A Stochastic Non-empirical approach in the problem of the reaction path seeking

In the atomistic simulation methods, the escaping trajectories, which is rendered rare because of the potential energy barrier, and free-energy landscape along them are usually calculated by applying artificial force and/or empirical collective variables. Our motivation is to develop the method free from such artificial forces and collective variables. We developed a non-empirical scheme to search for the minimum-energy escape paths from the minima of the potential surface to unknown saddle points nearby. This method employs only the local gradient and diagonal part of the Hessian matrix of the potential [R.Akashi, YSN, J. Phys. Soc. Jpn. 87, 063801 (2018)].
In our method we employ a stochastic equation, with which the distribution of the “walkers” representing atomic positions move up the potential surface through the valleys to the saddle points. The key to the successful tracking of the minimum-energy paths is the choice of the initial position. We designed a systematic method to generate initial atomic coordinates and efficiently simulate the paths to the saddle points starting from them. We demonstrate our method with several systems such as argon clusters.