Efficient two-step procedures for locating transition states of surface reactions

Using various two-step strategies, we examined how to accurately locate transition states (TS) of reactions using the example of eight reactions at metal surfaces with 14-33 moving atoms. These procedures combined four path-finding methods for locating approximate TS structures (nudged elastic band, standard string, climbing image string, and searching string, using a conjugate gradient or a modified steepest-descent method for optimization and two types of coordinate systems) with subsequent local refinement by two dimer methods. The dimer-Lanczos variant designed for this study required on average 20% fewer gradient calls than the standard dimer method. During the path finding phase, using mixed instead of Cartesian coordinates reduced the numbers of gradient calls on average by an additional 21%, while using a modified steepest-descent method improved that key efficiency criterion on average by 13%. For problematic cases we suggest strategies especially adapted to the problem at hand.