9-6 Lennard-Jones potential

The 9-6 Lennard-Jones potential (also known as the 6-9 potential) is a variant the more well known Lennard-Jones model. It is used for computing non-bonded interactions. The potential is given by  :

$\Phi _{12}(r)=\epsilon \left[2\left({\frac {r_{m}}{r}}\right)^{9}-3\left({\frac {r_{m}}{r}}\right)^{6}\right]$

or in terms of $\sigma$ (the value of $r$ at which $\Phi _{12}(r)=0$) one has:

$\Phi _{12}(r)=6.75\epsilon \left[\left({\frac {\sigma }{r}}\right)^{9}-\left({\frac {\sigma }{r}}\right)^{6}\right]$

where

• $r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|$
• $\Phi _{12}(r)$ is the intermolecular pair potential between two particles or sites
• $r_{m}$ is the distance, $r$, at which $\Phi _{12}(r)$ is a minimum, which corresponds to $r_{m}=1.5^{1/3}\sigma$.
• $\epsilon$ is the well depth (energy)

It is worth noting that the inclusion of an odd power (here the 9) adds an additional computational overhead, and the 8-6 Lennard-Jones potential has been suggested as a viable alternative.