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 approximately 4.2 kilojoules per mole).

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.

This computational study is motivated by the apparent conflict between an experiment on dissociation of H 2 and D 2 on Pt͑111͒, which suggests a rather corrugated potential energy surface ͑PES͒ for the H 2 /Pt͑111͒ system, and an experiment showing only weak nonzero-order diffraction of HD scattering from Pt͑111͒. In the calculations we have used density functional theory ͑DFT͒ within the generalized gradient approximation ͑GGA͒, including scalar relativistic effects and modelling the Pt͑111͒ surface as a slab. We have found that the H 2 /Pt͑111͒ 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 H 2 on the Pt͑111͒ surface, but that there are other reaction paths with substantial barriers. By performing extensive calculations on H interacting with a Pt͑111͒ surface we have shown that a DFT/GGA approach that includes scalar relativistic effects is capable of describing the interaction between a hydrogen atom and a Pt͑111͒ surface in a way that is, for the most part, consistent with experiments.

The Born-Oppenheimer approximation of uncoupled electronic and nuclear motion is a standard tool of the computational chemist. However, its validity for molecule-metal surface reactions, which are important to heterogeneous catalysis, has been questioned because of the possibility of electron-hole pair excitations. We have performed experiments and calculations on the scattering of molecular hydrogen from a catalytically relevant metal surface, obtaining absolute probabilities for changes in the molecule's velocity parallel to the representative Pt(111) surface. The comparison for in-plane and out-of-plane scattering and results for dissociative chemisorption in the same system show that for hydrogen-metal systems, reaction and diffractive scattering can be accurately described using the Born-Oppenheimer approximation.