Intermolecular Interactions

To find out the roots of the above differences, we compare the force used in a typical force-field MD simulation with the force derived from the density-functional theory (DFT). In the latter, the force depends on the relative orientations between two molecules, while the Lennard-Jones force can be regarded as the average over all possible orientations between them. Table 3 lists the Lennard-Jones potential parameters of methane and water used in the plotting of Fig. 13. Fig. 17 compares the forces between methane and water. Water has a permanent dipole moment which can generate an induced dipole in a nearby methane molecule. We found that the Lennard-Jones force between water and methane is more repulsive at short distance than the force derived from DFT. This means, among other things, water molecules can stay closer to methane molecules (easier to squeeze in between two methane molecules). At distance between $3.6$ Å to $5.0$ Å, an important difference between Lennard-Jones potentials (less attractive) and DFT (strongly attractive) has the following consequence. When two methane molecules lie between $3.9$ Å to $5.4$ Å, there is a net attractive interaction between two methane molecules due to the water molecules in the middle. This should increase the depth of the contact potential minimum, in accord with the quantum-mechanical result.

Table 3: The Lennard-Jones potential parameters used in plotting Fig. 13. The cross parameters for methane-water are deduced from the Lorentz-Berthelot rules [4].

	$\epsilon/k_{B}(K)$	$\sigma$(Å)	partial charge ($e$)
H$_{2}$O	$78.22$	$3.165$	$0.41(H)$, $-0.82(O)$
CH$_{4}$	$147.5$	$3.730$	$0$