Computing tunneling paths with the Hamilton–Jacobi equation and the fast marching method

Efficient acceleration of the convergence of the minimum free energy path via a path-planning generated initial guess

We demonstrate that combining a shifted clustering algorithm with a fast-marching-based algorithm can generate accurate approximations of the minimum energy path (MEP) given a free energy landscape (FEL). Using this approximation as the initial guess for the MEP, followed by further refinement with the string method (referred to as the fast marching tree (FMT)-string combined approach), significantly reduces the number of iterations required for MEP convergence. This approach saves substantial time compared to using linear interpolation (LI) for the initial guess. Our method offers a viable solution for obtaining an effective initial guess of the MEP when an approximate or converged FEL is available. This work highlights the potential of applying FMT-based approaches to extract the MEP in chemical reactions.