Volcano plots in hydrogen electrocatalysis – uses and abuses

The volcano plot sits at the center of electrocatalysis textbooks — that elegant, symmetric curve showing reaction rate climbing as hydrogen binds more favorably to a surface, peaking in the middle, then falling as binding grows too strong. It is one of the field's most reproduced figures. Quaino, Juarez, Santos, and Schmickler looked carefully at the data behind it. Their conclusion is stark: once you remove the metals that are actually covered by oxide films during the hydrogen evolution reaction, the volcano disappears. The descending branch — the very feature that makes it a volcano — collapses. What generations of researchers have used to guide catalyst design may be an artifact of which metals were included in the plot. To understand why that matters, start with Sabatier's principle. For any reaction that proceeds through an adsorbed intermediate, there is an optimal binding strength. If it is too weak, the reactant won't stick — adsorption is slow. If it is too strong, the product won't leave — desorption is slow. In hydrogen evolution, the intermediate is a hydrogen atom on the metal surface, and the relevant quantity is the free energy of adsorption, written as delta G sub ad. Sabatier's principle says that at the equilibrium potential, delta G sub ad should be close to zero. Bind hydrogen just right, and both formation and release of the intermediate are fast. If you plot the exchange current density, which is the measure of reaction rate at equilibrium, against adsorption free energy for a range of metals, Sabatier's principle predicts a volcano. The parallel to Marcus theory, which governs outer-sphere electron transfer, is explicit in the paper. Marcus predicts a rate maximum when the reaction free energy equals minus the solvent reorganization energy, and predicts a fall-off for more exergonic reactions — the famous inverted region. Quaino and colleagues note that both the Marcus inverted region and the descending limb of the Sabatier volcano are difficult to observe in practice, because real systems can access alternative pathways that sidestep the predicted penalty. That observation turns out to be the key to everything that follows. Modern volcano plots are built from density functional theory — DFT — calculations of hydrogen adsorption free energy on densely packed metal surfaces. DFT is quite reliable for hydrogen, with an estimated error of plus or minus 0.1 electronvolt. That is important, because experimental reaction rates reported by different research groups can vary by up to two orders of magnitude — the uncertainty in the measurements dwarfs the uncertainty in the calculations. The plots by Quaino and colleagues draw on adsorption energies from Nørskov and colleagues, compared against experimental compilations from Trasatti and from Petrii and Tsirlina. Newer measurements from Chen and Kucernak and from Gasteiger and colleagues tend to run systematically higher than older values, because earlier experiments were limited by mass transport. What the modern DFT-based plots actually show is three clusters, not a smooth curve. Sp metals — elements like cadmium or mercury, where the d band lies far below the Fermi level — are the worst catalysts. The coinage metals, copper, silver, and gold, are intermediate. And the d-block transition metals contain the fastest catalysts, including platinum with an adsorption free energy of minus 0.2 electronvolt and copper at plus 0.1 electronvolt. Neither the acid nor the alkaline version of these plots, the authors state plainly, bears any resemblance to a volcano. The rate rises with more favorable adsorption on the left side, yes. But the right side — where Sabatier predicts rates should drop — simply does not show that decline, with two exceptions: nickel and cobalt. The reason is the oxide problem. Trasatti's original volcano, and many that followed it, included metals that are covered by oxide or hydroxide films under the conditions of hydrogen evolution. Oxide films suppress rates by orders of magnitude. When those metals occupy the region of strong hydrogen binding, they create the appearance of a descending branch — not because strong binding hurts catalysis, but because oxides hurt catalysis. Quaino and colleagues remove those metals, and the branch vanishes. The volcano was built on a selection artifact. This is not just a bookkeeping complaint. It has theoretical consequences. If the descending branch is not real for most metals, then Sabatier's principle alone cannot be the governing factor. Quaino and colleagues propose that three rules together determine whether a metal is a good hydrogen-evolution catalyst. First, delta G sub ad should be near zero at the equilibrium potential — the Sabatier condition. Second, a d band that spans the Fermi level, providing the right electronic states for adsorption and electron transfer. Third, strong and long-range coupling between that d band and the hydrogen 1s orbital. Long range matters because electron transfer to the proton happens at a distance of roughly 0.5 ångström from the adsorption site, and coupling that decays too quickly with distance makes both electron transfer and bond formation slow. The three rules together explain the pattern in the data. For sp metals, the d band lies too low to participate in bonding; in some cases, like cadmium, both bonding and antibonding hydrogen states are filled, so the d interaction contributes nothing to net binding. These metals follow Sabatier's principle closely, with the Volmer step — the initial proton discharge — typically rate-determining. For transition metals with d bands at the Fermi level, the situation is different. Many of them offer multiple adsorption sites, including a weakly adsorbed state called opd hydrogen alongside the strongly bound underpotential-deposited, or upd, hydrogen. When a metal can route the reaction through the weaker binding site, it sidesteps the Sabatier penalty entirely. On platinum, the strongly adsorbed species reaches about seventy percent surface coverage in the relevant potential range, while a weakly adsorbed species is already detectable. The system picks the favorable path. That is why the descending branch does not appear for most d metals — not because Sabatier is wrong, but because it is only one of several factors, and alternative pathways can outmaneuver it. Nickel and cobalt cannot. They are the exception the paper gives sustained attention to, and nickel becomes the worked example of what happens when the third rule fails. Nickel has its d band at the Fermi level — rule two is satisfied. But its 3d orbitals are compact. The coupling with the hydrogen 1s orbital decays rapidly with distance. And nickel is spin polarized: the d bands for spin-up and spin-down electrons are shifted relative to each other, and that asymmetry persists to shorter hydrogen-surface distances than on most metals. At 1.6 ångström from the surface, the two spin states of the hydrogen 1s orbital interact with their respective nickel d bands, producing distinct bonding and antibonding peaks. The spin polarization only disappears when hydrogen is fully adsorbed at 0.9 ångström. The practical consequence is that the weakly bound top-site adsorption on nickel(111) — the kind that would offer an alternative pathway — is energetically unfavorable under realistic conditions, with an adsorption energy of 0.9 electronvolt when strongly adsorbed hydrogen already occupies the surface. The reaction is forced through the hollow site, through the strongly bound state, with no escape route. Quaino and colleagues calculated the free-energy landscape for the Volmer reaction on nickel(111) explicitly. At the equilibrium potential, the activation energy at the saddle point is about 0.48 electronvolt, and the overall Volmer reaction is exergonic by about 0.32 electronvolt. The Volmer step itself is fast enough. Consistent with experiment, it is the subsequent Heyrovsky step — where adsorbed hydrogen reacts with another proton from solution — that is rate-determining on nickel. The mechanistic picture is a metal that looks electronically reasonable but is undone by poor spatial overlap between its orbitals and hydrogen. Volcano plots are not useless. They encode real chemistry, and they remain a sensible first screen when comparing many candidate materials. DFT adsorption energies are reliable at the 0.1 electronvolt level, and adsorption free energy does correlate with activity in a broad sense. But Quaino and colleagues argue that treating a single descriptor as a complete theory produces distorted expectations — the vanishing descending branch is proof of that. For oxygen reduction, the problem is worse still: multiple electron and chemical steps, an ambiguous choice of descriptor, and experimental scatter that dwarfs anything seen in hydrogen evolution. The framework they advance — three rules, not one — captures what a single-descriptor plot cannot: that orbital symmetry, d-band position, and coupling range all shape the outcome, sometimes overriding the thermodynamic optimum that Sabatier identifies. The volcano was never quite real. The chemistry underneath it is. This lecture was created by ennepō. Go to https://ennepo.ai to Discover, Create and Follow the latest research in your field. Read when you can. Listen when you want to.