Iterative minimization algorithm for efficient calculations of transition states

This paper presents an efficient algorithmic implementation of the iterative minimization formulation (IMF) for fast local search of transition state on potential energy surface. The IMF is a second order iterative scheme providing a general and rigorous description for the eigenvector-following (min-mode following) methodology. We offer a unified interpretation in numerics via the IMF for existing eigenvector-following methods, such as the gentlest ascent dynamics, the dimer method and many other variants. We then propose our new algorithm based on the IMF. The main feature of our algorithm is that the translation step is replaced by solving an optimization subproblem associated with an auxiliary objective function which is constructed from the min-mode information. We show that using an efficient scheme for the inexact solver and enforcing an adaptive stopping criterion for this subproblem, the overall computational cost will be effectively reduced and a super-linear rate between the accuracy and the computational cost can be achieved. A series of numerical tests demonstrate the significant improvement in the computational efficiency for the new algorithm.