Adsorption Scaling Relations
Adsorption scaling relations are approximately linear relationships between the adsorption energies of different species. They are useful because a few computed energies (or a single descriptor) can then predict many others, which reduces the cost of screening catalysts. Such relations are most often reported across many metal surfaces at a fixed coverage, but the same idea can be applied across adsorbate configurations and coverages on one surface. See also Coverage-dependent adsorption and d-Band model.
Configurational correlations across coverage (2009)
On Pd(111), Kitchin showed that the coverage-dependent adsorption energies of C and N in fcc sites are nearly linear functions of the O adsorption energy in the same configuration, because all three adsorbates modify the surface d band in a similar way. The correlations hold with LDA, PBE, revPBE and RPBE as well as PW91, and rescaling by each correlation’s slope and intercept reduces them to a single line. The paper argues that single-coverage scaling relations of the kind reported by Abild-Pedersen and co-workers are likely to remain valid at other coverages, provided the configurations are geometrically similar and share a d-mediated bonding mechanism (Kitchin 2009). Summary: kitchin2009.
The original Au/Pt configurational correlation (2009)
This paper introduced the configurational correlation: oxygen adsorption energies of the same configurations on Au(111) and Pt(111) fall on a near-linear line with slope 1.26, matching the ratio (1.28) of the two metals’ coverage slopes, and the relation holds even for configurations that are not ground states (Miller 2009). Fitting the line to only two configurations predicted the other 14 with mean absolute errors of 0.033 eV (Pt) and 0.038 eV (Au). The authors expected it to hold for similar sites and d-band dominated bonding on other late transition metals, a prediction later tested for other adsorbates and metals. Summary: miller2009.
Configurational correlations across metals (2011)
Miller, İnoğlu and Kitchin extended configurational correlations from adsorbate-to-adsorbate on one surface to metal-to-metal for one adsorbate: oxygen energies of 20 configurations on Rh, Ir, Pt, Cu, Ag and Au(111) are each linear in the energies of the same configurations on Pd(111). The fits are near DFT precision for Rh, Ir and Pt but degrade on the noble metals when relaxation produces geometrically dissimilar structures; fixing the atoms at scaled Pd geometries cut the errors (Au from 55 to 24 meV/O, Cu from 120 to 65 meV/O). An empirical model based on the d-orbital radius and d-band filling reproduces the slopes within 0.1 (Miller et al. 2011). Summary: miller2011.
Universal HO*/HOO* scaling on oxides (2011)
Across perovskites, rutiles, anatase, manganese oxides, Co3O4 and NiO, the HOO* adsorption energy follows the HO* adsorption energy with a slope of about one and an intercept of 3.2 eV (MAE 0.17 eV), the same offset seen on metals. The unit slope reflects a single O-surface bond in both species and a shared preference for the same site type. This universal relation reduces the OER free energy diagram to one free parameter and fixes a lower bound on the theoretical overpotential, so scaling relations act as a fundamental constraint on catalyst design rather than only a shortcut for screening (Man et al. 2011). Summary: man2011.
Outer electrons as the origin of ORR-OER scaling (2013)
Calle-Vallejo and co-workers showed with RPBE DFT that the adsorption energies of *O, *OH and *OOH on 3d metals, monoxides and perovskites all weaken roughly linearly with the number of outer electrons on the metal (valence electrons left after oxidation), with the *O slope about twice the *OH and *OOH slopes. This explains the familiar scaling slopes of about 0.5 (*OH or *OOH against *O) and 1 (*OOH against *OH). The data form an adsorption-energy grid (mean absolute error 0.20 eV for *OH), and overlapping two grids collapses them into one scaling line; the *OOH versus *OH intercept was 3.2 eV. The authors caution that scaling plots hide the underlying trends that the grids make explicit (Calle-Vallejo et al. 2013). Summary: callevallejo2013.
Coverage dependence of atomic scaling slopes (2014)
Xu and Kitchin tested whether scaling between atomic adsorbates holds beyond low coverage, using 896 PBE adsorption energies for eight atoms on seven fcc(111) metals at 0.25 to 1.0 ML. Correlations within the halogens weakened at high coverage, S-O stayed strong but changed slope, and among C, N and O only the N-O correlation could be described by one slope within the 95% confidence intervals at all coverages. Recasting the Abild-Pedersen bond-counting rule as a ratio of electrons missing from an octet, (8 - Yval)/(8 - Zval), reproduced the low-coverage S-O, C-O and N-O slopes well, but the agreement generally worsened with increasing coverage. The authors conclude that scaling relations persist at high coverage but are coverage dependent, so volcano peaks and selectivity boundaries built at low coverage will likely shift, and they suggest modeling the roughly linear change of slope with coverage (Xu 2014). Summary: xu2014a.
Robustness of oxide scaling to the Hubbard U (2015)
Xu, Rossmeisl and Kitchin asked whether OER scaling relations on rutile dioxides, established without a Hubbard U, survive DFT + U. For all 4d and 5d dioxides, raising U from 0 to 8 eV shifted OH, O and OOH adsorption energies together so that they stayed on the U = 0 scaling lines. The exceptions were 3d oxides: on MnO2 and CrO2 the OH/OOH relation broke only where OOH stopped binding stably at high U, and on d0 TiO2 scaling was not preserved (Xu et al. 2015). Summary: xu2015.
Single atom alloys as possible exceptions (2018)
Because hydrogen adsorption energies on single atom alloys did not correlate with the d-band center, Thirumalai and Kitchin suggested that single atom alloys may be able to break the linear scaling that limits transition metal catalysts. They also noted that water dissociation transition state energies on AuPd and AgPd decreased along with reaction energies, consistent with Brønsted-Evans-Polanyi relations (Thirumalai 2018). Summary: thirumalai2018.
Explicit barriers versus BEP relations in a large network (2025)
In a reaction network for CO hydrogenation on Rh(111) (61 intermediates, 174 dissociation or association reactions), Wander and coworkers computed barriers explicitly with ML-accelerated NEBs and found poor correlation between activation and reaction energies across diverse reactions. Even a BEP relation fit to the 102 converged DFT NEBs, an upper bound on BEP accuracy, had a mean absolute error of 0.20 eV, compared with 0.04 eV for the ML NEB plus DFT single point approach, and the choice changed which reactions passed a 0.75 eV feasibility cutoff (Wander et al. 2025). Summary: wander2025a.