HOMO—LUMO transition polyenes

We might, therefore, be emboldened to apply the model to predict absorption spectra in higher polyenes, CH2=(CH—CH =) -1CH2. For the molecule with 2n carbon atoms (n double bonds), the HOMO —LUMO transition corresponds to n —> n - - 1, thus... 

Essential features of the electronic spectra of linear polyenes have already been mentioned in Chapter 1. The HOMO LUMO transition is shifted to longer wavelengths as the number of conjugated double bonds increases, and this is easy to rationalize in the FEMO model. However, the next transition that is to be expected from the simple MO model is only allowed if the molecule does not have a center of symmetry that is, if it is not in the all-trans configuration. (Cf. Example 1.7.) The absorption spectrum of /S-caro-... 

Equation 4.22 HMO prediction for the wavelength of the HOMO LUMO transition of linear polyenes... 

Compounds with a narrow HOMO-LUMO gap (Figure 5.5d) are kinetically reactive and subject to dimerization (e.g., cyclopentadiene) or reaction with Lewis acids or bases. Polyenes are the dominant organic examples of this group. The difficulty in isolation of cyclobutadiene lies not with any intrinsic instability of the molecule but with the self-reactivity which arises from an extremely narrow HOMO-LUMO gap. A second class of compounds also falls in this category, coordinatively unsaturated transition metal complexes. In transition metals, the atomic n d orbital set may be partially occupied and/or nearly degenerate with the partially occupied n + 1 spn set. Such a configuration permits exceptional reactivity, even toward C—H and C—C bonds. These systems are treated separately in Chapter 13. 

However, the linear polyenes are more compUcated than just described in the one-electron model. There is another excited state at a low energy. This is a state with the same symmetry as the ground state. The transition to this state is thus forbidden in all polarizations. The wave function for this state is a superposition of two singly substituted Slater determinauts, corresponding to the HOMO - 1 LUMO and the HOMO LUMO -I-1 substitutions, respectively. The orbital energy differences are both larger than the HOMO LUMO substitution, of course, but the correlation... 

Fig. 1.55 Frequency of first n —> te transitions of some representative polyenes R(CH=CH) R plotted against LUMo - homo...

The free-electron model can also be applied to the electronic spectrum of butadiene and other linear polyenes. The lowest unoccupied molecular orbital (LUMO) in butadiene corresponds to the = 3 particle-in-a-box state. Neglecting electron-electron interaction, the longest-wavelength (lowest-energy) electronic transition should occur from n — 2, the highest occupied molecular orbital (HOMO), as shown below ... 

Figure 13.33 illustrates the transition between electronic energy states responsible for the 230-nm UV band of c/i -tra i -l,3-cyclooctadiene. Absorption of ultraviolet radiation excites an electron from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO). In alkenes and polyenes, both the HOMO... 

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