Reaction-Induced Excitations and Their Effect on Surface Chemistry

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Reaction-Induced Excitations and their Effect on Surface Chemistry Matthew M. Montemore, Robert A. Hoyt, Grigory Kolesov, and Efthimios Kaxiras ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.8b03266 • Publication Date (Web): 09 Oct 2018 Downloaded from http://pubs.acs.org on October 9, 2018

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Reaction-Induced Excitations and their Effect on Surface Chemistry Matthew M. Montemore,†,‡ Robert Hoyt,¶ Grigory Kolesov,‡ and Efthimios Kaxiras∗,¶,‡ †Department of Chemistry and Chemical Biology, Harvard University, Cambridge, MA 02138, USA ‡John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA ¶Department of Physics, Harvard University, Cambridge, MA 02138, USA E-mail: [email protected] Phone: (617) 495-7977

Abstract Despite intensive study of reactions on metals, it is unclear whether electronic excitations play an important role. Here, we show that nonadiabatic effects do indeed play a significant role in N2 and H2 dissociation on Ru nanoparticles. We employ nonadiabatic dynamical calculations based on real-time, time-dependent density functional theory to study energy dissipation during these exothermic reaction steps. We find that dissipation of the excess energy into excitation of electrons exceeds thermal dissipation into phonons. For isolated dissociation events, electronic friction can increase reaction barriers; further, the excitations induced by a dissociation event can affect other reacting molecules. Our studies suggest that, for exothermic reactions, metal catalysts in reaction conditions may be constantly experiencing electronic excitations, and these excitations can significantly affect

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surface chemistry.

Keywords: nonadiabatic dynamics; electronic excitations;

nanoparticles; energy dissipation; real-time time-dependent density functional theory

Both large-scale chemical processes and clean energy technologies rely critically on transition metal catalysts. Exothermic reaction steps on the surfaces of these catalysts can dissipate a large amount of energy in a short amount of time, which raises the question: do phonons absorb most or all of the energy, or can electronic excitations play a major role in the dissipation process? Excitations are expected when there is fast atomic motion and strongly coupled potential energy surfaces; both of these conditions are satisfied during dissociation on metal surfaces. Indeed, it has been shown experimentally that adsorption or reaction on a metal surface can induce excitations. 1–7 It has been suggested that the excitation of electrons is linked to the much lower heat capacity for electrons, as compared to phonons. 8 Along the same lines, thermal conduction in metals is dominated by electrons and electronic excitations. The prevalence, nature, and consequences of reaction-induced excitations are unclear and still debated. 9 Further, excitations induced in other ways, usually by exposure to light, have been repeatedly shown to affect surface chemistry. 10–15 This calls into question the use of ground-state quantum chemical calculations for transition metal catalysts, particularly given recent interest in understanding uncertainties in rate predictions based on density functional theory (DFT). 16,17 Here, we apply high-quality nonadiabatic calculations to a realistic and important catalytic system to show that electronic excitations represent a viable energy dissipation channel, and that these excitations can affect barriers and reactivity. Previous theoretical work has given useful insight into nonadiabatic effects; for example, it has been suggested that the current induced by chemisorption is related to the heat of adsorption by a power law. 18 Overall, this work suggests that reactions can induce electronic excitations in particular situations, for instance, when atoms approaching the surface undergo a spin transition, or when the charge state of the adsorbate depends sensitively on its interaction with the surface. 19–24 In some cases, nonadiabatic effects are thought to be small. 25–27 Much of this work has focused on simple systems and was


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based on simplifying assumptions, due to the challenging and computationally intensive nature of nonadiabatic dynamical calculations. This has prevented characterization of the prevalence and nature of these excitations, as well as their effect on surface chemistry, in more realistic catalytic systems. Here, we show the importance of excitations in a catalytically important system using Ehrenfest dynamics, a first-principles nonadiabatic method that is well-suited to describe excitations in metals 22,28,29 where many similar potential energy surfaces are accessed. In Ehrenfest dynamics, excited-state forces are calculated by explicitly propagating the electronic degrees of freedom.

This differs

from other treatments of quantum-classical dynamics, such as Langevin-type forces in electronic frictions, 30 or forces from a single adiabatic state in surface hopping. This method also allows us to characterize the excitations. Ammonia synthesis from N2 and H2 is a crucial industrial process, as it allows largescale fertilizer production. 31 Ru is the most effective monometallic catalyst for this reaction, in which the rate determining step is the rupture of the N−N bond; this has motivated the intensive study of N2 dissociation on Ru. Previous work has found indirect indications that the N2 /Ru(0001) system may exhibit nonadiabatic effects, but this is a controversial issue. 32–37 The model systems we consider are two Ru clusters consisting of 55 and 147 Ru atoms, on which we study N2 and H2 dissociation (Figure S1). The two different sizes give insight as to whether the results are sensitive to the particular nanoparticle size and shape. The surface of these nanoparticles closely mimic the active sites on Ru surfaces. In particular, the energetics of N2 dissociation on Ru55 and for one of the sites on Ru147 correspond closely to those previously identified as the active sites on Ru catalysts for ammonia synthesis. 38 To study energy dissipation during a typical dissociation event, we perform Ehrenfest dynamics simulations with the system initialized at the N2 dissociation transition state on the Ru55 nanoparticle. We assign small initial velocities on the N atoms to induce dissociation. Test calculations show that varying the initial kinetic energy on the N atoms between 0.01 and 0.1 eV has very little effect on the results. After the initial nonadiabatic run from this state, coordinates are extracted every 4.8 fs along the trajectory, and


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ground state calculations are performed with these coordinates. This procedure gives the energy of the system if it had followed the same trajectory but stayed in the electronic Born-Oppenheimer ground state. The difference in energy between the nonadiabatic and ground state energy represents the energy dissipated into electronic degrees of freedom. As shown in Figure 1, the system remains nearly in the ground state for roughly 100 fs, but excitations are induced as the dissociation proceeds. Overall, the ground state and nonadiabatic curves have similar shapes, suggesting that the excited-state potential energy surface is qualitatively similar to the ground state. Surprisingly, the dissociation process continues to excite electrons well after the initial dissociation event. Our analysis suggests that the rate of excitation is qualitatively linked to the kinetic energy of the N atoms, as the excitation rate peaks occur synchronously with peaks in the kinetic energy (see Figure S5). Because the N atoms retain high kinetic energy over the course of the simulation, they can continue to induce electronic excitations. By 500 fs, a significant amount of energy, > 1 eV, has been dissipated into electronic excitations. The energy dissipation into phonons can be calculated as the kinetic energy of the Ru atoms. The dissociating N atoms are able to excite significant Ru motion over short (< 200 fs) time scales, and yet the dissipation into electrons is at least as important as the dissipation into phonons. Similar results are obtained for the Ru147 nanoparticle (see Figure S2). Hence, electronic excitations are an important channel for energy dissipation during dissociation. This conclusion holds even if the Ru atoms are thermalized to 300 K prior to dissociation or fixed during dissociation (see Figure S3). Previous work using electronic frictions has found that N2 associative desorption from Ru(0001) has an expected energy dissipation into electrons of 0.5 eV, 36 and this was thought to be an underestimate of the true value. This is a roughly similar magnitude to our results. We also examined H2 dissociation, where the dissipation into phonons is expected to be small due to the small mass of the H atoms 39 (see Figure 1c, d). Since H2 dissociation is less exothermic than N2 dissociation, the amount of electronic excitation is also smaller, but it is somewhat higher than the phonon excitation. If the initial kinetic energy of the


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H atoms is increased, more electronic excitation is observed but the energy dissipated into phonons stays more constant (see Figure S4). Because H2 dissociation is barrierless on Ru and results in less electronic excitation, we focus on N2 dissociation in the rest of this work.

a)

c)

b)

d) (Ru K.E.) (Ru K.E.)

Figure 1: a,b) N2 dissociation on a Ru55 nanoparticle dissipates a significant amount of energy into electronic excitations. Initially, the N2 molecule is at its dissociation transition state and 0.05 eV of kinetic energy is imparted towards dissociation. a) Total potential energy for the nonadiabatic run and ground state energies along the same trajectory for comparison. A few snapshots along the trajectory are shown. b) Energy dissipated into electrons (the difference between the curves in part (a)) and energy dissipated into phonons (the kinetic energy of all Ru atoms) as a function of time. c,d) H2 dissociation on a Ru55 nanoparticle, initialized with 0.05 eV of kinetic energy towards the particle.

We expect our result, that exothermic reactions can induce significant electronic excitation on metal nanoparticles, to apply fairly generally, because the excitation is driven by the motion of the dissociating atoms. However, the de-excitation of the electrons is driven by the coupling of the electronic states to the metal substrate’s phonons. This coupling can vary significantly for different metallic systems. Ehrenfest dynamics does not correctly describe the de-excitation over extended time scales, so we applied a twotemperature model to our results to test their validity (see Figure S6). This analysis


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suggests that our results are at least qualitatively correct for the 500 fs we examine here, and perhaps for significantly longer. To gain insight into the spatial distribution of the excitations, we examined the difference in charge density between a nonadiabatic run and the ground state at configurations along the trajectory. The excitations quickly engulf the entire nanoparticle, as shown in Figure 2a (see also Movies S1 and S2). Surface Ru atoms tend to experience higher levels of excitation than bulk Ru atoms (see Figure S7a), which increases the likelihood that the excitations can affect surface chemistry. We further characterized the excitations by examining the occupation of electronic states as a function of their energy, and comparing to the Fermi-Dirac distribution that is expected for the ground state. We projected the nonadiabatic Kohn-Sham wavefunctions onto ground-state wavefunctions, which allowed us to calculate the occupations for a nonadiabatic state. When the system is nearly in the ground state, the resulting curve is the expected Fermi-Dirac distribution at the initial electronic temperature of 300 K (see Figure 2b). As the system becomes excited, these curves show well-defined peaks above the Fermi energy, as would be expected for an electron-hole pair excitation. As time progresses, these curves tend to resemble Fermi-Dirac distributions at higher temperatures, suggesting the existence of hot electrons. The kinetic analysis of catalytic surfaces relies on calculating activation barriers for elementary processes. Since the rates depend exponentially on these barriers, it is crucial to test whether nonadiabatic effects can change these barriers from predictions based on a ground-state treatment. First, we test whether a dissociating N2 molecule that is initially in the ground state experiences a different barrier than the ground-state barrier. Extracting a barrier directly from a molecular dynamics (MD) simulation is extremely challenging; however, we can take advantage of the fact that we have calculated the ground-state transition state. To do so, we first run a ground-state MD calculation, beginning at the transition state, with 0.10 eV of initial kinetic energy directed towards the initial, associated state. Once the system has reached a minimum in the initial state potential well, we extract the coordinates and velocities, reverse the velocities, and run a


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Figure 2: a) Charge density differences between the excited state and the ground state for Ru55 at different points in time. An isosurface at 10−4 e/˚ A3 is shown; the negative isosurface is omitted for clarity. b,c) Fractional occupation numbers as a function of energy for states on b) a surface atom and c) a bulk atom. The shaded areas show Fermi-Dirac distributions at 300 or 600 K for reference.


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nonadiabatic calculation with these initial conditions. If the system stays in the ground state, the N2 molecule will reach the transition state with the same potential energy as the initial state for the ground-state run, due to microscopic reversibility. This is not the case for dissociation on Ru147 : upon reaching the transition state, the potential energy of the system is 0.07 eV higher than the ground-state transition state, demonstrating that nonadiabatic effects indeed increase the barrier (Figure S5). Essentially, a high velocity is needed to reach the transition state, and at the high velocity excitations are induced. These excitations act as a frictional force on the system. 30 The effect of this change in barrier can be estimated by calculating the dissociation rate using harmonic transition state theory (Ae−Ea /kT ) and multiplying by the probability of dissociation (as opposed to desorption). This procedure predicts that, at 300-600 K, the rate is roughly 25-220 times slower than would be predicted from the ground-state barrier. Hence, while an error of 0.07 eV still allows ground-state DFT calculations to be useful for qualitative predictions of catalytic performance, it can have a significant impact on quantitative predictions. Our calculations for Ru55 show a similar barrier change of 0.04 eV. This barrier change also shows that Ehrenfest calculations that have only enough energy to reach the ground-state barrier will not result in dissociation, while Born-Oppenheimer calculations will, as we have explicitly confirmed in separate calculations. Therefore, nonadiabatic calculations can lead to qualitatively different results from ground-state calculations. Further, because the system does not remain in the Born-Oppenheimer ground state, a reaction could follow a different effective potential energy surface in the forward direction as compared to the reverse direction. Therefore reactions on metals may not always obey the principle of microscopic reversibility. While we have shown that the barrier for the dissociation of a molecule is affected by nonadiabaticity, it is equally important to consider whether or not the excitations induced by a dissociating molecule can affect other, nearby molecules. Indeed, excitations and hot electrons have been widely shown to affect surface chemistry. 10–15 We perform a simple test of this by examining how a dissociating N2 molecule affects another N2 molecule that is fixed at the transition state. By monitoring how the forces on this fixed N2 molecule


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are affected by excitations, we can test if the barrier and potential energy surface for dissociation are significantly affected by electronic excitations. This calculation models the many possible cases where an N2 molecule begins to dissociate, and then a nearby N2 molecule reaches the dissociation transition state shortly thereafter. This will become increasingly likely at higher pressures. As shown in Figure 3 and Movie S3, the excitations induced by a dissociating N2 molecule indeed affect the potential energy surface for other N2 molecules. The excitation-induced force (defined as the difference between the force found in the Ehrenfest simulation and the force at the same configuration but in the ground state) reaches as high as 0.2 eV/˚ A. For comparison, during the initial dissociation of an N2 molecule, the force on the N atoms is usually less than 1.5 eV/˚ A, and peaks at around 2 eV/˚ A. This effect may be particularly important for slower reaction steps, which are rare on microscopic timescales. These steps may be influenced by the excitations induced by other adsorption and reaction steps occurring in their vicinity, particularly those that are high energy, such as a fast-moving molecule impacting the surface. These forces can be qualitatively compared to Langevin dynamics, where a stochastic force is added to an MD simulation in order to simulate the effect of electronic excitations on the nuclear trajectory. As would be expected in Langevin dynamics, the force is highly fluctuating. However, in Langevin dynamics, there is no correlation between the forces at different times, while it is clear in Figure 3b that there is some short-time correlation, as well as longer time correlation (i.e., the moving average of the force is not constant). Our calculations show that the dissociation of N2 and H2 on Ru nanoparticles is highly nonadiabatic, and that nonadiabaticity can have significant effects for surface processes on metal nanoparticles. Therefore, it is not always safe to assume that metal nanoparticles in reactive conditions remain in the ground state, nor that molecules are always on the potential energy surface of the ground-state nanoparticle. Our results for multiple species on multiple nanoparticles suggest that this phenomenon may be quite general for exothermic reaction steps on metal nanoparticles. However, it is possible that much larger nanoparticles could behave somewhat differently, due to a higher density of electronic states and phonon modes. Further, while we expect the presence of a support


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Figure 3: a) Schematic showing the nanoparticle with two N2 molecules, one which is fixed in the transition state and one which is allowed to dissociate. b) The force on the N2 molecule that is fixed at the transition state induced by the excitation, defined as the difference between ground-state and nonadiabatic forces. c) Snapshots showing the direction of the forces on the fixed N2 molecule.

to have a small effect on the creation of excitations, it could affect their behavior. Our results, when taken in consideration along with previous studies, suggest that reactions on metals often induce electronic excitations. 1–7 We found that the kinetic energy of the reacting atoms is the primary factor determining the level of excitation. This is in qualitative agreement with previous studies, which tend to show higher nonadiabatic effects in systems with significant kinetic energy due to exothermicity or a high-energy molecular beam than in systems with little kinetic energy. 1,36,40,41 This suggests that metal catalysts in reaction conditions may be constantly experiencing electronic excitations, particularly at high temperature and for exothermic reactions. These electronic excitations can play a dominant role in dissipation and relaxation, and also affect surface chemistry. Isolated molecules experience somewhat higher barriers than those predicted by ground-state calculations, and excitations induced by one molecule can affect another. While ground-state DFT calculations have proven useful for qualitative predictions of transition metal catalysts, it may be necessary to account for these nonadiabatic effects in order to obtain quantitative agreement with experiment;


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this would be useful in improving catalytic performance through materials design based on highly accurate predictions. Accounting for these effects may improve the accuracy of predictions, and controlling them may improve catalytic performance. If properly harnessed, this effect may also prove useful for sensing technologies or the conversion of chemical energy to electrical energy.

Supporting Information Supplementary methods, description of the systems, movies, and further analysis as described in the text.

This material is available free of charge via the Internet at

http://pubs.acs.org.

Acknowledgements This work was performed as part of Integrated Mesoscale Architectures for Sustainable Catalysis, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award # DE-SC0012573. K. G. acknowledges funding from the Army Research Office Multidisciplinary University Research Initiative (MURI), Award No. W911NF-14-0247. Computational resources on the Odyssey cluster (FAS Division of Science, Research Computing Group at Harvard University), and at the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility (Office of Science of the U.S. Department of Energy, Contract No. DE-AC02-05CH11231), were used in this work.

Competing Interests The authors declare no competing financial interests.


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Graphical TOC Entry Exothermic Reaction

Electronic Excitation

Effects on Surface Chemistry

e-

ΔE, excited state

Energy

ΔE, ground state

Energy

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ACS Catalysis

Reaction Coordinate


Reaction-Induced Excitations and Their Effect on Surface Chemistry

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