Direct inversion in the iterative subspace-induced acceleration of the ridge method for finding transition states

Abstract

We extend the application of the direct inversion in the iterative subspace (DIIS) technique to the ridge method for finding transition states (TS). The latter is not a quasi-Newton-type algorithm, which is the only class of geometry optimization methods that has been combined with DIIS. With this new combination, we obtain a factor of two speedup due to DIIS, similar to the DIIS-related speedup achieved in other methods including quasi-Newton geometry optimization and self-consistent field iterations. We also demonstrate that DIIS is useful even in cases where optimization is started far from the quadratic region of the TS, provided that only one previous iteration is used in the DIIS expansion. We compare the performance of the new ridge-DIIS method to that of the TS algorithm utilized in GAUSSIAN 92. We find that the computational cost of the former is similar (when both methods converge) to that of the latter. The examples considered in the paper include a novel TS found for an isomerization of a cluster of six Na atoms. Locating such a TS poses a known problem for second-derivatives-based algorithms that fail on very flat potential energy surfaces. Thus, the gradient-based ridge-DIIS method is the only TS search method that is robust, does not need second derivatives and/or an initial guess for the TS geometry, and whose performance matches or exceeds that of a second-derivatives-based algorithm.