a minimum Φmax (i.e., maximum -Φmax) at each ΦN*, and thus a boundary that limits Φmax, beyond which no studied surfaces exist due to the inherent scaling relations between NRR intermediates. Because intermediates scale imperfectly with each other, some points deviate slightly above or below the boundary defined by the volcano (see section 2.3 in the SI). In contrast to previous studies where scaling between the adsorption energies of the N2H* intermediate and the NH2* intermediate limits the minimum overpotential, 8,9,28 several unique energetic span steps comprise this volcano and limit Φmax within certain N* adatom binding ranges. More reactive surfaces on the left side of the volcano are limited by the formation of solvated NH3 from the NH* (associative distal, dark blue scaling line) or NHNH2* (associative alternating, light blue scaling line) intermediates. This results from the overbinding of intermediate adsorbates associated with a more favorable N* adatom binding energy. The metals on the right side of the volcano are less reactive and thus tend to underbind the N2* and N2H* intermediates and are consequently limited by the NH3* → N2H* energetic span (orange scaling line) that proceeds through the bare surface state (See Figure ).