A Phase Space Theory for Roaming Reactions

We describe a new, simple theory for predicting the branching fraction of products in roaming reactions, compared to the analogous barrierless bond dissociation products. The theory uses a phase space theory (PST) formalism to divide reactive states in the bond dissociation channel into states with enough translational energy to dissociate and states that may roam. Two parameters are required, ?Eroam, the energy difference between the bond dissociation threshold and the roaming threshold, and the roaming probability, Proam, the probability that states that may roam do roam rather than recombine to form reactants. The PST-roaming theory is tested against experimental and theoretical data on the dissociation dynamics of H2CO, NO3, and CH3CHO. The theory accurately models the relative roaming to bond dissociation branching fraction over the experimental or theoretical energy range available in the literature for each species. For H2CO, fixing Delta E-roam = 146 cm(-1), the midpoint of the experimental bounds for the roaming threshold, we obtain P-roam = 1. The best-fit value, Delta E-roam = 161 cm(-1), is also consistent with the experimental bounds. Using this value, the relative roaming to dissociation branching ratios are predicted to be similar in D2CO and H2CO, consistent with experimental observation. For NO3, we fix ?Eroam = 258.6 cm(-1), the experimental threshold for NO + O-2 production, and we model low-temperature experimental branching fractions using the experimental rotational and vibrational temperatures of Trot = 0 K and T-vib = 300 K. The best fit to the experimental data is obtained for P-roam = 0.0075, with this very small Proam being consistent with the known geometric constraints to formation of NO + O-2. Using Proam = 0.0075, our PST-roaming theory also accurately predicts the low-temperature NO yield spectrum and quantum yield data for room-temperature NO3 photolysis. For CH3CHO, we fix Delta E-roam = 385 cm(-1), based on theoretical calculations, and obtain a best-fit value of P-roam = 0.21, fitting to reduced dimensional trajectory calculations. These values of Delta E-roam and P-roam yield PST-roaming theory results that are also consistent with two experimental room-temperature data points. The combination of other kinetic theories and the PST-roaming theory will provide rate coefficients for roaming reactions.