Saddle point sampling using scaled normal coordinates

Abstract

The sampling of saddle points (SPs) on a potential energy surface (PES) is critical for describing the dynamics and transport properties of materials. Here, we propose a saddle point search (SPS) method that enables efficient sampling of practically meaningful SPs around a local minimum by converting the PES to the scaled normal coordinates (SNCs), together with the dimer method. We find that the pathway leading to a SP using SNCs is highly efficient and is independent of the system size. This results in the significantly increased SPS efficiency and the enhanced possibility of a complete catalog of the SPs. In addition, we perform SPSs using the SNCs for the diffusion of a vacancy and a dumbbell in body-centered cubic Fe and demonstrate (1) the required number of system force evaluations for a SPS decreases by at least an order of magnitude, (2) the effects of the system size on the number of force evaluations are greatly decreased, and (3) the effects of the number of atoms involved in the SPS on the probability of finding practically meaningful SPs is mostly eliminated. We also discuss the computational cost of introducing the SNCs. It should be highlighted that the SNCs could also be applied to other minimum-mode following methods, demonstrating the general versatility of the proposed method.