Electron–hole pair creation by atoms incident on a metal surface

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.

Random Force in Molecular Dynamics with Electronic Friction

Originally conceived to describe thermal diffusion, the Langevin equation includes both a frictional drag and a random force, the latter representing thermal fluctuations first seen as Brownian motion. The random force is crucial for the diffusion problem as it explains why friction does not simply bring the system to a standstill. When using the Langevin equation to describe ballistic motion, the importance of the random force is less obvious and it is often omitted, for example, in theoretical treatments of hot ions and atoms interacting with metals. Here, friction results from electronic nonadiabaticity (electronic friction), and the random force arises from thermal electron-hole pairs. We show the consequences of omitting the random force in the dynamics of H-atom scattering from metals. We compare molecular dynamics simulations based on the Langevin equation to experimentally derived energy loss distributions. Despite the fact that the incidence energy is much larger than the thermal energy and the scattering time is only about 25 fs, the energy loss distribution fails to reproduce the experiment if the random force is neglected. Neglecting the random force is an even more severe approximation than freezing the positions of the metal atoms or modelling the lattice vibrations as a generalized Langevin oscillator. This behavior can be understood by considering analytic solutions to the Ornstein-Uhlenbeck process, where a ballistic particle experiencing friction decelerates under the influence of thermal fluctuations.

Configuration interaction approaches for solving quantum impurity models

We develop several configuration interaction approaches for characterizing the electronic structure of an adsorbate on a metal surface (at least in model form). When one can separate the adsorbate from the substrate, these methods can achieve a reasonable description of adsorbate on-site electron-electron correlation in the presence of a continuum of states. While the present paper is restricted to the Anderson impurity model, there is hope that these methods can be extended to ab initio Hamiltonians and provide insight into the structure and dynamics of molecule-metal surface interactions.

A practical ansatz for evaluating the electronic friction tensor accurately, efficiently, and in a nearly black-box format

It is well-known that under conditions of fast electronic equilibration and weak nonadiabaticity, nonadiabatic effects induced by electron-hole pair excitations can be partly incorporated through a frictional force. However, ab initio computation of the electronic friction tensor suffers from numerical instability and usually demands a convergence check. In this study, we present an efficient and accurate interpolation method for computing the electronic friction tensor in a nearly black-box manner as appropriate for molecular dynamics. In almost all cases, our method agrees quite well with the exact friction tensor which is available for several quadratic Hamiltonians. As such, we outperform more conventional approaches that are based on the introduction of a broadening parameter. Future work will implement this interpolation approach within ab initio software packages.

The Fate of Atomic Spin in Atomic Scattering off Surfaces

We explore model electron dynamics of an atom scattering off a surface within the time-dependent complete active space self-consistent field (TD-CASSCF) approximation. We focus especially on the scattering of a hydrogen atom and its resulting spin dynamics starting from an initially spin-polarized state. Our results reveal competing electronic time scales that are governed by the electronic structure of the surface as well as the character of the atom. The time scales and nonadiabaticity of the dynamics are reported on by the final spin polarization of the scattered atom, which may be probed in future experiments.

Unified description of H-atom-induced chemicurrents and inelastic scattering

The Born-Oppenheimer approximation (BOA) provides the foundation for virtually all computational studies of chemical binding and reactivity, and it is the justification for the widely used "balls and springs" picture of molecules. The BOA assumes that nuclei effectively stand still on the timescale of electronic motion, due to their large masses relative to electrons. This implies electrons never change their energy quantum state. When molecules react, atoms must move, meaning that electrons may become excited in violation of the BOA. Such electronic excitation is clearly seen for: (i) Schottky diodes where H adsorption at Ag surfaces produces electrical "chemicurrent;" (ii) Au-based metal-insulator-metal (MIM) devices, where chemicurrents arise from H-H surface recombination; and (iii) Inelastic energy transfer, where H collisions with Au surfaces show H-atom translation excites the metal's electrons. As part of this work, we report isotopically selective hydrogen/deuterium (H/D) translational inelasticity measurements in collisions with Ag and Au. Together, these experiments provide an opportunity to test new theories that simultaneously describe both nuclear and electronic motion, a standing challenge to the field. Here, we show results of a recently developed first-principles theory that quantitatively explains both inelastic scattering experiments that probe nuclear motion and chemicurrent experiments that probe electronic excitation. The theory explains the magnitude of chemicurrents on Ag Schottky diodes and resolves an apparent paradox--chemicurrents exhibit a much larger isotope effect than does H/D inelastic scattering. It also explains why, unlike Ag-based Schottky diodes, Au-based MIM devices are insensitive to H adsorption.

Energy dissipation to tungsten surfaces upon hot-atom and Eley–Rideal recombination of H2

Adiabatic and nonadiabatic quasi-classical molecular dynamics simulations are performed to investigate the role of electron–hole pair excitations in hot-atom and Eley–Rideal H₂ recombination mechanisms on H-covered W(100). The influence of the surface structure is analyzed by comparing with previous results for W(110).

Nonadiabatic Vibrational Damping of Molecular Adsorbates: Insights into Electronic Friction and the Role of Electronic Coherence

We present a perturbation approach rooted in time-dependent density-functional theory to calculate electron-hole (e-h) pair excitation spectra during the nonadiabatic vibrational damping of adsorbates on metal surfaces. Our analysis for the benchmark systems CO on Cu(100) and Pt(111) elucidates the surprisingly strong influence of rather short electronic coherence times. We demonstrate how in the limit of short electronic coherence times, as implicitly assumed in prevalent quantum nuclear theories for the vibrational lifetimes as well as electronic friction, band structure effects are washed out. Our results suggest that more accurate lifetime or chemicurrentlike experimental measurements could characterize the electronic coherence.

Dissipation of the excess energy of the adsorbate-thermalization via electron transfer

A new scenario for the thermalization process of adsorbates at solid surfaces is proposed. The scenario is based on the existence of an electric dipole layer in which the electron wavefunctions extend over the positive ions, creating a strong local electric field which drags the electrons into the solid interior and repels the positive ions. During adsorption the electrons tunnel into the solid interior, conveying the excess energy. The positive ions are retarded by the field, losing the excess kinetic energy, and are located smoothly into the adsorption sites. In such a scheme, the excess energy is not dissipated locally, avoiding melting or the creation of defects which is in accordance with experiments. The scenario is supported by ab initio calculation results, including density function theory of the slabs representing the AlN surface and the Schrodinger equation for the time evolution of hydrogen-like atoms at the solid surface.

Mixed Quantum-Classical Dynamics Using Collective Electronic Variables: A Better Alternative to Electronic Friction Theories

An accurate description of nonadiabatic dynamics of molecular species on metallic surfaces poses a serious computational challenge associated with a multitude of closely spaced electronic states. We propose a mixed quantum-classical scheme that addresses this challenge by introducing collective electronic variables. These variables are defined through analytic block-diagonalization applied to the time-dependent Hamiltonian matrix governing the electronic dynamics. We compare our scheme with a simplified Ehrenfest approach and with a full-memory electronic friction model on a 1D "adatom + atomic chain" model. Our simulations demonstrate that collective-mode dynamics with only a few (two to three) electronic variables is robust and can describe a variety of situations: from a chemisorbed atom on an insulator to an atom on a metallic surface. Our molecular model also reveals that the friction approach is prone to unpredictable and catastrophic failures.

Electronic Friction-Based Vibrational Lifetimes of Molecular Adsorbates: Beyond the Independent-Atom Approximation

We assess the accuracy of vibrational damping rates of diatomic adsorbates on metal surfaces as calculated within the local-density friction approximation (LDFA). An atoms-in-molecules (AIM) type charge partitioning scheme accounts for intramolecular contributions and overcomes the systematic underestimation of the nonadiabatic losses obtained within the prevalent independent-atom approximation. The quantitative agreement obtained with theoretical and experimental benchmark data suggests the LDFA-AIM scheme as an efficient and reliable approach to account for electronic dissipation in ab initio molecular dynamics simulations of surface chemical reactions.

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.

Electronic excitations induced by hydrogen surface chemical reactions on gold

Associated with chemical reactions at surfaces energy may be dissipated exciting surface electronic degrees of freedom. These excitations are detected using metal-insulator-metal (MIM) heterostructures (Ta-TaOx-Au) and the reactions of H with and on a Au surface are probed. A current corresponding to 5×10(-5) electrons per adsorbing H atom and a marked isotope effect are observed under steady-state conditions. Analysis of the current trace when the H atom flux is intermitted suggests that predominantly the recombination reaction creates electronic excitations. Biasing the front versus the back electrode of the MIM structure provides insights into the spectrum of electronic excitations. The observed spectra differ for the two isotopes H and D and are asymmetric when comparing negative and positive bias voltages. Modeling indicates that the excited electrons and the concurrently created holes differ in their energy distributions.

Quantum corrected Langevin dynamics for adsorbates on metal surfaces interacting with hot electrons

We investigate the importance of including quantized initial conditions in Langevin dynamics for adsorbates interacting with a thermal reservoir of electrons. For quadratic potentials the time evolution is exactly described by a classical Langevin equation and it is shown how to rigorously obtain quantum mechanical probabilities from the classical phase space distributions resulting from the dynamics. At short time scales, classical and quasiclassical initial conditions lead to wrong results and only correctly quantized initial conditions give a close agreement with an inherently quantum mechanical master equation approach. With CO on Cu(100) as an example, we demonstrate the effect for a system with ab initio frictional tensor and potential energy surfaces and show that quantizing the initial conditions can have a large impact on both the desorption probability and the distribution of molecular vibrational states.

Role of electron-hole pair excitations in the dissociative adsorption of diatomic molecules on metal surfaces

We quantitatively evaluate the contribution of electron-hole pair excitations to the reactive dynamics of H2 on Cu(110) and N2 on W(110), including the six dimensionality of the process in the entire calculation. The interaction energy between molecule and surface is represented by an ab initio six-dimensional potential energy surface. Electron friction coefficients are calculated with density functional theory in a local density approximation. Contrary to previous claims, only minor differences between the adiabatic and nonadiabatic results for dissociative adsorption are found. Our calculations demonstrate the validity of the adiabatic approximation to analyze adsorption dynamics in these two representative systems.

Spectrum of electronic excitations due to the adsorption of atoms on metal surfaces

The time-dependent, mean-field Newns-Anderson model for a spin-polarized adsorbate approaching a metallic surface is solved in the wide-band limit. Equations for the time evolution of the electronic structure of the adsorbate-metal system are derived and the spectrum of electronic excitations is found. The behavior of the model is demonstrated for a set of physically reasonable parameters.

Femtosecond laser induced associative desorption of H2 from Ru(0001): Comparison of “first principles” theory with experiment

A three dimensional model based on molecular dynamics with electronic frictions is developed to describe the femtosecond laser induced associative desorption of H2 from Ru(0001)(1 x 1)H. Two molecular coordinates (internuclear separation d and center of mass distance to surface z) and a single phonon coordinate are included in the dynamics. Both the potential energy surface and the electronic friction tensor are calculated by density functional theory so that there are no adjustable parameters in the comparison of this model with the wide range of experiments available for this system. This "first principles" dynamic model gives results in semiquantitative agreement with all experimental results; nonlinear fluence dependence of the yield, isotope effect, two pulse correlation, and energy partitioning. The good agreement of theory with experiment supports a description of this surface femtochemistry in terms of thermalized hot electron induced chemistry with coupling to nuclear coordinates through electronic frictions. By comparing the dynamics with the analytical one dimensional frictional model used previously to fit the experiments for this system, we show that the success of the one dimensional model is based on the rapid intermixing of the z and d coordinates as the H-H climbs out of the adsorption well. However, projecting the three dimensional dynamics onto one dimension introduces a fluence (adsorbate temperature) dependent "entropic" barrier in addition to the potential barrier for the chemistry. This implies that some caution must be used in interpreting activation energies obtained in fitting experiments to the one dimensional model.

Theoretical evidence for nonadiabatic vibrational deexcitation in H2(D2) state-to-state scattering from Cu(100)

Dynamical calculations are presented for electronically nonadiabatic vibrational deexcitation of H2 and D2 in scattering from Cu(111). Both the potential energy surface and the nonadiabatic coupling strength were obtained from density functional calculations. The theoretically predicted magnitude of the deexcitation and its dependence on incident energy and isotope are all in agreement with state-to-state scattering experiments [on Cu(100)], and this gives indirect evidence for a nonadiabatic mechanism of the observed deexcitation. Direct evidence could be obtained by measuring the chemicurrent associated with the deexcitation, and its properties have been predicted.

Theoretical calculations of CH4 and H2 associative desorption from Ni(111): Could subsurface hydrogen play an important role?

The results of theoretical calculations of associative desorption of CH(4) and H(2) from the Ni(111) surface are presented. Both minimum-energy paths and classical dynamics trajectories were generated using density-functional theory to estimate the energy and atomic forces. In particular, the recombination of a subsurface H atom with adsorbed CH(3) (methyl) or H at the surface was studied. The calculations do not show any evidence for enhanced CH(4) formation as the H atom emerges from the subsurface site. In fact, there is no minimum-energy path for such a concerted process on the energy surface. Dynamical trajectories started at the transition state for the H-atom hop from subsurface to surface site also did not lead to direct formation of a methane molecule but rather led to the formation of a thermally excited H atom and CH(3) group bound to the surface. The formation (as well as rupture) of the H-H and C-H bonds only occurs on the exposed side of a surface Ni atom. The transition states are quite similar for the two molecules, except that in the case of the C-H bond, the underlying Ni atom rises out of the surface plane by 0.25 A. Classical dynamics trajectories started at the transition state for desorption of CH(4) show that 15% of the barrier energy, 0.8 eV, is taken up by Ni atom vibrations, while about 60% goes into translation and 20% into vibration of a desorbing CH(4) molecule. The most important vibrational modes, accounting for 90% of the vibrational energy, are the four high-frequency CH(4) stretches. By time reversibility of the classical trajectories, this means that translational energy is most effective for dissociative adsorption at low-energy characteristic of thermal excitations but energy in stretching modes is also important. Quantum-mechanical tunneling in CH(4) dissociative adsorption and associative desorption is estimated to be important below 200 K and is, therefore, not expected to play an important role under typical conditions. An unexpected mechanism for the rotation of the adsorbed methyl group was discovered and illustrated a strong three-center C-H-Ni contribution to the methyl-surface bonding.

How adiabatic is activated adsorption/associative desorption?

Using density-functional theory we calculate friction coefficients describing the damping of nuclear motion into electron-hole pair excitation for the two best-known examples of activated adsorption: H2 dissociation on a Cu(111) surface and N2 dissociation on a Ru(0001) surface. In both cases, the frictions increase dramatically along the reaction path towards the transition state and can be an order of magnitude larger there than typical in the molecularly adsorbed state. In addition, the frictions for N2/Ru(0001) are typically an order of magnitude larger than for H2/Cu(111). We rationalize these trends in terms of the electron structure as the systems proceed to dissociation along the reaction paths. Combining these friction coefficients with the potential-energy surface in quasiclassical dynamics allows first-principles studies of the importance of the breakdown in the Born-Oppenheimer approximation in describing the chemistry. We find that nonadiabatic effects are minimal for the H2/Cu(111) system, but are quite important for N2/Ru(0001).

Electronic nonadiabatic effects in the adsorption of hydrogen atoms on metals

The time-dependent, mean-field Newns-Anderson model for a spin-polarized adsorbate approaching a metallic surface is solved in the wide-band limit. Equations for the time evolution of the occupation of the spin dependent adsorbate states and for the nonadiabatic and nearly adiabatic adsorbate-surface energy transfer rates are derived. Numerical solutions are obtained using characteristic parameters derived from density functional theory calculations for the H/Cu(111) system. The time evolution of the model system is shown to be strongly nonadiabatic in the vicinity of the transition point between spin-polarized and nonpolarized ground states. Away from the spin transition the nonadiabatic energy transfer is in close agreement with the nearly adiabatic limit. Near the transition, nonadiabatic effects are large and the nearly adiabatic approximation fails.

Real-time study of the adiabatic energy loss in an atomic collision with a metal cluster

Gas-phase hydrogen atoms are accelerated towards metallic surfaces in their vicinity. As it approaches the surface, the velocity of an atom increases and this motion excites the metallic electrons, causing energy loss to the atom. This dissipative dynamics is frequently described as atomic motion under friction, where the friction coefficient is obtained from ab initio calculations assuming a weak interaction and slow atom. This paper tests the aforementioned approach by comparing to a real-time Ehrenfest molecular dynamics simulation of such a process. The electrons are treated realistically using standard approximations to time-dependent density functional theory. We find indeed that the electronic excitations produce a friction-like force on the atom. However, the friction coefficient strongly depends on the direction of the motion of the atom: it is large when the atom is moving towards the cluster and much smaller when the atom is moving away. It is concluded that a revision of the model for energy dissipation at metallic surfaces, at least for clusters, may be necessary.

Scattering of O2 from AL111

Experimental results are presented for the scattering of well-defined beams of molecular oxygen incident on clean Al(111). The data consist of scattered angular distributions measured as a function of incident angle, and for fixed incident angle, the dependence on surface temperature of the angular distributions. The measurements are interpreted in terms of a scattering theory that treats the exchange of energy between the translational and rotational motions of the molecule and the phonons of the surface using classical dynamics. The dependence of the measured angular distributions on incident beam angle and temperature is well explained by the theory. Rotational excitation and quantum excitation of the O(2) internal stretching mode are briefly discussed.

The surface temperature dependence of the inelastic scattering and dissociation of hydrogen molecules from metal surfaces

High-dimensional, wave packet calculations have been carried out to model the surface temperature dependence of rovibrationally inelastic scattering and dissociation of hydrogen molecules from the Cu(111) surface. Both the molecule and the vibrating surface are treated fully quantum-mechanically. It is found, in agreement with experimental data, that the surface temperature dependence of a variety of dynamical processes has an Arrhenius form with an activation energy dependent on molecular translational energy and on the initial and final molecular states. The activation energy increases linearly with decreasing translational energy below the threshold energy. Above threshold the behavior is more complex. A quasianalytical model is proposed that faithfully reproduces the Arrhenius law and the translational energy dependence of the activation energy. In this model, it is essential to include quantized energy transfer between the surface and the molecule. It further predicts that for any process characterized by a large energy barrier and multiphonon excitation, the linear change in activation energy up to threshold has slope-1. This explains successfully the universal nature of the unit slope found experimentally for H2 and D2 dissociation on Cu.