A Theoretical Study on the Mechanism of the Superacid-Catalyzed Unimolecular Isomerization of<i>n</i>-Alkanes and<i>n</i>-Alkenes. Comparison between ab Initio and Density Functional Results

The mechanism of the branching rearrangement of the 2-pentyl cation has been studied theoretically using both ab initio and density functional theory based methods which include electron correlation and extended basis sets. Two different reaction paths have been considered. In one of them the secondary linear cation is converted through a protonated cyclopropane ring into the secondary branched cation, which is converted into the tertiary cation by a 1,2-H shift. In the other one the secondary linear cation is directly converted into the tertiary cation through the primary cation. Comparison of the calculated activation energies for both reaction paths with the experimental value indicates that the studied reaction occurs via the first mechanism. It has also been found that the protonated 1,2-dimethylcyclopropane ring is not a common intermediate for the reaction, because it is a transition state and not a minimum on the potential energy surface of C5H11+. In relation with the performance of DFT methods it has been found that the local SVWN and nonlocal BP86 and B3P86 optimized geometries are in excellent agreement with the MP2 structures, while the BLYP method tends to reproduce the HF results. From an energetic point of view, the DFT-calculated barrier heights are in better agreement with experiment than the ab initio values.