Surface molecule limit

The state 6) represents the particular linear combination of metal states which actually participates in the chemisorption bond and may be considered to be localised at the surface in the vicinity of the adatom. It follows from Eq. (11) that the energy distribution of the photoemission current depends not only on both the real and imaginary parts of Gaa(w — wo) but also on the properties of the propagator g(w — wo). In the surface molecule limit (13—15)... 

Figures 4.3c, d and e illustrate changes in electronic structure of cluster 3a when the cluster atoms become part of a surface. Three physically different situations have to be distinguished surface molecule limit, intermediate adsorption and weak adsorption. Figure 4.3c schematically presents the electronic structure in the surface molecule limit. Then the interaction between adatom and surface atoms P is significantly larger than p ...

In the surface molecule limit, the first term dominates and the last term is small compared to the localization-energy. 

Hence in the surface molecule limit the interaction-energy between adsorbate and surface decreases when the number of surface neighbour atoms (z) of the interacting surface atom increases. 

Tamm Surface States, Surface Molecule Limit. 

E)quation (2.196) can be recognized as the equation for the molecular orbital energies of a diatomic molecule formed by the adsorbate atomic orbital 0 and surface atom 1 (see q.(2.53) 5 ss 0). For this reason conditions Eq.(2.195) are identified with the surface molecule limit. ... 

Figure 2.42. Bond-order overlap population density between adatom and endatom, one-dimensional chain (schematic), a weak adsorption limit b surface molecule limit.

It is of interest to discuss the poles (the values E for which Goo becomes infinite) in two limits, the ideal weak adsorption limit and the quasi-surface molecule limit. The solutions for both limits are sketched in Fig.(2.48). The explicit expressions for A and r are given in the caption of Fig.(2.48). In the weak adsorption limit, the width of undisturbed surface LDOS Pw E T = a) is larger than or + — oro ... 

Figure 2.48. Ideal weak adsorption limit (a) and quasi surface molecule limit (b) solutions (schematic).

The quasi-surface molecule limit occurs if interaction of the metal surface atoms with the rest of the lattice is small compared to the interaction with the adsorbate. This situation may arise if the surface atoms become highly unsaturated. In that event Z is much smaller than Z and the width F / of the surface atom local density... 

In the quasi-surface molecule limit F is much smaller than the line-width computed in the "ideal weak adsorption case. We will discuss the behavior of the chemisorption energy as a function of Z and Z in a later section. The expressions and general relations for the chemisorption energy have to be derived first. 

Interpretation of the first three terms in Eq.(2.229a) is straightforward. Term (1) results from the assumption that in the adsorbate no levels higher than Ef were occupied before adsorption. If such terms were occupied a correction to account for electron transfer from the adsorbate to the Fermi-level has to be introduced. Term (1) reflects electron transfer front the occupied undisturbed adsorbate levels to the Fermi level, term (2) electron transfer from a surface electronic state present before chemisorption to the Fermi level and term (3) electron transfer from the Fermi level to a surface molecule- or chemisorption- induced surface state level. In the surface molecule limit the contribution to the chemisorption energy is easy to calculate for s-type orbitals. If an orbital has Z" metal atom neighbors, the solutions cf become the solution of Ek. (2.215) ... 

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... 

Figure 2.51. Quasi-surface molecule limit solutions of fj B) as calculated according to Eq.(2.241).

Ek]uation (2.245) relates the chemisorption energy to the group orbital density of states at the Fermi level in similar fashion to Eq.(2.237b). Equation (2.248) is often satisfied for the occupied molecular orbital levels as well as unoccupied molecular orbitals of an adsorbate with respect to the d-valence electron levels of the surface. Its use is limited, because the interaction with the d-valence electrons is better described in the quasi-surface molecule limit. We will return to this later. In the second-order perturbation theory expression, one ignores the repulsive interaction of two orbitals that are doubly occupied (see also section 2.2.7). 

It follows that the poles of the Green s function Goo z) determine the time dependence of an electron localized in the adsorbate orbital o We will compute Eq.(2.276c) in the limit of weak chemisorption fo(ty) and in the surface molecule limit... 

In this subsection, we will analyze CO and H chemisorption using the Bethe lat tice approximation (section 2.5.1) for d- and s-metal valence electrons. First we will discuss chemisorption of CO with atop and bridge coordination to the (111) surface of platinum. Initially the interaction with the d- and s-valence electrons will be considered separately. We will focus on an analysis that makes explicit the concepts of weak chemisorption and the quasi-surface molecule limit that we also... 

Z is the number of surface metal atoms involved in the chemisorptive bond. The surface molecule limit condition Eq.(2.195a) can be written as ... 

Adding the three terms gives for the chemisorptive bond strength in the surface molecule limit the approximate expression ... 

The formulae apply to the (111) surface of an f.c.c. metal. E M — M) and E A — A) are the bond strengths of diatomic molecules of metal atoms and adsorbing atoms respectively and X f and their respective chemical affinities. i/ is the metal atomic valency. Since t/ < I2y according to both formulae the chemisorptive bond strength is smaller than that of the corresponding free surface molecule. It is revealing to understand the physical basis of Eqs.(3.6). Equation (3.6a) is valid in the surface molecule limit. It ignores Equation (3.6b) applies in the weak... 

When the overlap energy f increases, the adatom local electron density of states bandwidth increases gradually until a limiting value of f is crossed. This is called the surface molecule limit [18] ... 

One concludes that bonding is covalent When surface atom coordination changes, the increased localization of the electrons is responsible for increased adsorption energies. The actual position of is not of dominating importance, it merely reflects the decrease in d-valence band width W. The Newns-Anderson model applies and the chemical bond in the surface complex approximates the surface molecule limit... 

Bonding in the surface molecule limit is illustrated in a different way by the surface bond formation scheme presented in Fig. 3.30. Step 1 represents the localization of an electron on a surface atom, with complete rupture of the chemical bonds with neighboring atoms. Step 2 represents the formation of the molecule complex between the adatom and the surface atoms. Step 3 involves the formation of the adsorption complex by embedding of the surface molecule complex into the vacancy of the surface atom. 

In the surface molecule limit, Ema S> Eioc and Eemb E oc- This implies that the dominant correction to the surface-molecule complex energy Ema is Eioc, which is proportional to the sublimation energy of a surface atom, which increases with increasing coordinative saturation as y/ri. The embedding energy is equal to the weakened metal... 

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