Finding Reaction Pathways and Transition States: r‑ARTn and d‑ARTn as an Efficient and Versatile Alternative to String Approaches

Finding transition states and diffusion pathways is essential to understand the evolution of materials and chemical reactions. Such characterization is hampered by the heavy computation costs associated with exploring energy landscapes at ab initio accuracy. Here, we revisit the activation-relaxation technique (ARTn) to considerably reduce its costs when used with the density functional theory and propose three adapted versions of the algorithm to efficiently (i) explore the energy landscape of complex materials with the knowledge of a single minimum (ARTn); (ii) identify a transition state when two minima or a guess transition state is given (refining ART or r-ART); and (iii) reconstruct complex pathways between two given states (directed ART or d-ART). We show the application of these three variants on benchmark examples and on various complex defects in silicon. For the latter, the presented improvements to ART lead to much more precise transition states while being 2 to 6 times faster than the commonly used string methods such as the climbing image nudged elastic band method (CI-NEB).