(10e) An Adaptive Acceleration Routine for Efficient MEP Discovery

Efficient exploration of the potential energy surface (PES) and evaluation of the minimum energy path (MEP) facilitates the understanding of reaction mechanism(s) and catalyst design. A popular MEP finding technique is the NEB, which involves optimizing a chain of images connected by artificial springs [1]. Even with its robustness, employing ab initio computations to obtain energy and forces demands substantial computational efforts. Therefore, selecting an efficient optimization algorithm is critical. Force-based optimizers are usually preferred for exploring the PES due to the computational complexity associated with obtaining the Hessian matrix. Among these optimizers, the fast inertial relaxation engine (FIRE) is a preferred method [2]. However, FIRE has certain drawbacks: (a) has an empirical parameter which is arbitrarily chosen, (b) slow convergence due to zeroing the velocity (uphill motion) and the latency time, and (c) overshooting due to increased time-step. Herein, we propose a new algorithm to relax MEP. The algorithm modifies the MD trajectory by employing an adaptive acceleration routine based on local information and conjugate-like direction. Similarly, we also improved the conventional CG method, using an acceleration scheme combining the Newton and Secant methods to compare the algorithms. The new algorithms were tested on 26 analytical test functions, and both the algorithms performed much better than FIRE. Since finding MEP also involves solving a constrained optimization problem that drives the force perpendicular to MEP zero, these algorithms are extended to NEB by replacing the gradient forces with NEB forces. The algorithms were tested on two analytical potentials, LEPS-I and LEPS-II, and for HCN - CNH isomerisation reaction for finding MEP. In all the cases tested, AARE-FR notably outperformed FIRE in terms of number of force evaluations.

References:
1. Henkelman and Jónsson, JCP (2000), 113, 9978.
2. Bitzek et al. PRL (2006), 97170201.