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I am puzzled by the derivation of the Lennard Jones 9-3 model. Many articles mentioned that the Lennard Jones 9-3 model is derived from the integration of a 3d half-lattice of Lennard-Jones 12-6 particles.

The 12-6 potential is:

[tex]

4\epsilon\left[\left(\frac{\sigma}{r}\right)^{12}-\left(\frac{\sigma}{r}\right)^6\right]

[/tex]

while the 9-3 model is:

[tex]

\epsilon\left[\frac{2}{15}\left(\frac{\sigma}{r}\right)^{9}-\left(\frac{\sigma}{r}\right)^3\right]

[/tex]

Can anyone point me to the right direction how should I perform integration of a 3d half-lattice of Lennard-Jones 12-6 particles? Do I change [tex]r[/tex] to [tex]r_x, r_y, r_z[/tex] and integrate with respect to [tex]dx, dy, dz[/tex]?

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# Derivation of Lennard Jones 9-3 model

Can you offer guidance or do you also need help?

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