Roar A. Olsen

Comparison of methods for finding saddle points without knowledge of the final states

Within the harmonic approximation to transition state theory, the biggest challenge involved in finding the mechanism or rate of transitions is the location of the relevant saddle points on the multidimensional potential energy surface. The saddle point search is particularly challenging when the final state of the transition is not specified. In this article we report on a comparison of several methods for locating saddle points under these conditions and compare, in particular, the well-established rational function optimization (RFO) methods using either exact or approximate Hessians with the more recently proposed minimum mode following methods where only the minimum eigenvalue mode is found, either by the dimer or the Lanczos method. A test problem involving transitions in a seven-atom Pt island on a Pt(111) surface using a simple Morse pairwise potential function is used and the number of degrees of freedom varied by varying the number of movable atoms. In the full system, 175 atoms can move so 525 degrees of freedom need to be optimized to find the saddle points. For testing purposes, we have also restricted the number of movable atoms to 7 and 1. Our results indicate that if attempting to make a map of all relevant saddle points for a large system (as would be necessary when simulating the long time scale evolution of a thermal system) the minimum mode following methods are preferred. The minimum mode following methods are also more efficient when searching for the lowest saddle points in a large system, and if the force can be obtained cheaply. However, if only the lowest saddle points are sought and the calculation of the force is expensive but a good approximation for the Hessian at the starting position of the search can be obtained at low cost, then the RFO approaches employing an approximate Hessian represent the preferred choice. For small and medium sized systems where the force is expensive to calculate, the RFO approaches employing an approximate Hessian is also the more efficient, but when the force and Hessian can be obtained cheaply and only the lowest saddle points are sought the RFO approach using an exact Hessian is the better choice. These conclusions have been reached based on a comparison of the total computational effort needed to find the saddle points and the number of saddle points found for each of the methods. The RFO methods do not perform very well with respect to the latter aspect, but starting the searches further away from the initial minimum or using the hybrid RFO version presented here improves this behavior considerably in most cases.

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).

Atomic and molecular hydrogen interacting with Pt(111).

This computational study is motivated by the apparent conflict between an experiment on dissociation of H2 and D2 on Pt(111), which suggests a rather corrugated potential energy surface (PES) for the H2/Pt(111) system, and an experiment showing only weak nonzero-order diffraction of HD scattering from Pt(111). In the calculations we have used density functional theory (DFT) within the generalized gradient approximation (GGA), including scalar relativistic effects and modelling the Pt(111) surface as a slab. We have found that the H2/Pt(111) PES is both energetically and geometrically corrugated. We have also found that there are reaction paths without or with very low barriers leading to dissociation of H2 on the Pt(111) surface, but that there are other reaction paths with substantial barriers. By performing extensive calculations on H interacting with a Pt(111) surface we have shown that a DFT/GGA approach that includes scalar relativistic effects is capable of describing the interaction between a hydro...

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...

CO on Pt(111): A puzzle revisited

Today’s state-of-the-art method for calculating the interaction of atoms or small molecules with metal surfaces is considered to be density functional theory (DFT) at the generalized gradient approximation (GGA) level employing a slab or supercell representation of the surface. The method is widely used and by many assumed to be both qualitatively and quantitatively accurate. This notion has recently been challenged by Feibelman et al. [J. Phys. Chem. B 105, 4018 (2001)] who suggest that the DFT/GGA method does not correctly predict the most stable adsorption site for the CO/Pt(111) system, and they conclude that the method is not qualitatively accurate. However, using a different calculational approach we find a good agreement between the calculated potential energy surface for this system and the one inferred from experiments, indicating that the evidence supporting the view of Feibelman et al. is not yet conclusive. On the contrary, we advocate the view that the DFT/GGA method should at the moment be c...

Rovibrationally inelastic scattering of (v=1, j=1) H-2 from Cu(100) experiment and theory

A comparison between experiment and theory is performed for the scattering of (v=1, j=1) H2 from Cu(100) at normal incidence. Experimentally, this system was studied using molecular beam techniques, with stimulated Raman pumping employed to overpopulate (v=1, j=1) in the incident beam, and resonance enhanced multi-photon ionization used to detect the H2 scattered in two (v=1, j) states, and two (v=0, j) states. Theoretically, six-dimensional wave packet calculations were performed, employing a new, extended potential energy surface that was computed with density functional theory, using the generalized gradient approximation and a slab representation of the metal surface. Theory and experiment are in good agreement for the survival probability, i.e., the probability for rovibrationally elastic scattering. However, the theory overestimates the probabilities for rotationally inelastic scattering (to v=1, j=3) and for rovibrationally inelastic scattering (to v=0, j=5 and 7) for channels that could be determi...

A multifaceted approach to hydrogen storage

The widespread adoption of hydrogen as an energy carrier could bring significant benefits, but only if a number of currently intractable problems can be overcome. Not the least of these is the problem of storage, particularly when aimed at use onboard light-vehicles. The aim of this overview is to look in depth at a number of areas linked by the recently concluded HYDROGEN research network, representing an intentionally multi-faceted selection with the goal of advancing the field on a number of fronts simultaneously. For the general reader we provide a concise outline of the main approaches to storing hydrogen before moving on to detailed reviews of recent research in the solid chemical storage of hydrogen, and so provide an entry point for the interested reader on these diverse topics. The subjects covered include: the mechanisms of Ti catalysis in alanates; the kinetics of the borohydrides and the resulting limitations; novel transition metal catalysts for use with complex hydrides; less common borohydrides; protic-hydridic stores; metal ammines and novel approaches to nano-confined metal hydrides.

Rotational Effects in Six-Dimensional Quantum Dynamics for Reaction of H2 on Cu (100).

We present results of six-dimensional (6D) quantum wave-packet calculations for the dissociative adsorption of (ν=0,j=4,mj) H2 on Cu(100). The potential-energy surface is a fit to points calculated using density-functional theory (DFT), with the generalized gradient approximation (GGA), and a slab representation for the surface. New aspects of the methodology we use to adapt the wave function to the symmetry of the surface, which relate to calculations for initial rotational states with odd mj (the magnetic quantum number), are explained. Invoking detailed balance, we calculate the quadrupole alignment for H2 as it would be measured in an associative desorption experiment. The reaction of the helicopter (ν=0,j=4,mj=4) state is preferred over that of the (ν=0,j=4,mj=0) cartwheel state for all but the lowest collision energies considered here. The energy dependence of the quadrupole alignment that we predict for (ν=0,j=4) H2 desorbing from Cu(100) is in good qualitative agreement with velocity-resolved asso...

Mechanisms of H2 dissociative adsorption on the Pt(211) stepped surface.

We utilize classical trajectory calculations to study the reaction dynamics of the dissociative adsorption of H2 on the stepped Pt(211) surface. The potential-energy surface has been obtained through an accurate interpolation of density-functional theory data at the generalized gradient approximation level, using the corrugation reduction procedure. New techniques for visualizing the collective dynamics of trajectories are introduced to elucidate the reaction mechanisms involved. Reaction exhibits a nonmonotonic dependence on collision energy, first decreasing with energy, and then increasing. A strong component of direct nonactivated reaction exists at the top edge of the step over the entire range of energies. The inverse relationship between reaction and collision energy at low energies is attributed to trapping in weak chemisorption wells. These wells also influence the direct reaction at the step, leading to a strong asymmetric dependence on incidence angle. Reaction on the terrace is activated, and only contributes significantly at high energies. Agreement with experiments on Pt(533) [A. T. Gee, B. E. Hayden, C. Mormiche, and T. S. Nunney, J. Chem. Phys. 112, 7660 (2000); Surf. Sci. 512, 165 (2002)] is good, and we are able to suggest new interpretations of the experimental data.

Direct subsurface absorption of hydrogen on Pd(111): Quantum mechanical calculations on a new two-dimensional potential energy surface

We have calculated a two-dimensional ~2D! potential energy surface ~PES! for H 2 interacting with aP d ~111! surface. The geometry considered is for H 2 approaching a bridge site and dissociating into neighboring hollow sites and the subsurface sites directly below these. Density functional calculations were performed using both the local density approximation ~LDA! and the generalized gradient approximation ~GGA!. The LDA PES gives the usual overbinding and shows no barrier ~relative to the bottom of the H2 potential! to subsurface absorption, while the GGA PES agrees with the experimental adsorption energies and has a large barrier. We have performed quantum mechanical wave packet calculations on the GGA PES to obtain the direct subsurface absorption probability. We have also calculated the barrier height’s dependence on a coordinate that can be associated with a local surface vibrational mode and the results suggest that this degree of freedom should be taken into account in the dynamical calculations.