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

摘要

Efficient identification of transition states is important for understanding reaction mechanisms. Mosttransition state search algorithms require long computational times and a good estimate of thetransition state structure in order to converge, particularly for complex reaction systems. Thegrowing string method (GSM) [B. Peters et al., J. Chem. Phys. 120, 7877 (2004)] does not requirean initial guess of the transition state; however, the calculation is still computationally intensive dueto repeated calls to the quantum mechanics code. Recent modifications to the GSM [A. Goodrow etal., J. Chem. Phys. 129, 174109 (2008)] have reduced the total computational time for convergingto a transition state by a factor of 2 to 3. In this work, three transition state-finding strategies havebeen developed to complement the speedup of the modified-GSM: (1) a hybrid strategy, (2) anenergy-weighted strategy, and (3) a substring strategy. The hybrid strategy initiates the stringcalculation 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 onthe energy at those points, leading to a higher density of points where the energy is highest and finerresolution of the transition state. The substring strategy is similar to the hybrid strategy, but only aportion of the low-level string is refined using a higher level of theory. These three strategies havebeen used with the modified-GSM and are compared in three reactions: alanine dipeptideisomerization, H-abstraction in methanol oxidation on VO_X/SiO_2catalysts, and C–H bondactivation in the oxidative carbonylation of toluene to p-toluic acid on Rh(CO)_2(TFA)_3catalysts. Ineach of these examples, the substring strategy was proved most effective by obtaining a betterestimate of the transition state structure and reducing the total computational time by a factor of 2to 3 compared to the modified-GSM. The applicability of the substring strategy has been extendedto three additional examples: cyclopropane rearrangement to propylene, isomerization ofmethylcyclopropane to four different stereoisomers, and the bimolecular Diels–Alder condensationof 1,3-butadiene and ethylene to cyclohexene. Thus, the substring strategy used in combination withthe modified-GSM has been demonstrated to be an efficient transition state-finding strategy for awide range of types of reactions.