Dissociative and diffractive scattering of H2 from Pt(111): A four-dimensional quantum dynamics study

Assessment of Two Problems of Specific Reaction Parameter Density Functional Theory: Sticking and Diffraction of H2 on Pt(111)

It is important that theory is able to accurately describe dissociative chemisorption reactions on metal surfaces, as such reactions are often rate-controlling in heterogeneously catalyzed processes. Chemically accurate theoretical descriptions have recently been obtained on the basis of the specific reaction parameter (SRP) approach to density functional (DF) theory (DFT), allowing reaction barriers to be obtained with chemical accuracy. However, being semiempirical, this approach suffers from two basic problems. The first is that sticking probabilities (to which SRP density functionals (DFs) are usually fitted) might show differences across experiments, of which the origins are not always clear. The second is that it has proven hard to use experiments on diffractive scattering of H₂ from metals for validation purposes, as dynamics calculations using a SRP-DF may yield a rather poor description of the measured data, especially if the potential used contains a van der Waals well. We address the first problem by performing dynamics calculations on three sets of molecular beam experiments on D₂ + Pt(111), using four sets of molecular beam parameters to obtain sticking probabilities, and the SRP-DF recently fitted to one set of experiments on D₂ + Pt(111). It is possible to reproduce all three sets of experiments with chemical accuracy with the aid of two sets of molecular beam parameters. The theoretical simulations with the four different sets of beam parameters allow one to determine for which range of incidence conditions the experiments should agree well and for which conditions they should show specific differences. This allows one to arrive at conclusions about the quality of the experiments and about problems that might affect the experiments. Our calculations on diffraction of H₂ scattering from Pt(111) show both quantitative and qualitative differences with previously measured diffraction probabilities, which were Debye-Waller (DW)-extrapolated to 0 K. We suggest that DW extrapolation, which is appropriate for direct scattering, might fail if the scattering is affected by the presence of a van der Waals well and that theory should attempt to model surface atom motion for reproducing diffraction experiments performed for surface temperatures of 500 K and higher.

Six-dimensional quantum dynamics of dissociative chemisorption of H2 on Co(0001) on an accurate global potential energy surface

Six-dimensional quantum dynamics of hydrogen dissociative chemisorption on Co(0001) is investigated on a DFT based potential energy surface.

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) H 2 if the calculations are based on accurately fitted density functional theory calculations that are performed using the generalized gradient approximation. The influence of the molecule's 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 H 2. 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 H 2 reacting on metal surfaces will likely be aimed at validating GGAs for molecule-surface interactions, and understanding trends in collisions of H 2 with complex metal surfaces.

Ab initio molecular dynamics of hydrogen dissociation on metal surfaces using neural networks and novelty sampling

We outline a hybrid multiscale approach for the construction of ab initio potential energy surfaces (PESs) useful for performing six-dimensional (6D) classical or quantum mechanical molecular dynamics (MD) simulations of diatomic molecules reacting at single crystal surfaces. The algorithm implements concepts from the corrugation reduction procedure, which reduces energetic variation in the PES, and uses neural networks for interpolation of smoothed ab initio data. A novelty sampling scheme is implemented and used to identify configurations that are most likely to be predicted inaccurately by the neural network. This hybrid multiscale approach, which couples PES construction at the electronic structure level to MD simulations at the atomistic scale, reduces the number of density functional theory (DFT) calculations needed to specify an accurate PES. Due to the iterative nature of the novelty sampling algorithm, it is possible to obtain a quantitative measure of the convergence of the PES with respect to the number of ab initio calculations used to train the neural network. We demonstrate the algorithm by first applying it to two analytic potentials, which model the H2/Pt(111) and H2/Cu(111) systems. These potentials are of the corrugated London-Eyring-Polanyi-Sato form, which are based on DFT calculations, but are not globally accurate. After demonstrating the convergence of the PES using these simple potentials, we use DFT calculations directly and obtain converged semiclassical trajectories for the H2/Pt(111) system at the PW91/generalized gradient approximation level. We obtain a converged PES for a 6D hydrogen-surface dissociation reaction using novelty sampling coupled directly to DFT. These results, in excellent agreement with experiments and previous theoretical work, are compared to previous simulations in order to explore the sensitivity of the PES (and therefore MD) to the choice of exchange and correlation functional. Despite having a lower energetic corrugation in our PES, we obtain a broader reaction probability curve than previous simulations, which is attributed to increased geometric corrugation in the PES and the effect of nonparallel dissociation pathways.

Multiconfiguration time-dependent Hartree method applied to molecular dissociation on surfaces: H2+Pt(111)

Four-dimensional quantum dynamics calculations are performed on the dissociative chemisorption of H(2) on Pt(111) using the multiconfiguration time-dependent Hartree method. The aim of this work is to study the performance of the multiconfiguration time-dependent Hartree method for a gas-surface reaction by comparison with the standard time-dependent wave-packet propagation method. The initial-state resolved dissociation probability of H(2) is calculated within two four-dimensional models. The first four-dimensional model treats explicitly the rotational motion of the molecule and the H(2) dissociation is studied above two different sites of the Pt(111). For this model, only a potential-energy surface of general form was available. This potential was refitted to a sum of product form to allow efficient calculations with the multiconfiguration time-dependent Hartree method. The second model focuses on the description of the center-of-mass motion parallel to the surface, the rotational motion of the molecule being frozen. These four-dimensional quantum dynamics calculations yield important insights which can help with performing full six-dimensional calculations on H(2) dissociating on Pt(111). The multiconfiguration time-dependent Hartree method is shown to be particularly efficient for computing initial-state selective dissociation probabilities for the system studied, with a good accuracy and a reduced amount of memory and computational time when compared to the standard time-dependent wave-packet method.

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.

Multiconfigurational time-dependent Hartree calculations for dissociative adsorption of H2 on Cu(100)

The efficiency of the multiconfigurational time-dependent Hartree (MCTDH) method for calculating the initial-state selected dissociation probability of H(2)(v=0,j=0) on Cu(100) is investigated. The MCTDH method is shown to be significantly more efficient than standard wave packet methods. A large number of single-particle functions is required to converge the initial-state selected reaction probability for dissociative adsorption. Employing multidimensional coordinates in the MCTDH ansatz (mode combination) is found to be crucial for the efficiency of these MCTDH calculations. Perspectives towards the application of the MCTDH approach to study dissociative adsorption of polyatomic molecules on surfaces are discussed.

Theoretical study of the H2 reaction with a Pt4 (111) cluster

The C(s) symmetry reaction of the H(2) molecule on a Pt(4) (111) clusters, has been studied using ab initio multiconfiguration self-consistent field plus extensive multireference configuration interaction variational and perturbative calculations. The H(2) interaction by the vertex and by the base of a tetrahedral Pt(4) cluster were studied in ground and excited triplet and singlet states (closed and open shells), where the reaction curves are obtained through many avoided crossings. The Pt(4) cluster captures and activates the hydrogen molecule; it shows a similar behavior compared with other Pt(n) (n=1,2,3) systems. The Pt(4) cluster in their lowest five open and closed shell electronic states: (3)B(2), (1)B(2), (1)A(1) (3)A(1), (1)A(1), respectively, may capture and dissociate the H(2) molecule without activation barriers for the hydrogen molecule vertex approach. For the threefolded site reaction, i.e., by the base, the situation is different, the hydrogen adsorption presents some barriers. The potential energy minima occur outside and inside the cluster, with strong activation of the H-H bond. In all cases studied, the Pt(4) cluster does not absorb the hydrogen molecule.

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.