Hydrogen Adsorption Free Energy
The hydrogen adsorption free energy (often written as the free energy of adsorbed H relative to the HER reactants and products) is a widely used descriptor for hydrogen electrocatalysis. It can be computed with density functional theory, which makes it possible to estimate trends in activity across many surfaces. See also Hydrogen evolution reaction and Volcano plot.
Definition from DFT chemisorption energies (2005)
In their study of HER exchange-current trends, Nørskov, Kitchin and coworkers computed hydrogen chemisorption energies with RPBE DFT on close-packed surfaces at 1/4 and 1 monolayer coverage, and converted them to adsorption free energies by adding a zero point energy difference (0.04 eV, from H on Cu(111)) and an entropy term of half the standard entropy of gas-phase H2. The result is the simple rule that the free energy equals the chemisorption energy plus 0.24 eV, assumed transferable across metals. A value near zero, found for Pt, corresponds to the top of the HER volcano (Nørskov et al. 2005). Summary: norskov2005.
Necessary but not sufficient, and the Au versus Ni contrast (2006)
Nørskov, Kitchin and coworkers state that a hydrogen adsorption free energy near zero is a necessary but not sufficient condition for a good HER catalyst. Defending their DFT databases, they argue that hydrogen binds much more weakly to Au than to Ni, which they attribute to d-band filling: Au has filled d bands, while Ni has partly empty d bands so that the H–Ni antibonding states are partly empty. They consider it unlikely that H–H interactions could shift the H free energy on Ni well above the reactant and product chemical potential (No̸rskov et al. 2006). Summary: norskov2006.
H binding across Pd-Sn intermetallic surfaces (2020)
For Pd-Sn intermetallics from the Materials Project, Lopato et al. computed H binding on all unique sites of surfaces with Miller indices up to 2 using RPBE DFT, supplemented by machine learning predictions, and added 0.24 eV to obtain free energies (Lopato et al. 2020). Binding strengthened with Pd content: the strongest site on PdSn was 0.6 eV stronger than on Sn2Pd, attributed to new Pd3 fcc hollow sites. A linear fit of the strongest binding free energy against Pd fraction (R2 = 0.90) crossed 0 eV near a Pd fraction of 0.5, the composition of highest measured photocatalytic activity. Summary: lopato2020.
Aggregating machine-learned hydrogen binding over sites and surfaces (2023)
Rather than one adsorption site on one facet, this work enumerated slabs and sites from Materials Project intermetallics, predicted hydrogen adsorption energies with an Open Catalyst-trained GemNet model (about 0.1 eV mean absolute error on validation data), took the strongest site on each surface, and chose the surface closest to the -0.24 eV optimum to describe a chemical system (Broderick et al. 2023). The aggregated descriptor captured the necessary condition for HER activity but not effects of coverage, strain, poisoning or surface area, which the authors identify as missing pieces. Summary: broderick2023.