Determining the adsorption energies of small molecules with the intrinsic properties of adsorbates and substrates

Adsorption is essential for many processes on surfaces; therefore, an accurate prediction of adsorption properties is demanded from both fundamental and technological points of view. Particularly, identifying the intrinsic determinants of adsorption energy has been a long-term goal in surface science. Herein, we propose a predictive model for quantitative determination of the adsorption energies of small molecules on metallic materials and oxides, by using a linear combination of the valence and electronegativity of surface atoms and the coordination of active sites, with the corresponding prefactors determined by the valence of adsorbates. This model quantifies the effect of the intrinsic properties of adsorbates and substrates on adsorbate–substrate bonding, derives naturally the well-known adsorption-energy scaling relations, and accounts for the efficiency and limitation of engineering the adsorption energy and reaction energy. All involved parameters are predictable and thus allow the rapid rational design of materials with optimal adsorption properties.


Supplementary Note 2: The derivation of LSRs and its generalized form
We will first use our model to derive the linear scaling relationships (LSRs) established by Nørskov et al. 1 and its generalized form established by Calle-Vallejo et al. 2 . On the basis of Equations (2) and (3) in the main text, the adsorption energies are given as: For the atoms' partially hydrogenated species, the adsorption energies are as follows: Comparing Supplementary Equations 6 with 7, we can naturally derive that: This expression is exactly the LSRs.
For the generalized LSRs form established by Calle-Vallejo et al. 2 , the offset ξ scales with coordination number for any pair of adsorbates (with X1 and X2) with the same central atom, that is: With Supplementary Equations 8 and 9, we obtain: Recalling Equations (4) and (5) in the main text for calculating b, of adsorbates (with X1 and X2) with the same central atom as,

Supplementary Note 3: Extension of our model for intermetallics and oxides
For a given adsorption site, it exhibits significantly different electronic structures on near-surface alloys (NSAs) and oxides compared with pure transition metals (TMs) and nanoparticles (NPs) due to its coordination environments. To incorporate the local environment effect of active centers, the electronic descriptor ψ is generalized by using the geometric mean of the valence number Sv and electronegativity χ of the given substrate atoms and their neighboring atoms, as (13) where N is the number of the atoms at active centers, while Svi and χi are the outer-electron number and electronegativity of the ith atom at active centers. It is noteworthy that Supplementary Equation

Supplementary Note 5: The gas-phase references for adsorption energies
The absolute values of adsorption energies are distinct depending on the adopted energy references for small molecules (see Supplementary Table 17 and references therein). To ensure the comparability of the cited data, we unified the energy references for the cited data by shifting the energy difference between the standard references that we choose and the original ones. In the case of molecular species binding with C terminal, we chose the gaseous CO, H2O and H2 as the references 8 .
For the molecular species binding with N terminal, N2 and H2 were taken as the references. In addition, the gas-phase references for the adsorption energies of *O, *OH, *OOH and *OCH3 were 1/2O2, OH, OOH and OCH3, respectively (see Supplementary Table 18). Consequently, the internal consistency and comparability have been found for the cited data, ensuring the validity of our model well.
All DFT calculations for the gas-phase references were performed by the spin-polarized PBE 9 exchange-correlation functional, implemented with the Vienna Ab Initio Simulation Package (VASP) 10 Table 8. Comparison between the predicted prefactors λ by the established relation and the fitted DFT-calculated ones for different adsorbates on transition-metal (TM) surfaces and nanoparticles. Column 2 shows the predicted results while Columns i-x show the fitted ones from Refs [20,[22][23][24][29][30][31][32] shown in Fig. 2      Comparison between the predicted slopes k by the established relation and the fitted DFT-calculated ones for different adsorbates on near-surface alloy (NSA) surfaces. Column 2 shows the predicted results, while Columns i-iv show the fitted ones from Refs [6,26,33,34] and Ref. [26] shown in Fig. 4 in the main text and Supplementary Figure 7. Note that all of the slopes k here are absolute values.

Species
Supplementary Table 13. Comparison between the predicted slopes k by the established relation and the fitted DFT-calculated ones for different adsorbates on surfaces of oxides. Column 2 shows the predicted results, while Columns i-iii show the fitted ones from Refs [3,5] shown in Fig. 5 in the main text, and Columns iv-v correspond to the fitted results from Refs [16,27] shown in Supplementary  Figure 8.      Introducing structural sensitivity into adsorption-energy scaling relations by means of coordination numbers 2 O2, OH, OOH, OCH3

Title Gas references
Understanding trends in electrochemical carbon dioxide reduction rates 12 CO, H2, H2O Origin of the overpotential for oxygen reduction at a fuel-cell cathode 15 H2O, H2 Scaling relationships for adsorption energies on transition metal oxide, sulfide, and nitride surfaces 16 AH x max , H2 Using scaling relations to understand trends in the catalytic activity of transition metals 17 AH x max , H2