Trapping, molecular adsorption, and precursors for nonactivated chemisorption

Modeling Surface Vibrations and Their Role in Molecular Adsorption: A Generalized Langevin Approach

The atomic vibrations of a solid surface can play a significant role in the reactions of surface-bound molecules, as well as their adsorption and desorption. Relevant phonon modes can involve the collective motion of atoms over a wide array of length scales. In this paper, we demonstrate how the generalized Langevin equation can be utilized to describe these collective motions weighted by their coupling to individual sites. Our approach builds upon the generalized Langevin oscillator (GLO) model originally developed by Tully. We extend the GLO by deriving parameters from atomistic simulation data. We apply this approach to study the memory kernel of a model platinum surface and demonstrate that the memory kernel has a bimodal form due to coupling to both low-energy acoustic modes and high-energy modes near the Debye frequency. The same bimodal form was observed across a wide variety of solids of different elemental compositions, surface structures, and solvation states. By studying how these dominant modes depend on the simulation size, we argue that the acoustic modes are frozen in the limit of macroscopic lattices. By simulating periodically replicated slabs of various sizes, we quantify the influence of phonon confinement effects in the memory kernel and their concomitant effect on simulated sticking coefficients.

Reflective epoxy resin/chitosan/PAA composite-functionalized fiber-optic interferometric probe sensor for sensitive heavy metal ion detection

A highly sensitive label-free chemical sensing platform for the detection of various metal ions is demonstrated. The chemical sensor was derived from a single-mode fiber that is inserted into the ceramic tube with epoxy resin (ER) on the end face for reflecting light and forms the Fabry-Perot (F-P) interferometric cavity. Multilayer chitosan (CS)/polyacrylic acid (PAA) were coated on the surface of the epoxy resin and act as the sensitive film. Based on the analysis of the sensing principle and the F-P cavity structure, the parameters were numerically simulated and experimentally evaluated, which enables ease of fabrication and real-time modulation of the cavity length. The sensitivity of sensing Ni²⁺, Zn²⁺, and Na⁺ reached 9.95 × 10^-4 nm ppb^-1, 2.31 × 10^-4 nm ppb^-1, and 4 × 10^-4 nm ppb^-1, respectively, and the sensing results were theoretically analyzed by the Langmuir adsorption model, which corresponds to the surface atom percentage results obtained by SEM and EDS measurements for sensing three types of metal ions. The proposed ER/CS/PAA multilayer film-coated F-P sensor can be employed as a probe, which features label-free, highly sensitivity, real-time monitoring, ease of measurement, stability, and therefore provides a remarkable analytical platform for chemical applications.

Time-dependent density functional theory calculations of electronic friction in non-homogeneous media

The excitation of low-energy electron-hole pairs is one of the most relevant processes in the gas-surface interaction. An efficient tool to account for these excitations in simulations of atomic and molecular dynamics at surfaces is the so-called local density friction approximation (LDFA). The LDFA is based on a strong approximation that simplifies the dynamics of the electronic system: a local friction coefficient is defined using the value of the electronic density for the unperturbed system at each point of the dynamics. In this work, we apply real-time time-dependent density functional theory to the problem of the electronic friction of a negative point charge colliding with spherical jellium metal clusters. Our non-adiabatic, parameter-free results provide a benchmark for the widely used LDFA approximation and allow the discussion of various processes relevant to the electronic response of the system in the presence of the projectile.

H atom scattering from W(110): A benchmark for molecular dynamics with electronic friction

Molecular dynamics with electronic friction (MDEF) at the level of the local density friction approximation (LDFA) has been applied to describe electronically non-adiabatic energy transfer accompanying H atom collisions with many solid metal surfaces. When implemented with full dimensional potential energy and electron density functions, excellent agreement with experiment is found. Here, we compare the performance of a reduced dimensional MDEF approach involving a simplified description of H atom coupling to phonons to that of full dimensional MDEF calculations known to yield accurate results. Both approaches give remarkably similar results for H atom energy loss distributions with a 300 K W(110) surface. At low surface temperature differences are seen; but, quantities like average energy loss are still accurately reproduced. Both models predict similar conditions under which H atoms that have penetrated into the subsurface regions could be observed in scattering experiments.

Molecular dynamics with electronic friction (MDEF) at the level of the local density friction approximation (LDFA) has been applied to describe electronically non-adiabatic energy transfer accompanying H atom collisions with many solid metal surfaces.

Computational approaches to dissociative chemisorption on metals: towards chemical accuracy

We review the state-of-the-art in the theory of dissociative chemisorption (DC) of small gas phase molecules on metal surfaces, which is important to modeling heterogeneous catalysis for practical reasons, and for achieving an understanding of the wealth of experimental information that exists for this topic, for fundamental reasons. We first give a quick overview of the experimental state of the field. Turning to the theory, we address the challenge that barrier heights (E_b, which are not observables) for DC on metals cannot yet be calculated with chemical accuracy, although embedded correlated wave function theory and diffusion Monte-Carlo are moving in this direction. For benchmarking, at present chemically accurate E_b can only be derived from dynamics calculations based on a semi-empirically derived density functional (DF), by computing a sticking curve and demonstrating that it is shifted from the curve measured in a supersonic beam experiment by no more than 1 kcal mol^-1. The approach capable of delivering this accuracy is called the specific reaction parameter (SRP) approach to density functional theory (DFT). SRP-DFT relies on DFT and on dynamics calculations, which are most efficiently performed if a potential energy surface (PES) is available. We therefore present a brief review of the DFs that now exist, also considering their performance on databases for E_b for gas phase reactions and DC on metals, and for adsorption to metals. We also consider expressions for SRP-DFs and briefly discuss other electronic structure methods that have addressed the interaction of molecules with metal surfaces. An overview is presented of dynamical models, which make a distinction as to whether or not, and which dissipative channels are modeled, the dissipative channels being surface phonons and electronically non-adiabatic channels such as electron-hole pair excitation. We also discuss the dynamical methods that have been used, such as the quasi-classical trajectory method and quantum dynamical methods like the time-dependent wave packet method and the reaction path Hamiltonian method. Limits on the accuracy of these methods are discussed for DC of diatomic and polyatomic molecules on metal surfaces, paying particular attention to reduced dimensionality approximations that still have to be invoked in wave packet calculations on polyatomic molecules like CH₄. We also address the accuracy of fitting methods, such as recent machine learning methods (like neural network methods) and the corrugation reducing procedure. In discussing the calculation of observables we emphasize the importance of modeling the properties of the supersonic beams in simulating the sticking probability curves measured in the associated experiments. We show that chemically accurate barrier heights have now been extracted for DC in 11 molecule-metal surface systems, some of which form the most accurate core of the only existing database of E_b for DC reactions on metal surfaces (SBH10). The SRP-DFs (or candidate SRP-DFs) that have been derived show transferability in many cases, i.e., they have been shown also to yield chemically accurate E_b for chemically related systems. This can in principle be exploited in simulating rates of catalyzed reactions on nano-particles containing facets and edges, as SRP-DFs may be transferable among systems in which a molecule dissociates on low index and stepped surfaces of the same metal. In many instances SRP-DFs have allowed important conclusions regarding the mechanisms underlying observed experimental trends. An important recent observation is that SRP-DFT based on semi-local exchange DFs has so far only been successful for systems for which the difference of the metal work function and the molecule's electron affinity exceeds 7 eV. A main challenge to SRP-DFT is to extend its applicability to the other systems, which involve a range of important DC reactions of e.g. O₂, H₂O, NH₃, CO₂, and CH₃OH. Recent calculations employing a PES based on a screened hybrid exchange functional suggest that the road to success may be based on using exchange functionals of this category.

Argon tagging of doubly transition metal doped aluminum clusters: The importance of electronic shielding

The interaction of argon with doubly transition metal doped aluminum clusters, Al_nTM₂ ⁺ (n = 1-18, TM = V, Nb, Co, Rh), is studied experimentally in the gas phase via mass spectrometry. Density functional theory calculations on selected sizes are used to understand the argon affinity of the clusters, which differ depending on the transition metal dopant. The analysis is focused on two pairs of consecutive sizes: Al_6,7V₂ ⁺ and Al_4,5Rh₂ ⁺, the largest of each pair showing a low affinity toward Ar. Another remarkable observation is a pronounced drop in reactivity at n = 14, independent of the dopant element. Analysis of the cluster orbitals shows that this feature is not a consequence of cage formation but is electronic in nature. The mass spectra demonstrate a high similarity between the size-dependent reactivity of the clusters with Ar and H₂. Orbital interactions provide an intuitive link between the two and further establish the importance of precursor states in the reactions of the clusters with hydrogen.

Nonthermalized Precursor-Mediated Dissociative Chemisorption at High Catalysis Temperatures

Quasiclassical trajectory calculations and vibrational-state-selected beam-surface measurements of CH₄ chemisorption on Ir(111) reveal a nonthermal, hot-molecule mechanism for C-H bond activation. Low-energy vibrationally excited molecules become trapped in the physisorption well and react before vibrational and translational energies accommodate the surface. The reaction probability is strongly surface-temperature-dependent and arises from the pivotal role of Ir atom thermal motion. In reactive trajectories, the mean outward Ir atom displacement largely exceeds that of the transition-state geometry obtained through a full geometry optimization. The study also highlights a new way for (temporary) surface defects to impact high-temperature heterogeneous catalytic reactivity. Instead of reactants diffusing to and competing for geometrically localized lower barrier sites, transient, thermally activated surface atom displacements deliver low-barrier surface reaction geometries to the physisorbed reactants.

Dynamics in reactions on metal surfaces: A theoretical perspective

Recent advances in theoretical characterization of reaction dynamics on metal surfaces are reviewed. It is shown that the widely available density functional theory of metals and their interactions with molecules have enabled first principles theoretical models for treating surface reaction dynamics. The new theoretical tools include methods to construct high-dimensional adiabatic potential energy surfaces, to characterize nonadiabatic processes within the electronic friction models, and to describe dynamics both quantum mechanically and classically. Three prototypical surface reactions, namely, dissociative chemisorption, Eley-Rideal reactions, and recombinative desorption, are surveyed with a focus on some representative examples. While principles governing gas phase reaction dynamics may still be applicable, the presence of the surface introduces a higher level of complexity due to strong interaction between the molecular species and metal substrate. Furthermore, most of these reactive processes are impacted by energy exchange with surface phonons and/or electron-hole pair excitations. These theoretical studies help to interpret and rationalize experimental observations and, in some cases, guide experimental explorations. Knowledge acquired in these fundamental studies is expected to impact many practical problems in a wide range of interfacial processes.

Stochastic wave packet approach to nonadiabatic scattering of diatomic molecules from metals

In this contribution, we present a quantum dynamical approach to study inelastic scattering of diatomic molecules from metal surfaces at normal incidence. The dissipative dynamics obeys a stochastic Schrödinger equation describing the time-evolution of the system as a piecewise deterministic process. Energy exchange between the molecular vibrational degrees of freedom and the metal electrons is represented using operators in tensor product form, which are coupled via anharmonic transition rates calculated from first-order perturbation theory. Full dimensional observables are obtained by averaging over simulations in 4D-including the internal stretch, the distance to the surface, and the orientation angles-at different surface sites. The method is applied to the state-resolved scattering of vibrationally excited NO from Au(111), revealing important channels for quantized energy relaxation.

Dynamics of N2 sticking on W(100): the decisive role of van der Waals interactions

The reactive dynamics of N₂ on W(100) has been investigated by means of quasi-classical trajectory calculations using an interpolated six-dimensional potential energy surface (PES) based on density functional theory energies obtained employing the vdW-DF2 functional.

Chaotic variations of electrical conductance in powdered Pd correlating with oscillatory sorption of D2

A microcalorimetric method has been combined with a potentiostatic method to measure simultaneously the rate of heat evolution and the electrical current in a powdered sample of palladium during thermokinetic oscillations accompanying the sorption of deuterium in the metal. Deterministic chaos has been confirmed in the temporal variations in current (of ca. 1-4 mA) on the onset of both the sorption and the desorption of deuterium from Pd. It has been found that the first derivative of the current in time, dI/dt, turns out to be correlated precisely with the periodicity of thermokinetic oscillations. The dI/dt curves consist of regularly timed outbursts of aperiodic, high frequency (HF) fluctuations, interlinked by calm periods. The calm periods correlate with the descending slopes of thermokinetic oscillations (i.e., with decrease in the rate of heat evolution) and their lengths depend on the frequency of thermokinetic oscillations. In turn, the outbursts of aperiodic HF fluctuations in the dI/dt derivatives correlate with the ascending slopes of thermokinetic oscillations (i.e., with increasing rate of heat production), but their length is practically constant, irrespective of the thermokinetic frequency. We propose a periodic mechanism of sorption including a collective action of adsorbed deuterium taking place on the Pd surface. The periodicity of this mechanism arises from the temporal separation of its two sub-processes. The sub-process (1) involves only the adsorption of molecular D₂ on the Pd surface and proceeds with little heat evolution until a critical coverage of D₂ is achieved. The sub-process (2) initiates the dissociation of the adsorbed D₂ and the penetration of the dissociated atomic D species into the Pd lattice. It is the more energetic of the two, but it only begins after a threshold coverage of D₂ on the Pd surface has been achieved. We suggest that these sub-processes occurring alternatingly may provide a kernel for the oscillatory behavior observed in Pd/H(D) systems.

Dissociative and non-dissociative adsorption of O2 on Cu(111) and CuML/Ru(0001) surfaces: adiabaticity takes over

Adiabatic molecular spin-quenching during the approach of O₂ to Cu(111) and Cu_ML/Ru(0001) surfaces.

Quantum and classical dynamics of reactive scattering of H2 from metal surfaces

State-of-the-art theoretical models allow nowadays an accurate description of H₂/metal surface systems and phenomena relative to heterogeneous catalysis. Here we review the most relevant ones investigated during the last 10 years.

Molecular dynamics simulation of O2 adsorption on Ag(110) from first principles electronic structure calculations

State of the art simulations show that the physisorption state could be important for O₂/Ag(110) adsorption.

Surface temperature effects on the dynamics of N2 Eley-Rideal recombination on W(100)

Quasiclassical trajectories simulations are performed to study the influence of surface temperature on the dynamics of a N atom colliding a N-preadsorbed W(100) surface under normal incidence. A generalized Langevin surface oscillator scheme is used to allow energy transfer between the nitrogen atoms and the surface. The influence of the surface temperature on the N(2) formed molecules via Eley-Rideal recombination is analyzed at T = 300, 800, and 1500 K. Ro-vibrational distributions of the N(2) molecules are only slightly affected by the presence of the thermal bath whereas kinetic energy is rather strongly decreased when going from a static surface model to a moving surface one. In terms of reactivity, the moving surface model leads to an increase of atomic trapping cross section yielding to an increase of the so-called hot atoms population and a decrease of the direct Eley-Rideal cross section. The energy exchange between the surface and the nitrogen atoms is semi-quantitatively interpreted by a simple binary collision model.

Towards chemically accurate simulation of molecule-surface reactions

This perspective addresses four challenges facing theorists whose aim is to make quantitatively accurate predictions for reactions of molecules on metal surfaces, and suggests ways of meeting these challenges, focusing on dissociative chemisorption reactions of H(2), N(2), and CH(4). Addressing these challenges is ultimately of practical importance to a more accurate description of overall heterogeneously catalysed reactions, which play a role in the production of more than 90% of man-made chemicals. One challenge is to describe the interaction of a molecule with a metal surface with chemical accuracy, i.e., with errors in reaction barrier heights less than 1 kcal mol(-1). In this framework, the potential of a new implementation of specific reaction parameter density functional theory (SRP-DFT) will be discussed, with emphasis on applications to reaction of H(2) with metal surfaces. Two additional challenges are to come up with improved descriptions of the effects of phonons and electron-hole pairs on reaction of molecules like N(2) on metal surfaces. Phonons can be tackled using sudden approximations in quantum dynamics, and through Ab Initio Molecular Dynamics (AIMD) calculations using classical dynamics. To additionally achieve an accurate description of the effect of electron-hole pair excitation on dissociative chemisorption within a classical dynamics framework, it may be possible to combine AIMD with electronic friction. The fourth challenge we will consider is how to achieve an accurate quantum mechanical description of the dissociative chemisorption of a polyatomic molecule, like methane, on a metal surface. A method of potential interest is the Multi-Configuration Time-Dependent Hartree (MCTDH) method.

Effect of surface motion on the rotational quadrupole alignment parameter of D2 reacting on Cu(111)

Ab initio molecular dynamics (AIMD) calculations using the specific reaction parameter approach to density functional theory are presented for the reaction of D2 on Cu(111) at high surface temperature (T(s)=925  K). The focus is on the dependence of reaction on the alignment of the molecule's angular momentum relative to the surface. For the two rovibrational states for which measured energy resolved rotational quadrupole alignment parameters are available, and for the energies for which statistically accurate rotational quadrupole alignment parameters could be computed, statistically significant results of our AIMD calculations are that, on average, (i) including the effect of the experimental surface temperature (925 K) in the AIMD simulations leads to decreased rotational quadrupole alignment parameters, and (ii) including this effect leads to increased agreement with experiment.

Competition between electron and phonon excitations in the scattering of nitrogen atoms and molecules off tungsten and silver metal surfaces

We investigate the role played by electron-hole pair and phonon excitations in the interaction of reactive gas molecules and atoms with metal surfaces. We present a theoretical framework that allows us to evaluate within a full-dimensional dynamics the combined contribution of both excitation mechanisms while the gas particle-surface interaction is described by an ab initio potential energy surface. The model is applied to study energy dissipation in the scattering of N(2) on W(110) and N on Ag(111). Our results show that phonon excitation is the dominant energy loss channel, whereas electron-hole pair excitations represent a minor contribution. We substantiate that, even when the energy dissipated is quantitatively significant, important aspects of the scattering dynamics are well captured by the adiabatic approximation.

Dynamics simulation of N(2) scattering onto W(100,110) surfaces: A stringent test for the recently developed flexible periodic London-Eyring-Polanyi-Sato potential energy surface

An efficient method to construct the six dimensional global potential energy surface (PES) for two atoms interacting with a periodic rigid surface, the flexible periodic London-Eyring-Polanyi-Sato model, has been proposed recently. The main advantages of this model, compared to state-of-the-art interpolated ab initio PESs developed in the past, reside in its global nature along with the small number of electronic structure calculations required for its construction. In this work, we investigate to which extent this global representation is able to reproduce the fine details of the scattering dynamics of N(2) onto W(100,110) surfaces reported in previous dynamics simulations based on locally interpolated PESs. The N(2)/W(100) and N(2)/W(110) systems are chosen as benchmarks as they exhibit very unusual and distinct dissociative adsorption dynamics although chemically similar. The reaction pathways as well as the role of dynamic trapping are scrutinized. Besides, elastic/inelastic scattering dynamics including internal state and angular distributions of reflected molecules are also investigated. The results are shown to be in fair agreement with previous theoretical predictions.

Experimental evidence of dynamic trapping in the scattering of H2 from Pd(110)

We have performed H2(D2) diffraction experiments on a Pd(110) surface using two different high-sensitivity set-ups. We have found that, although the total reflectivity of Pd(110) is comparable to that observed in other reactive systems, the corresponding H2(D2) diffraction patterns are quite different: no diffraction peak, including the specular one, is observed on Pd(110). This unexpected result is the consequence of dynamic trapping. Such interpretation is supported by classical dynamics calculations based on accurate ab initio potential energy surfaces.

Why N2 molecules with thermal energy abundantly dissociate on W(100) and not on W(110)

Low-energy N2 molecules easily dissociate on W(100) but not on W(110). In this Letter, the six-dimensional potential energy surface for the dissociation of N2 molecules on W(110) has been determined by density functional calculations. Results are compared to those of N2 dissociation on W(100). The difference in reactivity between the two faces is shown to arise from the characteristics of the potential energy surface far from the surface (>3 A) and not from the properties of a precursor well or those of the final atomic adsorption sites.

Relaxation of hot atoms following H2 dissociation on a Pd(111) surface

We study the relaxation of hot H atoms produced by dissociation of H2 molecules on the Pd111 surface. Ab initio density-functional theory calculations and the "corrugation reducing procedure" are used to determine the interaction potential for a H atom in front of a rigid surface as well as its modification under surface-atom vibrations. A slab of 80 Pd atoms is used to model the surface together with "generalized Langevin oscillators" to account for energy dissipation to the bulk. We show that the energy relaxation is fast, about 75% of the available energy being lost by the hot atoms after 0.5 ps. As a consequence, the hot atoms do not travel more than a few angstroms along the surface before being trapped into the potential well located over the hollow site.