The 1,5-H-shift in 1-butoxy: A case study in the rigorous implementation of transition state theory for a multirotamer system

The rigorous implementation of transition state theory (TST) for a reaction system with multiple reactant rotamers and multiple transition state conformers is discussed by way of a statistical rate analysis of the 1,5-H-shift in 1-butoxy radicals, a prototype reaction for the important class of H-shift reactions in atmospheric chemistry. Several approaches for deriving a multirotamer TST expression are treated: oscillator versus (hindered) internal rotor models; distinguishable versus indistinguishable atoms; and direct count methods versus degeneracy factors calculated by (simplified) direct count methods or from symmetry numbers and number of enantiomers, where applicable. It is shown that the various treatments are fully consistent, even if the TST expressions themselves appear different. The 1-butoxy H-shift reaction is characterized quantum chemically using B3LYP-DFT; the performance of this level of theory is compared to other methods. Rigorous application of the multirotamer TST methodology in an harmonic oscillator approximation based on this data yields a rate coefficient of k(298 K,1 atm)=1.4x10(5) s(-1), and an Arrhenius expression k(T,1 atm)=1.43x10(11) exp(-8.17 kcal mol(-1)/RT) s(-1), which both closely match the experimental recommendations in the literature. The T-dependence is substantially influenced by the multirotamer treatment, as well as by the tunneling and fall-off corrections. The present results are compared to those of simplified TST calculations based solely on the properties of the lowest energy 1-butoxy rotamer. (C) 2003 American Institute of Physics.