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

Abstract

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 VO(x)/SiO(2) 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.

Following atomistic kinetics on experimental timescales with the kinetic Activation–Relaxation Technique

“…A number of algorithms have been proposed in the past to accomplish this task, many of them being very similar in their spirit and their e ciency. [20][21][22] Here, we use ART nouveau [23][24][25], an e cient Lanczosbased activation-relaxation technique that was developed and improved over the past 20 years in our group (see, for a comparison with other methods, Refs. 25, 26 as well as a few papers in this issue.…”

Implementation of an algorithm based on the Runge‐Kutta‐Fehlberg technique and the potential energy as a reaction coordinate to locate intrinsic reaction paths

“…(12) is close in its structure with the main equation of the NEB and related algorithms. [14][15][16][17][18][19][20][21] As far as we known it is the first time that the basic equation of this set of algorithms is derived rigorously from the theory of calculus of variations. In addition it is expressed as a function of the PES rather than other parameter allowing its use to locate the IRC curves using the potential energy as the parameter of the curve.…”

“…Because of this minimization procedure, these methods are named ''nudged elastic band'' (NEB). [14][15][16][17][18][19][20][21] Using the NEB method, in the converged path the set of equally spaced points characterizing the curve possesses a zero forces or gradient components of the PES in the orthogonal path direction. Further improvements of NEB technique imply the definition of tangent vector direction and estimation of transition state.…”

Reaction Path Optimization and Sampling Methods and Their Applications for Rare Events

“…Growing string methods (GSM) were proposed (Peters et al 2004) and are under continuous development to address these issues. (Goodrow et al , 2009(Goodrow et al , 2010Quapp 2005Quapp , 2009 The basic idea is to gradually grow two strings separately from two minima by continuously adding replicas to each string until both strings merge. The GSM generally comprises five steps.…”

“…4. In various developments, Newton projector, (Quapp 2005) internal coordinate, ) conjugate gradient method, ) and different TS search strategies (Goodrow et al 2009(Goodrow et al , 2010 are implemented in GSM for better performance. The major goal of GSM is improving the calculation efficiency of the ZTS framework for systems involving expensive QM calculations.…”