In this framework, the coordinate r N represents the N Cartesian coordinates pertinent to each particle. The λ-dependent potential energy function U (r N ; λ) is characterized such that U (r N ; 0) = U 0 (r N ) and U (r N ; 1) = U 1 (r N ), which represent the potential energy functions for the initial and final states, respectively. Throughout the TI simulation, mean values of ∂U (r N ;λ) ∂λ are derived for each λ interval "λ i ", where i = 1, ..., m with corresponding weights