DFT and SISSO studies on the CO₂ cycloaddition reaction to ethylene oxide catalyzed by intraframework M(<scp>ii</scp>)-BEA zeolites

CO₂ cycloaddition with EO over M(II)-intraframework BEA zeolites, with and without TMAI as a co-catalyst, is investigated using the M06-L functional. Without a co-catalyst, the catalytic process occurs through a concerted mechanism. The activation energy is calculated to be 39.9, 38.9, 38.6, and 39.6 kcal mol^-1 for M-DeAlBEA zeolites (M = Ni, Cu, Zn, and Mg), respectively. In the presence of the co-catalyst, the catalytic process proceeds through three consecutive steps: ring opening, CO₂ activation, and ring closure, with the latter being the rate-determining step (RDS) of the reaction. The incorporation of TMAI plays a crucial role in activating EO and CO₂, leading to a more kinetically favorable formation of ethylene carbonate compared to the concerted pathway. From the energy span model, the activation energies of the RDS for the stepwise CO₂ cycloaddition are 16.8, 24.7, 14.7, and 14.1 kcal mol^-1, respectively. The SISSO algorithm has been employed to develop a mathematical expression for predicting the highest activation energy required for EC production <i>via</i> two pathways. The highest activation energy for CO₂ cycloaddition can be approximated using the molecular orbital (MO) energies of the zeolite and co-catalyst, along with the EO and CO₂ adsorption free energies. The SISSO-derived activation energies closely match the DFT-calculated values, achieving an <i>R</i>² value of 0.998 and an RMSE of 1.52 kcal mol^-1.