We observe that Eq. 3 gives the same quantities as a 1 2 9 i=1 ln λ i , with eigenvalues λ 1 , ..., λ 9 obtained from diagonalizing J T J , where J ∈ R 9×10 is the Jacobian of Eq. 2 given by automatic differentiation. Eq. 3 was therefore evaluated when reconstructing a water molecule (i.e., mapping x mol → r mol ). When mapping in the opposite direction (i.e., r mol → x mol ), as defined in Ref. , the log volume change of -ln γ x mol →r mol was used. In model H, all of the intramolecular DOFs (i.e., the bond lengths and angles [d 1 , d 2 , θ] ×n mol , see Fig. ) were directly concatenated to the whitened Cartesian coordinates of the oxygen atoms (c O ), with the latter being treated in the same way as in model C.