Lennard-Jones model

Lennard-Jones Potential:

$V(r)=4ϵ[{(\frac{\sigma }{r})}^{12}-{(\frac{\sigma }{r})}^6]$

where:

• $V(r)$ : Potential energy of interaction betweeen two particles at a distance r;

• $\sigma$ : Diameter (length);

• $ϵ$ : well depth (energy)

Reduced units:

• Density, ${\rho }^{*}\equiv \rho {\sigma }^3$, where $\rho =N/V$ (Number of particles $N$ divided by the volume $V$.)

• Temperature; $T^{*}\equiv k_{B}T/ϵ$, where $T$ is the absolute temperature and $k_B$ is the Boltzmann constant

References

J. E. Lennard-Jones "Cohesion", Proc. Phys. Soc. Lond. volume 43 pages 461 (1931)