A critical assessment of theoretical methods for finding reaction pathways and transition states of surface processes

The performance of a variety of techniques for locating transition states on potential energy surfaces is evaluated within the density functional theory framework. Diffusion of a water molecule across NaCl(001) and HCl bond breaking on the same surface are treated as general test cases; the former is an example of a low barrier diffusion process and the latter an example of a relatively high barrier covalent bond rupture event. The methods considered include the nudged elastic band (NEB), Dewar, Healy and Stewart (DHS), dimer, constrained optimization (CO), activation–relaxation technique (ART) and one-side growing string (OGS) as well as novel combinations of the DHS with growing string (DHS + GS) and DHS plus climbing image (CI-DHS). A key conclusion to come from this study is that the NEB method is relatively fast, especially when just a single (climbing) image is used. Indeed, using more images represents an unnecessary computational burden for our set of processes. The dimer method exhibits variable performance; being poor for the water diffusion processes, which have small activation energies, but much more efficient for the HCl bond breaking process which has a higher barrier. When only a poor initial guess of the transition state geometry is available, the CI-DHS scheme is one of the most efficient techniques considered. And as a means to quickly establish an approximate minimum energy pathway the DHS + GS scheme offers some potential.