Resonant level model

A good starting point for discussing chemisorption is the resonant level model. The substrate metal is jellium, implying that we look at metals without d-electrons, and the adsorbate is an atom. We focus on only two electron levels of the atom. Level 1 is occupied and has ionization potential / level 2 is empty and... 

Figure A.9 A potential energy diagram of an atom chemisorbed on the model metal jellium shows the broadening of the adsorbate orbitals in the resonant level model.

The resonant level model readily explains the change in work function associated with chemisorption. It is well known that alkali atoms such as potassium lower the work function of the substrate, whereas electronegative atoms such as chlorine increase the work function [2,8,19]. Figure A. 10 indicates that potassium charges positively and chlorine negatively when adsorbed on jellium. Remember that the surface contribution to the work function is caused by... 

Although the resonant level model successfully explains a few general aspects of chemisorption, it has nevertheless many shortcomings. The model gives no information on the electronic structure of the chemisorption bond it does not tell where the electrons are. Such information is obtained from a more refined model, called the density functional method. We will not explain how it works but merely give the results for the adsorption of Cl and Li on jellium, reported by Lang and Williams [20]. 

H2, N2, or CO dissociates on a surface, we need to take two orbitals of the molecule into account, the highest occupied and the lowest unoccupied molecular orbital (the HOMO and LUMO of the so-called frontier orbital concept). Let us take a simple case to start with the molecule A2 with occupied bonding level a and unoccupied anti-bonding level a. We use jellium as the substrate metal and discuss the chemisorption of A2 in the resonant level model. What happens is that the two levels broaden because of the rather weak interaction with the free electron cloud of the metal. 

Obviously, chemisorption on d-metals needs a different description than chemisorption on a jellium metal. With the d-metals we must think in terms of a surface molecule with new molecular orbitals made up from d-levels of the metal and the orbitals of the adsorbate. These new levels interact with the s-band of the metal, similarly to the resonant level model. We start with the adsorption of an atom, in which only one atomic orbital is involved in chemisorption. Once the principle is clear, it is not difficult to invoke more orbitals. 

Crlm heat capacity from resonant level model Taf antiferromagnetic ordering temperature ... 

Fig. 12. Total heat capacity of a single crystal of PrFe4Pi2 vs. temperature in various applied magnetic fields (a) low fields and (b) high fields. The dashed fines in (b) correspond to the best fit of the heavy fermion state to die resonant level model (Crlm)-Cph is the estimate of die phonon contribution to the heat capacity (Aoki et al., 2002).

Fig. A.10 Potential energy diagrams of atoms chemisorbed on jellium in the resonant level model. The situation under (a) corresponds to Figure A.9. In (b) the adatom has a low ionization potential and consequently it donates charge to the metal (as with alkalis on metal), whereas in (c) the adatom has a high electron affinity such that it becomes negatively charged (as with fluorine on metals).

The Schottky-like anomaly observed in the specific heat of the compounds discussed in this section can be derived phenomenologically using (a) the resonance-level model, (b) the spin glass behaviour, (c) the crystal field (Schottky) contribution or even (d) low-dimensional magnetic fluctuations. The cases where an HF behaviour is deduced from a large value will be discussed in sect. 9, in connection with the contribution to of the excited crystal field levels. It is clear that complementary techniques, such as NMR, AC susceptibility and electrical resistivity, can easily reveal the magnetic character of the microscopic interactions. In some of the HF compounds the ratio between the y term and the (( -> 0) = Xo value of the susceptibility, and between the / term and the coefficient of the resistivity. A, have values predicted by... 

Under an applied magnetic field is shifted to higher temperatures, while the value of Cm at 7 is found to decrease in CePd3Beo.45 and CePdjBeo.ss (Sereni et al. 1986) or to remain constant as in CeCue.jAlg 5 (Rauchschwalbe et al 1985). The resonance-level model for Kondo impurities predicts the narrowing and the increase of Cm (at T ) with field, as verified by Bredl et al. (1978) for (La, Ce)Al2 such a behaviour is also followed by CePd3B. 

Derived from T = 5 K [as obtained from the residual quasielastic neutron line width (HWHM) as well as by using a resonance level model via T = r /0.68, corresponding to the Bethe-ansatz results, see Andrei et al. (1983)], in line with the definition used throughout this article. 

The simple model for studying chemisorption is the so-called resonant level model, it is illustrated in Figure 26.7. Once again, the metal is described by... 

The resonant-level model can be extended to the adsorption of molecules for example, it can be used to explain why a diatomic molecule (e.g. H2 or CO)... 

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