Development and application of a hybrid method involving interpolation and <i>ab initio</i> calculations for the determination of transition states

Transition state search algorithms, such as the nudged elastic band can fail, if a good initial guess of the transition state structure cannot be provided. The growing string method (GSM) [J. Chem. Phys. 120, 7877 (2004)] eliminates the need for an initial guess of the transition state. While this method only requires knowledge of the reactant and product geometries, it is computationally intensive. To alleviate the bottlenecks in the GSM, several modifications were implemented: Cartesian coordinates were replaced by internal coordinates, the steepest descent method for minimization of orthogonal forces to locate the reaction path was replaced by the conjugate gradient method, and an interpolation scheme was used to estimate the energy and gradient, thereby reducing the calls to the quantum mechanical (QM) code. These modifications were tested to measure the reduction in computational time for four cases of increasing complexity: the Müller–Brown potential energy surface, alanine dipeptide isomerization, H abstraction in methanol oxidation, and C–H bond activation in oxidative carbonylation of toluene to p-toluic acid. These examples show that the modified GSM can achieve two- to threefold speedups (measured in terms of the reduction in actual QM gradients computed) over the original version of the method without compromising accuracy of the geometry and energy of the final transition state. Additional savings in computational effort can be achieved by carrying out the initial search for the minimum energy pathway (MEP) using a lower level of theory (e.g., HF/STO-3G) and then refining the MEP using density functional theory at the B3LYP level with larger basis sets (e.g., 6-31G∗, LANL2DZ). Thus, a general strategy for determining transition state structures is to initiate the modified GSM using a low level of theory with minimal basis sets and then refining the calculation at a higher level of theory with larger basis sets.