In the context of classical mechanics, qq and pp represent the generalized positions and momenta, while λi\lambda_i denotes the Lagrange multiplier that enforces the ii-th constraint σi(q)\sigma_i(q). The reaction coordinate ξ(q)\xi(q) serves as a key parameter, which may reflect a straightforward geometric quantity like a bond distance or a more abstract variable. Notably, this reaction coordinate is typically not predetermined and must be selected thoughtfully, guided by chemical insight. Its choice should be carefully monitored to ensure it remains effective throughout the analysis.