A phase-space method for finding the accepting modes in a non-vertical radiationless vibronic transition and for recognizing the final state with the largest Franck-Condon factor is applied to a harmonic model of the S1 → S0 relaxation in trans-octatetraene. Input required for the analysis includes the energy gap between S1 and S0, normal mode frequencies, reduced masses, and eigenvectors (including the Duschinsky rotation matrix), and the molecule equilibrium configurations (bond lengths and angles) in S1 and S0. Some of these data are taken from published experimental results and some are calculated in this work. The energy gap of 0.132 au is much larger than the energy of a vertical transition, which is only 0.047 au. The phase-space method gives a closed-form analytic solution for how to divide the excess energy between the accepting modes. The final distribution includes a large excitation of the two CH2 end groups, where the motion of the two hydrogen atoms within each quasilocal CH2 group is antisymmetric; a symmetric stretch of the two central C-H bonds of the molecule; and small totally symmetric bending of the whole molecule. Comparison of Franck-Condon factors (exact within the harmonic model) of the final state obtained by the phase-space analysis and of other similar isoenergetic states shows that the phase-space method indeed chooses the most probable final energy distribution. Possible modifications of these results due to anharmonic effects are discussed.
ASJC Scopus subject areas
- Chemistry (all)