The dependence of the ultrafast relaxation kinetics of the $S2$ and $S1$ states in $β$-carotene homologs and lycopene on conjugation length studied by femtosecond time-resolved absorption and Kerr-gate fluorescence spectroscopies

The ultrafast relaxation kinetics of all-trans-$β$-carotene homologs with varying numbers of conjugated double bonds $n(n=7–15)$ and lycopene $(n=11)$ has been investigated using femtosecond time-resolved absorption and Kerr-gate fluorescence spectroscopies, both carried out under identical excitation conditions. The nonradiative relaxation rates of the optically allowed $S2(1Bu+1)$ state were precisely determined by the time-resolved fluorescence. The kinetics of the optically forbidden $S1(2Ag−1)$ state were observed by the time-resolved absorption measurements. The dependence of the $S1$ relaxation rates upon the conjugation length is adequately described by application of the energy gap law. In contrast to this, the nonradiative relaxation rates of $S2$ have a minimum at $n=9$ and show a reverse energy gap law dependence for values of $n$ above 11. This anomalous behavior of the $S2$ relaxation rates can be explained by the presence of an intermediate state (here called the $Sx$ state) located between the $S2$ and $S1$ states at large values of $n$ (such as $n=11$⁠). The presence of such an intermediate state would then result in the following sequential relaxation pathway $S2→Sx→S1→S0$⁠. A model based on conical intersections between the potential energy curves of these excited singlet states can readily explain the measured relationships between the decay rates and the energy gaps.