Unimolecular Rate Constants versus Energy and Pressure as a Convolution of Unimolecular Lifetime and Collisional Deactivation Probabilities. Analyses of Intrinsic Non-RRKM Dynamics

Following work by Slater and Bunker, the unimolecular rate constant versus collision frequency, k_uni(ω,E), is expressed as a convolution of unimolecular lifetime and collisional deactivation probabilities. This allows incorporation of nonexponential, intrinsically non-RRKM, populations of dissociating molecules versus time, N(t)/N(0), in the expression for k_uni(ω,E). Previous work using this approach is reviewed. In the work presented here, the biexponential f₁exp(-k₁t) + f₂exp(-k₂t) is used to represent N(t)/N(0), where f₁k₁ + f₂k₂ equals the RRKM rate constant k(E) and f₁ + f₂ = 1. With these two constraints, there are two adjustable parameters in the biexponential N(t)/N(0) to represent intrinsic non-RRKM dynamics. The rate constant k₁ is larger than k(E) and k₂ is smaller. This biexponential gives k_uni(ω,E) rate constants that are lower than the RRKM prediction, except at the high and low pressure limits. The deviation from the RRKM prediction increases as f₁ is made smaller and k₁ made larger. Of considerable interest is the finding that, if the collision frequency ω for the RRKM plot of k_uni(ω,E) versus ω is multiplied by an energy transfer efficiency factor β_c, the RRKM k_uni(ω,E) versus ω plot may be scaled to match those for the intrinsic non-RRKM, biexponential N(t)/N(0), plots. This analysis identifies the importance of determining accurate collisional intermolecular energy transfer (IET) efficiencies.