Association rate constants for reactions between resonance-stabilized radicals: C₃H₃ + C₃H₃, C₃H₃ + C₃H₅, and C₃H₅ + C₃H₅

Reactions between resonance-stabilized radicals play an important role in combustion chemistry. The theoretical prediction of rate coefficients and product distributions for such reactions is complicated by the fact that the initial complex-formation steps and some dissociation steps are barrierless. In this paper direct variable reaction coordinate transition state theory (VRC-TST) is used to predict accurately the association rate constants for the self and cross reactions of propargyl and allyl radicals. For each reaction, a set of multifaceted dividing surfaces is used to account for the multiple possible addition channels. Because of their resonant nature the geometric relaxation of the radicals is important. Here, the effect of this relaxation is explicitly calculated with the UB3LYP/cc-pvdz method for each mutual orientation encountered in the configurational integrals over the transition state dividing surfaces. The final energies are obtained from CASPT2/cc-pvdz calculations with all π-orbitals in the active space. Evaluations along the minimum energy path suggest that basis set corrections are negligible. The VRC-TST approach was also used to calculate the association rate constant and the corresponding number of states for the C₆H₅ + H → C₆H₆ exit channel of the C₃H₃ + C₃H₃ reaction, which is also barrierless. For this reaction, the interaction energies were evaluated with the CASPT2(2e,2o)/cc-pvdz method and a 1-D correction is included on the basis of CAS+1+2+QC/aug-cc-pvtz calculations for the CH₃ + H reference system. For the C₃H₃ + C₃H₃ reaction, the VRC-TST results for the energy and angular momentum resolved numbers of states in the entrance channels and in the C₆H₅ + H exit channel are incorporated in a master equation simulation to determine the temperature and pressure dependence of the phenomenological rate coefficients. The rate constants for the C₃H₃ + C₃H₃ and C₃H₅ + C₃H₅ self-reactions compare favorably with the available experimental data. To our knowledge there are no experimental rate data for the C₃H₃ + C₃H₅ reaction.