Local Density Friction Approximation Research Articles

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.

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

We assess the reliability of the local density friction approximation and show that, despite the strong approximations involved, it is able to provide a good estimate of the friction force suffered by an atomic particle at a metal surface.

Adsorbate modification of electronic nonadiabaticity: H atom scattering from p(2 × 2) O on Pt(111).

We report inelastic differential scattering experiments for energetic H and D atoms colliding at a Pt(111) surface with and without adsorbed O atoms. Dramatically, more energy loss is seen for scattering from the Pt(111) surface compared to p(2 × 2) O on Pt(111), indicating that O adsorption reduces the probability of electron-hole pair (EHP) excitation. We produced a new full-dimensional potential energy surface for H interaction with O/Pt that reproduces density functional theory energies accurately. We then attempted to model the EHP excitation in H/D scattering with molecular dynamics simulations employing the electronic density information from the Pt(111) to calculate electronic friction at the level of the local density friction approximation (LDFA). This approach, which assumes that O atoms simply block the Pt atom from the approaching H atom, fails to reproduce experiment due to the fact that the effective collision cross section of the O atom is only 10% of the area of the surface unit cell. An empirical adiabatic sphere model that reduces electronic nonadiabaticity within an O-Pt bonding length scale of 2.8 Å reproduces experiment well, suggesting that the electronic structure changes induced by chemisorption of O atoms nearly remove the H atom's ability to excite EHPs in the Pt. Alternatives to LDFA friction are needed to account for this adsorbate effect.

Vibrational response and motion of carbon monoxide on Cu(100) driven by femtosecond laser pulses: Molecular dynamics with electronic friction

Carbon monoxide on copper surfaces continues to be a fascinating, rich microlab for many questions evolving in surface science. Recently, hot-electron mediated, femtosecond-laser pulse induced dynamics of CO molecules on Cu(100) were the focus of experiments [Inoue et al., Phys. Rev. Lett. 117, 186101 (2016)] and theory [Novko et al., Phys. Rev. Lett. 122, 016806 (2019)], unraveling details of the vibrational nonequilibrium dynamics on ultrashort (subpicoseconds) timescales. In the present work, full-dimensional time-resolved hot-electron driven dynamics are studied by molecular dynamics with electronic friction (MDEF). Dissipation is included by a friction term in a Langevin equation which describes the coupling of molecular degrees of freedom to electron-hole pairs in the copper surface, calculated from gradient-corrected density functional theory (DFT) via a local density friction approximation (LDFA). Relaxation due to surface phonons is included by a generalized Langevin oscillator model. The hot-electron induced excitation is described via a time-dependent electronic temperature, the latter derived from an improved two-temperature model. Our parameter-free simulations on a precomputed potential energy surface allow for excellent statistics, and the observed trends are confirmed by on-the-fly ab initio molecular dynamics with electronic friction (AIMDEF) calculations. By computing time-resolved frequency maps for selected molecular vibrations, instantaneous frequencies, probability distributions, and correlation functions, we gain microscopic insight into hot-electron driven dynamics and we can relate the time evolution of vibrational internal CO stretch-mode frequencies to measured data, notably an observed redshift. Quantitatively, the latter is found to be larger in MDEF than in experiment and possible reasons are discussed for this observation. In our model, in addition we observe the excitation and time evolution of large-amplitude low-frequency modes, lateral CO surface diffusion, and molecular desorption. Effects of surface atom motion and of the laser fluence are also discussed.

Orbital-Dependent Electronic Friction Significantly Affects the Description of Reactive Scattering of N2 from Ru(0001).

Electron–hole pair (ehp) excitation is thought to substantially affect the dynamics of molecules on metal surfaces, but it is not clear whether this can be better addressed by orbital-dependent friction (ODF) or the local density friction approximation (LDFA). We investigate the effect of ehp excitation on the dissociative chemisorption of N2 on and its inelastic scattering from Ru(0001), which is the benchmark system of highly activated dissociation, with these two different models. ODF is in better agreement with the best experimental estimates for the reaction probabilities than LDFA, yields results for vibrational excitation in better agreement with experiment, but slightly overestimates the translational energy loss during scattering. N2 on Ru(0001) is thus the first system for which the ODF and LDFA approaches are shown to yield substantially different results for easily accessible experimental observables, including reaction probabilities.

Energy Dissipation Effects on the Adsorption Dynamics of N2 on W(100)

Adsorption dynamics of N2 on the W(100) surface is studied by means of quasi-classical trajectories making use of a six-dimensional potential energy surface obtained from density functional theory calculations. In our simulations, van der Waals (vdW) interactions are accounted for by using the vdW-DF2 functional. In view of the comparison with experiments, we show that this leads to a good description of the adsorption dynamics, providing a significant improvement with respect to semi-local exchange–correlation functionals used in the past. Particular emphasis is placed on the description of nonactivated pathways, leading to either dissociation or molecular adsorption. Dynamics calculations are performed within the generalized Langevin oscillator (GLO) model in order to simulate the energy exchange between molecule and surface atoms. Electron–hole (e–h) pair excitations are also implemented in the dynamics via the local density friction approximation (LDFA). Overall adsorption probability, including disso...

Transferability of the Specific Reaction Parameter Density Functional for H2 + Pt(111) to H2 + Pt(211).

The accurate description of heterogeneously catalyzed reactions may require chemically accurate evaluation of barriers for reactions of molecules at the edges of metal nanoparticles. It was recently shown that a semiempirical density functional describing the interaction of a molecule dissociating on a flat metal surface (CHD3 + Pt(111)) is transferable to the same molecule reacting on a stepped surface of the same metal (Pt(211)). However, validation of the method for additional systems is desirable. To address the question whether the specific reaction parameter (SRP) functional that describes H2 + Pt(111) with chemical accuracy is also capable of accurately describing H2 + Pt(211), we have performed molecular beam simulations with the quasi-classical trajectory (QCT) method, using the SRP functional developed for H2 + Pt(111). Our calculations used the Born–Oppenheimer static surface model. The accuracy of the QCT method was assessed by comparison with quantum dynamics results for reaction of the ro-vibrational ground state of H2. The theoretical results for sticking of H2 and D2 on Pt(211) are in quite good agreement with the experiment, but uncertainties remain because of a lack of accuracy of the QCT simulations at low incidence energies and possible inaccuracies in the reported experimental incidence energies at high energies. We also investigated the nonadiabatic effect of electron–hole pair excitation on the reactivity using the molecular dynamics with the electron friction (MDEF) method, employing the local density friction approximation (LDFA). Only small effects of electron–hole pair excitation on sticking are found.

Analysis of Energy Dissipation Channels in a Benchmark System of Activated Dissociation: N2 on Ru(0001).

The excitation of electron–hole pairs in reactive scattering of molecules at metal surfaces often affects the physical and dynamical observables of interest, including the reaction probability. Here, we study the influence of electron–hole pair excitation on the dissociative chemisorption of N2 on Ru(0001) using the local density friction approximation method. The effect of surface atom motion has also been taken into account by a high-dimensional neural network potential. Our nonadiabatic molecular dynamics simulations with electronic friction show that the reaction of N2 is more strongly affected by the energy transfer to surface phonons than by the energy loss to electron–hole pairs. The discrepancy between the computed reaction probabilities and experimental results is within the experimental error both with and without friction; however, the incorporation of electron–hole pairs yields somewhat better agreement with experiments, especially at high collision energies. We also calculate the vibrational efficacy for the N2 + Ru(0001) reaction and demonstrate that the N2 reaction is more enhanced by exciting the molecular vibrations than by adding an equivalent amount of energy into translation.

Effects of surface motion and electron-hole pair excitations in CO2 dissociation and scattering on Ni(100).

The energy transfer between different channels is an important aspect in chemical reactions at surfaces. We investigate here in detail the energy transfer dynamics in a prototypical system, i.e., reactive and nonreactive scattering of CO2 on Ni(100), which is related to heterogeneous catalytic processes with Ni-based catalysts for CO2 reduction. On the basis of our earlier nine-dimensional potential energy surface for CO2/Ni(100), dynamical calculations have been done using the generalized Langevin oscillator (GLO) model combined with local density friction approximation (LDFA), in which the former accounts for the surface motion and the latter accounts for the low-energy electron-hole pair (EHP) excitation. In spite of its simplicity, it is found that the GLO model yields quite satisfactory results, including the significant energy loss and product energy disposal, trapping, and steering dynamics, all of which agree well with the ab initio molecular dynamics ones where many surface atoms are explicitly involved with high computational cost. However, the GLO model fails to describe the reactivity enhancement due to the lattice motion because it intrinsically does not incorporate the variance of barrier height on the surface atom displacement. On the other hand, in LDFA, the energy transferred to EHPs is found to play a minor role and barely alter the dynamics, except for slightly reducing the dissociation probabilities. In addition, vibrational state-selected dissociative sticking probabilities are calculated and previously observed strong mode specificity is confirmed. Our work suggests that further improvement of the GLO model is needed to consider the lattice-induced barrier lowering.

Testing Electronic Friction Models: Vibrational De-excitation in Scattering of H2 and D2 from Cu(111).

At present, molecular dynamics with electronic friction (MDEF) is the workhorse model to go beyond the Born–Oppenheimer approximation in modeling dynamics of molecules at metal surfaces. Concomitant friction coefficients can be calculated with either the local density friction approximation (LDFA) or orbital-dependent friction (ODF), which, unlike LDFA, accounts for anisotropy while relying on other approximations. Due to the computational cost of ODF, extensive high-dimensional MDEF trajectory calculations of experimentally measurable observables have hitherto only been performed based on LDFA. We overcome this limitation with a continuous neural-network-based representation. In our first application to the scattering of vibrationally excited H2 and D2 from Cu(111), we predict up to three times higher vibrational de-excitation probabilities with ODF than with LDFA. These results indicate that anisotropic electronic friction can be important for specific molecular observables. Future experiments can test for this “fingerprint” of different approximations underlying state-of-the-art MDEF.

Hydrogen collisions with transition metal surfaces: Universal electronically nonadiabatic adsorption.

Inelastic scattering of H and D atoms from the (111) surfaces of six fcc transition metals (Au, Pt, Ag, Pd, Cu, and Ni) was investigated, and in each case, excitation of electron-hole pairs dominates the inelasticity. The results are very similar for all six metals. Differences in the average kinetic energy losses between metals can mainly be attributed to different efficiencies in the coupling to phonons due to the different masses of the metal atoms. The experimental observations can be reproduced by molecular dynamics simulations based on full-dimensional potential energy surfaces and including electronic excitations by using electronic friction in the local density friction approximation. The determining factors for the energy loss are the electron density at the surface, which is similar for all six metals, and the mass ratio between the impinging atoms and the surface atoms. Details of the electronic structure of the metal do not play a significant role. The experimentally validated simulations are used to explore sticking over a wide range of incidence conditions. We find that the sticking probability increases for H and D collisions near normal incidence-consistent with a previously reported penetration-resurfacing mechanism. The sticking probability for H or D on any of these metals may be represented as a simple function of the incidence energy, Ein, metal atom mass, M, and incidence angle, 𝜗in. S=(S0+a⋅Ein+b⋅M)*(1-h(𝜗in-c)(1-cos(𝜗in-c)d⋅h(Ein-e)(Ein-e))), where h is the Heaviside step function and for H, S0 = 1.081, a = -0.125 eV-1, b=-8.40⋅10-4 u-1, c = 28.88°, d = 1.166 eV-1, and e = 0.442 eV; whereas for D, S0 = 1.120, a = -0.124 eV-1, b=-1.20⋅10-3 u-1, c = 28.62°, d = 1.196 eV-1, and e = 0.474 eV.

Stereodynamics of Diatom Formation through Eley–Rideal Abstraction

Using adiabatic and nonadiabatic quasiclassical molecular dynamics simulations within the single adsorbate limit, we study the dependence on the incidence angle of the Eley–Rideal (ER) recombination of H2 and N2 on the (100) and (110) tungsten surfaces. In the nonadiabatic simulations, effects due to electron–hole pair excitations and the energy exchange between the recombination partners and the surface lattice are included in the dynamics by combining the local density friction approximation and the generalized Langevin oscillator model. Our adiabatic and nonadiabatic results, which are qualitatively similar, show that the incidence angle affects much more N2 recombination than H2 recombination due mainly to the higher corrugation of the potential energy surface for the former case. In particular, for N abstraction from W(110), we find a very efficient ER recombination pathway at grazing incidence angles. This new mechanism significantly influences the energy partition among the different degrees of fre...

Energy Dissipation during Diffusion at Metal Surfaces: Disentangling the Role of Phonons versus Electron-Hole Pairs.

Helium spin echo experiments combined with abinitio based Langevin molecular dynamics simulations are used to quantify the adsorbate-substrate coupling during the thermal diffusion of Na atoms on Cu(111). An analysis of trajectories within the local density friction approximation allows the contribution from electron-hole pair excitations to be separated from the total energy dissipation. Despite the minimal electronic friction coefficient of Na and the relatively small mass mismatch to Cu promoting efficient phononic dissipation, about (20±5)% of the total energy loss is attributable to electronic friction. The results suggest a significant role of electronic nonadiabaticity in the rapid thermalization generally relied upon in adiabatic diffusion theories.

Femtosecond-laser induced dynamics of CO on Ru(0001): Deep insights from a hot-electron friction model including surface motion

A Langevin model accounting for all six molecular degrees of freedom is applied to femtosecond-laser induced, hot-electron driven dynamics of Ru(0001)($2\ifmmode\times\else\texttimes\fi{}2$):CO. In our molecular dynamics with electronic friction approach, a recently developed potential energy surface based on gradient-corrected density functional theory accounting for van der Waals interactions is adopted. Electronic friction due to the coupling of molecular degrees of freedom to electron-hole pairs in the metal are included via a local density friction approximation, and surface phonons by a generalized Langevin oscillator model. The action of ultrashort laser pulses enters through a substrate-mediated, hot-electron mechanism via a time-dependent electronic temperature (derived from a two-temperature model), causing random forces acting on the molecule. The model is applied to laser induced lateral diffusion of CO on the surface, ``hot adsorbate'' formation, and laser induced desorption. Reaction probabilities are strongly enhanced compared to purely thermal processes, both for diffusion and desorption. Reaction yields depend in a characteristic (nonlinear) fashion on the applied laser fluence, as well as branching ratios for various reaction channels. Computed two-pulse correlation traces for desorption and other indicators suggest that aside from electron-hole pairs, phonons play a non-negligible role for laser induced dynamics in this system, acting on a surprisingly short time scale. Our simulations on precomputed potentials allow for good statistics and the treatment of long-time dynamics (300 ps), giving insight into this system which hitherto has not been reached. We find generally good agreement with experimental data where available and make predictions in addition. A recently proposed laser induced population of physisorbed precursor states could not be observed with the present low-coverage model.

Electron-hole pair effects in methane dissociative chemisorption on Ni(111).

The dissociative chemisorption of methane on metal surfaces has attracted much attention in recent years as a prototype of gas-surface reactions in understanding the mode specific and bond selective chemistry. In this work, we systematically investigate the influence of electron-hole pair excitations on the dissociative chemisorption of CH4/CH3D/CHD3 on Ni(111). The energy dissipation induced by surface electron-hole pair excitations is modeled as a friction force introduced in the generalized Langevin equation, in which the independent atomic friction coefficients are determined within the local-density friction approximation. Quasi-classical trajectory calculations for CH4/CH3D/CHD3 have been carried out on a recently developed twelve-dimensional potential energy surface. Comparing the dissociation probabilities obtained with and without friction, our results clearly indicate that the electron-hole pair effects are generally small, both on absolute reactivity of each vibrational state and on the mode specificity and bond selectivity. Given similar observations in both water and methane dissociation processes, we conclude that electron-hole pair excitations would not play an important role as long as the reaction is direct and the interaction time between the molecule and metal electrons is relatively short.

Surface electron density models for accurateab initiomolecular dynamics with electronic friction

Ab initio molecular dynamics with electronic friction (AIMDEF) is a valuable methodology to study the interaction of atomic particles with metal surfaces. This method, in which the effect of low-energy electron-hole (e-h) pair excitations is treated within the local density friction approximation (LDFA) [Juaristi et al., Phys. Rev. Lett. 100, 116102 (2008)], can provide an accurate description of both e-h pair and phonon excitations. In practice, its applicability becomes a complicated task in those situations of substantial surface atoms displacements because the LDFA requires the knowledge at each integration step of the bare surface electron density. In this work, we propose three different methods of calculating on-the-fly the electron density of the distorted surface and we discuss their suitability under typical surface distortions. The investigated methods are used in AIMDEF simulations for three illustrative adsorption cases, namely, dissociated ${\mathrm{H}}_{2}$ on Pd(100), N on Ag(111), and ${\mathrm{N}}_{2}$ on Fe(110). Our AIMDEF calculations performed with the three approaches highlight the importance of going beyond the frozen surface density to accurately describe the energy released into e-h pair excitations in case of large surface atom displacements.

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.

Energy Dissipation to Tungsten Surfaces upon Eley–Rideal Recombination of N2 and H2

Quasiclassical molecular dynamics simulations are performed to investigate energy dissipation to the (100) and (110) tungsten surfaces upon Eley–Rideal (ER) recombination of H2 and N2. Calculations are carried out within the single adsorbate limit under normal incidence. A generalized Langevin surface oscillator (GLO) scheme is used to simulate the coupling to phonons, whereas electron–hole (e-h) pair excitations are implemented using the local density friction approximation (LDFA). Phonon excitations are found to reduce the ER reactivity for N2 recombination, but do not affect H abstraction. In contrast, the effect of e-h pair excitations on the ER recombination cross section is small for N2, but can be important for H2. The analysis of the energy lost by the recombined species shows that most of the energy is dissipated into phonon excitations in the N2 recombination and into electronic excitations in the H2 recombination. In all cases, the energy dissipated into e-h pairs is taken away from the translational kinetic energy of the formed molecules, whereas dissipation to phonons, only significant for N2, also affects vibration. Interestingly, the electron mediated energy losses are found to be smaller in the case of N2 when surface motion is allowed.