Nuclear quantum effects on zeolite proton hopping kinetics explored with machine learning potentials and path integral molecular dynamics

Abstract

Proton hopping is a key reactive process within zeolite catalysis. However, the accurate determination of its kinetics poses major challenges both for theoreticians and experimentalists. Nuclear quantum effects (NQEs) are known to influence the structure and dynamics of protons, but their rigorous inclusion through the path integral molecular dynamics (PIMD) formalism was so far beyond reach for zeolite catalyzed processes due to the excessive computational cost of evaluating all forces and energies at the Density Functional Theory (DFT) level. Herein, we overcome this limitation by training first a reactive machine learning potential (MLP) that can reproduce with high fidelity the DFT potential energy surface of proton hopping around the first Al coordination sphere in the H-CHA zeolite. The MLP offers an immense computational speedup, enabling us to derive accurate reaction kinetics beyond standard transition state theory for the proton hopping reaction. Overall, more than 0.6 μs of simulation time was needed, which is far beyond reach of any standard DFT approach. NQEs are found to significantly impact the proton hopping kinetics up to ~473 K. Moreover, PIMD simulations with deuterium can be performed without any additional training to compute kinetic isotope effects over a broad range of temperatures.

Computing Surface Reaction Rates by Adaptive Multilevel Splitting Combined with Machine Learning and Ab Initio Molecular Dynamics

“…This issue might be alleviated by the use of machine learning force fields (MLFFs), which can approach the accuracy of DFT force calculations at a much smaller computational cost. It also provides the opportunity to accurately describe nuclear quantum effects using path integral molecular dynamics such as in ref 69. Some active learning schemes to train MLFFs have been proposed recently, and they could articulate well with the present method.…”

Operando Modeling of Zeolite-Catalyzed Reactions Using First-Principles Molecular Dynamics Simulations

“…However, we recently performed a proof-of-concept study where the forces were evaluated using an MLP, which made it possible to obtain the kinetic rate constant directly using the BC approach. 4 In most of the cases, one resorts to the transition state theory (TST) approximation, whereby setting the chances of barrier recrossing to zero, the following expression can be obtained:…”

“…Although such force fields are specifically parametrized to reach high accuracy for a set of systems or conditions, they are often not transferable to other systems . Lastly, there are some notable examples of reactive force fields which allow simulation of reactive events within the field of catalysis, but still the overall outcome depends on the parametrization of the force field. − Interesting new directions are currently being explored to derive machine learning potentials (MLPs), where starting from underlying quantum-mechanical data sets a numerical potential is derived to describe the PES using a nonlinear regression method. − This approach is very promising, but the applications in the field of zeolite catalysis, which is characterized by an enormous complexity at various levels, is nearly nonexistent. ,− We elaborate in Outlook and Future Directions on new possibilities within the field of modeling zeolite catalysis when having access to cheaper methods to evaluate the PES.…”

“…While it is tempting to assume that nuclear quantum effects might not be of major importance in the field of zeolite catalysis, given the relatively higher temperatures involved, it was recently shown that the kinetics of proton hoppings may still be seriously impacted by the inclusion of nuclear quantum effects at temperatures of ca. 473 K. Given the fact that zeolites will also be used in future technologies under milder conditions, it might be interesting to also consider these effects …”

“…473 K. Given the fact that zeolites will also be used in future technologies under milder conditions, it might be interesting to also consider these effects. 4 Referring back to the initial question, namely, how firstprinciples MD methods may help to understand the catalytic function at operating conditions, we further elaborate on the various levels of complexities occurring within catalysis taking place in nanoporous materials. This Perspective focuses primarily on zeolite catalysis; however, many concepts discussed are much more broadly applicable to catalysis taking place in other materials such as metal−organic frameworks and covalent organic frameworks, which all belong to the class of nanoporous materials.…”