respectively, are of comparable energy (eq 4 and ref 36). In fact, the "doubly excited" state was found50 to be the lowest excited singlet state in some systems with a small HOMO-LUMO energy gap «, and a large number of photoreactions initiated in the St (50) B.
We have fitted over 160 electronic absorption spectra of over 95 aromatic compounds and some other substances with lognormal distribution curves to evaluate the shapes of the bands. The compounds include simple benzene derivatives, phenols, anilines, benzaldehyde, benzoic acid, nitrobenzene, and potassium permanganate. The well-defined n-π* transitions of acetone, benzaldehyde, nitrobenzene, and pyrazine are included. Effects of solvents have been studied in a number of cases. The fitting of absorption bands with lognormal curves is compared with resolution with Gaussian curves or with other types of skewed Gaussian curves. We conclude that the lognormal curve provides an excellent approximation to the shapes of spectral bands in aromatic as well as many other organic and inorganic compounds. The ability to analyze complex spectra by resolution with lognormal curves may be usefully applied in a number of ways.
A mathematical treatment of mixed potential generation is developed from basic electrochemical theories, such that the relationships between rest, mixed, and Nernst potentials are evident. Various approximations of the general mixed potential equations are also developed and discussed.
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