Constrained Broyden Minimization Combined with the Dimer Method for Locating Transition State of Complex Reactions

To determine transition state (TS) and, thus, to predict chemical activity has been a challenging topic in theoretical simulations of chemical reactions. In particular, with the difficulty to compute the second derivative of energy (Hessian) in modern quantum mechanics packages with a non-Gaussian basis set, the location usually involves a high demand in computational power and lacks stability in the algorithm, especially for complex reaction systems with many degrees of freedom. Here, an efficient TS searching method is developed by combining the constrained Broyden minimization algorithm with the dimer method that was first proposed by Henkelman and Jonsson. In the new method, the rotation of the dimer needs only one energy and gradient calculation for determining a rotation angle; the translation of the dimer is continually carried out until a termination criterion is met, and the translational force parallel to the dimer direction is damped to optimize the searching trajectory. Based on our results of the Baker reaction system and of a heterogeneous catalytic reaction, our method is shown to increase the efficiency significantly and is also more stable in finding TSs.