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

First-Principles Insights into Adiabatic and Nonadiabatic Vibrational Energy-Transfer Dynamics during Molecular Scattering from Metal Surfaces: The Importance of Surface Reactivity

Energy transfer is ubiquitous during molecular collisions and reactions at gas-surface interfaces. Of particular importance is vibrational energy transfer because of its relevance to bond forming and breaking. In this Perspective, we review recent first-principles studies on vibrational energy-transfer dynamics during molecular scattering from metal surfaces at the state-to-state level. Taking several representative systems as examples, we highlight the intrinsic correlation between vibrational energy transfer in nonreactive scattering and surface reactivity and how it operates in both electronically adiabatic and nonadiabatic pathways. Adiabatically, the presence of a dissociation barrier softens a bond in the impinging molecule and increases its couplings with other molecular modes and surface phonons. In the meantime, the stronger interaction between the molecule and the surface also changes the electronic structure at the barrier, resulting in an increase of nonadiabatic effects. We further discuss future prospects toward a more quantitative understanding of this important surface dynamical process.

Computational approaches to dissociative chemisorption on metals: towards chemical accuracy

We review the state-of-the-art in the theory of dissociative chemisorption (DC) of small gas phase molecules on metal surfaces, which is important to modeling heterogeneous catalysis for practical reasons, and for achieving an understanding of the wealth of experimental information that exists for this topic, for fundamental reasons. We first give a quick overview of the experimental state of the field. Turning to the theory, we address the challenge that barrier heights (E_b, which are not observables) for DC on metals cannot yet be calculated with chemical accuracy, although embedded correlated wave function theory and diffusion Monte-Carlo are moving in this direction. For benchmarking, at present chemically accurate E_b can only be derived from dynamics calculations based on a semi-empirically derived density functional (DF), by computing a sticking curve and demonstrating that it is shifted from the curve measured in a supersonic beam experiment by no more than 1 kcal mol^-1. The approach capable of delivering this accuracy is called the specific reaction parameter (SRP) approach to density functional theory (DFT). SRP-DFT relies on DFT and on dynamics calculations, which are most efficiently performed if a potential energy surface (PES) is available. We therefore present a brief review of the DFs that now exist, also considering their performance on databases for E_b for gas phase reactions and DC on metals, and for adsorption to metals. We also consider expressions for SRP-DFs and briefly discuss other electronic structure methods that have addressed the interaction of molecules with metal surfaces. An overview is presented of dynamical models, which make a distinction as to whether or not, and which dissipative channels are modeled, the dissipative channels being surface phonons and electronically non-adiabatic channels such as electron-hole pair excitation. We also discuss the dynamical methods that have been used, such as the quasi-classical trajectory method and quantum dynamical methods like the time-dependent wave packet method and the reaction path Hamiltonian method. Limits on the accuracy of these methods are discussed for DC of diatomic and polyatomic molecules on metal surfaces, paying particular attention to reduced dimensionality approximations that still have to be invoked in wave packet calculations on polyatomic molecules like CH₄. We also address the accuracy of fitting methods, such as recent machine learning methods (like neural network methods) and the corrugation reducing procedure. In discussing the calculation of observables we emphasize the importance of modeling the properties of the supersonic beams in simulating the sticking probability curves measured in the associated experiments. We show that chemically accurate barrier heights have now been extracted for DC in 11 molecule-metal surface systems, some of which form the most accurate core of the only existing database of E_b for DC reactions on metal surfaces (SBH10). The SRP-DFs (or candidate SRP-DFs) that have been derived show transferability in many cases, i.e., they have been shown also to yield chemically accurate E_b for chemically related systems. This can in principle be exploited in simulating rates of catalyzed reactions on nano-particles containing facets and edges, as SRP-DFs may be transferable among systems in which a molecule dissociates on low index and stepped surfaces of the same metal. In many instances SRP-DFs have allowed important conclusions regarding the mechanisms underlying observed experimental trends. An important recent observation is that SRP-DFT based on semi-local exchange DFs has so far only been successful for systems for which the difference of the metal work function and the molecule's electron affinity exceeds 7 eV. A main challenge to SRP-DFT is to extend its applicability to the other systems, which involve a range of important DC reactions of e.g. O₂, H₂O, NH₃, CO₂, and CH₃OH. Recent calculations employing a PES based on a screened hybrid exchange functional suggest that the road to success may be based on using exchange functionals of this category.

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.

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

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

Vibrational Excitation of H2 Scattering from Cu(111): Effects of Surface Temperature and of Allowing Energy Exchange with the Surface

In scattering of H₂ from Cu(111), vibrational excitation has so far defied an accurate theoretical description. To expose the causes of the large discrepancies with experiment, we investigate how the feature due to vibrational excitation (the "gain peak") in the simulated time-of-flight spectrum of (v = 1, j = 3) H₂ scattering from Cu(111) depends on the surface temperature (T_s) and the possibility of energy exchange with surface phonons and electron-hole pairs (ehp's). Quasi-classical dynamics calculations are performed on the basis of accurate semiempirical density functionals for the interaction with H₂ + Cu(111). The methods used include the quasi-classical trajectory method within the Born-Oppenheimer static surface model, the generalized Langevin oscillator (GLO) method incorporating energy transfer to surface phonons, the GLO + friction (GLO+F) method also incorporating energy exchange with ehp's, and ab initio molecular dynamics with electronic friction (AIMDEF). Of the quasi-classical methods tested, comparison with AIMDEF suggests that the GLO+F method is accurate enough to describe vibrational excitation as measured in the experiments. The GLO+F calculations also suggest that the promoting effect of raising T_s on the measured vibrational excitation is due to an electronically nonadiabatic mechanism. However, by itself, enabling energy exchange with the surface by modeling surface phonons and ehp's leads to reduced vibrational excitation, further decreasing the agreement with experiment. The simulated gain peak is quite sensitive to energy shifts in calculated vibrational excitation probabilities and to shifts in a specific experimental parameter (the chopper opening time). While the GLO+F calculations allow important qualitative conclusions, comparison to quantum dynamics results suggests that, with the quasi-classical way of describing nuclear motion and the present box quantization method for assigning the final vibrational state, the gain peak is not yet described with quantitative accuracy. Ways in which this problem might be resolved in the future are discussed.

Quantum and classical dynamics of reactive scattering of H2 from metal surfaces

State-of-the-art theoretical models allow nowadays an accurate description of H₂/metal surface systems and phenomena relative to heterogeneous catalysis. Here we review the most relevant ones investigated during the last 10 years.

Chemical energy dissipation at surfaces under UHV and high pressure conditions studied using metal–insulator–metal and similar devices

Thin film metal heterostructures have allowed new light to be shed on the dissipation of chemical energy into electric excitations on metal surfaces.

Electronic energy dissipation during scattering of vibrationally excited molecules at metal surfaces: ab initio simulations for HCl/Al(111)

In this Letter, ab initio molecular dynamics simulations based on time-dependent density functional theory for the electrons and Ehrenfest dynamics for the nuclei are reported that detail the interaction of a vibrating HCl molecule with an Al(111) substrate. The mechanism responsible for the strong electron-hole-pair (EHP)-vibrational coupling in case of highly vibrationally excited molecules is traced back to a large eigenenergy shift of the spz*-like antibonding HCl lowest unoccupied molecular orbital with the bond length. As a consequence of this mechanism, the electronic excitation spectra turn out to be highly asymmetric. The simulations suggest an explanation of how to reconcile a strong EHP-vibrational coupling in case of highly vibrationally excited molecules with the small, but clearly evident, electronic contribution to the v=0 → v=1 vibrational excitation observed experimentally during the scattering of HCl molecules at a hot Au surface by Ran et al. [Phys. Rev. Lett. 98 237601 (2007)].

Electronic excitations induced by hydrogen surface chemical reactions on gold

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

Apparent failure of the Born-Oppenheimer static surface model for vibrational excitation of molecular hydrogen on copper

The accuracy of dynamical models for reactive scattering of molecular hydrogen, H(2), from metal surfaces is relevant to the validation of first principles electronic structure methods for molecules interacting with metal surfaces. The ability to validate such methods is important to progress in modeling heterogeneous catalysis. Here, we study vibrational excitation of H(2) on Cu(111) using the Born-Oppenheimer static surface model. The potential energy surface (PES) used was validated previously by calculations that reproduced experimental data on reaction and rotationally inelastic scattering in this system with chemical accuracy to within errors ≤ 1 kcal/mol ≈ 4.2 kJ/mol [Díaz C, et al. (2009) Science 326:832-834]. Using the same PES and model, our dynamics calculations underestimate the contribution of vibrational excitation to previously measured time-of-flight spectra of H(2) scattered from Cu(111) by a factor 3. Given the accuracy of the PES for the experiments for which the Born-Oppenheimer static surface model is expected to hold, we argue that modeling the effect of the surface degrees of freedom will be necessary to describe vibrational excitation with similar high accuracy.

Density functional theory for transition metals and transition metal chemistry

We introduce density functional theory and review recent progress in its application to transition metal chemistry. Topics covered include local, meta, hybrid, hybrid meta, and range-separated functionals, band theory, software, validation tests, and applications to spin states, magnetic exchange coupling, spectra, structure, reactivity, and catalysis, including molecules, clusters, nanoparticles, surfaces, and solids.

Efficient vibrational and translational excitations of a solid metal surface: State-to-state time-of-flight measurements of HCl(v=2,J=1) scattering from Au(111)

We report high resolution state-to-state time-of-flight (TOF) measurements for scattering of HCl(v=2, J=1) from a Au(111) single crystal surface for both vibrationally elastic (v=2-->2) as well as inelastic (v=2-->1) channels at seven incidence energies between 0.28 and 1.27 eV. The dependences of the TOF results on final HCl rotational state and surface temperature are also reported. The translational energy transferred to the surface depends linearly on incidence energy and is close to the single surface-atom impulse (Baule) limit over the entire range of incidence energies studied. The probability of vibrational relaxation is also large. For molecules that relax from v=2 to v=1, the fraction of vibrational energy that is transferred to the surface is approximately 74%. We discuss these observations in terms of an impulse approximation as well as the possible role of translational and vibrational excitations of electron-hole pairs in the solid.

Dissociative chemisorption of H2 on the Cu(110) surface: a quantum and quasiclassical dynamical study

Six-dimensional quantum dynamical and quasiclassical trajectory (QCT) calculations are reported for the reaction and vibrationally inelastic scattering of (v = 0,1,j = 0) H(2) scattering from Cu(110), and for the reaction and rovibrationally elastic and inelastic scattering of (v = 1,j = 1) H(2) scattering from Cu(110). The dynamics results were obtained using a potential energy surface obtained with density functional theory using the PW91 functional. The reaction probabilities computed with quantum dynamics for (v = 0,1,j = 0) were in excellent agreement with the QCT results obtained earlier for these states, thereby validating the QCT approach to sticking of hydrogen on Cu(110). The vibrational de-excitation probability P(v=1,j = 0 --> v = 0) computed with the QCT method is in remarkably good agreement with the quantum dynamical results for normal incidence energies E(n) between 0.2 and 0.6 eV. The QCT result for the vibrational excitation probability P(v = 0,j = 0 --> v = 1) is likewise accurate for E(n) between 0.8 and 1 eV, but the QCT method overestimates vibrational excitation for lower E(n). The QCT method gives probabilities for rovibrationally (in)elastic scattering, P(v = 1,j = 1 --> v('),j(')), which are in remarkably good agreement with quantum dynamical results. The rotationally averaged, initial vibrational state-selective reaction probability obtained with QCT agrees well with the initial vibrational state-selective reaction probability extracted from molecular beam experiments for v = 1, for the range of collision energies for which the v=1 contribution to the measured total sticking probability dominates. The quantum dynamical probabilities for rovibrationally elastic scattering of (v = 1,j = 1) H(2) from Cu(110) are in good agreement with experiment for E(n) between 0.08 and 0.25 eV.

An advanced molecule-surface scattering instrument for study of vibrational energy transfer in gas-solid collisions

We describe an advanced and highly sensitive instrument for quantum state-resolved molecule-surface energy transfer studies under ultrahigh vacuum (UHV) conditions. The apparatus includes a beam source chamber, two differential pumping chambers, and a UHV chamber for surface preparation, surface characterization, and molecular beam scattering. Pulsed and collimated supersonic molecular beams are generated by expanding target molecule mixtures through a home-built pulsed nozzle, and excited quantum state-selected molecules were prepared via tunable, narrow-band laser overtone pumping. Detection systems have been designed to measure specific vibrational-rotational state, time-of-flight, angular and velocity distributions of molecular beams coming to and scattered off the surface. Facilities are provided to clean and characterize the surface under UHV conditions. Initial experiments on the scattering of HCl(v = 0) from Au(111) show many advantages of this new instrument for fundamental studies of the energy transfer at the gas-surface interface.

Observation of a change of vibrational excitation mechanism with surface temperature: HCl collisions with Au(111)

We have measured the vibrational excitation probability (Pv) of HCl incident on a Au(111) surface at kinetic energies (Ei) of 0.59 eV to 1.37 eV and surface temperatures (Ts) of 273 K to 1073 K. For all energies, the slope of the Pv as a function of Ts exhibits a sharp increase above Ts approximately 800 K. We show this change in slope and the threshold behavior of Pv to be consistent with a change in excitation mechanism from an electronically adiabatic mechanical mechanism to an electronically nonadiabatic mechanism involving excited electron-hole pairs.

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

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