E. Pijper

Chemically Accurate Simulation of a Prototypical Surface Reaction: H2 Dissociation on Cu(111)

Simulating Surfaces Although modern computational chemistry can often match or even exceed experimental accuracy in modeling gas phase reactions, the surface-bound processes involved in most practical catalysis pose a substantially greater challenge to theory (see the Perspective by Hasselbrink). Díaz et al. (p. 832) show that a modification to standard density functional methods can predict reaction barrier heights to within 1 kilocalorie per mole for the widely studied dissociative adsorption of dihydrogen on copper. In a complementary study, Shenvi et al. (p. 829) apply an efficient algorithmic framework to model transitions among multiple electronic states at a metal surface and successfully account for the complex dependence of nitric oxide scattering on the small molecules vibrations and rotations. The use of a fitting parameter produces a much-improved potential energy surface for describing a surface reaction. Methods for accurately computing the interaction of molecules with metal surfaces are critical to understanding and thereby improving heterogeneous catalysis. We introduce an implementation of the specific reaction parameter (SRP) approach to density functional theory (DFT) that carries the method forward from a semiquantitative to a quantitative description of the molecule-surface interaction. Dynamics calculations on reactive scattering of hydrogen from the copper (111) surface using an SRP-DFT potential energy surface reproduce data on the dissociative adsorption probability as a function of incidence energy and reactant state and data on rotationally inelastic scattering with chemical accuracy (within ~4.2 kilojoules per mole).

Reactive and diffractive scattering of H2 from Pt(111) studied using a six-dimensional wave packet method

We present results of calculations on dissociative and rotationally (in)elastic diffractive scattering of H2 from Pt(111), treating all six molecular degrees of freedom quantum mechanically. The six-dimensional (6D) potential energy surface was taken from density functional theory calculations using the generalized gradient approximation and a slab representation of the metal surface. The 6D calculations show that out-of-plane diffraction is very efficient, at the cost of in-plane diffraction, as was the case in previous four-dimensional (4D) calculations. This could explain why so little in-plane diffraction was found in scattering experiments, suggesting the surface to be flat, whereas experiments on reaction suggested a corrugated surface. Results of calculations for off-normal incidence of (v=0,j=0) H2 show that initial parallel momentum inhibits dissociation at low normal translational energies, in agreement with experiment, but has little effect for higher energies. Reaction of initial (v=1,j=0) H2 ...

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.

Rotational effects in dissociation of H2 on Pd(111): Quantum and classical study

We study rotational effects in dissociation of H2 on Pd(111) through six-dimensional quantum dynamical and classical trajectory calculations. The potential energy surface was obtained from density functional theory. Quantum dissociative adsorption and rotational excitation probabilities are compared with initial-rotational-state-selective measurements. At low energies, dynamic trapping plays an important role, promoting reaction. For low values of the rotational quantum number J, the trapping is mainly due to translation to rotation energy transfer. The decreasing role of trapping when J increases contributes to the decrease of the dissociation probability. For larger values of J trapping is the result of energy transfer to parallel translational motion. Because trapping due to energy transfer to parallel translational motion is only effective at very low energies, the change in trapping mechanism with J causes the minimum of the reaction probability versus collision energy curve to shift to lower energie...

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, H2, 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 H2 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 H2 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.

The effect of corrugation on the quantum dynamics of dissociative and diffractive scattering of H2 from Pt(111)

We present results of two dimensional (2D) and three dimensional (3D) calculations for dissociative and diffractive scattering of H2 from Pt(111), using a potential energy surface obtained from density functional theory (DFT) employing the generalized gradient approximation (GGA) in conjunction with a slab representation of the metal surface. The present study is motivated by the importance of Pt as a hydrogenation catalyst, and by a paradox regarding the amount of corrugation of the H2+Pt(111) potential energy surface (PES). Molecular beam experiments on dissociation of D2 from a Pt(111) surface suggest a rather corrugated PES, which is at odds with results from molecular beam experiments on rotationally inelastic diffraction of HD from Pt(111), where only very little diffraction is found, suggesting a weakly corrugated PES. Results of our 3D calculations for off-normal incidence show that the present 3D model does not obey normal energy scaling, and that parallel motion inhibits dissociation at low coll...

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

Following earlier three-dimensional (3D) calculations, we present results of four-dimensional (4D) calculations on dissociative and diffractive scattering of H2 from Pt(111) by extending the 3D model with a second degree of freedom parallel to the surface. A 4D potential energy surface (PES) is constructed by interpolating four 2D PESs obtained from density-functional theory calculations using the generalized gradient approximation and a slab representation of the metal surface. The 4D calculations show that out-of-plane diffraction is much more efficient than in-plane diffraction, providing a partial explanation for the paradox that diffraction experiments measure little in-plane diffraction, whereas experiments on reaction suggest the surface to be corrugated. Calculations for off-normal incidence of v=0 H2 show that, in agreement with experiment, initial parallel momentum inhibits dissociation at low normal translational energies, and enhances reaction for higher energies. Our 4D calculations also show...

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...

First principles theory for reactive scattering of H2 from Cu(111)

Improving the accuracy of methods for computing the interaction of molecules with metal surfaces is critical to progress in describing molecule-surface reactions, which are important to heterogeneous catalysis. The use of a new density functional within a static surface, electronically adiabatic model allows reaction probabilities measured in molecular beam experiments to be reproduced with chemical accuracy for a prototype molecule-surface reaction, the dissociation of H2(D2) on Cu(111).