Free-end adaptive nudged elastic band method for locating transition states in minimum energy path calculation

A free-end adaptive nudged elastic band (FEA-NEB) method is presented for finding transition states on minimum energy paths, where the energy barrier is very narrow compared to the whole paths. The previously proposed free-end nudged elastic band method may suffer from convergence problems because of the kinks arising on the elastic band if the initial elastic band is far from the minimum energy path and weak springs are adopted. We analyze the origin of the formation of kinks and present an improved free-end algorithm to avoid the convergence problem. Moreover, by coupling the improved free-end algorithm and an adaptive strategy, we develop a FEA-NEB method to accurately locate the transition state with the elastic band cut off repeatedly and the density of images near the transition state increased. Several representative numerical examples, including the dislocation nucleation in a penta-twinned nanowire, the twin boundary migration under a shear stress, and the cross-slip of screw dislocation in face-centered cubic metals, are investigated by using the FEA-NEB method. Numerical results demonstrate both the stability and efficiency of the proposed method.