Machine learning thermodynamic perturbation theory offers accurate activation free energies at the RPA level for alkene isomerization in zeolites

Abstract

The determination of accurate free energy barriers for reactions catalyzed by proton-exchanged zeolites by quantum chemistry approaches is a challenge. While \textit{ab initio} molecular dynamics is often required to sample correctly the various states described by the system, the level of theory also has a crucial impact. In the present work, we report the determination of accurate barriers for a type B isomerization of a monobranched C7 alkene (4-methyl-hex-1-ene) into a dibranched tertiary cation inside a protonated chabazite zeolite. This is done by using the Machine Learning Thermodynamic Perturbation Theory (MLPT) at the Random Phase Approximation (RPA) level, on the basis of blue-moon sampling dynamic data obtained at the Generalized Gradient Approximation (GGA) level (PBE+D2). The compararizon of PBE+D2 and RPA profiles shows that the former overstabilizes cationic intermediates with respect to neutral ones. The transition state of the isomerization is a non-classical edge protonated cyclopropane, which stabilization is, according to our RPA results, lower than that of the π-complex, but higher than that of the classical tertiary carbenium ion, decreasing thus the backward isomerization barrier. Applying the MLPT approach to recompute the free energy barriers with various dispersion correction schemes to the PBE energies shows that none of the schemes is sufficient to improve both the forward and backward barriers with respect to the RPA reference. These data complement previously determined alkene cracking barriers [Rey et al., Angew. Chem., Int. Ed., 2024, 63, e202312392], thanks to which it is possible to compare the presently determined barriers with reference experimental data. The agreement with experiments is significantly improved at the RPA with respect to GGA. Chemical accuracy is approached (maximum deviation of 6.4 kJ/mol), opening the door to predictive kinetic modelling starting from first principles approaches.