Accelerated relaxation engines for optimizing to a minimum energy path†

In the last few decades, several novel algorithms have been designed for finding critical points on a potential energy surface (PES) and the minimum energy paths connecting them. This has led to a considerable improvement in our understanding of reaction mechanisms and the kinetics of the underlying processes. These methods implicitly rely on computation of energy and forces on the PES, which are usually obtained via computationally demanding wave-function- or density-function-based ab initio methods. To mitigate the computational cost, efficient optimization algorithms are needed. Herein, we present two new first-order optimization algorithms: the adaptively accelerated relaxation engine (AARE), an enhanced molecular dynamics (MD) scheme, and the accelerated conjugate-gradient (Acc-CG) method, an improved version of the traditional conjugate gradient (CG) algorithm. We show the efficacy of these algorithms for unconstrained optimization on 2-dimensional and 4-dimensional test functions. Additionally, we also show the efficacy of these algorithms for optimizing an elastic band of images to the minimum energy path on 2-dimensional analytical potentials, heptamer island transitions, the HCN/CNH isomerization reaction, and the keto–enol tautomerization reaction.