Intensities of Electronic Transitions in Molecular Spectra III. Organic Molecules with Double Bonds. Conjugated Dienes
Authors: Mulliken Robert S. 
Published: January 2005

This paper is the first of a series on the application of intensity calculations to the spectra and related properties of organic compounds containing conjugated or resonating double bonds. It is concluded that in most cases the characteristic strong absorption of such compounds (giving color if the number of conjugated double bonds is large enough) is due to an N→V transition (homopolar normal state→ionic excited state) similar to those already identified in paper II for I2, O2, C2H4, and other molecules.
The present paper is devoted primarily to conjugated dienes. Unconjugated dienes and polyenes are treated incidentally, and it is shown theoretically that their ultraviolet spectra should be similar to those of alkenes (C2H4 and derivatives). There should be no strong absorption peak above λ2000, and the intensity per double bond should be about the same as in alkenes. These conclusions are in agreement with the rather scanty experimental data (examples, diallyl, rubber).
Detailed calculations are made on 1, 3-butadiene by the molecular orbital method, assuming all the atoms to be in one plane. The results are applicable also to other conjugated dienes. Four N→V transitions must occur for the unsaturation electrons, i.e., those electrons which make the second or weaker bond in double bonds. This group of four transitions corresponds to the one N→V transition in alkenes; according to the calculations, the total absorption intensity per double bond is considerably increased by conjugation, especially if the molecules are in the transform. Conjugation causes the frequencies of the four transitions to scatter toward both longer and shorter wave-lengths as compared with alkenes, as Hückel's work implicitly shows. Although the calculated frequencies of the four transitions are independent of the shape of the molecule (within the range of reasonable assumptions), their intensities are very different for the cis- and trans-forms, and are also very sensitive to the bond angles. There is a marked tendency for the intensity to concentrate in the longer wave-length at the expense of the shorter wave-length N→V transitions, especially for the trans-form. In the latter, nearly all the intensity is concentrated in the longest wave-length of the four N→V transitions. This gives an essential clue to the explanation of the spectra of molecules containing conjugated polyene chains, e.g., carotene and related pigments, as will be shown in VI of this series.
Comparison of the theoretical predictions with available data on the ultraviolet spectra of dienes shows in general good agreement if we suppose that butadiene and its derivatives exist in the trans-form, except that perhaps its centrally-substituted derivatives (e.g., isoprene) exist partly in the cis-form. This conclusion is in line with other evidence. The available data are, however, somewhat conflicting, and systematic new measurements on the ultraviolet spectra of dienes and polyenes would be extremely valuable. The cyclic dienes, which are necessarily cis, show much weaker absorption in their longest wave-length N→V absorption region than do the open-chain dienes, just as predicted; the cyclopentadiene absorption is half as strong as that of cyclohexadiene, also as predicted in view of the different bond angles in the two rings. The absorption in both these molecules, begins, however, at abnormally long wave-lengths. This can be explained by ``hyperconjugation,'' as will be shown in IV of this series.
Application of the electron-pair bond method to the problem of the spectra of polyenes is briefly discussed. Sklar has suggested that transitions to excited states which are predicted by consideration of resonance among neutral canonical structures can account for long wave-length absorption and color in organic compounds. It is here tentatively concluded, however, that such transitions are probably in general weak, and that they are not always the longest wave-length absorption transitions.