EXCITATION OF POLYENES AND PORPHYRINS 87 



molecule is the fg triplet ^B. Numerical calculations by the LCAO 

 molecular-orbital method first gave this result for ethylene (see Mulliken 

 and Roothaan, 1947). 



The Theorem of Longuet-Higgins. Longuet-Higgins (1950a) generahzed 

 the result, showing by the LCAO method that, when an essential double 

 bond^ in any chain or even-ring hydrocarbon is twisted by 90°, the P and 

 fg configuration energies coincide. The ground state is necessarily a 

 triplet, and ^A and ^B must be low and close together. 



A molecule excited to the ^B state may then during its excited life- 

 time twist in an essential double bond to the minimum energy for that 

 state, near 90°. Thence it may return to the ground state either at 0° 

 or at 180° with about equal probability. Trans-substituted ethylenes 

 will be partly converted to cis after excitation, and vice versa. No fluo- 

 rescence seems to have been observed in ethylene, which may mean that 

 the twisting motion of the hydrogens has produced internal quenching. 

 But the fluorescence is quite strong in the diphenyl polyenes, where the 

 twisting motion of the heavier rings should be about a hundred times 

 slower. 



This indicates that in the latter compounds the quenching time due 

 to twisting is probably between 10~^ sec, the fluorescence lifetime, and 

 10"^^ sec. Any molecules that reach the longer-lived phosphorescent state 

 will therefore probably be twisted to 90° before they can radiate. It 

 would be interesting to know how long they can remain in the 90° con- 

 figuration, where this triplet state is the lowest. 



As Fig. 2-9 shows, thermal twisting in the 0° configuration will pro- 

 duce only second-order changes in the frequency of the first transition. 

 If the equilibrium configuration is twisted, as by steric hindrance or some 

 other constraint, not only will the frequency be shifted to the red, but 

 thermal twisting will now produce first-order changes. This is presuma- 

 bly the explanation of the red shift of the spectrum from cis-butene to 

 cyclohexene, where an equilibrium twist of about 20° is to be expected, 

 and of the unusually long absorption "tail" on the cyclohexene spectrum, 

 extending into the quartz ultraviolet (Piatt et al., 1949). A similar tail 

 extends into the visible region for cyclooctatetraene, making the color of 

 the compound yellow; here a puckered configuration is favored, with each 

 ethylene twisted about 40° (American Petroleum Institute, 1947, 1948).^ 



2 One that remains a double bond in every principal or nonionic resonance structure, 

 e.g., the center bond in stilbene but not the center bond in biphenyl. 



^ The great width of individual vibration bands in the long-wave-length polyene 

 transitions at room temperatures, as compared with the bands of condensed-ring 

 systems, may be evidence of thermal twisting, with consequent variations in the 

 excited-state energy. It seems to be a general rule that the sharpest bands in solu- 

 tions are those of rigid planar systems, with maximum resistance to twist. Substitu- 

 tion of methyl or alkyl groups, which have free rotation but little conjugation, broad- 

 ens the bands. The vibrational structure frequently disappears entirely with more 



