LUMO levels

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. 

Electron donor molecules are oxidized in solution easily. Eor example, for TTE is 0.33V vs SCE in acetonitrile. Similarly, electron acceptors such as TCNQ are reduced easily. TCNQ exhibits a reduction wave at — 0.06V vs SCE in acetonitrile. The redox potentials can be adjusted by derivatizing the donor and acceptor molecules, and this tuning of HOMO and LUMO levels can be used to tailor charge-transfer and conductivity properties of the material. Knowledge of HOMO and LUMO levels can also be used to choose materials for efficient charge injection from metallic electrodes. 

Calculations for Ceo in the LDA approximation [62, 60] yield a narrow band (- 0.4 0.6 eV bandwidth) solid, with a HOMO-LUMO-derived direct band gap of - 1.5 eV at the X point of the fee Brillouin zone. The narrow energy bands and the molecular nature of the electronic structure of fullerenes are indicative of a highly correlated electron system. Since the HOMO and LUMO levels both have the same odd parity, electric dipole transitions between these levels are symmetry forbidden in the free Ceo moleeule. In the crystalline solid, transitions between the direct bandgap states at the T and X points in the cubic Brillouin zone arc also forbidden, but are allowed at the lower symmetry points in the Brillouin zone. The allowed electric dipole... 

A < 640 nm (or 1.9 < E < 2.5 eV), weak absorption takes plaee, and is associated with electric dipole-forbidden transitions between the one-electron HOMO level w ith /i symmetry and the one-electron Uu LUMO level. 

Figure 4-4. Schematic rcprcsenlalion of ihc one-clcclron structure of a single siilbcnc molecule and that of a cofacial dimer formed by iwo chains separated by 4 A. lire INDO-ealculated energy splil ot the HOMO and LUMO levels when going from Ihc isolated molecule to the dimer are also given.

Table 2.2 contains mean values of the Cu—Oz bond lengths ((<7Cu—())), copper valence index [11] (FCu) and partial charge (<2Cu), one-electron energies of the HOMO and LUMO ( HOmo> lumo) levels along with the bonding energy of Cu1 to the hosting cluster. 

From the comparison of the results, it can be inferred that copper ions exchanged in the ZSM-5 zeolites assumes a bidentate (sites 12 and II) or tridentate coordination (sites M5, Z6, and M7). These two groups differ also in the molecular properties (Table 2.2). The I-centers are characterized by lower values of the valence index and greater partial charges, QCu, in comparison to the M and Z centers, which is associated with the deeper laying HOMO and LUMO levels. In the M5, Z6, and M7 sites Cu1 ions exhibit more covalent character, and the frontier orbitals have less negative energies. As a result, the chemical hardness of the I-centers, located at the channel intersections, is smaller than those located on the walls of the ZSM-5 zeolite. 

Theoretical calculations demonstrated that the energy gap between HOMO and LUMO levels is not particularly affected by pH variations, but a systematic downshift is recorded with increasing pH. The energetic levels are not influenced by the substituent, which is usually a glucosidic unit, even though has been widely demonstrated that it increases dye stability [34]. 

One more step provides an operational definition. The HOMO level lies, I = ionization energy, below the vacuum level, while the LUMO level lies, A = electron affinity, below it. Thus, the chemical hardness lies midway in the gap and usually is given in units of eV. 

Figure 1 shows the electron attachment energies (AE) and ionization potentials (IP) of silyl substituted 7t-systems and related compounds [4], AE can be correlated with the energy level of the LUMO (lowest unoccupied molecular orbital) and IP can be correlated with the energy level of the HOMO (highest occupied molecular orbital). For a-substituted 7t-systems, the introduction of a silyl group produces a decrease in the tc -(LUMO) level. This effect is attributed to the interaction between a low-lying silicon-based unoccupied orbital such as the empty d orbital of silicon and the it orbital (d -p interaction) as shown in Fig. 2. Recent investigations on these systems, however, indicate that d orbitals on silicon are not necessarily required for interpreting this effect a-effects of SiR3 can also be explained by the interaction between Si-R a orbitals and the 7r-system.

Owing to such orbital interactions, a-silyl substitution causes the decrease in the LUMO level of the 7t-system and enhances the electron accepting ability of the 7i-system. Therefore, the reduction potentials of a-silyl-substituted 7t-systems are less negative than those of the parent jr-systems, although the magnitude of this effect is not large. 

Another interesting feature of Si-Si bonds is the low energy level of the LUMO. The LUMO levels decrease with increasing chain length of polysilanes (Fig. 10). Because of the low lying LUMO, polysilanes can be reduced by both... 

The redox properties of cyclic polysilanes are interesting because they resemble those of aromatic hydrocarbons. For instance, cyclic polysilanes can be reduced to anion radicals or oxidized to cation radicals. ESR spectra for both the cation and anion radicals indicate that the unpaired electron is fully delocalized over the ring [17,19,20]. The aromatic properties of the cyclic polysilanes are ascribed to a high energy delocalized HOMO and a relatively low energy LUMO. Because the HOMO and LUMO levels lie at similar level to those of benzene, cyclic polysilanes can serve either as electron donors or electron acceptors. 

MEH-PPV 13, which raises the HOMO and also unexpectedly brings down the LUMO level of the copolymer (see Section 2.2.3) (Chart 2.10). 

Jin and coworkers [123] synthesized PPV 67, containing an oxadiazole and an alkoxy group. According to UPS study, the HOMO and LUMO levels in 67 (-6.32 and -3.98 eV) are within the band gap of the parent polymer 61 without alkoxy substituents (Scheme 2.14). The external QE of PLEDs based on polymer 67 is about one order of magnitude higher than that for 61 (0.045% for ITO/67/Li Al) and a maximum brightness of up to 7570 cd/m2 was achieved for this material (using Ca cathode). 

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