Quantum effects in thermal reaction rates at metal surfaces

Six-dimensional quantum dynamics of an Eley-Rideal reaction between gaseous and adsorbed hydrogen atoms on Cu(111)

In the form of direct abstraction of a surface adsorbate by a gaseous projectile, the Eley-Rideal (ER) reaction at the gas-surface interface manifests interesting dynamics. Unfortunately, high-dimensional quantum dynamical (QD) studies for ER reactions remain very challenging, which demands a large configuration space and the coordinate transformation of wavefunctions. Here, we report the first six-dimensional (6D) fully coupled quantum scattering method for studying the ER reaction between gas phase H(D) atoms and adsorbed D(H) atoms on a rigid Cu(111) surface. Reaction probabilities and product rovibrational state distributions obtained by this 6D model are found to be quite different from those obtained by reduced-dimensional QD models, demonstrating the high-dimensional nature of the ER reaction. Using two distinct potential energy surfaces (PESs), we further discuss the influence of the PES on the calculated product vibrational and rotational state distributions, in comparison with experimental results. The lateral corrugation and the exothermicity of the PES are found to play a critical role in controlling the energy disposal in the ER reaction.

Spiers Memorial Lecture: New directions in molecular scattering

The field of molecular scattering is reviewed as it pertains to gas-gas as well as gas-surface chemical reaction dynamics. We emphasize the importance of collaboration of experiment and theory, from which new directions of research are being pursued on increasingly complex problems. We review both experimental and theoretical advances that provide the modern toolbox available to molecular-scattering studies. We distinguish between two classes of work. The first involves simple systems and uses experiment to validate theory so that from the validated theory, one may learn far more than could ever be measured in the laboratory. The second class involves problems of great complexity that would be difficult or impossible to understand without a partnership of experiment and theory. Key topics covered in this review include crossed-beams reactive scattering and scattering at extremely low energies, where quantum effects dominate. They also include scattering from surfaces, reactive scattering and kinetics at surfaces, and scattering work done at liquid surfaces. The review closes with thoughts on future promising directions of research.

Optimization of Quantum Nuclei Positions with the Adaptive Nuclear-Electronic Orbital Approach

The use of multicomponent methods has become increasingly popular over the last years. Under this framework, nuclei (commonly protons) are treated quantum mechanically on the same footing as the electronic structure problem. Under the use of atomic-centered orbitals, this can lead to some complications as the ideal location of the nuclear basis centers must be optimized. In this contribution, we propose a straightforward approach to determine the position of such centers within the self-consistent cycle of a multicomponent calculation, making use of individual proton charge centroids. We test the method on model systems including the water dimer, a protonated water tetramer, and a porphine system. Comparing to numerical gradient calculations, the adaptive nuclear-electronic orbital (NEO) procedure is able to converge the basis centers to within a few cents of an Ångström and with less than 0.1 kcal/mol differences in absolute energies. This is achieved in one single calculation and with a small added computational effort of up to 80% compared to a regular NEO- self-consistent field run. An example application for the human transketolase proton wire is also provided.

In situ observation of the on-surface thermal dehydrogenation of n-octane on Pt(111)

The catalytic dehydrogenation of alkanes constitutes a key step for the industrial conversion of these inert sp3-bonded carbon chains into other valuable unsaturated chemicals. To this end, platinum-based materials are among the most widely used catalysts. In this work, we characterize the thermal dehydrogenation of n-octane (n-C8H18) on Pt(111) under ultra-high vacuum using synchrotron-radiation X-ray photoelectron spectroscopy, temperature-programmed desorption and scanning tunneling microscopy, combined with ab initio calculations. At low activation temperatures, two different dehydrogenation stages are observed. At 330 K, n-C8H18 effectively undergoes a 100% regioselective single C-H bond cleavage at one methyl end. At 600 K, the chemisorbed molecules undergo a double dehydrogenation, yielding double bonds in their carbon skeletons. Diffusion of the dehydrogenated species leads to the formation of carbon molecular clusters, which represents the first step towards poisoning of the catalyst. Our results reveal the chemical mechanisms behind the first stages of alkane dehydrogenation on a platinum model surface at the atomic scale, paving the way for designing more efficient dehydrogenation catalysts.

Ring Polymer Molecular Dynamics Approach to Quantum Dissociative Chemisorption Rates

A ring polymer molecular dynamics (RPMD) method is proposed for the calculation of the dissociative chemisorption rate coefficient on surfaces. The RPMD rate theory is capable of handling quantum effects such as the zero-point energy and tunneling in dissociative chemisorption, while it relies on classical trajectories for the simulation. Applications to H2 dissociative chemisorption are demonstrated. For the highly activated process on Ag(111), strong deviations from Arrhenius behavior are found at low temperatures and attributed to tunneling. On Pt(111), where the dissociation has a barrierless pathway, the RPMD rate coefficient is found to agree with the experimentally derived thermal sticking coefficient within a factor of 2 over a large temperature range. Significant quantum effects are also found.

Spin-dependent reactivity and spin-flipping dynamics in oxygen atom scattering from graphite

The formation of two-electron chemical bonds requires the alignment of spins. Hence, it is well established for gas-phase reactions that changing a molecule's electronic spin state can dramatically alter its reactivity. For reactions occurring at surfaces, which are of great interest during, among other processes, heterogeneous catalysis, there is an absence of definitive state-to-state experiments capable of observing spin conservation and therefore the role of electronic spin in surface chemistry remains controversial. Here we use an incoming/outgoing correlation ion imaging technique to perform scattering experiments for O(³P) and O(¹D) atoms colliding with a graphite surface, in which the initial spin-state distribution is controlled and the final spin states determined. We demonstrate that O(¹D) is more reactive with graphite than O(³P). We also identify electronically nonadiabatic pathways whereby incident O(¹D) is quenched to O(³P), which departs from the surface. With the help of molecular dynamics simulations carried out on high-dimensional machine-learning-assisted first-principles potential energy surfaces, we obtain a mechanistic understanding for this system: spin-forbidden transitions do occur, but with low probabilities.

First-principles surface reaction rates by ring polymer molecular dynamics and neural network potential: role of anharmonicity and lattice motion

Elementary gas-surface processes are essential steps in heterogeneous catalysis. A predictive understanding of catalytic mechanisms remains challenging due largely to difficulties in accurately characterizing the kinetics of such steps. Experimentally, thermal rates for elementary surface reactions can now be measured using a novel velocity imaging technique, providing a stringent testing ground for ab initio rate theories. Here, we propose to combine ring polymer molecular dynamics (RPMD) rate theory with state-of-the-art first-principles-determined neural network potential to calculate surface reaction rates. Taking NO desorption from Pd(111) as an example, we show that the harmonic approximation and the neglect of lattice motion in the commonly-used transition state theory overestimates and underestimates the entropy change during the desorption process, respectively, leading to opposite errors in rate coefficient predictions and artificial error cancellations. Including anharmonicity and lattice motion, our results reveal a generally neglected surface entropy change due to significant local structural change during desorption and obtain the right answer for the right reasons. Although quantum effects are found to be less important in this system, the proposed approach establishes a more reliable theoretical benchmark for accurately predicting the kinetics of elementary gas-surface processes.

Factorized Electron-Nuclear Dynamics with an Effective Complex Potential

We present a quantum dynamics approach for molecular systems based on wave function factorization into components describing the light and heavy particles, such as electrons and nuclei. The dynamics of the nuclear subsystem can be viewed as motion of the trajectories defined in the nuclear subspace, evolving according to the average nuclear momentum of the full wave function. The probability density flow between the nuclear and electronic subsystems is facilitated by the imaginary potential, derived to ensure a physically meaningful normalization of the electronic wave function for each configuration of the nuclei, and conservation of the probability density associated with each trajectory in the Lagrangian frame of reference. The imaginary potential, defined in the nuclear subspace, depends on the momentum variance in the nuclear coordinates averaged over the electronic component of the wave function. An effective real potential, driving the dynamics of the nuclear subsystem, is defined to minimize motion of the electronic wave function in the nuclear degrees of freedom. Illustration and the analysis of the formalism are given for a two-dimensional model system of vibrationally nonadiabatic dynamics.

Binding Energy and Diffusion Barrier of Formic Acid on Pd(111)

Velocity-resolved kinetics is used to measure the thermal rate of formic acid desorption from Pd(111) between 228 and 273 K for four isotopologues: HCOOH, HCOOD, DCOOH, DCOOD. Upon molecular adsorption, formic acid undergoes decomposition to CO₂ and H₂ and thermal desorption. To disentangle the contributions of individual processes, we implement a mass-balance-based calibration procedure from which the branching ratio between desorption and decomposition for formic acid is determined. From experimentally derived elementary desorption rate constants, we obtain the binding energy 639 ± 8 meV and the diffusion barrier 370 ± 130 meV using the detailed balance rate model (DBRM). The DBRM explains the observed kinetic isotope effects.

Analysis of Temperature-Programmed Desorption via Equilibrium Thermodynamics

Temperature-programmed desorption (TPD) experiments in surface science are usually analyzed using the Polanyi-Wigner equation and/or transition-state theory. These methods are far from straightforward, and the determination of the pre-exponential factor is often problematic. We present a different method based on equilibrium thermodynamics, which builds on an approach previously used for TPD by Kreuzer et al. (Surf. Sci. 1988). Equations for the desorption rate are presented for three different types of surface-adsorbate interactions: (i) a 2D ideal hard-sphere gas with a negligible diffusion barrier, (ii) an ideal lattice gas, that is, fixed adsorption sites without interaction between the adsorbates, and (iii) a lattice gas with a distribution of (site-dependent) adsorption energies. We show that the coverage dependence of the sticking coefficient for adsorption at the desorption temperature determines whether the desorption process can be described by first- or second-order kinetics. The sticking coefficient at the desorption temperature must also be known for a quantitative determination of the adsorption energy, but it has a rather weak influence (like the pre-exponential factor in a traditional TPD analysis). Quantitative analysis is also influenced by the vibrational contributions to the energy and entropy. For the case of a single adsorption energy, we provide equations to directly convert peak temperatures into adsorption energies. These equations also provide an approximation of the desorption energy in cases that cannot be described by a fixed pre-exponential factor. For the case of a distribution of adsorption energies, the desorption spectra cannot be considered a superposition of desorption spectra corresponding to the different energies. Nevertheless, we present a method to extract the distribution of adsorption energies from TPD spectra, and we rationalize the energy resolution of TPD experiments. The analytical results are complemented by a program for simulation and analysis of TPD data.

Adsorption and Absorption Energies of Hydrogen with Palladium

Thermal recombinative desorption rates of HD on Pd(111) and Pd(332) are reported from transient kinetic experiments performed between 523 and 1023 K. A detailed kinetic model accurately describes the competition between recombination of surface-adsorbed hydrogen and deuterium atoms and their diffusion into the bulk. By fitting the model to observed rates, we derive the dissociative adsorption energies (E _0, ads ^H₂ = 0.98 eV; E _0, ads ^D₂ = 1.00 eV; E _0, ads ^HD = 0.99 eV) as well as the classical dissociative binding energy ϵ_ads = 1.02 ± 0.03 eV, which provides a benchmark for electronic structure theory. In a similar way, we obtain the classical energy required to move an H or D atom from the surface to the bulk (ϵ_sb = 0.46 ± 0.01 eV) and the isotope specific energies, E _0, sb ^H = 0.41 eV and E _0, sb ^D = 0.43 eV. Detailed insights into the process of transient bulk diffusion are obtained from kinetic Monte Carlo simulations.