Chemisorption Energy Scaling Relations

We next consider situations where there is considerable interaction between adsorbate and adsorbent. The sttength of the interaction is such that the elechonic structure of the adsorbate changes significantly and a chemical bond is formed. In Chapters 8 and 12, we will see how to understand the bonding between adsorbates and surfaces in more detail. 

FIGURE 6.3 DFT-calculated adsorption energies of CH species plotted against the adsorption energy of C for a number of different transition metals. The black and gray symbols indicate close-packed and stepped surfaces, respectively. The lines show the best fits to the points. Adapted from Abild-Pedersen et al. (2007). 

The simplest way to understand this is to say that the N levels are degenerate, separable, and linearly independent such that each contributes with the same amount to the total binding energy when A couples to a surface. Saturating one of these energy levels by bonding to H or another atom wiU remove it from the equation and hence reduce the number of bonds the element can make with the surface. 

We note that the scaling parameter is independent of the surface. The cutoff, in Equation (6.1), on the other hand, depends on the surface structure. Hence, in order to obtain information about how weU a given structure binds an adsorbate, given that one knows how all the base elements (C, O, N, S, etc.) bind, one needs to do only a single value measurement or calculation of the adsorption energy, and the rest can be scaled from the binding of the base elements. This enables us to write a simple expression for the reaction energy of an elementary step as 

the sum is over all atoms, i, forming bonds to the surface. Ay. is the change in the scaling slope or valency parameter during the reaction, AE denotes the binding energy of the base elements relevant for the reaction, and A is a constant that one has to measure or calculate for a single system. 

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