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Derivation of Lennard Jones 9-3 model

  1. Aug 3, 2010 #1
    Dear all,

    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]?
     
  2. jcsd
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