HOMO-LUMO gaps

FMO theory requires that a HOMO of one reactant has to be correlated with the LUMO of the other reactant. The decision between the two alternatives - i.e., from which reactant the HOMO should be taken - is made on the basis of which is the smaller energy difference in our case the HOMO of the electron rich diene, 3.1, has to be correlated with the LUMO of the electron-poor dienophile, 3.2. The smaller this HOMO-LUMO gap, the higher the reactivity will be. With the HOMO and LUMO fixed, the orbital coefficients of these two orbitals can explain the regios-electivity of the reaction, which strongly favors the formation of 3.3 over 3.4. 

Hydrogen bonding of water to the activating group of (for normal-electron demand Diels-Alder reactions) the dienophile constitutes the second important effect". Hydrogen bonds strengthen the electron-withdrawing capacity of this functionality and thereby decrease the HOMO-LUMO gap... 

Most of the semiempirical methods are not designed to correctly predict the electronic excited state. Although excited-state calculations are possible, particularly using a CIS formulation, the energetics are not very accurate. However, the HOMO-LUMO gap is reasonably reproduced by some of the methods. 

Since the optical transitions near the HOMO-LUMO gap are symmetry-forbidden for electric dipole transitions, and their absorption strengths are consequently very low, study of the absorption edge in Ceo is difficult from both an experimental and theoretical standpoint. To add to this difficulty, Ceo is strongly photosensitive, so that unless measurements arc made under low light intensities, photo-induced chemical reactions take place, in some cases giving rise to irreversible structural changes and polymerization of the... 

For C70, molecular orbital calculations [60] reveal a large number of closely-spaced orbitals both above and below the HOMO-LUMO gap [60]. The large number of orbitals makes it difficult to assign particular groups of transitions to structure observed in the solution spectra of C70. UV-visible solution spectra for higher fullerenes (C n = 76,78,82,84,90,96) have also been reported [37, 39, 72]. 

As shown in Fig. 7, a large increase in optical absorption occurs at higher photon energies above the HOMO-LUMO gap where electric dipole transitions become allowed. Transmission spectra taken in this range (see Fig. 7) confirm the similarity of the optical spectra for solid Ceo and Ceo in solution (decalin) [78], as well as a similarity to electron energy loss spectra shown as the inset to this figure. The optical properties of solid Ceo and C70 have been studied over a wide frequency range [78, 79, 80] and yield the complex refractive index n(cj) = n(cj) + and the optical dielectric function... 

Another characteristic of aromatic compounds is a relatively large HOMO-LUMO gap, which can be expressed in terms of hardness, t] (see p. 21 for the definition of hardness) ... 

The numerical value of hardness obtained by MNDO-level calculations correlates with the stability of aromatic compounds. The correlation can be extended to a wider range of compounds, including heterocyclic compounds, when hardness is determined experimentally on the basis of molar reffactivity. The relatively large HOMO-LUMO gap also indicates the absence of relatively high-energy, reactive electrons, in agreement with the reduced reactivity of aromatic compounds toward electrophilic reagents. 

Electron-donor and electron-acceptor substituents selectively interact with different ring orbitals. Compare the HOMO and LUMO of azobenzene with the corresponding orbitals of the two substituted molecules. Which orbitals show signficant substituent contributions What are the nature of these contributions, bonding or antibonding Try to relate this to the effect which the substituents have on orbital energies and on the HOMO-LUMO gap in azobenzene. 

Figure 12-8 summarizes the information available as far as the HOMO/LUMO positions of the compounds is concerned. Being inferred from oxidation/rcduction potentials measured by cyclic voltammetry in polar solution and from HOMO/ LUMO gaps, respectively, absolute values should be viewed with some caution. 

Electrical measurements on devices with different layer thickness have shown that the diode current depends on the applied field rather than the drive voltage. This is similar to what has been observed with our alternating PPV copolymers [68]. It indicates that field-driven injection determines the electrical characteristics. From Figure 16-39 it is evident that U-OPV5 has the lowest onset for both current and emission. By means of Fowler-Nordhcini analysis of the /-V -charac-teristics and optical absorption measurements, wc estimated the injection barrier for holes and the HOMO-LUMO gap, respectively [119]. The results of... 

Tabic 16-7. Estimated HOMO-LUMO gaps and hole injection barriers. 

FIGURE 3.41 In large molecules, there are many closely spaced energy levels and the HOMO-LUMO gap is quite small. Such molecules are often colored because photons of visible light can be absorbed when electrons are excited from the HOMO to the LUMO. 

The HOMO/LUMO gaps of these isomeric sulfur molecules of branched rings and chains are considerably smaller than that of the crown-shaped Ss ring [35]. Therefore, the UV-Vis spectra of these species are expected to exhibit absorption bands at longer wavelengths than the ground state structure... 

Khanna et al. [136] proposed a mechanism of the reactions of aluminum based clusters with O, which lends a physical interpretation as to why the HOMO-LUMO gap of the clusters successfully predicts the oxygen etching behaviors. The importance of the HOMO-LUMO gap strongly suggests that the reactions of the metal clusters belong to the pseudoexcitation band. 

Metal surfaces and clusters are readily pseudoexcited. The band gaps of the surface states and the HOMO-LUMO gaps of metal clusters will be found to be important for more and more reactions in future. 

The and dianions have 20 (= 6 x 1 + 14) valence electrons and satisfy the 6N + 14 valence electron rule. The Al dianion possesses an geometry [60], Wade rules are not applicable to the stable geometry of Al ". The instability of the 0 geometry of Ga in disagreement with the rule can be attributed to similar magnitudes of the interaction between the p -orbitals and that between the p-orbitals which gives a very small HOMO-LUMO gap [8],... 

Akiba investigated the electrochemical behavior of a variety of phosphorus octaethylporphyrin derivatives all compounds showing a single reversible oxidation wave [91]. The absolute difference in potential between the first ring-centered oxidation and reduction varies from 2.19 to 2.36 V in dichloromethane. These values are within the range of the HOMO-LUMO gap observed for most metalloporphyrins. 

Quadratic hyperpolarisability DCJTB 4-(Dicyanomethylene)-2-tert-butyl-6 (l,l,7,7-tetrametbyljulolidyl-9-enyl)-4H-pyran Disperse red 1 HOMO-LUMO gap Electroluminescence Indium-tin-oxide Nonlinear optic... 

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