Electron delocalised

Metallic bonding is the electrostatic force of attraction between positively charged metal cations and the delocalised electrons between them. 

The bonding in a metal such as aluminium consists of Al3+ cations (1) in a sea of delocalised electrons (1). Therefore, current can flow due to the presence of mobile electrons (three per Al atom) (1). 

Bonding In benzene can be described In terms of sp hybridisation, o-bonds and a 71 molecular orbital containing delocalised electrons. 

Benzene is unusually stable and it is the delocalised electrons that account for this stability. The presence of the delocalised electrons also explains why benzene does not undergo addition reactions. Addition reactions would disrupt the electron delocalisation and so reduce the stability of the ring. Substitution reactions, on the other hand, can occur without any such disruption and the stability of the benzene ring is maintained. The delocalised electrons in the % molecular orbital make benzene susceptible to attack by electrophiles (electron pair acceptors). As a result, benzene undergoes electrophilic substitution reactions and some of these are outlined at the top of the next page. Note that the electrophiles are shown in red, the reagents in blue and the reaction names in green. 

Both benzene and graphite contain delocalised electrons. Why does graphite conduct electricity, yet benzene does not ... 

Graphite has a layer structure and each layer can be regarded as a network of fused benzene rings. The delocalised electrons extend over the whole layer and allow graphite to conduct electricity. The benzene molecule also contains delocalised electrons and this would imply that individual molecules would conduct electricity. However, a collection of benzene molecules, such as in a beaker of benzene liquid, does not conduct. This is because the delocalised electrons are confined to the individual benzene molecules and cannot jump from one molecule to another. 

Very broadly speaking, two situations have to be considered in explaining devices such as those we have mentioned. In the first, which is relevant to the ruby laser and to phosphors for fluorescent lights, the light is emitted by an impurity ion in a host lattice. We are concerned here with what is essentially an atomic spectrum modified by the lattice. In the second case, which applies to LEDs and the gallium arsenide laser, the optical properties of the delocalised electrons in the bulk solid are important. 

In phosphors and in the ruby laser, light was absorbed and emitted by electrons localised on an impurity site, but in other optical devices, delocalised electrons emit the radiation. In the next section, therefore, we shall consider the absorption and emission of radiation in solids with delocalised electrons, particularly in semiconductors. 

Pauli paramagnetism + 10 Independent None Spin and orbital motion of delocalised electrons... 

Note that the conduction which takes place in the electrodes is due to the movement of delocalised electrons (pp. 51 and 55) whereas in the electrolyte, as stated earlier, the charge carriers are ions. 

The reader is probably familiar with a simple picture of metallic bonding in which we imagine a lattice of cations M"+ studded in a sea of delocalised electrons, smeared out over the whole crystal. This model can rationalise such properties as malleability and ductility these require that layers of atoms can slide over one another without-undue repulsion. The sea of electrons acts like a lubricating fluid to shield the M"+ ions from each other. In contrast, distortion of an ionic structure will necessarily lead to increased repulsion between ions of like charge while deformation of a molecular crystal disrupts the Van der Waals forces that hold it together. It is also easy to visualise the electrical properties of metals in... 

What factors determine whether an elemental substance adopts a metallic or a covalent structure From the simple model for metallic bonding, which views a metal as a lattice of cations embedded in a sea of delocalised electrons, it may be supposed that atoms having low ionisation potentials are most likely to become assembled as metallic substances. This correlation is far from perfect, however. Thus the first and second ionisation energies of mercury are comparable with those of sulphur, but the alchemists viewed elemental mercury and sulphur as the quintessential metal and nonmetal respectively. A closely-related correlation can be found with electronegativity. 

Lithium is exceptional in forming molecular alkyls with oligomeric structures, for example, the tetrameric Li4(CH3)4(3). Bonding in the cubane -like framework is provided by delocalised electrons. 

While the Overhauser shift is due to delocalised electrons, the ENDOR experiments require more localised electrons. Both groups were able to observe ENDOR on the effective mass donor resonance but not on the deep donor signal. An illustrative ENDOR spectrum is shown in FIGURE 4, in which the 69 71Ga ENDOR lines are observed. The 69Ga line is clearly split by quadrupole interactions just as in the Oveihauser shift measurements, while the quadrupolar interaction is much less resolved in the 71 Ga line, due to its smaller quadrupole moment. In the three samples investigated by the two groups, the linewidths were all too broad to resolve any hyperfine interaction and so no definitive identification of the residual donor was possible. 

In a semiconductor, as discussed in the previous section, localisation can also occur as the width of the allowed energy band is reduced, and this was defined in terms of a limiting mobility. The Anderson model shows that disorder can lead to localisation in metals as well as semiconductors. In metals, since conduction is due only to electrons within a partially filled band, the energy in the band tail that separates localised from delocalised electron states is termed the mobility edge. The onset of localisation in a metal occurs at a minimum conductivity. This can be seen as follows. For an electron at the Fermi energy its mean free path, l, is just the scattering time, r, multiplied by the electron velocity at the Fermi energy, vF. Then, from Equations (4.1) and (4.2) it follows that ... 

Finally a method which shows promise for the future is d5mamic mean field theory. Dynamical mean field theory uses an approximation to the local spectral density functional (rather than energy density functional) and a set of correlated local orbitals. For solids this local description is combined with a periodic description such as DFT using EDA to provide a method of dealing with both localised and delocalised electrons." Anisimov et applied this method to the photo-... 

The majority of the reactions of benzene are substitution reactions and not. as might be expected, addition reactions. The reason is that the continuous cloud of electrons above and below the carbon hexagon is very stable and it takes energy to break it. The preferred reaction is to replace a hydrogen atom so that the delocalised ring structure is kept intact. This is best achieved by substitution reactions. Addition across the double bonds would destroy the delocalised electron cloud of the ring. These addition reactions are not very common for benzene and similar compounds, although they are possible. 

The conducting AFM method has revealed interesting details of the single molecule conductance of carotene molecules. The electronic properties of carotenoids are of interest since they play a role in their biological function, especially their optical properties which are a manifestation of their delocalised electron structure. The structure of the dithiolated carotenoid used in a study by Ramachandran et al. is shown in Fig. 7-21. A synthetic molecular wire 2,5-di(phenylethynyl-4 -thioacetyl)benzene, also appraised by conducting AFM is also shown in Fig. 7-21. The measured low bias resistance of the carotenoid molecule was found to be (4.9 0.2) GQ. After... 

Although less stackable than the other systems considered here, fullerenes, in other respects, also qualify as clusters, for several reasons. First, they do so because of their large size and symmetrical shapes. Second, there can exist similarly formed groupings of C atoms with diverse numbers (70, 120, etc) and related properties. Third the p bonds of C give rise to a delocalised electronic shell structure similar in many respects to the closed shells of metallic clusters each carbon atom donates four electrons to a shell whose precise shape is determined by the fullerene structure, but which is closed, has a thickness of about one atom, and is very similar to the closed shells of metallic clusters. 

We suppose that there is only one delocalised electron per site (an appropriate assumption for an alkali cluster). The Hiickel Hamiltonian for the cluster can then be written as ... 

Fig. 12.15. Example of a giant dipole resonance in a metal cluster with a closed shell, in this case a singly ionised K cluster with eight delocalised electrons (after C. Brechignac and J.-P. Connerade [714]).

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