Valence electrons in metals

For high-density electron ensembles such as valence electrons in metals, Fermi statistics are applicable. In a thermodynamic sense, the Fermi level, E (defined at 0 K as the energy at which the probability of finding an electron is 0.5) can be regarded as the electrochemical potential of the electron in a particular phase (in this... 

The valence electrons in metals (shown in blue) are evenly distributed among the metallic cations (shown in red). Attractions between the positive cations and negative "sea" hold the metal atoms together in a lattice. 

The valence electrons in metals have considerable freedom of movement (see Section 1.3.4). This contrasts with ionic crystals where the bonding electrons are normally locahzed within the ions, and with covalent and molecular crystals where electrons are localized in the constituent bonds. 

Most properties of metals, nonmetals, and metalloids are determined by their valence electron configurations. The number of valence electrons that a metal has varies with its position in the periodic table. Valence electrons in metal atoms tend to be loosely held. Nonmetals have four or more tightly held electrons, and metalloids have three to seven valence electrons. 

For high density electron ensembles such as valence electrons in metals, Fermi statistics is applicable. In a thermodynamic sense, the Fermi level, Ey (defined at 0 K... 

For a meaningful discussion of electronic factors in catalysis it is necessary to briefly review the nature of chemisorption bonds. Two theories of the metallic state have been accepted, the electron band theory and the valence bond theory. Both theories recognize the existence of two separate functions for valence electrons in metals one function is to bind the atoms together and the other is to account for magnetic and conductive properties. In the electron band theory, as particularly applied to the transition metals, the s-electron energy band is broad with a low maximum... 

Metallic bonds pose a greater challenge than ionic bonds to the standard MO theory approach because the LCAO method we normally use to build the molecular orbitals from atomic orbitals turns out to be an inefficient way of treating the valence electrons in metal-metal bonds. The LCAO method relies on basis functions that position the electrons near the nuclei, with exponentially decreasing density as the distance from the nuclei increases. This contrasts with the qualitative picture of bonding in a network of metal atoms. 

P4) is closely similar with P-P distances of 216 pm (smaller than for P4 itself, 221pm). Indeed, a whole series of complexes has now been established with the same structure-motif and differing only in the number of valency electrons in the cluster some of these are summarized in Table 13.11. The number of valence electrons in all these complexes falls in the range 30-34 as predicted by R. Hoffmann and his colleagues.Many other cluster types incorporating differing numbers of Group 15 and transition metal atoms are now known and have been fully reviewed. ... 

This type of argument leads us to picture a metal as an array of positive ions located at the crystal lattice sites, immersed in a sea of mobile electrons. The idea of a more or less uniform electron sea emphasizes an important difference between metallic bonding and ordinary covalent bonding. In molecular covalent bonds the electrons are localized in a way that fixes the positions of the atoms quite rigidly. We say that the bonds have directional character— the electrons tend to remain concentrated in certain regions of space. In contrast, the valence electrons in a metal are spread almost uniformly throughout the crystal, so the metallic bond does not exert the directional influence of the ordinary covalent bond. 

The mobility of the valence electrons in a metal accounts for its electrical... 

The 8V + 6 valence electron rule has been completely substantiated by the calculated four-membered species in Table 2 [7], Boldyrev, Wang, and their collaborators presented experimental and theoretical evidence of aromaticity in the Al/ [19] Ga/" [20], In " [20] and isoelectronic heterosystems, XAl [21], The Al/" unit (14e) was found to be square planar and to possess two n electrons, thus conforming to the (An + 2)n electron counting rule for aromaticity. The n electron counting rule would be more powerful if we could predict the number of n electrons of metal atomic rings in an unequivocal manner. Our SN+6 electron rule only requires the number of valence electrons in Al/, which is easy to count. 

All these properties of metals are consistent with a bonding description that places the valence electrons in delocalized orbitals. This section describes the band theory of solids, an extension of the delocalized orbital ideas... 

In tier (1) of the diagram (for the electronic structure of iron(III)), only the total energy of the five metal valence electrons in the potential of the nucleus is considered. Electron-electron repulsion in tier (2) yields the free-ion terms (Russel-Saunders terms) that are usually labeled by term ° symbols (The numbers given in brackets at the energy states indicate the spin- and orbital-multiplicities of these states.)... 

The structure of MnP is a distorted variant of the NiAs type the metal atoms also have close contacts with each other in zigzag lines parallel to the a-b plane, which amounts to a total of four close metal atoms (Fig. 17.5). Simultaneously, the P atoms have moved up to a zigzag line this can be interpreted as a (P-) chain in the same manner as in Zintl phases. In NiP the distortion is different, allowing for the presence of P2 pairs (P ). These distortions are to be taken as Peierls distortions. Calculations of the electronic band structures can be summarized in short 9-10 valence electrons per metal atom favor the NiAs structure, 11-14 the MnP structure, and more than 14 the NiP structure (phosphorus contributes 5 valence electrons per metal atom) this is valid for phosphides. Arsenides and especially antimonides prefer the NiAs structure also for the larger electron counts. 

How then, can one recover some quantity that scales with the local charge on the metal atoms if their valence electrons are inherently delocalized Beyond the asymmetric lineshape of the metal 2p3/2 peak, there is also a distinct satellite structure seen in the spectra for CoP and elemental Co. From reflection electron energy loss spectroscopy (REELS), we have determined that this satellite structure originates from plasmon loss events (instead of a two-core-hole final state effect as previously thought [67,68]) in which exiting photoelectrons lose some of their energy to valence electrons of atoms near the surface of the solid [58]. The intensity of these satellite peaks (relative to the main peak) is weaker in CoP than in elemental Co. This implies that the Co atoms have fewer valence electrons in CoP than in elemental Co, that is, they are definitely cationic, notwithstanding the lack of a BE shift. For the other compounds in the MP (M = Cr, Mn, Fe) series, the satellite structure is probably too weak to be observed, but solid solutions Coi -xMxl> and CoAs i yPv do show this feature (vide infra) [60,61]. 

The representative elements have valence electrons in. v or. v and p orbitals in the outermost occupied energy level, whereas the /-transition metals must have a partially filled set of d orbitals. 

The behaviour of electrons in metals shows the translational properties of quantum particles having quantized energy levels. These cannot be approximated to the continuous distribution describing particles in a gas because of the much smaller mass of the electron when compared with atoms. If one gram-atom of a metal is contained in a cube of length L, the valence electrons have quantum wavelengths, X, described by the de Broglie equation... 

In metals the electrons lose their association with individual atoms and the number of valence electrons is often used in rationalization schemes. Estimated enthalpies of formation for equi-atomic alloys, MM, of two elements of the first transition metal series are given as a function of the difference in number of valence electrons in Figure 7.13 [8], Compounds of a given common metal are given a specific symbol. For example, the scandium compounds ScM where M = Ti, V, Cr, Mn, Fe, Co, Ni and Zn, are given by open circles. The metal M of the compound MM is... 

The rare earth elements (REE) are the lanthanides (defined as those elements with valence electrons in 4/orbitals), La, Ce, Pr, Nd, (Pm), Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, and Yb. Often included for analysis, because they behave in a chemically similar way, although strictly not REE, are the Group 3 transition metals Y and Lu. The radioactive lanthanide element promethium (Pm) is excluded from analysis, since it is not found in samples because of its short half-life. 

The first transition would be expected to be of higher energy than the second from simple atomic charge considerations. Because the two atoms are of equal abundance, the two peaks have essentially equal intensities. Unfortunately, the observation of two XPS peaks does not rule out the possibility of delocalized valence electrons in the ground state. Two transitions are expected even in that case because of polarization of the excited state by the core ionization 123 The ground state of a delocalized mixed valence compound can be crudely represented by the formula M-M, where the intermediate position of the dot indicates that the odd valence electron is equally shared by the two metal atoms. The two XPS transitions can then be represented as follows,... 

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