Mark F. Somers

Constructing accurate potential energy surfaces for a diatomic molecule interacting with a solid surface: H2+Pt(111) and H2+Cu(100)

By applying a corrugation-reducing procedure we have interpolated the six-dimensional (6D) potential energy surfaces for the H2/Pt(111) and H2/Cu(100) systems from data obtained by density functional theory (DFT) calculations. We have compared interpolated values with a large number of DFT results not used in the basis for the interpolation and we have obtained an average error below 20 meV and a maximum error of about 30 meV in the regions important for dissociative adsorption. Near the surface the corrugation-reducing procedure gives excellent results using only data from high-symmetry sites. However, we show that to reach the above mentioned accuracy level far from the surface, it is necessary to include information from at least one low-symmetry site. Care has been taken to demonstrate the quality of the interpolation along all degrees of freedom in different regions of the configuration space. The strengths of the method are shown together with the aspects requiring careful handling. A comparison wit...

SIX-DIMENSIONAL DYNAMICS OF DISSOCIATIVE CHEMISORPTION OF H2 ON METAL SURFACES

The theory of time-dependent quantum dynamics of dissociative chemisorption of hydrogen on metal surfaces is reviewed, in the framework of electronically adiabatic scattering from static surfaces. Four implementations of the time-dependent wave packet (TDWP) method are discussed. In the direct product pseudo-spectral and the spherical harmonics pseudo-spectral methods, no use is made of the symmetry associated with the surface unit cell. This symmetry is exploited by the symmetry adapted wave packet and the symmetry adapted pseudo-spectral (SAPS) method, which are efficient for scattering at normal incidence. The SAPS method can be employed for potential energy surfaces of general form. Comparison to experiment shows that the TDWP method yields good, but not yet excellent, quantitative accuracy for dissociation of (ν = 0, j = 0)H2 if the calculations are based on accurately fitted density functional theory calculations that are performed using the generalized gradient approximation. The influence of the molecules vibration (rotation) is well (reasonably well) described. The theory does not yet yield quantitatively accurate results for rovibrationally inelastic scattering. The theory has helped with the interpretation of existing experimental results, for instance, by solving a parodox regarding the corrugation of Pt(111) as seen by reacting and scattering H2. The theory has also provided some exciting new predictions, for instance, concerning where on the surface of Cu(100)H2 reacts depending on its vibrational state. Future theoretical studies of H2 reacting on metal surfaces will likely be aimed at validating GGAs for molecule-surface interactions, and understanding trends in collisions of H2 with complex metal surfaces.

Diffractive and reactive scattering of H2 from Ru(0001): experimental and theoretical study

We present a combined experimental and theoretical study of the diffraction of H(2) from Ru(0001) in the incident energy range 78-150 meV, and a theoretical study of dissociative chemisorption of H(2) in the same system. Pronounced out-of-plane diffraction was observed in the whole energy range studied. The energy dependence of the elastic diffraction intensities was measured along the two main symmetry directions for a fixed parallel translational energy. The data were compared with quantum dynamics calculations performed by using DFT-based, six-dimensional potential energy surfaces calculated with both the PW91 and RPBE functionals, as well as with a functional obtained from a weighted average of both (the MIX functional, which was earlier shown to perform quite well for H(2) + Cu(111)). Our results show that the PW91 functional describes the H(2) diffraction intensities more accurately than the RPBE and the MIX functionals, although the absolute values of these intensities are overestimated in the calculations. For the reaction probabilities a preference for one or the other functional cannot be given over the entire energy range probed by the sticking experiments. The PW91 functional yields too high reaction probabilities over the entire investigated energy range, but is better than RPBE at low collision energies (<0.1 eV). The RPBE functional gives too low reaction probabilities at low energy and somewhat too high reaction probabilities at high energy, but agrees better with experiment than PW91 for energies >0.1 eV. The results suggest that, in order to get a better description of both H(2) diffraction and dissociative chemisorption for this system, a specific reaction parameter functional for H(2) + Ru(0001) is needed that is a weighted average of functionals other than PW91 and RPBE. We speculate that differences between the H(2) + Ru(0001) system (early and low reaction barrier) and H(2) + Cu(111) (late and high reaction barrier) may well lead to fundamentally different specific reaction parameter functionals, and that including a reasonable accurate description of the van der Waals interaction might be important for H(2) + Ru(0001) which has barriers localised far away from the surface. Based on our results we advocate new, systematic combined theoretical and experimental studies of H(2) interacting with transition metals in early and late barrier systems, with the aim of determining whether specific reaction parameter functionals for these systems might differ in a systematic way.

Signatures of site-specific reaction of H2 on Cu(100)

Six-dimensional quantum dynamical calculations are presented for the reaction of (v,j) H2 on Cu(100), at normal incidence, for v=0–1 and j=0–5. The dynamical calculations employed a potential energy surface computed with density functional theory, using the generalized gradient approximation and a slab representation for the adsorbate-substrate system. The aim of the calculations was to establish signatures from which experiments could determine the dominant reaction site of H2 on the surface and the dependence of the reaction site on the initial rovibrational state of H2. Two types of signatures were found. First, we predict that, at energies near threshold, the reaction of (v=1) H2 is rotationally enhanced, because it takes place at the top site, which has an especially late barrier and a reaction path with a high curvature. On the other hand, we predict the reaction to be almost independent of j for (v=0) H2, which reacts at the bridge site. Second, we predict that, at collision energies slightly above...

Diffractive and reactive scattering of (v=0, j=0) HD from Pt(111): Six-dimensional quantum dynamics compared with experiment

We present results of (v=0, j=0) HD reacting on and scattering from Pt(111) at off-normal angles of incidence, treating all six molecular degrees of freedom quantum mechanically. The six-dimensional potential energy surface (PES) used was obtained from density functional theory, using the generalized gradient approximation and a slab representation of the metal surface. Diffraction and rotational excitation probabilities are compared with experiment for two incidence directions, at normal incidence energies between 0.05–0.16 eV and at a parallel translational energy of 55.5 meV. The computed ratio of specular reflection to nonspecular in-plane diffraction for HD+Pt(111) is lower than found experimentally, and lower for HD+Pt(111) than for H2+Pt(111) for both incidence directions studied. The calculations also show that out-of-plane diffraction is much more efficient than in-plane diffraction, underlining that results from experiments that solely attempt to measure in-plane diffraction are not sufficient t...

Six-dimensional quantum dynamics of (v=0,j=0)D2 and of (v=1,j=0)H2 scattering from Cu(111)

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.

A classical dynamics method for H2 diffraction from metal surfaces.

We present a discretization method that allows one to interpret measurements on diffraction of diatomic molecules from solid surfaces using six-dimensional (6D) classical trajectory calculations. It has been applied to the D2NiAl(110) and H2Pd(111) systems (which are models for activated and nonactivated dissociative chemisorption, respectively) using realistic potential energy surfaces obtained from first principles. Comparisons with experimental results and 6D quantum dynamical calculations show that, in general, the method is able to predict the relative intensity of the most important diffraction peaks. We therefore conclude that classical mechanics can be an efficient guide for experimentalists in the search for the most significant diffraction channels.

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.

Performance of a Non-Local van der Waals Density Functional on the Dissociation of H2 on Metal Surfaces

van der Waals functionals have recently been applied to obtain a potential energy surface to describe the dissociation of H2 on Ru(0001), where an improvement was found for computed reaction probabilities compared to experiment, which could not be achieved with the use of other exchange-correlation functionals. It is, however, not yet clear to what extent van der Waals functionals give a better description of other molecule-metal surface systems. In this study, the optPBE-vdW-DF functional is compared to the SRP48 functional, which was originally fitted to describe the dissociation of H2 on Cu(111), in terms of the resulting potential energy surfaces and results of quasi-classical dynamics calculations and their agreement with experiment for different H2-metal surface systems. It is found that overall the optPBE-vdW-DF functional yields potential energy surfaces that are very similar to potential energy surfaces computed with the SRP48 functional. In dynamics calculations the optPBE-vdW-DF functional gives a slightly better description of molecular beam experiments. Also a different dependence of reaction on the rotational quantum number J is found, which is in better agreement with experimental data for H2 dissociation on Cu(111). The vibrational efficacy is found to be relatively insensitive to which of the two functionals is chosen.

7D Quantum Dynamics of H2 Scattering from Cu(111): The Accuracy of the Phonon Sudden Approximationy

Abstract The correct prediction of elementary processes occurring when H2 scatters from a metal surface is one of the main challenges of surface science. In the field, the scattering of H2 from Cu(111) has been considered a prototype system for activated dissociative chemisorption. Experimental and theoretical work suggested that a proper description of some scattering experiments on this system might require going beyond the static surface approximation, to consider how the motion of the Cu atoms affects the scattering event. Previous work suggested that important effects of phonons on the dynamics can be incorporated in the Potential Energy Surface (PES) by including four degrees of freedom, that have approximately additive couplings with the hydrogen molecule: the 3 dimensional motion of the nearest 1st layer copper atom and the displacement of the nearest 2nd layer copper atom along the direction perpendicular to the surface [3]. In the present work, we extend the 6D dynamical model by including the perpendicular motion of the 2nd layer surface atom and we study this novel dynamical model with two techniques: an approximate method based on the Phonon Sudden Approximation (PSA) and an exact description using 7D wavepacket quantum dynamics. We consider how the inclusion and the excitation of the lattice degree of freedom affect some relevant processes: dissociative chemisorption, vibrational excitation of H2 and state-to-state scattering probabilities fully resolved with respect to the vibrational states of the surface. We show that the PSA works in an excellent way for the system, thereby suggesting that this might be a viable way to study higher dimensional quantum models, incorporating four surface degrees of freedom that appear to be most relevant for H2 scattering.