Quantum-mechanical tunneling in the H 2 elimination from 2,3-dimethylbutane cation: (CH 3) 2CHCH(CH 3) +2→(CH 3) 2CC(CH 3) +2+H 2. An ab initio molecular orbital study

Abstract

Ab initio molecular orbital calculations were carried out for the H 2 elimination from 2,3-dimethylbutane cation (DMB +) to form tetramethylethylene cation (TME +): (CH 3) 2CHCH(CH 3) + 2→(CH 3) 2CC(CH 3) + 2+H 2. Geometry optimizations and vibrational analyses for DMB +, transition state, and TME + were performed at the UMP2/6-31G(d) level of theory and single-point energies were obtained at the UMP3/6-31G(d) and UMP4(SDTQ)/6-31G(d) levels. Moreover, in order to examine the basis-set dependence of energetics, single-point energies were calculated at the UMP2/6-31G(d,p) and UMP2/6-311G(d,p) levels for the UMP2/6-31G(d) optimized geometries. The calculated barrier height was found to be sensitive to basis sets and it was estimated to be 17.3 kcal mol −1. Thermal rate constants with quantum-mechanical correction factor were calculated using standard transition-state theory. At low temperatures a remarkable deviation from the Arrhenius law was seen and a large isotope effect was obtained by replacing the eliminating H 2 molecule with D 2. The rate constants for the DMB + and deuterated DMB + reactions at 77 K were calculated to be about 10 −9 and 10 −16 s −1, respectively, which are significantly smaller than the observed values of Miyazaki et al. [J. Phys. Chem. 98 (1994) 10767] However, it is expected that using larger basis sets can further improve the calculated values for the barrier height.