Two-dimensional ring polymer molecular dynamics determination of the MnO⁺ + H₂/D₂ reaction rates on a Δ-machine learned potential energy surface

In this work, we investigate the impact of nuclear quantum effects in the kinetics of the MnO⁺ + H₂ reaction, a prototypical system for gas-phase H₂ activation by transition metal oxide ions. The DFT based potential energy surfaces (PESs) for the lowest-lying quintet and septet spin states reported in our previous work [Y. Liu <i>et al.</i>, <i>J. Phys. Chem. A</i>, 2025, <b>129</b>, 6306-6314] are improved by 2953 newly calculated CCSD(T)/AVDZ points using a delta-machine learning (Δ-ML) method. To examine nuclear quantum effects, the rate coefficients are computed using ring-polymer molecular dynamics (RPMD). Due to the mechanistic complexity of the reaction, two reaction coordinates are necessary to map out the free-energy surface and an extended RPMD rate theory is developed. The calculated RPMD rate coefficients on the new PES are in better agreement with experimental data. The calculated kinetic isotope effects (KIEs) range from 1.6 to 1.8, also in good agreement with the experimental values. In addition, the converged RPMD rate coefficients are 2.3 to 3.1 times higher than their classical counterparts across the studied temperature range, suggesting the presence of moderate nuclear quantum effects in this reaction.