Ring Polymer Molecular Dynamics in Gas–Surface Reactions: Inclusion of Quantum Effects Made Simple

Abstract

Accurately modeling gas-surface collision dynamics presents a great challenge for theory, especially in the low energy (or temperature) regime where quantum effects are important. Here, a path integral based non-equilibrium ring polymer molecular dynamics (NE-RPMD) approach is adapted to calculate dissociative initial sticking probabilities (S0) of H2 on Cu(111) and D2O on Ni(111), revealing distinct quantum nature in the two benchmark surface reactions. NE-RPMD successfully captures quantum tunneling in H2 dissociation at very low energies, where the quasi-classical trajectory (QCT) method suddenly fails. Additionally, QCT substantially overestimates S0 of D2O due to severe zero point energy (ZPE) leakage, even at collision energies higher than the ZPE-corrected barrier. Instead, NE-RPMD predicts S0 values of D2O in much improved agreement with reference results obtained by the quantum wavepacket method with reasonable corrections of the thermal contribution. Our results suggest NE-RPMD as a promising approach to model quantum effects in gas-surface reactions. TOC graphic3 Dissociative adsorption of small molecules at surfaces is the initial and often rate-limiting step in many interfacial processes such as heterogeneous catalysis and corrosion. Initial sticking probability (S0) is an important observable to reveal the adsorption mechanism and dynamics at solid surfaces, which can be now precisely measured as a function of incidence energy by molecular beam experiments 1-2 . S0 can be 10 -5 or even lower at low energies in many highly activated systems, e.g. methane and water dissociative chemisorption on metal surfaces 1, 3 , representing indispensable steps in methane steaming reforming. Given the large number of degrees of freedom (DOFs), however, it is very challenging to accurately predict S0 from first-principles calculations.Ideally, given an accurate global potential energy surface (PES), exact quantum initial sticking probabilities can be extracted by fully-coupled quantum dynamical (QD) methods, including both time-dependent 4-6 and time-independent 7 implementations. While such molecule-surface PESs can be now routinely developed 8-9 , high-dimensional QD calculations remain extremely difficult and are limited to involve at most nine molecular DOFs so far 10 , due to their poor scaling with dimensionality. Alternatively, the quasiclassical trajectory (QCT) method is much more efficient to model surface reaction dynamics and visualize the associated mechanism 4 . In QCT calculations, the zero point energy (ZPE) of the reactant is approximately included, while the atomic motion is evolved classically. Such QCT applications in H2 activated dissociation on various metal surfaces do reproduce the QD calculated S0 values above the ZPE-corrected barrier quite well 4, 11 .When explicit PESs are unavailable, ab initial molecular dynamics (AIMD) simulations, in which the energies and forces are calculated on-the-fly, have also been performed to study surface reactions 12 . Although AIMD is computationally expen...

Computational approaches to dissociative chemisorption on metals: towards chemical accuracy

“…133,596 There are now numerous instances in which initial-state resolved reaction probabilities computed with QCT have been compared with QD results for a diatomic molecule reacting on a metal surface to assess the accuracy of QCT. Examples include H 2 + Cu(111), 159,597 Ru(0001), 151 Ni(111), 476 Pd(111), 158 Pt(111), 156 Pt(211), 48 and D 2 + Ag (111). 186 Generally, very good agreement is obtained.…”

Nuclear quantum effects in state-selective scattering from ring polymer molecular dynamics

“…It incorporates ZPE effects and does not suffer from ZPE leakage. [49][50][51] Furthermore, it can incorporate some tunneling effects due to the extension of the ring polymer that can stretch over a barrier and thus lower the effective barrier height. 52 RPMD has been especially successful for the calculations of thermal rate constants in the form of RPMD rate theory.…”

“…55 Further numerical tests showed that one can expect similar accuracy of RPMD for calculations with equilibrium and non-equilibrium initial conditions. 55 Very recently, the non-equilibrium initial conditions have been used to obtain microcanonical rate constants from RPMD simulations; 50,57 however, initial state-selectivity could not be addressed in these works.…”

State‐selective cross sections from ring polymer molecular dynamics

“…ZPE effects are incorporated through the harmonic springs connecting the beads, and RPMD therefore respects ZPE constraints and does not suffer from ZPE leakage. [61][62][63] Tunneling effects are also incorporated due to the finite extension of the ring polymer, which can stretch over a barrier and therefore lower its effective height. [54,55,[64][65][66] Originally, RPMD was formulated for the calculation of real-time correlation functions associated with equilibrium initial conditions.…”

“…[75][76][77] Very recently, the nonequilibrium initial conditions have been used to obtain microcanonical rate constants from RPMD simulations; however, initial state selectivity could not be addressed in these works. [82,62] We have proposed an efficient approach that combines the RPMD approach with QCT simulations to obtain initial state-selective cross sections for bimolecular reactions. [83] Initial state-selective cross sections for the Mu/H/D + H 2 (ν = 0,1) reactions were calculated close to the threshold energy.…”