FIG. 3.

A simple staged transformation approach for computing the free energy difference at two levels (L/H) of theory, ΔG^L→H. (a) The staged thermodynamic path treats the selected degrees of freedom (X) separately from the rest (Y); X represents the degrees of freedom that lead to a large gap in the ΔU^LH distribution. Assuming that the free energy costs for confining X to values at (or near) the free energy minima are similar at the L and H levels, ΔG^L→H, is given by the sum of $\mathrm{\Delta }{G}_0^{L\to H}$, which converges readily since the sampling involves only Y, and the “reorganization free energy,” $\mathrm{\Delta }{G}_{\mathrm{\Lambda }}^L$, which is the free energy cost of changing X₀ to ${\mathbf{X}}_0^{\prime }$ at the low level of theory. (b) A simple one-dimensional illustration for the staged transformation approach: W(X) is the potential of mean force and the key approximation is that the configurational entropies for X are comparable at the L and H levels.