Surface Group Orbitals

we analyze in more detail the electronic features that determine low or high coordination of an adsorbate in relation to the symmetry of interacting adsorbate orbitals. For this, it is important to introduce the concept of surface group orbitals. 

We initially use the preference of the ammonia molecule to adsorb atop of a surface metal atom to introduce this concept. 

The a symmetric lone-pair orbital of ammonia is doubly occupied and hence as we discussed in Section 10.3.2 will experience a repulsive interaction with the metal free electrons. The attractive interaction to the chemisorption energy is mainly due to the interaction of the donative interaction of the ammonia a symmetric lone-pair molecular orbital with metal d-valence electrons. 

This schematic figure sketches differences in the metal valence band electron density structure based on a tight-binding description with one atomic orbital per metal atom [17]. For the generalization to d-atomic orbitals, we refer to [36]. 

When an s-type adsorbate orbitals interacts with a two- or threefold surface site, because of symmetry it will interact with orbital combinations (Eqs. (10.10a) and (10.10c)), respectively. Equations (10.10b) and (lO.lOd) give the corresponding group orbital energies. In Eqs. (lO.lOe) and (lO.lOf), the corresponding expressions for the asymmetric surface group orbital combinations are given  

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Fig. 4.3. Interaction of CO with a (100) surface in fourfold coordination. The 2na orbital interacts with the asymmetric surface group orbital = 6(

In the limit of ideal weak chemisorption, the chemisorption energy is proportional to the number of surface metal atom orbitals to which the adsorbate is coordinated, the interaction energy squared and two functions pi (n, Ep)y the corresponding surface group orbital local density of states at the Fermi level and a function that depends... 

In practice the conditions of ideal weak adsorptions are not usually satisfied, because the maximum in LDOS of the surface group orbitals is at a different position than the position of the adsorbate orbitals. Assumptions Eq.(2.233) then are not satisfied. The situation of the quasi-surface molecule limit, discussed in section 2.5.1, then applies has been sketched in Fig.(2.48b). Equation (2.219c) has to be evaluated explicitly accounting for the energy dependence of A(E). We will analyze the quasi-surface molecule limit within the Bet he lattice approximation Eq.(2.215). Let the eigenvalues of... 

The fact that or + is not a discrete level but the maximum local density distribution of the surface group orbital reduces the coupling between adsorbate orbital ao and surface orbital a + n. In order to compute the bond strength we have to return to Eq.(2.229b) ... 

In contrast to the preference for high coordination of adsorption of atoms as C, O, or N, the CO molecule generally prefers low-coordination sites. This is due to the different preferences of the HOMO and LUMO interactions for low and high coordination, respectively. The chemical bonding aspects that are basic to this phenomenon are discussed in detail in the next part of this subsection and also the following section on surface group orbitals. 

Figure 10.13 Schematic illustration of interaction of atomic orbital with metal surface group orbital local density of states. Metal orbitals are constructed from one s-atomic orbital per atom, a is adsorbate orbital energy with asymmetric orbital symmetry with respect to surface normal, is adsorbate orbitals with symmetric orbital symmetry. The drawn LDOS fi E) lines correspond to metal surface group orbital densities...

A similar process occurs on the ensemble of surface atoms that activates dissociation of a molecular k bond. Then, the antibonding unoccupied orbital of the molecule has to interact with surface group orbitals of similar symmetry on the ensemble of surface atoms. When the unoccupied molecular orbital becomes... 

Figure 3.12 illustrates the importance of the concept of surface group orbitals. A surface group orbital is defined as a symmetry combination of atomic orbitals on the metal atonos to which an adsorbed molecule or atom is attached. For example, the adsorption of a probe molecule such as CO at a three-fold coordination site results in an interaction between the 5(7 lone-pair orbital on CO, which is a symmetric, and, hence when we limit the example to the interaction with s-atomic metal orbitals with the symmetric combination of the s-atomic orbitals on the coordinating metal atom. 

Analogous surface group orbitals can be constructed from the d, or p-atomic orbitals. Figure 3.12 shows the local density of states of such group orbitals as a function of electron... 

Fig. 17., (E) and ,(E) for Bethe lattice calculations. q (E) are surface group orbital local density of states after chemisorption for atop (e (E)) and three-coordinate sorption, o(b) LDOS of the adsorbate orbital. Parameters used are the same as for figure 12.

The changes of the surface group-orbital local density of states at the Fermi level (see Sect. 2d for definition), computed in the presence of coadsorbates (e.g., S) [97] can be inserted into Eq. (28) to compute the resulting energy changes. 

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