Basins of attraction for stationary points on a potential-energy surface

Abstract

Methods to locate stationary points on model potential-energy surfaces, especially minima and transition states, are of great importance. Here we visualise the basins of attraction of such points, that is, the regions of the surface for which searches converge to a given structure. The results demonstrate the superiority of the eigenvector-following (EF) method over simple Newton–Raphson (NR) iteration. Furthermore, the boundaries between different basins of attraction may apparently be multifractal in character and highly complex. The results also provide some general rules for the efficient characterisation of potential-energy surfaces which are of practical value.