Accurate prediction of experimental free energy of activation barriers for the aliphatic-Claisen rearrangement through DFT calculations

A benchmarking study was performed to determine DFT methods that can accurately predict free energy of activation barriers (ΔG‡) for the aliphatic-Claisen rearrangement. Accurate experimental ΔG‡ values from eight gas-phase literature reactions were used for validation. Previously applied density functionals for this system and its variants, along with the Minnesota 2005/2006/2008 functionals, were tested using the 6-31+G** basis set. On B3LYP/6-31+G** geometries, M08-HX afforded the best results and gave a sevenfold increase in accuracy over the energies predicted by the robust B3LYP functional, which is routinely used for Claisen rearrangements. An investigation of whether improvements in ΔG‡ predictions could occur by optimizing structures with newer functionals then became of interest. For geometry validation, optimization and Bigeleisen–Mayer KIE calculations with M05/6-31+G** and M05-2X/6-31+G** for the rearrangement of allyl vinyl ether were performed and compared to previous experimental data, and both were found to predict new valid Claisen transition structures. All structures were then reoptimized, and it was found that M05-2X/6-31+G** geometries afforded worthwhile enhancement, where M08-HX/6-31+G**//M05-2X/6-31+G** yielded the most accurate and reliable results with a mean unsigned error (MUE) of 0.3 kcal/mol relative to experimental ΔG‡ values. These results should prove useful for Claisen rearrangement studies, and this is the first instance that the Minnesota 2008 functionals have been applied to the study of sigmatropic reactions.