Transition state-finding strategies for use with the growing string method

Efficient identification of transition states is important for understanding reaction mechanisms. Most transition state search algorithms require long computational times and a good estimate of the transition state structure in order to converge, particularly for complex reaction systems. The growing string method (GSM) [B. Peters et al., J. Chem. Phys. 120, 7877 (2004)] does not require an initial guess of the transition state; however, the calculation is still computationally intensive due to repeated calls to the quantum mechanics code. Recent modifications to the GSM [A. Goodrow et al., J. Chem. Phys. 129, 174109 (2008)] have reduced the total computational time for converging to a transition state by a factor of 2 to 3. In this work, three transition state-finding strategies have been developed to complement the speedup of the modified-GSM: (1) a hybrid strategy, (2) an energy-weighted strategy, and (3) a substring strategy. The hybrid strategy initiates the string calculation at a low level of theory (HF/STO-3G), which is then refined at a higher level of theory (B3LYP/6-31G∗). The energy-weighted strategy spaces points along the reaction pathway based on the energy at those points, leading to a higher density of points where the energy is highest and finer resolution of the transition state. The substring strategy is similar to the hybrid strategy, but only a portion of the low-level string is refined using a higher level of theory. These three strategies have been used with the modified-GSM and are compared in three reactions: alanine dipeptide isomerization, H-abstraction in methanol oxidation on VOx/SiO2 catalysts, and C–H bond activation in the oxidative carbonylation of toluene to p-toluic acid on Rh(CO)2(TFA)3 catalysts. In each of these examples, the substring strategy was proved most effective by obtaining a better estimate of the transition state structure and reducing the total computational time by a factor of 2 to 3 compared to the modified-GSM. The applicability of the substring strategy has been extended to three additional examples: cyclopropane rearrangement to propylene, isomerization of methylcyclopropane to four different stereoisomers, and the bimolecular Diels–Alder condensation of 1,3-butadiene and ethylene to cyclohexene. Thus, the substring strategy used in combination with the modified-GSM has been demonstrated to be an efficient transition state-finding strategy for a wide range of types of reactions.