Polyene transition energy

Table 1. Extrapolations of carotenoid/Iinear polyene transition energies to the infinite polyene limit...

Thus for the case of the linear polyene, the p-th transition energy Ep is given by... 

FIGURE 4. Observed 0-0 electronic transition energies (cm ) of linear polyenes ... 

The wavelength of a transition is directly proportional to the inverse of its transition energy hence HMO theory predicts that the absorption wavelengths of linear polyenes are linearly related to the number of carbon atoms n (Equation 4.22). 

Fig. 36.9. Sketch of the UV transition energies in polymethine dyes and in polyenes.

These equations have been tested for several short polyenes and for jS-carotene (Sklar et al., 1977 Snyder et al., 1985 Andersson et al., 1991). For So(l Ag) — SgCl BJ transitions, k s are typically lO" cm. In addition to the linear dependence of transition energies on solvent polarizability, another critical test of Eq. (1) is its abdity to predict gas phase (n= 1) transition energies. Forthe So(l Ag) - 2( u) transitions of diphenylpolyenes with one to four double bonds, extrapolations of solution data and transition energies obtained from gas phase measurements agree within experimental error (Hudson etal., 1976,1982). Equation 1 also accounts for the shifts in spectra in the few cases where solvent studies have been carried out on vibronically-resolved S,(2 Ag) ->So(l Ag) transitions. The k s are considerably smaller but not insignificant, -1000-2000 cm for unsubstituted polyenes (Snyder et al.,... 

Extrapolation ofS and S, Sq Transition Energies to Long Carotenoids The Infinite Polyene Limit... 

The early work of Hemley and Kohler (1977) used E = A + B/N to fit the S (l Ag) - S fl BJ, (0-0) transition energies of unsubstituted polyenes with four through ten double bonds in a common hydrocarbon solvent (isooctane). This laterprovedto be consistent with Kohler s simple theoretical model... 

Table 2. Energies (in cm" )oflow-lying electronic states of simple polyenes. Vertical transition energies (Franck-Condon maxima) are given in parentheses. Other energies refer to the electronic origins (0-0 bands) of S ->T, and Sq transitions. The O, perturbation spectra were obtained in chloroform all other energies refer to the gas phase.

Outstanding issues to be addressed by more accurate information on the electronic energies of long polyenes and carotenoids include a quantitative understanding of the differences between the S, S and S(, 83 transition energies of simple polyenes,... 

Table 2 SDMRG results for the lowest-lying excited state energies (in eV) of polyenes with 4 to 30 carbons. All the values correspond to the vertical transition energies from the lAg ground state.

Vertical and relaxed transitions are indicated by dashed and solid lines and open and solid symbols, respectively. Experimental values of the relaxed l B (x) and (+) state energies for polyenes in hydrocarbon solution (Kohler 1988). (b) Calculated transition energies for the l BF state (squares) and charge gap (circles). Reprinted with permission from W. Barford, R. J. Bursill, and M. Yu Lavrentiev, Phys. Rev. B 63, 195108, 2001. Copyright 2001 by the American Physical Society. 

Ag transition is not observed, because it is expected to be extremely weak. The transition energy for the 2 Ag excited state is always lower than that for the 1 B state for each polyene. 

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