On the Role of Electronic Friction for Dissociative Adsorption and

Article pubs.acs.org/JPCA

On the Role of Electronic Friction for Dissociative Adsorption and Scattering of Hydrogen Molecules at a Ru(0001) Surface Gernot Füchsel, Selina Schimka, and Peter Saalfrank* Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Straße 24-25, D-14476 Potsdam-Golm, Germany ABSTRACT: The role of electronic friction and, more generally, of nonadiabatic effects during dynamical processes at the gas/metal surface interface is still a matter of discussion. In particular, it is not clear if electronic nonadiabaticity has an effect under “mild” conditions, when molecules in low rovibrational states interact with a metal surface. In this paper, we investigate the role of electronic friction on the dissociative sticking and (inelastic) scattering of vibrationally and rotationally cold H2 molecules at a Ru(0001) surface theoretically. For this purpose, classical molecular dynamics with electronic friction (MDEF) calculations are performed and compared to MD simulations without friction. The two H atoms move on a six-dimensional potential energy surface generated from gradient-corrected density functional theory (DFT), that is, all molecular degrees of freedom are accounted for. Electronic friction is included via atomic friction coefficients obtained from an embedded atom, free electron gas (FEG) model, with embedding densities taken from gradient-corrected DFT. We find that within this model, dissociative sticking probabilities as a function of impact kinetic energies and impact angles are hardly affected by nonadiabatic effects. If one accounts for a possibly enhanced electronic friction near the dissociation barrier, on the other hand, reduced sticking probabilities are observed, in particular, at high impact energies. Further, there is always an influence on inelastic scattering, in particular, as far as the translational and internal energy distribution of the reflected molecules is concerned. Additionally, our results shed light on the role played by the velocity distribution of the incident molecular beam for adsorption probabilities, where, in particular, at higher impact energies, large effects are found. are found in surface photochemistry,6 where the explicit participation of electronically excited states is the rule rather than the exception. On the other hand, no clear evidence exists so far if nonadiabatic effects affect the dynamics of elementary steps of heterogeneous catalysis involving metal surfaces. In this case, molecules, often closed-shell and of thermal energies, that is, in low-energy vibrational and rotational states and with moderate kinetic energies, interact with a metal substrate. Similarly, it is not entirely clear if electronic nonadiabaticity plays a role in molecular beam experiments with molecules in low vibrational states (notably ν = 0 or 1). In ref 7, experimental (for Cu(100)) and theoretical evidence (for Cu(111)) was provided, showing that for H2 (ν = 1) or D2 (ν = 1) scattering at the surface, an observed de-excitation to ν = 0 of the reflected species is due to EHP creation in the metal. For H2(ν = 0) on Pt(111), Kroes and co-workers argued on the basis of (adiabatic) wavepacket propagation, including all six degrees of freedom of the molecule relative to the rigid surface, that both reactive (dissociative sticking) and nonreactive scattering proceed electronically adiabatically.8 In ref 9, dissociation of H2 on Cu(111) and of N2, both vibrationally unexcited, on Ru(0001) was studied by a

1. INTRODUCTION In many theoretical studies on the reaction dynamics of molecules at surfaces, the validity of the Born−Oppenheimer or adiabatic, approximation1 is tacitly assumed. This simplifies the treatment of adsorbate motion near surfaces considerably because only the ground-state potential energy surface (PES) needs to be accounted for. However, in particular, at metal surfaces with their characteristic electronic excitation continuum, the Born−Oppenheimer approximation may break down. Several examples exist that illustrate the importance of nonBorn−Oppenheimer effects at the molecule/metal interface. A striking case is line broadening in vibrational spectroscopy, which is often dominated by energy losses and dephasing due to vibration−electron hole pair (EHP) coupling.2 Another example is the fast quenching of adsorbed, vibrationally excited molecules. Here, the relaxation of molecular vibrations often proceeds on a picosecond time scale and even below when EHP excitations are effective.3 Vibrational relaxation due to vibration−EHP coupling was also seen in molecular beam scattering experiments, that is, in cases where the contact time between the molecule and surface is short. This has impressively been demonstrated by Wodtke and co-workers, who studied vibrationally highly excited NO molecules (typically ν ≈ 15) scattering off of Au(111).4,5 There, huge losses of vibrational energy into the EHP continuum were observed. As a side effect, also exoelectron emission has been seen as a more direct proof for nonadiabaticity when the surface was covered with a low-work-function material such as Cs. Not surprisingly, the most prominent signatures of nonadiabaticity © 2013 American Chemical Society

Special Issue: Structure and Dynamics: ESDMC, IACS-2013 Received: April 18, 2013 Revised: June 10, 2013 Published: June 10, 2013 8761

dx.doi.org/10.1021/jp403860p | J. Phys. Chem. A 2013, 117, 8761−8769

The Journal of Physical Chemistry A

Article

sticking probabilities is also addressed. Section 4 summarizes and concludes this work.

molecular dynamics with electronic friction (MDEF) approach,10 albeit in reduced dimensions. The friction model does not explicitly account for EHP pair excitations (i.e., other potential surfaces), but rather the metal excitations are treated in a mean-field way, which results in damped motion on a single potential surface. Also, quantum effects like tunneling are neglected. A conclusion of ref 9 was that for H2/Cu, nonadiabatic effects are indeed minimal, while they are important for N2 on Ru. This latter statement was challenged by Juaristi et al. in ref 11, who note that if all (six) degrees of freedom of a closedshell diatomic molecule (H2 on Cu(110) and N2 on W(110) in their work) are accounted for, nonadiabatic effects are marginal, even for N2. In ref 11, the MDEF approach was used as well, however, with scalar atomic rather than tensorial molecular friction coefficients, which were adopted in ref 9. Moreover, the friction coefficients of ref 9 were computed from gradientcorrected density functional theory (DFT), while in ref 11, the local density approximation (LDA) was used instead. In response to ref 11, it was argued in ref 12 that the LDA atomic friction coefficients underestimate electronic damping in the entrance channel to scattering (in particular, around the barrier toward dissociation), thus leading to too low frictional forces. In passing, we note that experimentally, Wodtke and coworkers showed that molecules NO in ν = 0 states13 and even closed-shell CO(ν = 0)14 can also be excited to higher ν states (mostly ν = 1) in scattering from Au(111). They again ascribe this effect to the coupling of the adsorbate motion to EHP excitations in the metal. Finally, for adsorption of O2 on Pd(100), Meyer and Reuter argue on the basis of time-dependent perturbation theory that electronic nonadiabaticity is unimportant.15 This list of examples, which is far from complete, shows that the issue of nonadiabaticity for molecules in low-ν states scattering at metal surfaces is still controversial and needs further attention. The present work tries to shed some light on the issues raised above for the reactive (dissociative adsorption) and nonreactive (inelastic) scattering of H2 at Ru(0001). Diffractive and reactive scattering for this system has recently been studied experimentally in refs 16 and 17 and also theoretically by adiabatic, six-dimensional quantum wavepacket propagation in ref 18. For this system, no effects of (electronic) friction have been studied so far, at least as far as scattering and dissociation are concerned. There have been previous MDEF studies though to model femtosecond-laser-induced associative desorption in reduced19,20 and full dimensionality.21 Our goal is to address the question as to whether electronic friction has an impact on dissociative sticking probabilities and on inelastic scattering of H2 when approaching the surface in low vibrational and rotational states. We shall also address the validity of various friction models, discuss the reliability of PESs based on gradient-corrected DFT, and study temperature effects. The paper is organized as follows. In section 2, details of the model and the dynamics methods will be described. Special attention is devoted to the treatment of electronic friction. In section 3, we present and discuss results of MDEF calculations for dissociative adsorption and inelastic scattering of H2 at Ru(0001). While the comparison to experimental data is not our major concern, the role played by a realistic velocity distribution of molecules in the incident molecular beam on

2. METHOD AND MODEL 2.1. Potential Energy Surface. We use a six-dimensional PES fitted by Luppi et al.22,23 for a rigid ruthenium surface. The PES is based on ab initio calculations using periodic DFT and the RPBE functional24 at a coverage of 1/2 in a 2 × 2 unit cell. The potential is a function of the center-of-mass position of the molecule given by the coordinates X,Y,Z, and the relative orientation of the molecule to the ruthenium surface is denoted by r, θ, and ϕ. Here, X and Y are lateral components of the center-of-mass position relative to a ruthenium reference atom, and Z is its distance to the surface. The interatomic distance is labeled by r, the azimuthal orientation of the hydrogen molecule by ϕ ∈ [0,2π], and the polar orientation by θ ∈ [0,π]; see Figure 1. Close to the surface, the hydrogen molecule

Figure 1. (Left) Coordinate system for H2 on Ru(0001). Shown are the center-of-mass position relative to a ruthenium atom denoted by X,Y,Z and the relative orientation of the molecule to the surface described by the coordinates r, θ, and ϕ. (Right) A molecule approaching the surface along the minimum-energy path shown in Figure 2, that is, with the molecule oriented parallel to the surface and both hydrogen atoms end up in two adjacent fcc sites.

dissociates, and at its most stable position, the atoms occupy two adjacent face-centered cubic (fcc) sites, with r = 2.745 Å, X = ϕ = 0, Y = 2.745√3/6 Å, θ = π/2, and Z = 1.05 Å. This orientation is stabilized by a classical energy of Ebind = 856 meV compared to a molecule in the gas phase. However, the adsorption of hydrogen on ruthenium is an activated process, that is, incident particles experience a barrier in the entrance channel. Along the surface, the barrier height shows significant corrugation. For example at the top position, the activation energy is Ea = 80 meV, and it is 410 meV at a bridge position, both for θ = π/2 and ϕ = 0. (Barriers can be slightly lower if ϕ is relaxed.18,22) This emphasizes the importance of the impact site for the adsorption of impinging molecules. When averaged over (10000) X and Y positions of a unit cell (with θ = π/2 and ϕ = 0 kept fixed and r and Z optimized), the average adsorption barrier is 273 meV. Figure 2 outlines the situation. There, we show a minimum pathway as a function of Z obtained from a two-dimensional PES cut (r,Z) at a certain impact site for a molecule approaching the surface in parallel orientation (θ = 0, ϕ = 0, X = 0, and Y = √3d/6) and passing through the global minimum. This specific (not global) minimum-energy path is also schematically illustrated in Figure 1, right. As can be seen, the barrier extends relatively far into the gas phase, that is, the barrier is “early” from the viewpoint of adsorption. At the transition state at r‡ = 0.77 Å and Z‡ = 2.25 Å, the activation energy is Ea = 186 meV in this case. Further details of the adopted potential can be found in ref 23. In passing, we only 8762



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Figure 2. A minimum-energy path along a 2D potential cut (at X = 0, Y = √3d/6, ϕ = 0, black, left scale) as a function of Z for a molecule approaching Ru(0001) in parallel orientation from the gas phase. At small Z, the molecule reaches the global minimum, with two (dissociated) H atoms. Also shown for this path is the corresponding electronic friction coefficient η (red, right scale) for one single hydrogen atom as a function of Z.

⎛ 3 ⎞1/3 ⎟⎟ rs = ⎜⎜ ⎝ 4πρemb ⎠

note that the potential used in ref 19 is slightly different because it was calculated with the PW91 functional and for a different coverage. 2.2. Molecular Dynamics with Electronic Friction. We study adsorption and scattering of hydrogen molecules at Ru(0001) by classical, adiabatic molecular dynamics (MD) and by the MDEF approach.10 The latter is an extension of MD by including nonadiabatic couplings between adsorbate and surface electrons via effective electronic friction coefficients η. In particular, the force acting on atom i with mass mi along the corresponding atom coordinate r̲i = (xi,yi,zi) (i = 1,2 for a diatomic system) is given by a Langevin equation mi

d2 r̲ i dt

2

=−

d r̲ ∂V ( r̲ 1 , r̲ 2) − ηi( r̲ i) i + R̲ i(t ; T ) dt ∂ r̲ i

is the Wigner−Seitz radius depending on the embedding electron density ρemb. We assume that the latter is adsorbateindependent and can be represented by the electron density of the bare Ru(0001) surface, that is, only a single DFT calculation, here on the RPBE level of theory, is required. This assumption has been tested in ref 30 for H atoms on Pd and is expected to hold here also. The use of atomic friction coefficients ηi according to eq 3, dependent on the coordinates of a single adsorbate atom only, is an approximation to using N2 tensorial friction elements ηij(q1, ..., qN) (i,j = 1, ..., N) instead, which depend on all N dynamical variables qi (in our case, six). This latter, more exact approach was followed in ref 19, albeit for a reduced model including r and Z coordinates only. We have tested, again for a reduced-dimensional model, the tensorial versus the atomic/ FEG model for hot-electron-mediated desorption of H2 from Ru(0001) in ref 21. We found that computed properties of desorbing particles were in good (sometimes very good) agreement for both methods (see Figure 3 in ref 21). Still, it must be noted that the atomic/FEG friction model is an approximation, in which friction is a result of separable, atomic contributions. As demonstrated in Figure 2, where η is shown as a function of Z for a single hydrogen atom moving along the selected minimal-energy pathway of above, the FEG model predicts significant electronic friction of hydrogen atoms close to the surface, near the adsorption well. From there, η decreases monotonically away from the substrate, without a maximum around the transition state. (The same function is obtained for the second H atom.) In contrast, in ref 19, the tensorial friction model (in reduced dimensions) hints to the possibility that electronic friction can behave nonmonotonically, exhibiting a maximum at least for some tensor elements, near the barrier region. Quantitatively, the (local) damping rate Γ = η/m = 1/τ21 (where m is the mass of the damped particle/ vibration and τ a vibrational lifetime) is about Γ ≈ 2.7 × 10−5Eh/ℏ near the transition state according to Figure 2. In the

(1)

The first term on the right-hand side is the force arising from the potential, the second one is a frictional force acting against the atomic motion, and R̲ i(t;T) is a random force. The latter is present only at finite surface temperature T and calculated as white noise according to the second fluctuation−dissipation theorem25 as ⟨R̲ i(t )R̲ i(t ′)⟩ = 2kBTηδ (t − t ′) i

(2)

Note that in eq 1, only molecular degrees of freedom are accounted for while surface phonons are neglected. Of course, this is an approximation, but it allows us to study effects of dissipation due to EHPs, separately from contributions of phonons. In the following, the electronic friction term η is calculated according to an embedding free electron gas (FEG) model11,26−29 ηi( r̲ ) =

(4)

1/3 ∞ 3ℏ ⎛ 4 ⎞ ⎜ ⎟ ∑ (l + 1) sin 2[δl ,i(rs) − δl+ 1,i(rs)] rs2( r̲ ) ⎝ 9π ⎠ l = 0

(3)

Here, δl,i are phase shifts tabulated for various atom types i (here, H) and different l in ref 28 and 8763



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Figure 3. Decay of the initial vibrational energy Evib(0) of a single H atom on Ru(0001) when displaced along z (perpendicular, upper curve, symbols) and x (parallel, lower curve, symbols) directions. For the symbols, a 6D Langevin simulation with atomic/FEG friction was used. Dashed lines indicate exponential fits to the computed values, giving τ∥ = 227 fs and τ⊥ = 211 fs, respectively.

(molecular) r and Z modes, 200 (for r) and 700 fs (for Z), respectively.21 This was also in reasonable agreement with a Golden Rule type treatment (300 and 800 fs, respectively), also reported in ref 21. In summary, the atomic friction/FEG model yields the same order of magnitude of vibrational relaxation rates near the surface when compared to more sophisticated models (with their own approximations, though), without necessarily accounting for possible differences in different molecular modes. 2.3. Simulation Details. We simulate the scattering/ adsorption of hydrogen on Ru(0001) for different initial translation energies E0 and angles of incidence, α. We perform 10000 trajectories for each (E0,α) pair and average final scattering and adsorption events over all trajectories. The trajectories differ in initial lateral positions (X,Y) and initial relative orientations (θ,ϕ). In the sense of a quasi-classical treatment, we choose a Wigner distribution to simulate impinging hydrogen molecules in the quantum mechanical vibrational ground state, ν = 0. That is, the zero-point vibrational energy of the H2 molecule (about 260 meV) is accounted for in addition to the initial translational energy E0, but no extra vibrational excitation and also no rotational energy are considered. Due to the different adsorption barriers in the entrance channel, we ensure a complete sampling of the ruthenium surface by using a random sampling of the (1 × 1) surface subcell. Each trajectory starts at a surface−molecule distance at Z = 20 a0 and with randomly chosen θ and ϕ values. In case of off-normal incidence (α ≠ 0), the azimuthal impact direction is chosen randomly. We use the Velocity-Verlet based Ermak−Buckholtz Propagator31 to solve eq 1. A time step of 0.5ℏ/Eh (∼0.012 fs) is adopted. This ensures energy conservation of less than 1 meV in the case of ordinary MD up to the final propagation time, tf = 10 ps. We count trajectories as scattered when a surface−molecule distance Z reaches a value of 21 a0 at some point, after which the trajectory is terminated. We count molecules as being adsorbed/dissociated when trajectories reach r values larger than 2.745 Å, after which the propagation

tensorial friction model of ref 19, it shows a maximum near the transition state with a value about three times higher than that for the atomic friction/FEG model, namely, Γ ≈ 9 × 10−5Eh/ℏ, for both the molecular r and Z modes studied there. It should be stated, though, that this is not necessarily a general observation also for other systems, for example, H2 on Cu(110).12 In order to account for possible inaccuracies of the atomic friction model and to address the effects of altered friction in general, without the claim to model tensorial friction here, below, we will also consider situations in which the atomic friction coefficients are scaled by factors of 3 and 10, respectively. A scaling factor of 10 probably grossly overestimates the effects of electronic friction, thus providing an upper bound of what can be expected from frictional forces. Before doing so, we study in Figure 3 the vibrational relaxation for a single adsorbed hydrogen atom adsorbed in the fcc site, when displaced from its equilibrium geometry, using unscaled friction coefficients. In one case, the atom was displaced along the z-coordinate by an amount corresponding to a potential energy of ℏωZ01/2, where ℏωZ01 = 127.3 meV is the anharmonic vibrational quantum of an adsorbed (dissociated) H2 molecule vibrating perpendicular to the surface (along Z).23 In the other case, the H atom was displaced along a parallel (x) coordinate, to a point corresponding to a potential energy gain of ℏωr01/2, where ℏωr01 = 94.3 meV is the vibrational quantum of H2 with two H’s vibrating parallel to the surface (along r).23 The simulations were performed by Langevin dynamics in six dimensions at T = 0 K. Due to the presence of electronic friction, the vibrational energy decays with time, in excellent approximation exponentially as ⎛ −t ⎞ Evib = Evib(0) exp⎜ ⎟ ⎝ τ ⎠

(5)

The resulting lifetime for the perpendicular (z, ⊥) mode is τ⊥ = 211 fs, and the lifetime for the parallel mode (x, ∥) is τ∥ = 227 fs. Using tensorial friction based on gradient-corrected DFT and a 2D (r,Z) Langevin model, comparable but slightly longer lifetimes were found for two H atoms vibrating along the 8764



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Figure 4. Adsorption probabilities for impinging hydrogen molecules on Ru(0001) obtained from 6D MD (black, circle) and MDEF simulations (red, squares). (a) The adsorption probability as a function of α for molecules approaching the surface with initial translational energies E0 = 250 and 600 meV. (b) Experimental adsorption probabilities (exp., triangle) taken from ref 17 as function of E0 at normal incidence (α = 0) are compared with previous 6D QD (empty squares, from refs 17 and 18), MD, and MDEF simulations. For the latter one, we plot results obtained with the FEG friction model and from enhanced friction models (“medium” and “strong” regime, with η′ = 3η and 10η).

3. RESULTS AND DISCUSSION 3.1. Dissociative adsorption. In Figure 4, some results of 6D MDEF and (adiabatic) MD simulations for hydrogen adsorption are presented. In panel (a), we show the dissociative adsorption probability Pads as a function of the angle of incidence α. Two incident kinetic energies have been chosen, E0 = 250 and 600 meV; the first is close to and the second is clearly above the average adsorption barrier of 273 meV. The temperature was T = 0 K. From this panel, we first of all note that the dissociation probability is higher for the higher incidence energy (close to 1 at α = 0), and it decreases with increasing impact angle α in both cases. Normal energy scaling

is stopped also. At the energies considered here, this can happen only close to the surface. Real experiments are done with molecular beams with a certain velocity distribution. In order to account for this, we also calculate adsorption probabilities Pads(⟨E⟩) of a molecular beam at normal incidence as a function of the average (translational) collisional energy ⟨E⟩. For this purpose, we simulate the outcome (scattering or adsorption) of N = 106 trajectories with initial translational energies randomly chosen between Ei ∈ [50,2500] meV. Initial vibrational energies are calculated by using a Wigner distribution according to a harmonic oscillator as well. Pads(⟨E⟩) is than determined according to N

Pads(⟨E⟩) =

Pads(α) = Pads(0) cos2(α)

∑i =ads1 f (vi , T ) N ∑ j = 1 f (vj ,

T)

is not quite realized, but the strong α dependence of the dissociative sticking curves indicates that the component normal to the surface of the translational energy is decisive. Most importantly, we note from comparing MD and MDEF results that friction plays only a minor role. There is a small effect, visible for the E0 = 250 meV curve at low impact angles, where the dissociative sticking probability decreases by a few percent in the MDEF case. In Figure 4b, dissociative adsorption probabilities are plotted for normal incidence α = 0 as a function of initial translational energy E0 for both MD and MDEF cases. For comparison, we also show experimental values taken from ref 17 and results of (frictionless) QD wavepacket simulations.17,18 According to the MD/MDEF simulations, Pads increases with increasing energy, and the curvature is of sigmoidal shape, with almost complete dissociative adsorption at E0 = 600 meV. The quantum dynamics results, obtained with the same RPBE PES as that used here, agree semiquantitatively with our classical simulations. However, we find a more rapid increase of Pads with E0. For example, at 500 meV, the classical sticking probabilities are about 0.97, and they are only 0.83 in the QD simulation. Again, MD and MDEF calculations are strikingly similar, suggesting that electronic friction has only a small influence also here. Closer inspection shows that Pads values according to MDEF tend to be slightly lower than those obtained from MD, similar to what has been seen in Figure 4a. This comes from the fact that friction forces act on the particle and lead to a reduction of translational and internal energies when approaching the surface. Consequently, particles pass through

(6)

Here, f(vi,T) is the probability to find a particle with velocity vi + dvi at a nozzle or beam temperature T, Nads is the number of dissociatively adsorbed trajectories, and N = 106 is the total number of calculated trajectories. Two cases were considered. In the case of an ideal Maxwell−Boltzmann distribution (MBD) ∑Nj=1i f(vj,T) has the meaning of a partition function Ni

Ni

∑ f (vj , T ): = ∑ j=1

j=1

⎛ − (E − E 0 ) ⎞ j ⎟ exp⎜⎜ ⎟ k BT ⎝ ⎠

(7)

where E0 = 50 meV is the lowest kinetic energy that we assume, that is, we consider a distribution with a constant stream velocity. The corresponding average collisional energy is given by ⟨E⟩ = E 0 + kBT

(8)

Second, we used modified velocity distributions similar to previous quantum dynamical (QD) simulations, more compatible with the experiments of ref 16, called time-of-flight (TOF) distributions ⎡ −(v − v )2 ⎤ i 0 ⎥ f (vi , T ) ≈ vi3 exp⎢ 2 α ⎦ ⎣

(10)

(9)

Parameters v0, α, T as well as the corresponding averaged collisional energy are tabulated in ref 18. 8765



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Figure 5. Adsorption probability as a function of the average collisional energy ⟨E⟩ for a molecular beam of H2 molecules scattering at Ru(0001). In panel (a), we compare experimental (green) and QD results (blue) with nondistributed classical values taken from Figure 4 (black, dot) and classical (black line) and MDEF (red) simulations for a molecular beam energy distribution according to experimental TOF measurements. In panel (b), the same values are compared with classical and MDEF simulations for a molecular beam distribution according to a MBD. For MDEF simulations, we plot results with the normal friction (red line) taken from the FEG model and artificially enhanced friction (red dashed lines), that is, the medium (η′ = 3η) and strong friction regimes (η′ = 10η).

quantum mechanical simulations based on a PES calculated with periodic DFT and the PW91 functional32 instead overestimates the adsorption probability at all collisional energies due to lower adsorption barriers obtained with this functional.18 An empirical mixture of both the PW91 and RPBE PES shows the best results at low collisional energies18 but remains inaccurate at high energies. Although our strong friction model is somewhat ad hoc and conclusions drawn from it should be taken with care, we note that electronic friction is an alternative way to explain reduced sticking probabilities at higher impact energies, similar to those in experiment. So far, we investigated adsorption with classical simulations for a molecular beam with fixed (rather than a distribution of) translational energies. However, previous QD simulations take the spread of the experimental beam into account. As we show in Figure 5, the shape of the beam distribution influences values for Pads significantly at normal incidence. In fact, this effect is much stronger than the effect of friction. In Figure 5a, we compare QD and experimental results with classical “nondistributed” and classical and MDEF simulations for molecular beam energy distributions according to TOF measurements. As can be seen from purely classical calculations, Pads is lower for a TOF distributed beam, especially at high collisional energies, than that for nondistributed calculations. The results come closer to QD calculations. We also find that inclusion of “normal friction” has only a small influence on the results as before when no velocity distribution was accounted for. Also in agreement with our previous calculations, increasing the friction reduces the adsorption probability. In Figure 5b, we compare again QD and experimental values with calculations for a molecular beam that is distributed according to a flux-weighted MBD. We see a dramatic reduction of the adsorption probabilities at high impact energies, relative to the TOF case. While results for TOF distributed beams overestimate experimental values at high impact energies, MB distributed beams underestimate them only slightly. We point out that the distributions according to MBD are broader than the ones according to TOF. We finally study the effect of surface temperature. In our approach, which neglects phonons, temperature has only an influence through nonvanishing random forces in the Langevin equation, which are absent at T = 0. Using the strong friction model, the dissociative sticking probabilities at two impact

effectively larger barriers than the potential predicts, and consequently, Pads decreases. Following eq 1, the effective adsorption barriers are of dynamical height and increase proportional to η and the velocity of the incident particles. From a MDEF calculation during a scattering event, one observes a translational energy loss of ∼30 meV at an impact energy of E0 = 500 meV and of ∼4 meV at E0 = 120 meV (see below). We expect a similar increase of the effective barrier toward dissociation. However, the barrier increase ΔEa is typically much lower than E0, and therefore, effects of friction on dissociation probabilities are comparatively small in the atomic friction/FEG model. We shall see below that this energy loss does have an impact on inelastic scattering though. Before considering scattering, let us discuss possible influences of electronic friction on dissociative adsorption in some more detail. As mentioned above, the friction around the barrier region could be underestimated by the atomic friction/ FEG model. In Figure 4b, we therefore investigated the adsorption process also within a “medium friction model” and a “strong friction model” by artificially increasing η determined from the FEG model by a factor of 3 and 10, respectively. The latter is probably unrealistically large, serving as an upper limit for effects of electronic friction. From the curvatures in Figure 4b (dashed, red) calculated for enhanced friction models, we note the expected effect, namely, a shift of the Pads(E0) curve to higher energies. For example, Pads = 0.5 is reached at ∼220 meV in both MD and MDEF, but it is only reached at ∼240 meV in the medium friction and at ∼270 meV in the strong friction, scaled MDEF cases. The impact of friction is less severe at lower initial energies, that is, the curve becomes also flatter with increasing friction. The reason for this is as before, that is, a velocity-dependent increase of the effective barrier by friction. At this point, a comparison of experimental and theoretical sticking probabilities is appropriate. Both the MD/MDEF (with “normal” friction) and QD calculations are in qualitative agreement with experiment but predict a rise of the Pads(E0) curve that is too steep as compared to experiment. The latter is characterized by relatively higher sticking probabilities at energies below about 200 meV and relatively lower probabilities at energies of around 250 meV and higher. The fact that QD calculations, for example, deviate from experiment in this respect has been suggested to be due to possible shortcomings of the RPBE functional.18 On the other hand, 8766



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Table 1. Dissociative Sticking Probabilities of H2 at Ru(0001), Obtained with the Strong Friction MDEF Model for Two Impact Energies (Normal Incidence) and Various Surface Temperatures T/K E0 = 250 meV E0 = 80 meV

0

100

200

300

400

500

600

700

0.4508 0.0076

0.4495 0.0122

0.4504 0.0215

0.4506 0.0260

0.4436 0.0312

0.4518 0.0363

0.4515 0.0401

0.4589 0.0457

Figure 6. Translational (Etrans) and internal energies (Eint, sum of rotational and vibrational energy) for scattered hydrogen molecules obtained from MD (black, circle) and MDEF simulations (red squares). (a) Etrans and Eint as a function of the angle of incidence α for an initial translational energy E0 = 250 meV. (b) The translational energy of scattered H2 as a function of E0 at normal incidence is shown.

energies, E0 = 80 and 250 meV (normal incidence), are shown in Table 1 for various surface temperatures up to 700 K. From the table, we note that at the larger impact energy, the random forces have only a marginal influence on sticking probabilities, slightly enhancing or lowering the T = 0 value of 0.4508. At the lower impact energy, however, the effect is comparatively large and monotonic, gradually increasing the dissociation probability from 0.0076 at T = 0 K, to 0.0457 at T = 700 K. This is due to the fact that random “kicks” of the particles help to overcome the barrier at higher temperatures. Again, overall effects are not large; however, they may also contribute to larger sticking probabilities at low impact energies. 3.2. Inelastic Scattering. It has been mentioned that even in low rovibrational states, inelastic scattering probabilities can be affected by electronic friction, the energy loss of H2(ν = 1) at Cu(100)/Cu(111) being a classic example.7 Here, we study the role of electronic friction for inelastic scattering of H2(ν = 0) at Ru(0001). In panel (a) of Figure 6, we plot translational (Etrans) as well as internal energies (vibrational and rotational, Eint) of H2 molecules, after they have been reflected from the substrate. An initial energy E0 = 250 meV and various impact angles α have been chosen in this case. Considering the frictionless nondistributed MD simulations first, we note that the translational energy of the reflected particles depends only weakly on the impact angle, while a tendency of increasing internal energies with increasing α is found. This is due to the classical nature of the simulations. We have used a Wigner distribution to account for the vibrational zero-point energy of the free hydrogen molecule, which is about 260 meV. It is clear that a Wigner distribution allows for large vibrational energies. Not surprisingly, highly excited molecules dissociate more easily. As a consequence, scattered trajectories have a lower internal energy on average. This effect is strong in a classical simulation when the adsorption channel is an important alternative to scattering, that is, at low angles of incidence. In the MDEF simulations (nondistributed with unscaled friction coefficients and T = 0 K), we observe a loss of energy in both the translational and internal molecular motions,

with both curves being shifted to lower energies. There is only a moderate variation of the energy loss with angle α; at α = 0°, the total energy loss is about 17 meV, and at 45°, it is about 27 meV. At lower impact energies, the effect is somewhat smaller. For example, at E0 = 160 meV and α = 0, which is close to the experimental conditions, the loss of energy amounts to around 7 meV for translational and 10 meV for internal motion. This shows that the energy loss is about equal for translational and internal energies, that is, the simple friction model adopted here predicts no preference of coupling of EHPs to either translation or internal degrees of freedom. In panel (b) of Figure 6, we show the translational energy Etrans of reflected particles as a function of initial translational energy E0 (for normal incidence), as obtained with the MD and MDEF models. The effect mentioned above is visible, namely, a larger loss of energy at higher E0, and there is only a small influence at low E0. As stated earlier, at E0 = 500 meV, the translational energy loss is 30 meV for the reflected particles. The loss of internal energy is about the same. That indicates that an appreciable amount of initial energy (on the order of 10% at higher initial energies) is transferred into EHPs of the metal. While transitions in internal degrees will be restricted in quantum mechanics by quantization, an appreciable, measurable cooling of translation motion is expected for H2 scattering off of Ru(0001) when electronic friction is accounted for. This effect will be even larger for strong friction.

4. SUMMARY AND CONCLUSIONS In this work, we reported on classical molecular dynamics simulations without (MD) and with electronic friction (MDEF) to investigate the dissociative adsorption and inelastic scattering of hydrogen molecules at a Ru(0001) surface. All six molecular degrees of freedom were accounted for but no phonon modes. MDEF calculations using the FEG friction model show only small differences for dissociative adsorption probabilities compared to MD simulations. There is, however, clear evidence that electronic friction plays a role for inelastic scattering, with the expectation of cooling of reflected molecules. When these are in low rovibrational states initially, 8767



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(7) Luntz, A. C.; Persson, M.; Sitz, G. O. Theoretical Evidence for Nonadiabatic Vibrational Deexcitation in H2 (D2) State-to-State Scattering from Cu(100). J. Chem. Phys. 2006, 124, 091101−4. (8) Nieto, P.; Pijper, E.; Barredo, D.; Laurent, G.; Olsen, R.; Baerends, E. J.; Kroes, G. J.; Farías, D. Reactive and Nonreactive Scattering of H2 from a Metal Surface Is Electronically Adiabatic. Science 2006, 312, 86−89. (9) Luntz, A. C.; Persson, M. How Adiabatic Is Activated Adsorption/Associative Desorption? J. Chem. Phys. 2005, 123, 074704/1−074704/6. (10) Head-Gordon, M.; Tully, J. C. Molecular Dynamics with Electronic Frictions. J. Chem. Phys. 1995, 103, 10137−10145. (11) Juaristi, J. I.; Alducin, M.; Díez Muiño, R.; Busnengo, H. F.; Salin, A. Role of Electron−Hole Pair Excitations in the Dissociative Adsorption of Diatomic Molecules on Metal Surfaces. Phys. Rev. Lett. 2008, 100, 116102/1−116102/4. (12) Luntz, A.; Makkonen, I.; Persson, M.; Holloway, S.; Bird, D.; Mizielinski, M. Comment on “Role of Electron−Hole Pair Excitations in the Dissociative Adsorption of Diatomic Molecules on Metal Surfaces”. Phys. Rev. Lett. 2009, 102, 109601/1. (13) Cooper, R.; Bartels, C.; Kandratsenka, A.; Rahinov, I.; Shenvi, N.; Golibrzuch, K.; Li, Z.; Auerbach, D.; Tully, J.; Wodtke, A. Multiquantum Vibrational Excitation of NO Scattered from Au(111): Quantitative Comparison of Benchmark Data to Ab Initio Theories of Nonadiabatic Molecule-Surface Interactions. Angew. Chem., Int. Ed. 2012, 124, 5038−5042. (14) Schäfer, T.; Bartels, N.; Golibrzuch, K.; Bartels, H.; Köckert; Auerbach, D.; Tully, J.; Kistsopoulos, T.; Wodtke, A. Observation of Direct Vibrational Excitation in Gas-Surface Collisions of CO with Au(111): A New Model System for Surface Dynamics. Phys. Chem. Chem. Phys. 2013, 15, 1863−1867. (15) Meyer, J.; Reuter, K. Electron−Hole Pairs during the Adsorption Dynamics of O2 on Pd(100): Exciting or Not? New J. Phys. 2011, 13, 085010/1−085010/20. (16) Groot, I.; Ueta, H.; van der Niet, M.; Kleyn, A.; Juurlink, L. Supersonic Molecular Beam Studies of Dissociative Adsorption of H2 on Ru(0001). J. Chem. Phys. 2007, 127, 244701/1−244701/7. (17) Farías, D.; Miranda, R. Diffraction of Molecular Hydrogen from Metal Surfaces. Prog. Surf. Sci. 2011, 86, 222−254. (18) Nieto, P.; Farías, D.; Miranda, R.; Luppi, M.; Baerends, E. J.; Somers, M. F.; van der Niet, M. J. T. C.; Olsen, R. A.; Kroes, G. J. Diffractive and Reactive Scattering of H 2 from Ru(0001): Experimental and Theoretical Study. Phys. Chem. Chem. Phys. 2011, 13, 8583−8597. (19) Luntz, A. C.; Persson, M.; Wagner, S.; Frischkorn, C.; Wolf, M. Femtosecond Laser Induced Associative Desorption of H2 from Ru(0001): Comparison of “First Principles” Theory with Experiment. J. Chem. Phys. 2006, 124, 244702/1−244702/9. (20) Vazhappilly, T.; Klamroth, T.; Saalfrank, P.; Hernandez, R. Femtosecond-Laser Desorption of H2 (D2) from Ru(0001): Quantum and Classical Approaches. J. Phys. Chem. C 2009, 113, 7790−7801. (21) Füchsel, G.; Klamroth, T.; Monturet, S.; Saalfrank, P. Dissipative Dynamics within the Electronic Friction Approach: The Femtosecond Laser Desorption of H2/D2 from Ru(0001). Phys. Chem. Chem. Phys. 2011, 13, 8659−8670. (22) Luppi, M.; Olsen, R. A.; Baerends, E. J. Six-Dimensional Potential Energy Surface for H2 at Ru(0001). Phys. Chem. Chem. Phys. 2006, 8, 688−696. (23) Füchsel, G.; Klamroth, T.; Tremblay, J. C.; Saalfrank, P. Stochastic Approach to Laser-Induced Ultrafast Dynamics: The Desorption of H2/D2 from Ru(0001). Phys. Chem. Chem. Phys. 2010, 12, 14082−14094. (24) Hammer, B.; Hansen, L. B.; Norskov, J. K. Improved Adsorption Energetics within Density-Functional Theory Using Revised Perdew−Burke−Ernzerhof Functionals. Phys. Rev. B 1999, 59, 7413−7421. (25) Kubo, R. The Fluctuation-Dissipation Theorem. Rep. Prog. Phys. 1966, 29, 255−284.

we expect translational cooling to dominate. Because the atomic/FEG friction model cannot well account for molecular properties as observed by tensorial, frictional ab initio models,19 we also adopted an enhanced friction model either in the medium or strong regime to roughly account for enhanced friction in the transition state region. Then, one finds that also dissociative sticking can be influenced to a measurable extent, in particular, at higher impact energies. As a result, the sticking curve increases more slowly with energy, bringing experiment and theory in closer agreement. Therefore, electronic friction is a possible candidate to explain differences between frictionless theory (both classical and quantum) and experiment, in addition to the known deficiencies of the gradient-corrected DFT PESs.17 Even stronger effects are found for the shape of the velocity distribution of the incident molecular beam. Broader distributions yield lower reaction probabilities. We also note that experiments in ref 16 were done at surface temperatures of 180 K, where we find some effects due to random forces related to electronic friction at low impact energies. Of course, a bigger influence of surface temperature is expected from the action of phonons, which were neglected here. To conclude, our work shows that electronic friction has probably only a small or moderate, influence on certain observables of H2 molecules interacting with Ru(0001) (e.g., the dissociative sticking probability) and larger effects on others (e.g., the energy distribution in reflected molecules). Interesting challenges for the future are, among others, the impact of electronic friction on molecular diffraction patterns,17 the development of more reliable potential and friction models, the simultaneous inclusion of electronic friction and phonons, and, finally, the treatment of dissipation and nonadiabaticity in a quantum mechanical context.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was funded by the Deutsche Forschungsgemeinschaft through Project Sa 547/8-1 and in part by the Leibniz Graduate School “Dynamics in new Light (DinL)”.

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REFERENCES

(1) Born, M.; Oppenheimer, J. Zur Quantentheorie von Molekeln. Ann. Phys. 1927, 84, 457−484. (2) Langreth, D. C. Energy Transfer at Surfaces: Asymmetric Line Shapes and the Electron−Hole-Pair Mechanism. Phys. Rev. Lett. 1985, 54, 126−129. (3) Morin, M.; Levinos, N. J.; Harris, A. L. Vibrational Energy Transfer of CO/Cu(100): Nonadiabatic Vibration/Electron Coupling. J. Chem. Phys. 1992, 96, 3950−3956. (4) Huang, Y.; Rettner, C.; Auerbach, D.; Wodtke, A. Vibrational Promotion of Electron Transfer. Science 2000, 290, 111−114. (5) White, J.; Chen, J.; Matsiev, D.; Auerbach, D.; Wodtke, A. Conversion of Large-Amplitude Vibration to Electron Excitation at a Metal Surface. Nature 2005, 433, 503−505. (6) Saalfrank, P. Quantum Dynamical Approach to Ultrafast Molecular Desorption from Surfaces. Chem. Rev. 2006, 106, 4116− 4159. 8768



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On the Role of Electronic Friction for Dissociative Adsorption and

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