Energy Dependence of Ensemble-Averaged Energy Transfer Moments and Its Effect on Competing Decomposition Reactions

We carried out a direct dynamics study on the internal-energy dependence of the ensemble-averaged energy transfer moments of the isobutyl radical in collisions with N₂ bath gas. We find a linear dependence of the downward moment ⟨Δ<i>E</i>_d⟩ and the root-mean-square moment <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msqrt><mml:mrow><mml:mo>⟨</mml:mo><mml:mi>Δ</mml:mi><mml:msup><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo>⟩</mml:mo></mml:mrow></mml:msqrt></mml:math> on the initial internal energy, but the upward moment ⟨Δ<i>E</i>_u⟩ is found to be independent of the molecule's internal energy. We improved the exponential-down relaxation model by including a linear dependence of ⟨Δ<i>E</i>_d⟩ on the initial energy, and we used the improved treatment in the 1D master equation for isobutyl radical decomposition reactions and for a model of competitive reactions with a larger difference in barrier heights. We calculated phenomenological rate constants and branching ratios from chemically significant eigenmodes of the master equation and showed that the energy dependence of ⟨Δ<i>E</i>_d⟩ has a greater influence on channels with higher barriers in competitive reactions. Rate constants and branching ratios from master equation calculations indicate that for a given temperature and pressure, there is a constant ⟨Δ<i>E</i>_d⟩ that can reproduce results obtained with an <i>E</i>-dependent ⟨Δ<i>E</i>_d⟩. But a constant ⟨Δ<i>E</i>_d⟩ cannot do this for all temperatures and pressures, with larger differences when the barriers for the competing channels differ more. We conclude that when the branching ratio of competitive reactions is sensitive to pressure, including the energy dependence of ⟨Δ<i>E</i>_d⟩ in master equation simulations can make a significant difference in the results.