Population distributions in the vibrational deactivation of benzene and benzene-d6. First and second moments derived from two-color infrared fluorescence measurements

Abstract

Time-resolved two-color infrared fluorescence (IRF) from highly vibrationally excited benzene and benzene-d6 has been used to determine means and variances of the excited molecule population distributions over the majority of the energy range during deactivation via collisional energy transfer to unexcited molecules. These measurements extend the IRF technique to produce information about the first two moments of energy transfer induced population distributions present during the collisional deactivation process. A simple means of analysis of IRF from multiple emission bands is presented, which in principle yields information about higher moments, as well as increasingly precise determination of lower moments. Results from this analysis are independent of any assumed models for collisional energy transfer. In the experiments, simultaneous monitoring of IRF from the C–H (C–D) stretching mode fundamental region at ≈3060 cm−1 (≈2290 cm−1) and first overtone region at ≈6000 cm−1 (≈4500 cm−1), allows independent observation of two subsets of the total population of excited molecules, each containing the vibrational energy required to emit photons in the observed bands. Similar results are obtained from analysis of the time- and wavelength-resolved Δv= −1 C–H stretch emission spectrum of highly excited benzene-h6 as it is deactivated by collisions. The two-color results are shown to provide meaningful information about the first two moments of the energy population distribution over much of the energy range. Knowledge of the population distribution is important since it results directly from the form of Pc(E′, E), the step size probability distribution function for collisional energy transfer. Master equation simulations are used together with these results in order to derive some limitations on the possible forms of Pc(E′, E).