Reactive scattering of H2 from Cu(100): six-dimensional quantum dynamics results for reaction and scattering obtained with a new, accurately fitted potential-energy surface

Six-dimensional quantum dynamical calculations are reported for the dissociative chemisorption of (v=0, 1, j=0) H(2) on Cu(100), and for rovibrationally inelastic scattering of (v=1, j=1) H(2) from Cu(100). The dynamics results were obtained using a new potential-energy surface (PES5), which was based on density-functional calculations using a slab representation of the adsorbate-substrate system and a generalized gradient approximation to the exchange-correlation energy. A very accurate method (the corrugation reducing procedure) was used to represent the density-functional theory data in a global potential-energy surface. With the new, more accurately fitted PES5, the agreement between the dynamics results and experimental results for reaction and rovibrationally elastic scattering is not as good as was obtained with a previous potential-energy surface (PES4), which was based on a subset of the density-functional theory data not yet including the results for the low-symmetry Cu sites. Preliminary density-functional theory results suggest that the agreement between theory and experiment will improve over that obtained with PES5 if the density-functional calculations are repeated using a larger basis set and using more copper layers than employed in PES4 and PES5.     

State-to-state scattering of D2 from Cu(100) and Pd(111)

Results from state resolved experiments are presented for the interaction of D2(v=1,J=2) with Cu(100) and Pd(111). The reflected molecules were probed using quantum state specific spectroscopy. For D2 scattered from Cu(100) the vibrational survival probability and some transition inelastic probabilities were measured for incident energies from 70-200 meV. The survival probability was found to be larger then that found previously for H2(v=1) scattered from the same surface; these differences are discussed in terms of the lower zero point energy and smaller vibrational energy spacings of D2. D2 translational energy exchange was studied for several different scattering channels and interpreted using simple classical calculations. The survival probability was also measured for D2(v=1) scattered from Pd(111) at one incident energy. Pd is reactive for D2 dissociation and this survival probability was measured to be small and also to be much smaller than that for H2(v=1) under similar conditions. Vibrational relaxation channels were studied for D2 scattering from both Cu(100) and Pd(111). The vibrational relaxation probability on both surfaces was also found to be smaller than that measured for comparable channels for H2. The smaller survival probability and vibrational relaxation probability for D2 on Pd(111) cannot be easily accounted for by the difference in zero point energy and vibrational energy spacings.     

The effect of phonon modes on the H2(v, j)/D2(v, j)-Cu(1nn) scattering processes

We include the effect of the phonon modes originating from the three layers of Cu(1nn) surface atoms on the dynamics of incoming molecular [H(2)(v, j)/D(2)(v, j)] degrees of freedom (DOFs) through a mean-field approach, where the surface temperature is incorporated into the effective potential by considering Bose-Einstein probability (BEP) factor for the initial state distribution of the surface modes calculated within harmonic approximation. Such time and temperature dependent effective Hamiltonian is further subdivided assuming a weak coupling between the two sets of molecular DOFs, namely, (x, y, z, Z) and (X, Y), respectively, in particular, to reduce the computational cost and the corresponding coupled quantum dynamical equations of motion have been formulated in terms of Time Dependent Discrete Variable Representation (TDDVR) approach. We demonstrate the workability of TDDVR method to investigate the scattering of H(2)(v, j) on Cu(1nn) surface by calculating the reaction probabilities and scattering cross-sections. Calculated results show that the phonon modes affect (a) the state-to-state transition probabilities of the scattered H(2) molecule substantially but chemisorption and physisorption processes negligibly and (b) the reaction probability of the incoming D(2) molecule noticeably.     

On the dynamics of H2 adsorption on the Pt(111) surface

The dynamics and kinetics of the dissociation of hydrogen over the hexagonal close packed platinum (Pt(111)) surface are investigated using Car–Parrinello molecular dynamics and static density functional theory calculations of the potential energy surfaces. The calculations model the reference energy‐resolved molecular beam experiments, considering the degrees of freedom of the catalytic surface. Two‐dimensional potential energy surfaces above the main sites on Pt(111) are determined. Combined with Car–Parrinello trajectories, they confirm the dissociative adsorption of H₂ as the only adsorption pathway on this surface at H₂ incindence energies above 5 kJ/mol. A direct determination of energy‐resolved sticking coefficients from molecular dynamics is also performed, showing an excellent agreement with the experimental data at incidence energies in the 5–30 kJ/mol range. Application of dispersion corrections does not lead to an improvement in the prediction of the H₂ sticking coefficient. The adsorption reaction rate obtained from the calculated sticking coefficients is consistent with experimentally derived literature values.     

Surface temperature effect on the scattering of D2(v = 0, j = 0)-Cu(111) system

We perform four-dimensional (4D?2D) as well as six-dimensional (6D) quantum dynamics on a parametrically time- and temperature-dependent effective Hamiltonian for D(2)(v, j)-Cu(111) system, where such effective potential has been derived through a mean-field approach between molecular degrees of freedom and surface modes with Bose-Einstein probability factor for their initial state distribution. We present the convergence of the theoretically calculated sticking probabilities employing 4D?2D quantum dynamics with increasing number of surface atoms as well as layers for rigid surface and the surface at a particular temperature, where the temperature-dependent sticking probabilities appear exclusively dictated by those surface modes directed along the Z-axis. The sticking and state-to-state transition probabilities obtained from 6D quantum dynamics are shown as a function of initial kinetic energy of the diatom at different surface temperature. Theoretically calculated sticking probabilities display the similar trend with the experimentally measured one.     

Static surface temperature effects on the dissociation of H(2) and D(2) on Cu(111)

A model for taking into account surface temperature effects in molecule-surface reactions is reported and applied to the dissociation of H(2) and D(2) on Cu(111). In contrast to many models developed before, the model constructed here takes into account the effects of static corrugation of the potential energy surface rather than energy exchange between the impinging hydrogen molecule and the surface. Such an approximation is a vibrational sudden approximation. The quality of the model is assessed by comparison to a recent density functional theory study. It is shown that the model gives a reasonable agreement with recently performed ab initio molecular dynamics calculations, in which the surface atoms were allowed to move. The observed broadening of the reaction probability curve with increasing surface temperature is attributed to the displacement of surface atoms, whereas the effect of thermal expansion is found to be primarily a shift of the curve to lower energies. It is also found that the rotational quadrupole alignment parameter is generally lowered at low energies, whereas it remains approximately constant at high energies. Finally, it is shown that the approximation of an ideal static surface works well for low surface temperatures, in particular for the molecular beams for this system (T(s) = 120 K). Nonetheless, for the state-resolved reaction probability at this surface temperature, some broadening is found.     

Dynamical study of H2 and D2 desorbing from a Cu(111) surface

A theoretical study of H(2) and D(2) desorbing from Cu(111) is reported. The study makes use of the LEPS PES of Dai and Zhang [J. Chem. Phys. 1995, 102, 6280]. The LEPS parameters have been modified in order to lower the barrier threshold in conformity with accurate ab initio electronic structure calculations. The topological study of the modified PES by the CHAIN method reveals unambiguously that the transition state (TS) is located at the top of a unique early barrier along the desorption path. The adsorbed H atoms are supposed to be in thermal equilibrium with the metal surface. Batches of classical trajectories (CT) are then carried out from the TS onto the products with their initial conditions canonically distributed and the effect of their possible recrossing of the TS taken into account according to Keck's method [Discuss. Faraday Soc. 1962, 33, 173]. Product state distributions are then calculated using the Gaussian weighting procedure [Chem. Phys. Lett. 2004, 397, 106] to account for the quantization of the vibration motion of the desorbed diatom. These distributions are in overall good agreement with experimental measurements. On average, the early barrier to desorption results in a significant vibrational excitation of the final diatom and a strong deexcitation of its rotational angular momentum J from the TS onto the products. Moreover, the orientation of the rotation plane is roughly random for low values of J (both cartwheel and helicopter motions are observed) while it is more likely parallel to the metal surface for large values of J (predominance for helicopter motion). These findings are analyzed in some details.     

A six-dimensional H(2)-H(2) potential energy surface for bound state spectroscopy

We present a six-dimensional potential energy surface for the (H(2))(2) dimer based on coupled-cluster electronic structure calculations employing large atom-centered Gaussian basis sets and a small set of midbond functions at the dimer's center of mass. The surface is intended to describe accurately the bound and quasibound states of the dimers (H(2))(2), (D(2))(2), and H(2)-D(2) that correlate with H(2) or D(2) monomers in the rovibrational levels (v,j)=(0,0), (0,2), (1,0), and (1,2). We employ a close-coupled approach to compute the energies of these bound and quasibound dimer states using our potential energy surface, and compare the computed energies for infrared and Raman transitions involving these states with experimentally measured transition energies. We use four of the experimentally measured dimer transition energies to make two empirical adjustments to the ab initio potential energy surface; the adjusted surface gives computed transition energies for 56 experimentally observed transitions that agree with experiment to within 0.036 cm(-1). For 26 of the 56 transitions, the agreement between the computed and measured transition energies is within the quoted experimental uncertainty. Finally, we use our potential energy surface to predict the energies of another 34 not-yet-observed infrared and Raman transitions for the three dimers.     

Off-normal incidence dissociative sticking of H2 on Cu(100) studied using six-dimensional quantum calculations

Six-dimensional quantum calculations of the sticking probability for H2 hitting a Cu(100) surface with off-normal incidence are presented. The multiconfiguration time-dependent Hartree approach is employed for an efficient wave-packet propagation. The sticking probability is calculated for different initial momenta parallel to the surface. In contrast with the picture described in the literature, the sticking probability was found to depend on the parallel momentum. The results are explained by the topology of the potential-energy surface, which shows significant corrugation with a moderate variation of the barrier height with the surface site.     

Application of the modified Shepard interpolation method to the determination of the potential energy surface for a molecule-surface reaction: H2 + Pt(111)

We have used a modified Shepard (MS) interpolation method, initially developed for gas phase reactions, to build a potential energy surface (PES) for studying the dissociative chemisorption of H2 on Pt(111). The aim was to study the efficiency and the accuracy of this interpolation method for an activated multidimensional molecule-surface reactive problem. The strategy used is based on previous applications of the MS method to gas phase reactions, but modified to take into account special features of molecule-surface reactions, like the presence of many similar reaction pathways which vary only slightly with surface site. The efficiency of the interpolation method was tested by using an already existing PES to provide the input data required for the construction of the new PES. The construction of the new PES required half as many ab initio data points as the construction of the old PES, and the comparison of the two PESs shows that the method is able to reproduce with good accuracy the most important features of the H2 + Pt(111) interaction potential. Finally, accuracy tests were done by comparing the results of dynamics simulations using the two different PESs. The good agreement obtained for reaction probabilities and probabilities for rotationally and diffractionally inelastic scattering shows clearly that the MS interpolation method can be used efficiently to yield accurate PESs for activated molecule-surface reactions.     

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

Dynamical calculations are presented for electronically nonadiabatic vibrational deexcitation of H2 and D2 in scattering from Cu(111). Both the potential energy surface and the nonadiabatic coupling strength were obtained from density functional calculations. The theoretically predicted magnitude of the deexcitation and its dependence on incident energy and isotope are all in agreement with state-to-state scattering experiments [on Cu(100)], and this gives indirect evidence for a nonadiabatic mechanism of the observed deexcitation. Direct evidence could be obtained by measuring the chemicurrent associated with the deexcitation, and its properties have been predicted.     

On the determination of absolute vibrational excitation probabilities in molecule-surface scattering: Case study of NO on Au(111)

We describe a method to obtain absolute vibrational excitation probabilities of molecules scattering from a surface based on measurements of the rotational state, scattering angle, and temporal distributions of the scattered molecules and apply this method to the vibrational excitation of NO scattering from Au(111). We report the absolute excitation probabilities to the v = 1 and v = 2 vibrational states, rotational excitation distributions, and final scattering angle distributions for a wide range of incidence energies and surface temperatures. In addition to demonstrating the methodology for obtaining absolute scattering probabilities, these results provide an excellent benchmark for theoretical calculations of molecule-surface scattering.     

Vibrational deexcitation and rotational excitation of H(2) and D(2) scattered from Cu(111): Adiabatic versus non-adiabatic dynamics

We have studied survival and rotational excitation probabilities of H(2)(v(i) = 1, J(i) = 1) and D(2)(v(i) = 1, J(i) = 2) upon scattering from Cu(111) using six-dimensional (6D) adiabatic (quantum and quasi-classical) and non-adiabatic (quasi-classical) dynamics. Non-adiabatic dynamics, based on a friction model, has been used to analyze the role of electron-hole pair excitations. Comparison between adiabatic and non-adiabatic calculations reveals a smaller influence of non-adiabatic effects on the energy dependence of the vibrational deexcitation mechanism than previously suggested by low-dimensional dynamics calculations. Specifically, we show that 6D adiabatic dynamics can account for the increase of vibrational deexcitation as a function of the incidence energy, as well as for the isotope effect observed experimentally in the energy dependence for H(2)(D(2))/Cu(100). Furthermore, a detailed analysis, based on classical trajectories, reveals that in trajectories leading to vibrational deexcitation, the minimum classical turning point is close to the top site, reflecting the multidimensionally of this mechanism. On this site, the reaction path curvature favors vibrational inelastic scattering. Finally, we show that the probability for a molecule to get close to the top site is higher for H(2) than for D(2), which explains the isotope effect found experimentally.     

Rotationally inelastic scattering of HD from Cu(100) and Pd(111)

Rotational excitation of HD scattered from Cu(100), Pd(111), and Pd(111):H(D) was measured using molecular beam and quantum-state-specific laser spectroscopy techniques. Greater than 91% of the incident HD population was in the v = 0, J = 0 state. The final rotational distributions from Cu(100), Pd(111), and Pd(111):H(D) were compared for a HD beam at an incident energy of 74 meV. For all the three surfaces studied, rotationally inelastic scattering probabilities were large. We find that the final HD rotational distributions are remarkably similar for the three surfaces even though Pd(111) is very reactive to dissociative adsorption of HD whereas Cu(100) and Pd(111):H(D) are chemically inert.     

吸附氢气后的钯团簇在氧化亚铜表面上的稳定性研究

为了探究吸附H2后的Pdn团簇在Cu2O（111）完整表面和铜缺陷表面上的稳定性,计算了负载在Cu2O（111）完整表面和铜缺陷表面上的Pdn（n=1-4）对H2分子的最稳定吸附结构;利用在给定H2压力和温度下Pdn / Cu2O表面吸附H2的相图揭示了Pdn团簇在Cu2O（111）两个表面的变化情况。结果表明,在吸附了H2分子以后,Pdn团簇更倾向于保持原有的结构,且随着Pd团簇的增大,吸附H2的数量也逐渐增长。     

Six-dimensional quantum dynamics of (v=0,j=0)D2 and of (v=1,j=0)H2 scattering from Cu111

We report six-dimensional quantum dynamics calculations of the dissociative scattering of molecular hydrogen from the copper111 surface. Two potential energy surfaces are investigated and the results are compared with experiment. Our study completes the preliminary work of Somers et al. [Chem. Phys. Lett. 360, 390 (2002)] and focuses on the role of initial vibrational excitation and on isotopic effects. None of the two investigated potential energy surfaces is found satisfactory: the use of neither potential yields reaction and vibrational excitation probabilities and vibrational efficacies that are in close agreement with experiment. In addition to showing the shortcomings of existing potential energy surfaces we point out an inconsistency in the experimental fits for D2.     

Inelastic scattering and chemisorption of CO on a Pt(111) surface

A semiclassical model is used to calculate energy transfer in collisions between CO and a Pt(111) surface. The sticking probability is found to be as large as 0.7–0.8 for small collision energies (≈0.14 eV). At higher energies (≈5 eV) it decreases to ≈0.3. Strong interaction between the adsorbed molecule and the phonons is observed.     

Adsorption and scattering of H2 and D2 by NiAl(110)

We present quasiclassical dynamics calculations of H2 and D2 scattering by the NiAl(110) surface using a recently proposed six-dimensional potential-energy surface (PES) obtained from density-functional theory calculations. The results for dissociative adsorption confirm several experimental predictions using (rotationally hot) D2 beams, namely, the existence of a dissociation barrier, the small isotopic effect, the importance of vibrational enhancement, and the existence of normal energy scaling. The latter conclusion shows that normal energy scaling is not necessarily associated with weak corrugated surfaces. The results for rotationally elastic and inelastic diffractions are also in reasonable agreement with experiment, but they show that many more diffractive transitions are responsible for the observed structures than previously assumed. This points to the validity of the PES recently proposed [P. Riviere, H. F. Busnengo, and F. Martin, J. Chem. Phys. 121, 751 (2004)] to describe dissociative adsorption as well as rotationally elastic and inelastic diffractions in the H2NiAl(110) system.     

Interface-controlled synthesis of CeO2(111) and CeO2(100) and their structural transition on Pt(111)

Ceria-based catalytic materials are known for their crystal-face-dependent catalytic properties. To obtain a molecular-level understanding of their surface chemistry, controlled synthesis of ceria with well-defined surface structures is required. We have thus studied the growth of CeO_x nanostructures (NSs) and thin films on Pt(111). The strong metal-oxide interaction has often been invoked to explain catalytic processes over the Pt/CeO_x catalysts. However, the Pt-CeO_x interaction has not been understood at the atomic level. We show here that the interfacial interaction between Pt and ceria could indeed affect the surface structures of ceria, which could subsequently determine their catalytic chemistry. While ceria on Pt(111) typically exposes the CeO₂(111) surface, we found that the structures of ceria layers with a thickness of three layers or less are highly dynamic and dependent on the annealing temperatures, owing to the electronic interaction between Pt and CeO_x. A two-step kinetically limited growth procedure was used to prepare the ceria film that fully covers the Pt(111) substrate. For a ceria film of ~3–4 monolayer (ML) thickness on Pt(111), annealing in ultrahigh vacuum (UHV) at 1000 K results in a surface of CeO₂ (100), stabilized by a c-Ce₂O₃(100) buffer layer. Further oxidation at 900 K transforms the surface of the CeO₂(100) thin film into a hexagonal CeO₂(111) surface.     

A surface hopping quasiclassical trajectory study of the H2+ + H2 and (H2 + D2)+ systems

In this work we use a complete surface hopping quasiclassical trajectory method to determine cross sections for the reactions H₂⁺ + H₂ → H₃⁺ + H and the isotopic variants (H₂⁺ + D₂ and D₂⁺ + H₂). Initial translational energies ranged between 0.5 and 6 eV. The vibrational quantum number (v⁺) of the charged diatom is either 0 or 3. Comparing these results with our previous results with a partial treatment of surface hopping, we find essentially no change for v⁺ = 0 and reductions in cross sections of up to 30% for v⁺ = 3 trajectories.