Chemisorption functions

Figure 2.12 Chemisorption functions for the model metal band structure.

Having established the expressions for the chemisorption functions of an AB-type chain, we can now employ them in calculating AE (4.101) and Aq (4.102) for oxygen on narrow-gap III-V semiconductors. Specifically, we are interested in GaSb, InAs and InSb. The choice of narrow-gap substrates ensures that the approximation made regarding the contour C in (4.92) remains valid. Results are presented for the 47-case only. 

Here, the first factor in square brackets represents the adsorption of a single atom at site m. The second factor represents the adsorption of a second atom at site —n. Substituting (8.52) into (8.43), and invoking the chemisorption functions (4.68), (4.69), (8.16), (8.17), along with (8.46), results in... 

The subscripts 1 and 2 on the chemisorption functions refer to single- and double-adsorption, respectively. Note, however, that eaa and ha are given by (8.2), where the indicated occupancies are both for the double-chemisorption... 

It can be seen that the chemisorption function, A(e), can be regarded as a local projection of the metal density of states around the adsorbate. 

Introducing the matrix element Vad = a H d), we can rewrite the chemisorption function as ... 

Figure 4.5 shows solutions to the Newns-Anderson model using a semi-elliptical model for the chemisorption function. The solution is shown for different surface projected density of states, nd(e), with increasing d band centers sd. For a given metal the band width and center are coupled because the number of d electrons must be conserved. 

The d band center is given by the first moment of the chemisorption function, Eq. (10). We therefore need to understand qualitatively how ( ) behaves for a multi-component system. To see this it is useful to expand the metal wave functions... 

The simplest electrochemical reaction is an outer sphere electron transfer where the interactions with the electrode are weak. Hence, the details of the band structure are not important we can ignore the k dependence of the coupling constants and replace them by a single effective value. The sum over k in Eq. (16) then reduces to the surface density of states corresponding to the electrode and the chemisorption function h.(e) can be taken as constant. It corresponds to the interaction with a wide, stractureless band on the electrode. In this approximation" " the chemisorption K(s) functions vanishes (see Fig. 8a) ... 

Figure 8. Different approaches to describe the electronic structure of the metal through the chemisorption functions A(6 ) (full lines) and A(s) (dotted lines).

Here the Heaviside function 6 ensures that the contribution vanishes outside the bands. Sc and w indicate the center and the half width of the band, respectively. We still neglect any dependence of the couphng constants on k and consider an effective value, which is a good approximation for most cases. Then A sJ is proportional to Pe/s J but no more constant can be easily obtained from equation (16). The effect on the density of states of the reactant Pa sJ depends on the relative values of the parameters and w. In Fig. 8b and 8c we show the chemisorption functions for two semielliptic bands with different width, a wide band (Fig. 8b), which can represent a sp band, and a thinner one (Fig. 8c), which can describe a d band. 

In all cases the system has to overcome a saddle point situated at an intermediate value of the solvent coordinate q and the bond distance r. We note that the surfaces in this figure are meant to demonstrate the typical reactions paths, therefore they have been calculated for a constant chemisorption function A, which corresponds to the non-catalytic coupling to a sp wide band and to the absence of a band. Model calculations performed for reactions on a metal surface in the gas phase, which can nowadays be routinely performed with the aid of quantum-chemical packages, can only describe the pure dissociation A2 2A, but not electron... 

Figure 17. Chemisorption functions A and A, for the semiel-lipic model in the case of a superposition of a wide sp band and a thin d hand.

---