Nudged-elastic band method with two climbing images: finding transition states in complex energy landscapes.

The nudged-elastic band (NEB) method is modified with concomitant two climbing images (C2-NEB) to find a transition state (TS) in complex energy landscapes, such as those with a serpentine minimal energy path (MEP). If a single climbing image (C1-NEB) successfully finds the TS, then C2-NEB finds it too. However, improved stability of C2-NEB makes it suitable for more complex cases, where C1-NEB misses the TS because the MEP and NEB directions near the saddle point are different. Generally, C2-NEB not only finds the TS, but also guarantees, by construction, that the climbing images approach it from the opposite sides along the MEP. In addition, C2-NEB provides an accuracy estimate from the three images: the highest-energy one and its climbing neighbors. C2-NEB is suitable for fixed-cell NEB and the generalized solid-state NEB.