“…Notice that in case of a truly separable potential, we could write V 3 ( q̃ 3 ) – V 3 ( q̃ 3 eq ) = V ( q̃ 1 , q̃ 2 , q̃ 3 ) – V ( q̃ 1 , q̃ 2 , q̃ 3 eq ) and V 1,2 ( q̃ 1 , q̃ 2 ) – V 1,2 ( q̃ 1 eq , q̃ 2 eq ) = V ( q̃ 1 , q̃ 2 , q̃ 3 ) – V ( q̃ 1 eq , q̃ 2 eq , q̃ 3 ). These last expressions correspond to the “projected potentials” used to compute the vibrational spectroscopic features of molecules as large as G-quadruplex in solution with the Divide-and-Conquer SemiClassical Initial Value Representation (DC-SCIVR) method. ,, While the DC-SCIVR method simulates the dynamics of a system under a full dimensional potential and then approximates the classical action with a potential projected into subspaces, the algorithm we are presenting here evolves the dynamics entirely under the subspace-projected potential (or partially projected, when α ≠ 0). Furthermore, the decoupling could be applied to all the degrees of freedom pertaining to two atoms, that is, for instance, to the Cartesian product ( x 1 , y 1 , z 1 ) × ( x 2 , y 2 , z 2 ), to decouple atoms 1 and 2.…”