(669d) Development and Application of a Hybrid Method Involving Interpolation and Ab Initio Calculations for the Determination of Transition States

Determination of transition states (TS) is important for understanding the kinetics of chemical reactions. Methods such as the nudged-elastic band (NEB) require an intial guess for the geometry of the TS and electronic structure calculations can fail if the guess is not correct. By contrast, the growing-string method (GSM) requires only reactant and product geometries in order to initiate the search for the TS; however this method is computationally intensive because a large number of gradient calculations need to be made. Several modifications have been implemented in order to reduce the computational cost of the GSM. First, internal coordinates have replaced Cartesian coordinates because they are better able to describe the movement of atom(s) during elementary reactions. Second, the conjugate gradient method has replaced the steepest descent method during the minimization of orthogonal forces in the search of points along the minimum energy path (MEP). Third, an interpolation scheme has been implemented to estimate the energy and gradient rather than using quantum mechanics (QM) code, thereby saving significant computational time. The interpolation scheme that was implemented was adopted from work previously done on reaction dynamics [M. A. Collins, Theor. Chem. Acc. 2002, 108, 313]. The modified GSM has been tested on four cases of increasing complexity: the Müller-Brown potential energy surface, alanine dipeptide isomerization, H-abstraction during methanol oxidation on isolated vanadate species supported on silica [A. Goodrow, A. T. Bell, J. Phys. Chem. C 2007, 111, 14753], and C-H bond activation in the oxidative carbonylation of toluene to p-toluic acid by Rh complexes [X. Zheng, A. T. Bell, J. Phys. Chem. C 2008, 112, 2129]. The modified GSM represents a 2-3 time reduction in computational effort over the previous method as measured by the number of QM gradients computed, without a sacrifice in the accuracy of the geometry and energy of the final TS. Additional savings in computational effort can be achieved by carrying out the initial search for the MEP using a lower level of theory, e.g. HF/STO-3G, and then refining the MEP using DFT at the B3LYP level with larger basis sets.