Jellium 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. 

As shown in Fig. 5-20, the effective image plane is located close to but away from the jellium metal edge. CombiiungEqns. 5-27 and 5-28 yields the surface potential Xm as a fiinction of Om in Eqn. 5-29 ... 

Fig. 6-20. Charge distribution profile across an interface between metal and vacuum (MAO (a) ionic pseudo-potential in metal, (b) diffuse electron tailing away from the jellium metal edge, (c) excess charge profile. n(x) s electron density at distance x = electron density in metal x, = effective image plane On = differential excess charge On = 0 corresponds to the zero charge interface.

Table 6-3. The effective image plane position of a metal in vacuum estimated as a function of electron density in metal x, distance at the effective image plane fiom the jellium metal edge rws = Wigner-Seitz radius (a sphere containing one electron) which is related to electron density n, in metal (1 / n, = 4 n / 3 ) au = atomic unit (0.529 A). [From Schmickler, 1993.]...

The interfacial solution layer contains h3 ated ions and dipoles of water molecules. According to the hard sphere model or the mean sphere approximation of aqueous solution, the plane of the center of mass of the excess ionic charge, o,(x), is given at the distance x. from the jellium metal edge in Eqn. 5-31 ... 

Next, we discuss the plane of the closest approach (x = of water molecules to the jellium metal edge (x = 0). At the zero charge interface, this plane of closest approach of water molecules is separated by a distance equal to the radius of water molecules from the metal siuface. As the interfadal excess charge increases, the electrostatic pressure (electrostriction pressiue) reduces the distance of Xdip in prop>ortion to the square of the interfadal charge, a (= om = - os) the electrostatic force in the compact layer is proportional to om x as. The change in Xitp due to the interfadal charge is then given by Eqn. 5-32 ... 

A nonprimitive model for the jellium metal-liquid electrolyte interface similar to but more general than that of BRYB was developed by Schmickler and Henderson [132,133]. Their hard sphere ions and solvent molecules had different diameters and the construction of the jellium edge was different. Also their electronic density profile had two adjustable parameters and they assumed that the dependence on metal charge of the nearest distance of approach of solvent molecules to the metal was not important. In one paper [132b] the trial function in Eq. (21) was generalized for x < 0 to read... 

Schaich W L 2000 Calculations of second-harmonic generation for a jellium metal surface Phys. Rev. B 61 10 478-83... 

For systems of a certain symmetry such as closed shell atoms, jellium metal clusters, jellium metal surfaces, open-shell atoms in the central-field approximation, etc., the work Wee(r) and W, (r) are separately path-independent since Vx[Pg.185]

For the nonuniform electron density system at a jellium-metal surface, it is generally accepted [5-7,9,31-33] that the asymptotic structure of the Kohn-Sham exchange-correlation potential is the image potential ... 

In the mean field of N liquid molecules, the electron density, (r), of the jellium metal is obtained from Kohn-Sham density functional the-QPy.54,55,57,65-67 consisting of the Schrodinger-type equation... 

Fig. 11 The center of mass of excess charge distribution as a function of the net charge on jellium metals. At zero charge, it is located outside the jellium with negative charging, it moves further out. 1 a.u. of surface charge = 5.710 pCcm . ...

Figure 2. Sketch of an uncharged metal surface (simulated by the jellium model) covered by a macroscopic solvent layer, showing the components of the electric potential drop. 8%M is the surface potential of the metal modified by the solvent layer %s + 6%s is the surface potential of the solvent modified by the contact with the metal %s is the unmodified surface potential of the solvent layer at the external surface.

Schmidder and Henderson282 have studied several solvents and metals, using the jellium model for the metal and the MSA for the solution. Deviations of the Parsons-Zobel plot from linearity in the experimental results72,286-288 at the highest concentration have been attributed to the onset of ion-specific adsorption. However, data at other electrode charges... 

According to Vitanov et a/.,61,151 C,- varies in the order Ag(100) < Ag(lll), i.e., in the reverse order with respect to that of Valette and Hamelin.24 63 67 150 383-390 The order of electrolytically grown planes clashes with the results of quantum-chemical calculations,436 439 as well as with the results of the jellium/hard sphere model for the metal/electro-lyte interface.428 429 435 A comparison of C, values for quasi-perfect Ag planes with the data of real Ag planes shows that for quasi-perfect Ag planes, the values of Cf 0 are remarkably higher than those for real Ag planes. A definite difference between real and quasi-perfect Ag electrodes may be the higher number of defects expected for a real Ag crystal. 15 32 i25 401407 10-416-422 since the defects seem to be the sites of stronger adsorption, one would expect that quasi-perfect surfaces would have a smaller surface activity toward H20 molecules and so lower Cf"0 values. The influence of the surface defects on H20 adsorption at Ag from a gas phase has been demonstrated by Klaua and Madey.445... 

The C, values for Sb faces are noticeably lower than those for Bi. Just as for Bi, the closest-packed faces show the lowest values of C, [except Bi(lll) and Sb(lll)].28,152,153 This result is in good agreement with the theory428,429 based on the jellium model for the metal and the simple hard sphere model for the electrolyte solution. The adsorption of organic compounds at Sb and Bi single-crystal face electrodes28,152,726 shows that the surface activity of Bi(lll) and Sb(lll) is lower than for the other planes. Thus the anomalous position of Sb(lll) as well as Bi(lll) is probably caused by a more pronounced influence of the capacitance of the metal phase compared with other Sb and Bi faces28... 

Figure 5.7. Schematic representation of the definitions of work function O, chemical potential of electrons i, electrochemical potential of electrons or Fermi level p = EF, surface potential %, Galvani (or inner) potential

The hypothetical metal jellium consists of an ordered array of positively charged metal ions surrounded by a structureless sea of electrons that behaves as a free electron gas (Fig. 6.13). 

Figure 6.13. The electron distribution in the model metal jellium gives rise to an electric double layer at the surface, which forms the origin of the surface contribution to the work function. The electron wave function reaches...

When an atom with a filled level at energy approaches a metal surface it will first of all chemisorb due to the interaction with the sp electrons of the metal. Consider for example an oxygen atom. The 2p level contains four electrons when the atom is isolated, but as it approaches the metal the 2p levels broaden and shift down in energy through the interaction with the sp band of the metal. Fig. 6.28(a) and (b) show this for adsorption on jellium, the ideal free-electron metal. 

A simple metal like lithium or aluminum should best reveal the properties of the jellium model. To be sure, all long range order influence has been switched off, we measured S(q, co) of liquid A1 (T = 1000K). Figure 6 shows the result of a measurement for q = 1.5 a.u. together with theoretical calculations. 

The picture of the compact double layer is further complicated by the fact that the assumption that the electrons in the metal are present in a constant concentration which discontinuously decreases to zero at the interface in the direction towards the solution is too gross a simplification. Indeed, Kornyshev, Schmickler, and Vorotyntsev have pointed out that it is necessary to assume that the electron distribution in the metal and its surroundings can be represented by what is called a jellium the positive metal ions represent a fixed layer of positive charges, while the electron plasma spills over the interface into the compact layer, giving rise to a surface dipole. This surface dipole, together with the dipoles of the solvent molecules, produces the total capacity value of the compact double layer. 

With respect to the thermodynamic stability of metal clusters, there is a plethora of results which support the spherical Jellium model for the alkalis as well as for other metals, like copper. This appears to be the case for cluster reactivity, at least for etching reactions, where electronic structure dominates reactivity and minor anomalies are attributable to geometric influence. These cases, however, illustrate a situation where significant addition or diminution of valence electron density occurs via loss or gain of metal atoms. A small molecule, like carbon monoxide,... 

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