Vibronic Coupling through the In-Phase, CC Stretching Mode Plays a Major Role in the 2Ag⁻ to 1Ag⁻ Internal Conversion of all-trans-β-Carotene

The major role of vibronic coupling through the in-phase, CC stretching (ν1) mode in the 2Ag- to 1Ag- internal conversion of all-trans-β-carotene has been shown by the use of isotopic effects on the rate of internal conversion and on the strength of vibronic coupling as follows: (1) The rates of internal conversion for all-trans-β-carotene having natural abundance isotope composition [NA], along with 2H-labeled [2H], 13C-labeled [13C], and 2H,13C-doubly labeled [2H,13C] all-trans-β-carotenes, were determined, by subpicosecond time-resolved absorption spectroscopy, to be in the ratio [NA]/[2H]/[13C]/[2H,13C] = 1:0.92:0.70:0.64. (2) The strength of vibronic coupling was estimated for each isotope species by using the frequency difference between the 2Ag- and 1Ag- states, which was determined, by picosecond Raman spectroscopy, to be in the ratio, [NA]/[2H]/[13C]/[2H,13C] = 1:1.21:0.89:1.07. On the other hand, a theory was presented to show that the nonadiabatic vibronic-coupling constant that determines the rate of internal conversion is proportional to the adiabatic vibronic-coupling constant that determines the frequency difference. The application of the observed relative strength of vibronic coupling to the Englman−Jortner equation, for a single mode ν1, predicted the relative rates of internal conversion to be 1:0.80:0.72:0.60, which are in good agreement with those observed above. (3) A theory showing that the adiabatic vibronic-coupling constant is proportional to the product of the transition bond-order matrix and the L matrix was also presented. In a polyene model, the relative rates of internal conversion were predicted to be 1:0.94:0.68:0.64, which are in excellent agreement with the above observed values.