Article pubs.acs.org/JPCC
NO Vibrational Energy Transfer on a Metal Surface: Still a Challenge to First-Principles Theory Bastian C. Krüger,†,‡ Nils Bartels,†,‡ Christof Bartels,†,‡ Alexander Kandratsenka,†,‡ John C. Tully,§ Alec M. Wodtke,†,‡ and Tim Schaf̈ er*,†,‡ †
Max-Planck-Institut für biophysikalische Chemie, Karl-Friedrich-Bonhoeffer-Institut, Am Faßberg 11, 37077 Göttingen, Germany Institut für Physikalische Chemie, Georg-August-Universität Göttingen, Tammannstr. 6, 37077 Göttingen, Germany § Department of Chemistry, Yale University, 225 Prospect Street, PO Box 208107, New Haven, Connecticut 06520-8107, United States ‡
ABSTRACT: During a collision of highly vibrationally excited NO with a Au(111) surface, the molecule can lose a large fraction of its vibrational energy into electronic excitation of the metal. This process violates the Born−Oppenheimer approximation and represents a major challenge to theories of molecule−surface interaction. Two ab initio approaches to this problem, one using independent electron surface hopping (IESH) and the other electronic friction, previously reported good agreement with the limited available data on multiquantum vibrational relaxation; however, at that time only experiments for NO(vi = 15) at an incidence translational energy of Ei = 0.05 eV were available. In this work, we report a comparison of recently reported experiments characterizing the multiquantum vibrational relaxation of NO on Au(111) for a wider range of incidence translational and vibrational energies to IESH and molecular dynamics with electronic friction (MDEF) calculations for these conditions. Both theories fail to explain the large amount of vibrational energy transferred from NO to the solid.
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INTRODUCTION More than three decades ago, experiments on the vibrational lifetime of CO on Cu(100)1 presented evidence for the coupling of molecular vibration to electronic degrees of freedom in molecule−surface interactions. In comparison to vibrationally excited adsorbates on insulators, for example, CO on NaCl,2 the vibrational lifetime of an adsorbate at a metal surface is shortened by 9 orders of magnitude. This could be explained by a coupling of the adsorbate vibrational degrees of freedom to electron−hole pairs.3−6 Note that this relaxation process cannot be explained within the framework of the Born−Oppenheimer approximation.7 A description based on a single potential energy surface (PES) is not sufficient; therefore, accurate theoretical models need to include electronically nonadiabatic effects. Vibrational excitation has been experimentally observed in direct scattering, that is, without trapping/desorption, of nitric oxide (NO) from Ag(111)8 as well as Au(111)9,10 surfaces, and these observations are also considered clear examples of coupling between metallic electrons and molecular vibration. For the case of NO on Au(111), experiment was compared to two ab initio theories of electronically nonadiabatic molecule− surface interaction,9 IESH11 and molecular dynamics with electronic friction (MDEF).12 Only IESH could explain the magnitude of the large excitation probability.9 The main differences between IESH and MDEF concern how the vibrational−electronic coupling is treated. The MDEF approach utilizes a weak coupling approximation, considering the metal electrons implicitly on the level of a frictional force © 2015 American Chemical Society
with the propagation of nuclei happening on a single PES. In contrast, the IESH theory considers the nuclear dynamics on multiple PESs and solves the electron motion equations explicitly: in a first step, PESs are obtained from density functional theory (DFT) for the neutral NO molecule and its negative ion,13 and in a second step, the continuum of electronic states of the metal is approximated by multiple discrete states and electronically nonadiabatic transitions are treated by a surface hopping procedure.14 One of the most startling experimental observations for the NO/Au system was multiquantum vibrational relaxation.15 NO molecules initially prepared in vibrational state vi = 15 with Ei = 0.05 eV incidence translational energy lose on average 8 quanta of vibrational energy in direct scattering events at a Au(111) surface. Under otherwise similar conditions, NO vibrational relaxation on an insulator is dramatically reduced.16 Two reports, one employing the IESH theory17 and the other employing electronic friction-based theory,18 appeared to show semiquantitative agreement with the results of the multiquantum relaxation experiments. Recently, new experiments on NO(vi = 3) scattered from Au(111) have provided a much richer set of dynamical observations to which theory can be compared.19−23 Using a new experimental technique, “optical state selection with adiabatic orientation”,24 a strong influence of molecular Received: January 14, 2015 Revised: January 16, 2015 Published: January 16, 2015 3268
DOI: 10.1021/acs.jpcc.5b00388 J. Phys. Chem. C 2015, 119, 3268−3272
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The Journal of Physical Chemistry C orientation on relaxation probabilities was found,19,20 qualitatively in agreement with the predictions of IESH.17 Beyond this, state-to-state time-of-flight measurements gave detailed information on the coupling between translational, rotational, and vibrational degrees of freedom induced by NO collision at a gold surface.21,22 Vibrational relaxation studies from NO(vi = 3) were also compared to IESH and MDEF.23 This revealed a strong disagreement regarding the translational energy dependence of vibrational relaxation during the collision. The theoretical simulations displayed multibounce trajectories inconsistent with experimentally measured narrow angular distributions clearly indicating a direct “single-bounce” scattering mechanism. The agreement between experiment and theory was significantly improved when multibounce trajectories were artificially excluded from the analysis. The fraction of multibounce collisions was independent of the electronically nonadiabatic dynamics model employed and thus attributed to errors in the ground-state PES used in both approaches. A correct theoretical description of multiquantum vibrational relaxation is particularly interesting because stretching during the large-amplitude motion of NO in this case closely resembles bond dissociation. Hence, electronically nonadiabatic influences on bond breaking and making in surface chemistry at metals might be better understood. While agreement between experiment and theory has been reported,17,18 it is unfortunate that previous comparison could be made only at low incidence translational energy,17 where we now know multibounce effects seen in the simulations can be a problem. The multibounce events are much less important at high incidence energy.23 This suggests that comparisons between electronically nonadiabatic dynamics theories and experiments at incidence energies higher than those explored experimentally before could be informative. Recently, advances in optical preparation methods for highly vibrationally excited NO25 have allowed us to extend multiquantum vibrational relaxation experiments to a wide range of incidence translational and vibrational energies as well as to investigate the influence of the NO molecule incidence orientation.26 In this work, we report a comparison of experiments on the scattering of highly vibrationally excited NO from Au(111) to theory. For incidence energies up to Ei = 1 eV and vibrational excitation varying between vi = 3 and 16, vibrational relaxation distributions are obtained. We compare ab initio theories of electronically nonadiabatic molecule−surface interactions under conditions where multibounce events are unimportant in the theory. We find that neither IESH nor MDEF, as they are presently implemented, can explain the large amount of vibrational energy transferred from the NO molecule to the gold solid.
ular dynamics, BOMD) for NO in vi = 0. First, we recapitulate the experimental conditions applied to obtain vibrational state distributions in collisions of highly vibrationally excited NO molecules with a single-crystal Au(111) surface. Second, we refer to references describing the theory used in this work. We use a molecular beam surface scattering apparatus to reveal the scattering process. A pulsed molecular beam of rotationally cold NO molecules is produced by expanding mixtures of 1% and 10% NO seeded in H2 through a piezoelectric valve (1 mm diameter nozzle, 10 Hz, 3 atm stagnation pressure). At a distance of 3 cm downstream, the molecules enter a differential chamber (10−8 Torr) via a 2 mm electro-formed skimmer (Ni Model 2, Beam dynamics, Inc.). Here, highly vibrationally excited NO(vi = 11; 16) molecules are prepared in the ground electronic and rotational state X2Π1/2(J = 0.5). We employ the pump−dump−sweep method,25 which includes both stimulated emission pumping27 (pump−dump) via the A2Σ+(v = 2, J = 0.5) state and subsequent depletion of the excited-state population by further excitation to a dissociative state (sweep). The output of a Nd:YAG (Spectra Physics, Quanta Ray Lab 170-10, 10 Hz, 10 ns pulse width (fwhm) of the fundamental) pumped home-built optical parametric oscillator28 (OPO) is mixed with the fourth harmonic of the Nd:YAG to obtain suitable radiation for the pump step. The output of a second home-built OPO of the same type is frequency doubled, for NO(vi = 16) preparation, or mixed with the second harmonic of the Nd:YAG, for NO(vi = 11) preparation. Radiation produced in this way (NO(vi = 16), 450.50 nm; NO(vi = 11), 336.10 nm) connects the A2Σ+(v = 2, J = 0.5) state with the desired high v-state of the ground electronic state. A Nd:YAG (Spectra Physics, Quanta Ray PRO-270-10) pumped dye laser (Sirah, Precision Scan, PRSCDA-24) supplies radiation for the Sweep step (450.87 nm). As the preparation of NO(vi = 16) requires dump and sweep radiation of similar wavelengths, the function of the dye laser and OPO system can be switched. Experimentally, a slightly better performance was observed for the dye laser undertaking the dump step. Subsequently, the molecules enter the surface chamber (10−10 Torr) via an aperture of 2 mm. The NO molecules collide with the surface at close to normal incidence and are scattered back in various rovibrational states. Detection of incoming and scattered molecules is achieved by performing (1 + 1) resonance enhanced multiphoton ionization (REMPI) spectroscopy via the A2Σ+(v = 0−7) state. Suitable radiation between 235 and 350 nm is delivered by a commercial OPO laser system (Continuum Sunlite Ex, 3 GHz bandwidth, 2 mJ/ pulse @ 255 nm). Produced ions are accelerated onto a microchannel plate detector (Tectra MCP 050 in chevron assembly), and the signal is visualized and recorded with an oscilloscope (LeCroy Waverunner LT344) interfaced to an electronic computer. From a fit to the recorded (1 + 1) REMPI spectrum of scattered NO ground electronic state molecules we are able to derive their final vibrational state distribution. Cleanliness of the Au(111) surface is ensured by Argon-ion sputtering (LK Technologies NGI3000, 3 kV, 20 min) followed by annealing at 970 K for 20 min and verified with Auger electron spectroscopy. The IESH calculations were performed using the same code as used in ref 17. Additionally, we have performed a provisional multibounce correction as reported in ref 23.
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EXPERIMENTAL AND THEORETICAL METHODS In the experiments, NO molecules are prepared in vi = 3, 11, or 16 and collide with the Au(111) surface with incidence translational energies of either 0.5 or 1.0 eV.26 Results for vi = 3 come from refs 22 and 23. We performed IESH and MDEF calculations for these experimental conditions. Both IESH and MDEF rely on the same electronic ground-state PES reported in ref 13. In this way, the comparison of the two methods is not strongly dependent on the DFT input data that both methods require because it comes from the same DFT calculation. Additionally, we have performed IESH and purely adiabatic molecular dynamics calculations (Born−Oppenheimer molec3269
DOI: 10.1021/acs.jpcc.5b00388 J. Phys. Chem. C 2015, 119, 3268−3272
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The Journal of Physical Chemistry C MDEF is governed by equations11,12 which we recapitulate briefly: M·R̈ = −
∂E0 − K(R) ·Ṙ + FL (t ) ∂R
(1)
In eq 1, R is a column-vector of all nuclear coordinates, M a mass matrix, and E0 the ground-state potential energy surface. K(R) = π ℏd(R)d(R)
(2)
is a friction matrix in the Markovian limit approximated by the outer product of the nonadiabatic coupling vector d(R) of adiabatic orbitals just below and just above the Fermi level. A random (Langevin) force FL(t) FL (t ) = r(t )d(R) π ℏkBT
(3)
is defined in terms of the stochastic process r(t) with the standard normal distribution (⟨r(t)⟩ = 0 and ⟨r(t)r(t′)⟩ = δ(t − t′)) in agreement with the fluctuation−dissipation theorem
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⟨FL(t )FL(t ′)⟩ = kBT K(R)δ(t − t ′)
(4)
RESULTS The experimental and theoretical results are compared in Figure 1. We emphasize several key observations. At Ei = 0.5 eV (left panels), the influence of multibounce events in the simulations is seen clearly (compare open to closed symbols). At Ei = 1.0 eV (right panels), multibounce events are of minor importance. For both MDEF and IESH, multibounce events increase the amount of vibrational energy transferred; this is especially clear for Ei = 0.5 eV. Both MDEF as well as IESH reasonably describe vibrational relaxation of NO from vi = 3 at both translational energies. However, at Ei = 1.0 eV, where little influence of multibounce events is present, neither theory predicts as much multiquantum vibrational relaxation as is observed in experiment for vi = 11. The deviation is even more severe for vi = 16. Interestingly, IESH and MDEF give quite similar predictions of vibrational relaxation under conditions where multibounce effects are unimportant. We conclude that previously reported agreement between experiment and theory at low incidence translational energies17 was accidental and strongly influenced by multibounce events. Additionally, we compare the theoretically predicted final translational energy distribution for vibrational elastic collisions to the experimental observations (Figure 2). Both the BOMD and the IESH simulations predict a very similar translational energy distribution. This distribution is significantly shifted to lower translational energies with respect to the experimental values, which we assign to a too soft gold surface in the DFTbased PES.
Figure 1. Final vibrational state distributions: comparing experiment (black, filled circles) and results of IESH (red, triangles) as well as MDEF (blue, squares) calculations. Empty symbols indicate the results corrected for multibounce events as described in ref 23. Vibrationally excited NO is prepared in its electronic ground state with the vibrational quantum number vi and incidence translational energy Ei = 0.5 eV (left panels) and Ei = 1.0 eV (right panels), respectively. Arrows indicate the initial vibrational state.
experiment and calculations displayed in Figure 1 is solely due to the PES, we may identify the qualitative characteristics of the PES that could be in error and lead to an overestimation of multibounce events: (1) the gold surface is too soft and (2) the interaction potential between NO and Au is too corrugated. The assumption of the existence of error (1) is supported by the finding that the translational energy distribution for vibrational elastic collisions cannot be satisfactorily reproduced by theory. Figure 2 demonstrates that both adiabatic and nonadiabatic calculations consistently predict significantly smaller mean final translational energies compared to the experimental value. Moreover, it is likely that error (2) exists on the present PES because this is one of the most difficult aspects of molecule−surface interactions to model with DFT.13 Furthermore, for highly vibrationally excited NO(vi = 16), the corresponding vibrational energy (3.4 eV) is comparable to the barrier height for NO dissociation on Au(111), 3.5 eV, reported in ref 30. This barrier to dissociation is not captured in the PES used in the present theoretical implementations.
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DISCUSSION We now discuss the possible reasons for the disagreement between experiment and theory. Computational approaches consist of two major parts: the model for the electronically nonadiabatic propagation and the construction of the PES (or PESs) upon which the propagation happens. First, we consider possible errors in the PES. Note that the PES is constructed from energy values calculated from ab initio electronic structure theory, which are then fitted with an analytic function. Problems with either of these steps may lead to errors in the PES. Assuming that the disagreement between 3270
DOI: 10.1021/acs.jpcc.5b00388 J. Phys. Chem. C 2015, 119, 3268−3272
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The Journal of Physical Chemistry C
assign these deviations to significant errors in the PESs used in the simulations. Specifically, it appears that weak forces in the entrance channel that represent features of the PESs influencing multibounce events need to be improved. Furthermore, the dissociation of NO to form adsorbed atoms on the gold surface must likely also be built into the PES. Hence, the multiquantum vibrational relaxation of NO on Au(111) originally reported in ref 15 in 2000 remains to be fully explained. We hope that this work might stimulate future efforts to solve this outstanding problem.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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Figure 2. Final translational energy: comparison of theoretical predictions (IESH, red curve and BOMD, blue curve) to experimental observations (black curve) for vibrational elastic collisions of NO(vi = 3, Ji = 1.5) with an incidence translational energy of 1.0 eV. Experiments have been performed as described in detail in ref 21. In the experiment, NO is scattered back in the rotational states J = 1.5− 3.5. To obtain a reasonable comparison, the theoretical calculations consider only trajectories leading to a rotational excitation below 0.1 eV.
ACKNOWLEDGMENTS We acknowledge support from the Alexander von Humboldt Foundation. N.B. and T.S. acknowledge continuous motivation by M. Klose. The IESH method was developed under support from the U.S. DOE-BES, Grant DE-FG02-05ER15677.
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REFERENCES
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Vibrational energy transfer could be strongly enhanced by trajectories that resemble a failed attempt to traverse the transition state to dissociation, as has been seen for H2 interactions at Cu(111).29 The second component of theoretical modeling concerns the electronically nonadiabatic dynamics. Here, we are confident that the general approach followed by IESH is not responsible for the multibounce events. In comparing IESH, MDEF, and even fully adiabatic dynamics, it was seen that in all cases multibounce events are present in similar frequency.23 This is strong evidence that the (adiabatic) electronic ground-state PES used in these calculations has errors as described above. However, concerning the inability of IESH or MDEF to capture the large amount of vibrational energy transferred to the solid at high vi, the situation is not so clear. Correcting errors in the PES, for example, implementing a proper description of NO dissociation, could be important to solving this problem, but it cannot be ruled out that the large vibrational energy loss seen experimentally (Figure 1) reflects a nonadiabatic transfer process that is much more efficient than is included in the current implementation of IESH. The IESH simulations drastically simplify the electronic structure of NO. Only one excited electronic state of NO, the electron transfer NO anion state, was considered, and spin effects were ignored. It is conceivable that additional excited states must be included to fully describe the energy transfer, which is feasible in principle within the IESH framework but a daunting challenge.
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CONCLUSION We observe significant deviations between experimentally determined vibrational relaxation probabilities and predictions of state-of-the-art ab initio theoretical models of electronically nonadiabatic energy transfer. The deviations are most severe at high incidence energies of translation where single-bounce dynamics dominate and high incidence energies of vibration, conditions that are most likely to lead toward dissociation. We 3271
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