Quantum Instanton Method Research Articles

H Resurface and Hot H Promoted H2 Recombination on Ni(111): Effects of Arrangement, Surface Coverage, and Lattice Motion

Subsurface H can affect catalytic reactivity and selectivity. H resurface and H2 recombination with a subsurface H on Ni(111) were investigated by the quantum instanton method, and the arrangement,...

Physisorbed State Regulates the Dissociation Mechanism of H2O on Ni(100).

Water dissociation is a key step in many industrial catalytic processes. The dissociation of H2O on a rigid Ni(100) surface was investigated by the quantum instanton method with a full-dimensional potential energy surface. The calculated free-energy barrier maps showed that the free-energy barrier varied dramatically with the surface site. The free-energy well map demonstrated that the physisorption well of H2O was existent at all of the surface sites, and H2O could be dissociated by both the direct and steady-state processes. The calculated direct dissociation rate constants at different surface sites decreased rapidly in the order transition state (TS) > bridge > top > hollow. The steady-state dissociation rate constants had the same trend as that of the direct process but the steady-state dissociation rate constant at the top site became the largest at high temperatures. The direct dissociation rate constants were always larger than those of the steady-state process at a given temperature. The calculated kinetic isotope effects for the direct and steady-state processes were extremely large at low temperatures, which was caused by the zero-point energy correction and remarkable quantum tunneling. From low temperature to high temperature, H2O would undergo stable molecular adsorption at the top site, steady-state dissociation at the TS site, direct rupture at the TS site, and direct decomposition at the impact site.

A general non-adiabatic quantum instanton approximation.

We present a general quantum instanton approach to calculating reaction rates for systems with two electronic states and arbitrary values of the electronic coupling. This new approach, which we call the non-adiabatic quantum instanton (NAQI) approximation, reduces to Wolynes theory in the golden rule limit and to a recently proposed projected quantum instanton method in the adiabatic limit. As in both of these earlier theories, the NAQI approach is based on making a saddle point approximation to the time integral of a reactive flux autocorrelation function, although with a generalized definition of the projection operator onto the product states. We illustrate the accuracy of the approach by comparison with exact rates for one dimensional scattering problems and discuss its applicability to more complex reactions.

H2 Dissociation on H-Precovered Ni(100) Surface: Physisorbed State and Coverage Dependence

Hydrogen molecule dissociation on metal surfaces is a prototypical reaction for investigating the gas–surface interaction. To investigate the effect of lattice motion, the embedded cluster model is adopted to construct the quantum Ni(100) lattice, in which 11 Ni atoms are treated quantum mechanically. The direct and steady-state dissociation rates of H2 on H-precovered Ni(100) surface are calculated by quantum instanton method. Both the direct and steady-state dissociation rates on H-precovered Ni(100) are smaller than those on the clean Ni(100). This is because the repulsive interaction between H2 and the preadsorbed H raises the potential energy barrier. Moreover, this repulsive interaction is inversely proportional to the distance between H2 and the preadsorbed H. Owing to the classical relaxation and entropy effect of Ni atoms, the lattice motion promotes H2 dissociation by lowering the free-energy barrier but it hinders H2 recombination by raising the free-energy barrier. There are remarkable kinetic...

Photodissociation of phenol in the adiabatic representation: Tunneling, motions of phenyl ring, and kinetic isotope effects

AbstractThe photodissociation of phenol is a prototype of the photoinduced hydrogen detachment reaction. The dissociation rates of phenol through the excited S1 state are calculated with the quantum instanton method in full dimensionality. The Arrhenius plot of the rates shows that the quantum tunneling dominates the OH bond dissociation at low temperatures. The degrees of freedom of phenyl ring (C6H5) play extremely important roles in the dissociation of phenol. Fixing the phenyl ring at the equilibrium geometry can only provide reliable rates between 400 K and 800 K. The motions of phenyl ring have an impact on enhancing the dissociation by lowering the free energy barrier. The larger the amplitudes of the phenyl ring motions are, the more the free energy barrier will be reduced. The dissociation rates of C6H5OH are much larger than those of C6H5OD, which is due to the zero‐point energy and entropy effects.

H2 Dissociation on H Precovered Ni(111) Surfaces: Coverage Dependence, Lattice Motion, and Arrangement Effects

Hydrogen molecule dissociation on metal surfaces is a prototype reaction to study the gas–surface interaction. The dissociation rate constants of H2 on H atom precovered Ni(111) surfaces are calculated using the quantum instanton method in full dimensionality. Four different arrangements of the preadsorbed H and the dissociated H2, in which the preadsorbed H is located at the nearest (H2/H1–Ni(111)), second-nearest (H2/H2–Ni(111)), third-nearest (H2/H3–Ni(111)), and fourth-nearest (H2/H4–Ni(111)) neighbor sites of the bridge site where the H2 is dissociated, are considered. Compared to the dissociation rates of H2 on a clean Ni(111) surface (H2/Ni(111)), the dissociation rates of H2/H1–Ni(111) are much smaller. For instance, the former is 5.22 times larger than the latter at 300 K. This is because there is a strong repulsive interaction between the preadsorbed H and H2, which hinders the dissociation of H2. The dissociation rates of the four arrangements increase in the order of H2/H1–Ni(111), H2/H2–Ni(11...

The dissociation and recombination rates of CH4 through the Ni(111) surface: The effect of lattice motion.

Methane dissociation is a prototypical system for the study of surface reaction dynamics. The dissociation and recombination rates of CH4 through the Ni(111) surface are calculated by using the quantum instanton method with an analytical potential energy surface. The Ni(111) lattice is treated rigidly, classically, and quantum mechanically so as to reveal the effect of lattice motion. The results demonstrate that it is the lateral displacements rather than the upward and downward movements of the surface nickel atoms that affect the rates a lot. Compared with the rigid lattice, the classical relaxation of the lattice can increase the rates by lowering the free energy barriers. For instance, at 300 K, the dissociation and recombination rates with the classical lattice exceed the ones with the rigid lattice by 6 and 10 orders of magnitude, respectively. Compared with the classical lattice, the quantum delocalization rather than the zero-point energy of the Ni atoms further enhances the rates by widening the reaction path. For instance, the dissociation rate with the quantum lattice is about 10 times larger than that with the classical lattice at 300 K. On the rigid lattice, due to the zero-point energy difference between CH4 and CD4, the kinetic isotope effects are larger than 1 for the dissociation process, while they are smaller than 1 for the recombination process. The increasing kinetic isotope effect with decreasing temperature demonstrates that the quantum tunneling effect is remarkable for the dissociation process.

Thermal Rate Constants for the O(3P) + CH4 → OH + CH3 Reaction: The Effects of Quantum Tunneling and Potential Energy Barrier Shape.

The rate constants and kinetic isotope effects for the O(3P) + CH4 reaction have been investigated with the quantum instanton method in full dimensionality. The calculated rate constants are in good agreement with the experimental values above 400 K, below which the measured values are scattered. Compared to other theoretical approaches, the quantum instanton method predicts the largest quantum tunneling effect, so it gives the largest rate constants at low temperatures. The calculated kinetic isotope effects are always much larger than 1 and increase with decreasing temperature, due to the zero-point energy and quantum tunneling. Our calculations on different potential energy surfaces demonstrate that the potential energy barrier shape dominates the magnitude of quantum tunneling and has a great effect on the kinetic isotope effect.

Ring-polymer instanton theory of electron transfer in the nonadiabatic limit.

We take the golden-rule instanton method derived in the previous paper [J. O. Richardson, R. Bauer, and M. Thoss, J. Chem. Phys. 143, 134115 (2015)] and reformulate it using a ring-polymer instanton approach. This gives equations which can be used to compute the rates of electron-transfer reactions in the nonadiabatic (golden-rule) limit numerically within a semiclassical approximation. The multidimensional ring-polymer instanton trajectories are obtained efficiently by minimization of the action. In this form, comparison with Wolynes' quantum instanton method [P. G. Wolynes, J. Chem. Phys. 87, 6559 (1987)] is possible and we show that our semiclassical approach is the steepest-descent limit of this method. We discuss advantages and disadvantages of both methods and give examples of where the new approach is more accurate.

Dissociation rates of H2 on a Ni(100) surface: the role of the physisorbed state.

The dissociation and recombination rates of physisorbed H2, and the total dissociation rate of gas phase H2 on the rigid Ni(100) surface, as well as the corresponding kinetic isotope effects, are calculated by using the quantum instanton method, together with path integral Monte Carlo and adaptive umbrella sampling techniques. Both the dissociation and recombination rates of physisorbed H2 are dramatically enhanced by the quantum motions of H2 at low temperatures, for instance, the quantum rates are 43 and 7.5 times larger than the classical ones at 200 K, respectively. For the dissociation of gas phase H2, at high temperatures, the H2 can fly over the physisorbed state and dissociate directly, however, at low temperatures, the H2 is first physisorbed and then dissociates under steady state approximation. The total dissociation rate of gas phase H2 can be expressed as a combination of the direct and steady state dissociation rates. It has the form of an inverted bell with a minimum value at about 400 K, and detailed analysis shows that the dissociation of gas phase H2 is dominated by a steady state process below 400 K, however, both the steady state and direct processes are important above 400 K. The calculated kinetic isotope effects reveal that H2 always has larger rates than D2 no matter which dissociative process they undergo.

Effect of Lattice Motion on Dissociation and Recombination Rates of H2 on Ni(100) Surface

The rate constants and kinetic isotope effects of H2 dissociation and recombination on Ni(100) surface are calculated by using the quantum instanton method, together with path integral Monte Carlo and adaptive umbrella sampling techniques. The Ni(100) surface model containing 104 nickel atoms and the potential energy surface based on the embedded diatomics in molecules are used. For the H2 dissociation, the results on the rigid lattice are consistent with experimental data. Compared to the rigid lattice, the classical and quantum motions of the lattice further enhance the dissociation rates by 18 and 49% at 300 K. The calculated kinetic isotope effects show that the H2 always has the largest rate, while the D2 has the smallest one. For the H2 recombination, however, the effects of lattice motions on the rates are different from those for the dissociation, that is, compared to the rigid lattice, both the classical and quantum motions of the lattice lower the recombination rates. The possible mechanism is analyzed by the corresponding free energy profiles.

Quantum calculations of the temperature dependence of the rate constant and the equilibrium constant for the NH3 + H ⇌ NH2 + H2 reaction

Temperature dependence of the rate constant of the NH3+H→NH2+H2 reaction and its reverse was calculated for 200–1000K temperature range within the quantum instanton method. The potential energy surface PES-1997 was used. Not being of the heavy–light–heavy type, the hydrogen abstraction by another hydrogen allows safe neglection of recrossing effects. Curvature of the Arrhenius plot is present at low temperatures, which is indicative of quantum effects due to light hydrogen atoms. Additionally, a fully quantum mechanical method of calculating the temperature dependence of the equilibrium constant is presented and applied. The method is based upon path-integral Monte Carlo simulations and subsequently on thermodynamic integration.

Temperature dependence of the rate constant of ionic analogs of H + H2 → H2 + H reaction by quantum instanton method

AbstractRate constant ratios k(T)/k(1,500K) for two symmetrical reactions H− + H2 → H2 + H− and H+ + H2 → H2 + H+ are reported. Direct method based on quantum instanton approximation for evaluation of the temperature dependence of the quantum‐mechanical reaction rate constant is used. Implementation of the theory involves thermodynamic integration and path integral Monte Carlo method. Results of anionic case shows resemblance to neutral case, whereas cationic case is significantly different and below 1,000K rate constant shows strong deviation form linearity of Arrhenius plot due to high activation barrier. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012