Lowest HOMO-LUMO gap

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... 

FIGURE 3.4 Molecular level alignment diagrams constructed using the HOMO and vacuum levels measured using UPS. The lowest unoccupied molecular orbital LUMO positions are inferred assuming a HOMO/LUMO gap equal to the onset of optical absorption. The chemical structure of CuPc is shown. (From Hill, I.G. and Kahn, A., J. Appl. Phys., 86, 2116, 1991. With permission.)... 

Calculations of the HOMO-LUMO gap energy as a function of alkyl substituent size are in agreement with the experimentally observed increase in lowest energy UV Amax,231 and the effects of changing from alkyl to aryl side... 

The HOMO-LUMO gap calculated by an ah initio method using an STO-3G basis set26 seems to support these ideas. A more definitive test will be possible after the nature of the lowest excited state in carbon unsaturated systems is understood27). 

Comparison of the spectra of these Re(I)-containing polymers with those of the corresponding free oligomers demonstrates that metalation includes a substantial redshift of the lowest 71,71 absorption. Metalation forces the bipyridyl unit into a planar conformation, thereby effectively increasing the conjugation length [13, 69]. In addition to this effect, the electrophilic metal center likely decreases the LUMO energy and consequently decreases the HOMO-LUMO gap. 

In this context, interesting exhaustive QSAR studies dealing with the assessment of phototoxic hazards of PAHs to aquatic organisms such as Daphnia were published some years ago [12-14]. Authors chose a descriptor based on the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). They proposed that aromatic chemicals with a HOMO-LUMO gap energy in a window of 7.2 eV 0.4 eV have a high phototoxic potential. 

In spite of the absence of a typical chromophore, 1,2-dithiin is a bright reddish-orange color. Absorption maxima were found at 451 (2.75 eV), 279 (4.36 eV), and 248 nm (5.00 eV), and the colored band was assigned to a A excitation <1991JST(230)287>. The main reason for the colored absorption of 1,2-dithiin is the low HOMO-LUMO gap of the KS orbitals which amounts to only 3.6 eV (HOMO = highest occupied molecular orbital LUMO = lowest unoccupied molecular orbital KS = Kohn-Sham) <2000JMM177>. By comparison, saturated 1,2-dithiane is colorless (290 nm). 

Figure 6. Second total energy difference (upper panel) and HOMO-LUMO gap (lower panel) for the lowest energy equilibrium structures of AunTM+ clusters...

The Principle of Hard and Soft Acids and Bases states that hard acids form more stable complexes with hard bases and soft bases form more stable complexes with soft acids. In orbital terms hard molecules have a large gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), and soft molecules have a small HOMO-LUMO gap. In recent years it has been possible to correlate the hardness with the electronic properties of the atoms involved. Thus, if the enthalpy of ionisation (I) and the electron affinity (A) are known the so-called absolute hardness (t ) and absolute electronegativity (%) can be found from r = (I - A) / 2 and % = (I + A) / 2. For example, the first and second ionisation enthalpies of sodium are 5.14 and 47.29 eV. Thus for Na+, I = + 47.29 and A = + 5.14, so r = (47.29 - 5.14) / 2 = 21.1. Similarly for silver the first and second ionisation enthalpies are 7.58 and 21.49eV, so for Ag+ we have, n = (21.49 - 7.58) 12 = 6.9. 

The surface properties of alkanethiol SAMs have been studied thoroughly, and recently people have performed electrical characterizations and found the conduction mechanism through such self-assembled alkanethiol monolayers is tunneling due to its large HOMO-LUMO gap (HOMO highest occupied molecular orbital, LUMO lowest unoccupied molecular orbital) (>8 eV).28 Another type of molecular system is the so-called... 

Finally, let us consider how much of an energy off-set, eb, is required so that the lowest energy excited state is a charge-transfer state. For simplicity, we take the HOMO-LUMO gap on each monomer to be identical El, —Eha = ELb-EHb = AE and thus, ELb-EHa = AE-2eb and ELa-EHb = AE+2eb... 

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