Unbiased molecular dynamics for the direct determination of catalytic reaction times : paving the way beyond transition state theory

TL;DR

This work addresses the challenge of computing catalytic reaction rates beyond Transition State Theory by employing the Hill relation, which connects flux and committor probabilities to yield exact rates for stochastic dynamics. It couples AMS with ML-interatomic potentials, enabling feasible, unbiased estimation of reaction rates in complex systems. Two case studies—water formation on gamma-alumina and protonated isobutanol dehydration in the gas phase—demonstrate consistency with DFT results and reveal dynamical effects that TST can miss, while also illustrating the importance of robust CV construction. The framework promises to extend accurate rate constant calculations to more realistic catalytic environments (e.g., surfaces, zeolites) where traditional methods are computationally prohibitive, by leveraging MLIPs and path-sampling techniques to capture realistic reaction pathways and selectivity.

Abstract

This study address the computational determination of catalytic reaction rates by moving beyond traditional Transition State Theory (TST), addressing its limitations in complex systems. The Hill relation framework, integrated with Adaptive Multilevel Splitting (AMS), offers exact rate constants for stochastic dynamics, overcoming TST's assumptions and limitations such as recrossings and post-transition state bifurcations. Two case studies validate the approach: water formation on γ-alumina and protonated isobutanol dehydration in the gas phase, demonstrating consistency with DFT results and highlighting the importance of dynamical effects. This framework provides a robust, computationally feasible methodology for studying complex catalytic processes.

Figures (4)

• Figure 1: Schematic representation of (a) a loop trajectory starting in the reactant basin $R$, exiting and re-entering multiple times. The purple dot marks the first crossing of $\partial R_\varepsilon$ after leaving $R$ and (b) splitting estimators with interfaces $\Sigma_i$ taken as iso-levels of a reaction coordinate $\xi$. The reactant basin $R$ and product basin $P$ are represented as circles. Reactive trajectories (green) cross all interfaces and end in $P$, while non-reactive ones (orange, blue) return to $R$ after partial progress (the orange trajectory crosses $\Sigma_1$ but not $\Sigma_2$).
• Figure 2: $A_1$ (left) and dissociated water $D_1D_3$ (right) structures. Color legend: Grey: Al, Red: O, White: H.
• Figure 3: Key intermediates and saddle points (SP) involved in the transformation of two conformers ($c_1$ and $c_2$) of the protonated isobutanol into linear or branched butene in gaz phase. The curved arrows on top of the molecules schematically represent the motion leading to the various transformation observed in MD trajectories. Color legend: Grey: C, Red: O, White: H.
• Figure 4: Projection of 3D features on (a) dimensions 1 and 2, (b) dimensions 1 and 3, (c) dimensions 2 and 3, obtained after training the permutation invariant AE on all the training configurations (a subset of them are represented in blue). Additionally, the features of one (DH)I2 saddle points $\to$2BuOH2+ trajectory (red), one (DH)I2 saddle points $\to$iBuOH2+-$c_2$ (orange), one (DH)I2 saddle points $\to$ secondary cation (purple), one (DH)I1 saddle points $\to$iBuOH2+-$c_1$ (green), one (DH)I1 saddle points $\to$ tertiary cation (brown) are plotted on top. The (DH)I1 and (DH)I2 saddle points are plotted as black "x" and "+".