Minimum Free Energy Pathways of Reactive Processes with Nudged Elastic Bands

Abstract

The determination of minimum free energy pathways(MFEP) is one of the most widely used strategies to study reactiveprocesses. For chemical reactions in complex environments, thecombination of quantum mechanics (QM) with a molecularmechanics (MM) representation is usually necessary in a hybridQM/MM framework. However, even within the QM/MM approx-imation, the affordable sampling of the phase space is, in general, quiterestricted. To reduce drastically the computational cost of thesimulations, several methods such as umbrella sampling requireperforming a priori a selection of a reaction coordinate. The quality ofthe computed results, in an affordable computational time, isintimately related to the reaction coordinate election which is, ingeneral, a nontrivial task. In this work, we provide an approach tomodel reactive processes in complex environments that does not require the a priori selection of a reaction coordinate. The proposedmethodology combines QM/MM simulations with an extrapolation of the nudged elastic bands (NEB) method to the free energysurface (FENEB). We present and apply our own FENEB scheme to optimize MFEP in different reactive processes, using QM/MMframeworks at semiempirical and density functional theory levels. Our implementation is based on performing the FENEBoptimization by uncoupling the optimization of the band in a perpendicular and tangential direction. In each step, a full optimizationwith the spring force is performed, which guarantees that the images remain evenly distributed. The robustness of the method andthe influence of sampling on the quality of the optimized MFEP and its associated free energy barrier are studied. We show that theFENEB method provides a good estimation of the reaction barrier even with relatively short simulation times, supporting that itscombination with QM/MM frameworks provides an adequate tool to study chemical processes in complex environments.