Minimum free energy pathways with the nudged elastic band method in combination with a QM-MM Hamiltonian

The optimization of minimum free energy pathways (MFEP) is one of the most widely used strategies to study activated processes. For chemical reactions, this requires the use of quantum mechanics. Using quantum mechanics molecular mechanics (QM- MM) Hamiltionians allows the simulation of reactive processes in complex environments by treating with quantum mechanics only the chemically relevant part of the system. However, even within this approximation, the affordable simulation lenghts of QM-MM simulations is in general, quite limited. Free energy methods based on the sampling of the potential energy surface require long simulations times to provide converged and accurate results. As consequence, the combination of QM-MM methods and free energy calculations is computationally expensive. Moreover, the user usually needs to perform an a priori selection of the reaction coordinate. This may be not trivial for the general case. One of the most established methods for finding potential energy profiles without selecting a reaction coordinate is the nudged elastic band method (NEB). In this work, we used the extension of this method to the exploration of the free energy surface for finding MFEP (FENEB). We present and apply to reactive systems an improved version of the basic optimization scheme of FENEB that increases its robustness, and is based on decoupling the optimization of the band in the perpendicular direction to the band, from the optimization of the tangential direction. In each optimization step, a full optimization with the spring force is performed, in order to keep the images evenly distributed. Additionally, we evaluate the influence of sampling in the quality of the optimized MFEP and free energy barrier computed from it. We show and discuss that the FENEB method provides a good estimation of the reaction barrier even with relatively short simulations lenghts and that it scales better than umbrella sampling both with simulation lenght and with dimensionality. Overall, our results support that the combination of QM-MM methods and the FENEB provides an adequate tool study chemical processes in complex environments.