## Abstract

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 S_{1} → S_{0} relaxation in trans-octatetraene. Input required for the analysis includes the energy gap between S_{1} and S_{0}, normal mode frequencies, reduced masses, and eigenvectors (including the Duschinsky rotation matrix), and the molecule equilibrium configurations (bond lengths and angles) in S_{1} and S_{0}. 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 CH_{2} end groups, where the motion of the two hydrogen atoms within each quasilocal CH_{2} 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.

Original language | English |
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Pages (from-to) | 239-251 |

Number of pages | 13 |

Journal | Israel Journal of Chemistry |

Volume | 45 |

Issue number | 1-2 |

DOIs | |

State | Published - 1 Jan 2005 |

## ASJC Scopus subject areas

- Chemistry (all)

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