LUMO-HOMO difference

This expression is usually reduced to the superior order LUMO-HOMO difference... 

HOMO-LUMO energy difference in ethylene is greater than that of cis trans 1 3 cyclooctadiene... 

This idea can be quantitatively expressed by defining activation hardness as the difference between the LUMO-HOMO gap for the reactant and that for the rr-complex intermedi-... 

Lewis acids catalyze Diels-Alder reactions. Do they enhance overlap between diene and dienophile orbitals and/ or do they reduce the HOMO/LUMO energy difference ... 

These concepts play an important role in the Hard and Soft Acid and Base (HSAB) principle, which states that hard acids prefer to react with hard bases, and vice versa. By means of Koopmann s theorem (Section 3.4) the hardness is related to the HOMO-LUMO energy difference, i.e. a small gap indicates a soft molecule. From second-order perturbation theory it also follows that a small gap between occupied and unoccupied orbitals will give a large contribution to the polarizability (Section 10.6), i.e. softness is a measure of how easily the electron density can be distorted by external fields, for example those generated by another molecule. In terms of the perturbation equation (15.1), a hard-hard interaction is primarily charge controlled, while a soft-soft interaction is orbital controlled. Both FMO and HSAB theories may be considered as being limiting cases of chemical reactivity described by the Fukui ftinction. 

The LUMO-HOMO gap is approximately given by the spectroscopic properties of the SO group. Since DMSO absorbs in the region of 2380 and 2560 A, we obtain96 1.24 x 104/2560 = 4.8eV. This measures the drastic enhancement in redox properties anticipated for this compound. Indeed the 4.8 V value for the ground-state potential covers the whole range of usual redox potentials. The same principle applies to the sulfones because their electrode potential and absorption properties differ little from their sulfoxide analogues. 

Because EH calculations show that these factors strongly effect the HOMO-LUMO gaps, different absorption and emission energies are expected to exist. (Adapted from Rawashdeh-Omary et al., 2001)... 

Fig. 6 (a) Cyclic voltammograms Cgo (top) and Sc3N / ,-C8o (bottom) in a 0.050 M solution of TBAPFg in o-DCB. (b) Schematic energy diagram of HOMO-LUMO gaps difference between Cgo and Sc3N 4-Cgo... 

The potential difference between the first reduction and the first oxidation is a good measure of the HOMO-LUMO energy difference (the HOMO-LUMO gap) in solution. For Geo and G70, these gaps are 2.32 and 2.22 V, respectively, at room temperature in TGE [36]. 

Table 10 Comparison of LUMO-HOMO energy differences, (eV energy vaiues are taken from Table 9) for interaotions of 424, 422a, and 422d with 425c and 425d...

According to the frontier orbital theory,525 electron-withdrawing substituents lower the energies of the lowest unoccupied molecular orbital (LUMO) of the di-enophile thereby decreasing the highets occupied molecular orbital (HOMO)-LUMO energy difference and the activation energy of the reaction. 1,3-Butadiene itself is sufficiently electron-rich to participate in cycloaddition. Other frequently used dienes are methyl-substituted butadienes, cyclopentadiene, 1,3-cyclohexa-diene, and 1,2-dimethylenecyclohexane. 

The energy of electromagnetic radiation is inversely proportional to its wavelength. Since excitation of an electron for the tt — rr transition of ethylene occurs at a shorter wavelength (Amax = 170 nm) than that of cis, trans- 1,3-cyclooctadiene (Amax= 230 nm), the HOMO-LUMO energy difference in ethylene is greater. 

The HOMO (LUMO) of 12 having a different symmetry than the LUMO (HOMO) of ethylene, Reaction (4.1) is forbidden. In this particular case, the FO method is simpler than the PMO approach. 

For NCs, the electrochemically determined lumo- homo energy difference is, within experimental error, the same or very close to that measured optically. By both methods, the quantum confinement effect, characteristic of NCs, is evidenced.129 148 The same applies to conjugated oligomers (polymers), whose optically and electrochemically determined lumo- homo energies usually agree. 

This is considerably different from the recombination reaction with, for example, typical ruthenium dyes. This slow re-reduction of the dyad is explained by the low redox potential of the osmium center, the value of 0.66 V (vs. SCE) observed, points to a small driving force for the redox process. This observation is important for the design of dyes for solar cell applications. Osmium compounds have very attractive absorption features, which cover a large part of the solar spectrum. However, their much less positive metal-based oxidation potentials will result in a less effective re-reduction of the dyes based on that metal and this will seriously affect the efficiency of solar cells. In addition, for many ruthenium-based dyes, the presence of low energy absorptions, desirable for spectral coverage, is often connected with low metal-based redox potentials. This intrinsically hinders the search for dyes which have a more complete coverage of the solar spectrum. Since electronic and electrochemical properties are very much related, a lowering of the LUMO-HOMO distance also leads to a less positive oxidation potential. 

Fig. 12. Energy of relativistic (rei) and non-relativistic (nr) energy levels for MC15 (M = Nb, Ta, and Db) obtained from the DS-DV and HFS calculations. AE indicates the HOMO-LUMO energy difference. Reproduced from [117].

Comparison of HOMO-LUMO energy differences. In buta- 1,3-diene, the 77 — 77 transition absorbs at a wavelength of 217 nm (540 kJ/mol) compared with 171 nm (686 kJ/mol) for ethylene. This longer wavelength (lower-energy) absorption results from a smaller energy difference between the HOMO and LUMO in butadiene than in ethylene. 

The replacement of a tert-butyl group by SiMe3 going from di-ferf-butyl ketone to rerr-butanoyl trimethylsilane and from di-terf-butyl thioketone to ferf-thiobutanoyl trimethylsilane lg increased Xmax and deshielded the quaternary carbon. Furthermore, an inversion in polarization of the C=S bond and a decrease of the HOMO-LUMO energy differences were observed in the ferf-thiobutanoyl trimethylsilane with respect to di-rm-butyl thioketone. 

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