The graph above is for the PM6 model.

The difference in free energy for PHE is -1.8 kcal mol-1

The difference in free energy for TRP is -3.5 kcal mol-1

Question 5.1 - The PMFs plotted above are more curved than those calculated from the shorter simulation. This is because the short simulation is too short to allow the water molecules to adapt themselves to their most stable conformation for each value of λ. λ is used to scale linearly from the QM/MM to MM model of the side-chain. However, while this linear change may be expected to give a linear change in free energy (and hence a straight-line PMF), this neglects the affect of the change in model of the side-chain on the sampling of water. As λ moves from QM/MM to MM, the water will adopt a different equilibrium structure that is best adapted to the model of the side-chain at that value of λ. This change in structure of water is a non-linear effect, and thus introduces curvature into the PMF. You can only see this affect if you can sample the water at each value of λ, and you need long simulations to fully equilibrate the water (hence why the short simulations only showed minimum curvature). While the amount of curvature here is small, our experience is that the more polar the solute, the more curved the PMF (and hence the more important it is to sample fully across λ). This is perhaps why the TRP PMF is more curved than the PHE PMF. Note also that the increased curvature has reduced the difference in free energy between the MM and QM/MM models, e.g. for PHE, the free energy difference is reduced from -2.7 to -1.8 kcal mol-1, while for TRP the difference is reduced from -4.0 to -3.5 kcal mol-1.

Question 5.2 - The PMFs both show that the difference in free energy between the MM and QM/MM models is negative. This means that the free energy decreases (becomes more favourable) as we move from the QM/MM to MM model. This means that the MM model is more stable than the QM/MM model, hence that the MM model of each side-chain interacts more strongly with water than the QM/MM model.

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