Minimum mode saddle point searches using Gaussian process regression with inverse-distance covariance function

The minimum mode following method can be used to find saddle points on an energy surface by following a direction guided by the lowest curvature mode. Such calculations are often started close to a minimum on the energy surface to find out which transitions can occur from an initial state of the system, but it is also common to start from the vicinity of a first order saddle point making use of an initial guess based on intuition or more approximate calculations. In systems where accurate evaluations of the energy and its gradient are computationally intensive, it is important to exploit the information of the previous evaluations to enhance the performance. Here, we show that the number of evaluations required for convergence to the saddle point can be significantly reduced by making use of an approximate energy surface obtained by a Gaussian process model based on inverse inter-atomic distances, evaluating accurate energy and gradient at the saddle point of the approximate surface and then correcting the model based on the new information. The performance of the method is tested with start points chosen randomly in the vicinity of saddle points for dissociative adsorption of an H₂ molecule on the Cu(110) surface and three gas phase chemical reactions.