How a transition state tightens: The singlet photodissociation of ketene as a test case

The tightening of the transition state as energy increases above the dissociation threshold is studied for the dissociation of singlet ketene. Rate constants and quantum yields have been determined for the photodissociation of ketene to produce CH₂(ã¹A₁)(0,0,0) + CO(X̃ ¹∑⁺)(v=1). At 57, 110, 200, 357, and 490 cm^-1 above this threshold, vibrational branching ratios for the singlet products were measured and compared to theory. Above 100 cm^-1, the experimental values are consistent with the separate statistical ensembles (SSE) and variational RRKM models. CO(v=1,J) photofragment excitation (PHOFEX) spectra were observed up to 300 cm^-1 over the threshold for production of CO(v=1) and used to calculate the total yield of the state probed. The J dependence of these yields is statistical, consistent with the observed ¹CH₂ rotational distributions. Thus, the total CO(v=1) singlet yield and rate constant are determined as a continuous function of energy up to 300 cm^-1. Rate constants are given accurately by phase space theory (PST) up to 35 ± 5 cm^-1. The ab initio rate constants of Klippenstein, East, and Allen match the experimental rate constants from 10 to 6000 cm^-1 well within experimental uncertainty without any adjustment of parameters for the unified statistical model of Miller. Thus the rate appears to be controlled by an inner transition state near 3 Å and the outer PST transition state acting in series with the outer transition state dominating for energies below 50 cm^-1 and the inner for energies above a few hundred cm^-1. From the measured rate constants, an experimental density of states is calculated to be 0.94 times the anharmonic ab initio density of states. This allows the degeneracy g_t of the coupled triplet channels to be determined from the rates at the triplet threshold, g_t = 1.0 ± 0.1. The vibrational branching ratios and product yields for the vibrationally excited triplet products were also estimated and found to be nearly constant over this energy region. These values are about 17% of those predicted for vibrationally adiabatic dynamics in the exit valley after passage through the triplet transition state.