Theoretical Analysis of the Unimolecular Gas-Phase Decompositions of the Propane Molecular Ion

Abstract

Although the propane ion has been a long-standing model for RRKM/QET calculations, the validity of the transition states utilized in such calculations was unclear. To remedy this, we use potential energy barriers and harmonic vibrational frequencies calculated at the ab initio QCISD(T)/6-311+G(2d,2p) and UMP2/6-31G(d) levels of theory, respectively, as parameters to compute rate constants versus internal energy curves for the losses of the H atom, CH3•, and CH4 from the propane ion by a RRKM procedure. The results agree reasonably with experimental ones. The ab initio calculations confirm that H atom loss occurs from the middle carbon of the propane ion to form the sec-propyl cation. The rate constant of H atom loss increases slowly with increasing internal energy, which is surprising for a simple bond cleavage. This is shown to be due to the changes in vibrational frequencies between the propane ion and the transition state being small for this reaction. Methane elimination occurs in a stepwise fashion through a methyl radical−ethyl ion complex. Low frequencies arising from CC bond elongation in the rate determining step for this reaction give a faster rise in rate constant with increasing internal energy for this reaction than for H atom loss, despite the former reaction being an elimination. A number of frequencies are very low in the transition state for CH3• loss, taken to be a loosely bound methyl radical−ethyl ion complex. This gives a very rapid rise in the rate constant of this simple CC bond cleavage with increasing internal energy. Losses of single atoms by simple cleavages are predicted to be slower than most types of competing reactions due to changes in vibrational frequencies between the reactant and transition states being relatively small.