| This work focuses on the development of a novel approach to the study of the transition state region of gas phase chemical reactions. We refer to this approach as spectral quantization. The dynamics in the transition state region is studied by computing a hypothetical Franck-Condon spectrum, which is generated using a time-dependent wave packet method. The spectral features include resonances associated with dynamical barriers and trapped states. The resonance states are assigned by inspecting the stationary state wave functions obtained from the Fourier transform of the time evolving wave packet at the corresponding frequencies. Since the peak intensities are governed by the overlap of the resonance states with the initial wave packet, we can enhance the intensity of the peaks of particular interest by properly changing the characteristics of the initial wave packet. The spectral quantization method is applied here to a number of simple chemical reactions, such as collinear {dollar}H(D) + Hsb2{dollar} and three-dimensional {dollar}H + Hsb2.{dollar} These applications have revealed the existence of progressions of high energy resonances which were previously undiscovered. Furthermore, using an analytic treatment of a new model for dynamical trapping, an original line shape formula is derived, which fits well the peaks observed in the transition state spectrum and correctly yields the induction time associated with these resonances. |
