The notations in this study align with those in ref 1. An atomic system with n atoms atoms is represented by a 3n atoms dimensional vector x, which can also be expressed as a set of three-dimensional vectors r 1 , r 2 , • • • for individual atomic coordinates. Reactant and product structures are denoted by x r and x p , respectively. A path connecting these endpoints is described as x(t), where t ∈ [0, 1].