Transition state HOMO-LUMO energies

The features in Figure 15.2 are believed to be due to electron transitions from the highest occupied molecular orbital states to lowest unoccupied molecular orbital states (HOMO-LUMO). Specifically, for single molecules and dilute solutions, the absorption in the blue part of the spectrum is proposed to be caused by the aromatic structure of TNT [4], probably involving it to it transitions.1 In the solid state, where the molecules are stacked up on top of each other, interactions between the molecules occur causing the energy levels to split into higher... 

The fact that Cope rearrangements of alkynes proceed as readily as those of alkenes53 has been puzzling, since it would appear that the transition state would be more easily attained in the case of alkenes. However, our results indicate that considerable bending of the acetylenic units occurs easily in the transition state, since the energy required is counteracted by increased HOMO-LUMO interaction. Thus,... 

These bands are related to the four transitions, HOMO-LUMO, next-HOMO-LUMO, HOMO-next-LUMO, and next-HOMO-next-LUMO. The electron configurations of next-HOMO-LUMO and HOMO-next-LUMO are degenerate, and they split into two components by the Cl procedure, one of which lies below the transition of HOMO-LUMO with the lowest energy electron configuration. Therefore the lowest excited state (a band) is one component of the doublet pair (next-HOMO-LUMO and HOMO-next-LUMO). The second band (p band) corresponds to the transition of HOMO-LUMO. The third shortest wavelength and the strongest band (/3 band) is associated with the next HOMO-next-LUMO transition and another component of the doublet pair. 

As a result of the relativistic increase in the HOMO/LUMO energy gap AE, the energy of the lowest charge-transfer transitions 3p(ci)->d associated with the reduction of the metal also increases, which means that the stability of the maximum oxidation state increases. This is shown in Fig. 15 by a correlation between 3p(ci)->d and reduction potentials. E (V-rV) for MCI5 (M = V, Nb, Ta and Db). Thus, nonrelativistically, Db would have even been less stable than Nb ... 

After this, Martinez and Ben-Nun applied the method to the photoexcitation of ethylene [88,247]. The lowest energy excitation is the HOMO-LUMO n n transition. These states are labeled A and Close in energy to... 

Figure 10 12 shows the interaction between the HOMO of one ethylene molecule and the LUMO of another In particular notice that two of the carbons that are to become ct bonded to each other m the product experience an antibondmg interaction during the cycloaddition process This raises the activation energy for cycloaddition and leads the reaction to be classified as a symmetry forbidden reaction Reaction were it to occur would take place slowly and by a mechanism m which the two new ct bonds are formed m separate steps rather than by way of a concerted process involving a sm gle transition state... 

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... 

The energy of the frontier orbitals determines the reactivity. The small energy gap between the HOMO of electron donors and the LUMO of electron acceptors promotes the interaction and stabilizes the transition states. Electron donors react fast as the HOMO energy is high. Electron acceptors reacts fast as the LUMO energy is low. 

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