Oscillator phase and the reaction dynamics of HN3: A model for correlated motion

The reaction coordinate for a unimolecular dissociation reaction is intrins ically anharmonic, therefore the period of vibration depends upon the energ y in the bond. Consequently, the final few vibrations leading up to and inc luding reaction can occur over very different time scales, depending upon t he amount of vibrational energy in the reaction coordinate. In recent studi es, we have compared ensembles of reactive trajectories and have observed c orrelations in molecular motions during reaction leading up to the transiti on state. If the comparison is made in time, differences in the periods of the reaction coordinate vibration can obscure these correlations. However, if the reactions are compared vibration by vibration (i.e., coherently) cle ar patterns of vibrational motions emerge in the reaction dynamics. In this paper, we introduce a new application of the Hilbert transform to assign o scillator phases to the motions of anharmonic oscillators, which permits co herent comparison of trajectories. We also demonstrate by several examples that, when compared coherently, reaction dynamics of HN3 exhibit order whic h is not evident in time series comparisons. These orderly patterns of moti ons reflect the intramolecular conditions necessary for reaction to occur. We propose a model to account for the observed correlated motion in terms o f the requirements for intramolecular energy transfer. As a consequence of the constraints of energy transfer, the phases of several oscillators have clearly defined relative values. Physically this corresponds to a correlati on in the vibrations of several modes such that (for example) two key bonds always extend simultaneously during the course of reaction. Since the moti ons of atoms preceding reaction are not random, but rather follow a specifi c pattern, a restricted set of reactant states immediately precede reaction .