Electron density in metals

The value of the Fermi energy tp corresponding to the valence electron density in metals is of the order of a few eV. 

The real potential, a , of electrons in metals, as shown in Eqn. 2-4, comprises the electrostatic surface term, - ex, due to the surface dipole and the chemical potential term, M., determined by the bulk property of metal crystals. In general, the electrostatic surface term is greater the greater the valence electron density in metals whereas, the chemical potential term becomes greater the lower the valence electron density in metals. 

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 Electron Density in Metal-Metal Bonds of Transition Metal Complexes... 

Interatomic Distance Figure 56. Variation of electron density in metallic magnesium with distance between two neighbouring atoms A and B by Fourier anafysis)... 

In this connection, it is worth mentioning the role of the metallic bonding, which is one of the nonpolar components of the remainii (100 - I)% of the bondii in a semiconductor. X-ray diffraction studies of the distribution of the electron density in metals [15] indicate that free electrons are distributed throughout the whole volume of a crystal. Such a distribution of free electrons fills the dips in the potential more effectively than do the electron "bridges" of the covalent bonds. Therefore, the forbidden band should become narrower, decreasing to zero in the case of a pure metal. 

One disadvantage is that the lower levels of theory must be able to describe all atoms in the inner regions of the molecule. Thus, this method cannot be used to incorporate a metal atom into a force field that is not parameterized for it. The effect of one region of the molecule causing polarization of the electron density in the other region of the molecule is incorporated only to the extent that the lower levels of theory describe polarization. This method requires more CPU time than most of the others mentioned. However, the extra time should be minimal since it is due to lower-level calculations on smaller sections of the system. 

As a result of the systematic application of coordination-chemistry principles, dozens of previously unsuspected stnicture types have been synthesized in which polyhedral boranes or their anions can be considered to act as ligands which donate electron density to metal centres, thereby forming novel metallaboranc elusters, ". Some 40 metals have been found to act as acceptors in this way (see also p. 178). The ideas have been particularly helpful m emphasizing the close interconnection between several previously separated branches of chemistry, notably boron hydride clu.ster chemistry, metallaboranc and metallacarbaborane chemistry (pp. 189-95). organometallic chemistry and metal-metal cluster chemistry. All are now seen to be parts of a coherent whole. 

Some bis(dinitrogen) complexes exist, generally as m-isomers (presumably this minimizes competition for the metal t2g electron density in 7r-bonding). Unlike ruthenium, osmium(III) dinitrogen complexes do exist, showing osmium(III) to be a better 7r-donor not surprisingly, they are more labile than the osmium(II) species. 

In low oxidation states, transition metals possess filled or partly filled d shells. The Dewar-Chatt-Duncanson model envisages some of that electron density in (local) d (e.g. d., d y) orbitals being donated into the empty n orbitals of the carbon monoxide ... 

Instead of treating all electrons in the metal plus adsorbate system individually, one considers the electron density of the system. Hohenberg and Kohn (Kohn received the 1999 Nobel Prize in Chemistry for his work in this field) showed that the ground state Eq of a system is a unique functional of the electron density in its ground state Wq- Neglecting electron spin, the energy functional can be written as... 

Mijnarends, P.E., (1979) Electron momentum densities in metals and alloys. In Positrons in Solids, (Ed.) Hautojarvi, P., Springer. 

Calculations, which we shall discuss later, show30"32 that the direct contribution of the metal to the interfacial capacitance (from the conduction electrons) increases with the electron density, in... 

Through X-ray scattering studies of the electron densities in MgCu2, Kubota et al. (2000) found concentrations of electrons between the Cu atom pairs, but not between Mg—Cu pairs. They interpreted this as p3d3 covalent hybrid Cu—Cu bonds embedded in Mg metal. 

The importance of alkali metal binding with available 7r-electron density in the formation of CIPs was also demonstrated by Niemeyer in the structural elucidation of the first monomeric non-solvated lithium cuprate, [(2,6-Mcs2(LI L)2CuLi] 450, formed from the reaction of 2 equiv. of (2,6-Mcs2Gf,I L)Li with /-BuOCu in pentane.447 The complex crystallizes as two different independent molecules in which the C-Cu-C angles differ (171.1° and 173.8°) as does the mode of coordination to the Li cations C pso and rf to one pendant Ph in molecule 1, with an additional rf interaction to a second Ph group in molecule 2. In the second molecule, the Li site is 10% occupied by a Cu ion. 

Figure 3.4 Distribution of the electronic density in the jellium model the metal occupies the region x < 0. The unmarked curve is for an uncharged surface, the other two curves are for the indicated surface-charge densities. The distance along the x axis is measured in atomic units (a.u.), where 1 a.u. of length = 0.529 A.

This equation can be solved by several techniques, for example, by noting that it is a quadratic equation in a2. The sp metals that are relevant for electrochemistry have electronic densities in the range of 10-2 to 3 x 10 2 a.u., over which a is almost constant (see Table 17.1). From simple electrostatics it can be shown that the surface dipole potential... 

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