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  :

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

where

• $r:=|{\mathbf{r}}_1-{\mathbf{r}}_2|$
• ${\mathrm{\Phi }}_{12}(r)$ is the intermolecular pair potential between two particles or sites
• $\sigma$ is the diameter (length), i.e. the value of $r$ at which ${\mathrm{\Phi }}_{12}(r)=0$
• $ϵ$ 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.