Efficient methods for finding transition states in chemical reactions: Comparison of improved dimer method and partitioned rational function optimization method

A combination of interpolation methods and local saddle-point search algorithms is probably the most efficient way of finding transition states in chemical reactions. Interpolation methods such as the growing-string method and the nudged-elastic band are able to find an approximation to the minimum-energy pathway and thereby provide a good initial guess for a transition state and imaginary mode connecting both reactant and product states. Since interpolation methods employ usually just a small number of configurations and converge slowly close to the minimum-energy pathway, local methods such as partitioned rational function optimization methods using either exact or approximate Hessians or minimum-mode-following methods such as the dimer or the Lanczos method have to be used to converge to the transition state. A modification to the original dimer method proposed by [Henkelman and Jónnson J. Chem. Phys. 111, 7010 (1999)] is presented, reducing the number of gradient calculations per cycle from six to four gradients or three gradients and one energy, and significantly improves the overall performance of the algorithm on quantum-chemical potential-energy surfaces, where forces are subject to numerical noise. A comparison is made between the dimer methods and the well-established partitioned rational function optimization methods for finding transition states after the use of interpolation methods. Results for 24 different small- to medium-sized chemical reactions covering a wide range of structural types demonstrate that the improved dimer method is an efficient alternative saddle-point search algorithm on medium-sized to large systems and is often even able to find transition states when partitioned rational function optimization methods fail to converge.