Figure 4:

A staged transformation approach¹⁴¹ for computing the free energy difference at two levels (L/H) of theory, ΔG^L→H. (A) The staged thermodynamic path treats 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 $\Delta G_0^{L\to H}$, which converges readily since the sampling involves only Y, and the “reorganization free energy”, $\Delta G_{\Lambda }^L$, which is the free energy cost of changing X₀ to $X_0^{\prime }$ at the low level of theory. (b-c) Illustration of the impact of bond and angle restraints on the ΔU^LH distribution for a methyl diphosphate, which is treated with either DFTB3 (L) or B3LYP (H), solvated by TIP3P water.