A modification of the nudged elastic band method for finding minimum energy paths is presented. One of the images is made to climb up along the elastic band to converge rigorously on the highest saddle point. Also, variable spring constants are used to increase the density of images near the top of the energy barrier to get an improved estimate of the reaction coordinate near the saddle point. Applications to CH 4 dissociative adsorption on Ir͑111͒ and H 2 on Si͑100͒ using plane wave based density functional theory are presented.

We present a method for calculating the stability of reaction intermediates of electrochemical processes on the basis of electronic structure calculations. We used that method in combination with detailed density functional calculations to develop a detailed description of the free-energy landscape of the electrochemical oxygen reduction reaction over Pt(111) as a function of applied bias. This allowed us to identify the origin of the overpotential found for this reaction. Adsorbed oxygen and hydroxyl are found to be very stable intermediates at potentials close to equilibrium, and the calculated rate constant for the activated proton/electron transfer to adsorbed oxygen or hydroxyl can account quantitatively for the observed kinetics. On the basis of a database of calculated oxygen and hydroxyl adsorption energies, the trends in the oxygen reduction rate for a large number of different transition and noble metals can be accounted for. Alternative reaction mechanisms involving proton/electron transfer to adsorbed molecular oxygen were also considered, and this peroxide mechanism was found to dominate for the most noble metals. The model suggests ways to improve the electrocatalytic properties of fuel-cell cathodes.

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An improved way of estimating the local tangent in the nudged elastic band method for finding minimum energy paths is presented. In systems where the force along the minimum energy path is large compared to the restoring force perpendicular to the path and when many images of the system are included in the elastic band, kinks can develop and prevent the band from converging to the minimum energy path. We show how the kinks arise and present an improved way of estimating the local tangent which solves the problem. The task of finding an accurate energy and configuration for the saddle point is also discussed and examples given where a complementary method, the dimer method, is used to efficiently converge to the saddle point. Both methods only require the first derivative of the energy and can, therefore, easily be applied in plane wave based density-functional theory calculations. Examples are given from studies of the exchange diffusion mechanism in a Si crystal, Al addimer formation on the Al͑100͒ surface, and dissociative adsorption of CH 4 on an Ir͑111͒ surface.