Conclusion

We have carried out classical MD simulations using different functional forms of repulsions and found that the softer repulsions make the PMF resemble the shape of the PMF from the quantum-mechanical simulation. In general, the softer repulsive force results in a lower energy barrier between the two potential minima. This indicates that the repulsive part in the Lennard-Jones potential can cause qualitative effects in describing intermolecular interactions. We also compared the forces derived from the density functional theory with the forces used in the classical force-field MD simulation. The floppy nature of molecules should blur the barrier between contact configuration and solvent-separated configuration in the PMF.

Although the softer repulsion creates a lower energy barrier, the barrier between the two potential minima is still more significant in classical simulations than in quantum-mechanical results. From the comparison of Lennard-Jones potentials and interactions calculated by DFT, we find the Lennard-Jones potential is incorrect at short distances, and it has less binding at larger distances as well. The interaction calculated by DFT has a softer repulsion and a stronger attractive force than Lennard-Jones potential until $5.2$ Å. This may be the reason why the PMF calculated by quantum-mechanical simulation differs from the PMF in the classical force-field simulation.

From the variation of the hydrogen-bonded polygon distribution, we found the hydrogen-bond network is sensitive to the size of solutes. The ratio of pentagons to hexagons is larger when the separation is $4.8$ Å, which hints a stable cage structure forms at a specific solute size.