Degenerate delocalization

The delocalized n systems of I are similar to that of N3 (Table 3), while II and III have the non-degenerate delocalized orbitals shown in Table 4. II, which also contains a localized tt orbital, is the real structure of RN3 and so must be the most stable. 

The most important classes of functionalized [60]fullerene derivatives, e.g. methanofullerenes [341, pyrrolidinofullerenes [35], Diels-Alder adducts [34i] and aziridinofullerene [36], all give rise to a cancellation of the fivefold degeneration of their HOMO and tlireefold degeneration of their LUMO levels (figure Cl.2.5). This stems in a first order approximation from a perturbation of the fullerene s 7i-electron system in combination with a partial loss of the delocalization. 

Consider now the rr-system in benzene. The MO approach will generate linear combinations of the atomic p-orbitals, producing six rr-orbitals delocalized over the whole molecule with four different orbital energies (two sets of degenerate orbitals). Figure 7.3. The stability of benzene can be attributed to the large gap between the HOMO and LUMO orbitals. 

Returning to the Case 2 systems, one may expect that the large twist of the double bond should have strong effects on the electron distribution. A considerable fraction of the ir-electron density originally in the double bond must be delocalized into the acceptor part of the molecule. The effect of this delocalization has been studied in some twisted 1,1-diacetylethylenes (84), in which the partial negative charge makes the acceptor part Ac—C —Ac similar to an acetylace-tonate anion (89). In this anion as well as in 84, four rotamers (one degenerate... 

The concept of a mobility edge has proved useful in the description of the nondegenerate gas of electrons in the conduction band of non-crystalline semiconductors. Here recent theoretical work (see Dersch and Thomas 1985, Dersch et al. 1987, Mott 1988, Overhof and Thomas 1989) has emphasized that, since even at zero temperature an electron can jump downwards with the emission of a phonon, the localized states always have a finite lifetime x and so are broadened with width AE fi/x. This allows non-activated hopping from one such state to another, the states are delocalized by phonons. In this book we discuss only degenerate electron gases here neither the Fermi energy at T=0 nor the mobility edge is broadened by interaction with phonons or by electron-electron interaction this will be shown in Chapter 2. 

---