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  :

${\mathrm{\Phi }}_{12}(r)=ϵ[2{(\frac{r_m}{r})}^9-3{(\frac{r_m}{r})}^6]$

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

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

where

• $r:=|{\mathbf{r}}_1-{\mathbf{r}}_2|$
• ${\mathrm{\Phi }}_{12}(r)$ is the intermolecular pair potential between two particles or sites
• $r_m$ is the distance, $r$, at which ${\mathrm{\Phi }}_{12}(r)$ is a minimum, which corresponds to $r_m=1.5^{1/3}\sigma$.
• $ϵ$ 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.