The Lennard-Jones potential is typically expressed mathematically as:

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


  • $V(r)$ represents the potential energy as a function of the distance $r$ between two particles or molecules.
  • $\varepsilon$ is the depth of the potential well, representing the strength of the attractive forces.
  • $\sigma$ represents the distance at which the inter-particle potential is zero.
  • The first term, $\left(\frac{\sigma}{r}\right)^{12}$, represents the repulsive term responsible for Pauli repulsion.
  • The second term, $\left(\frac{\sigma}{r}\right)^{6}$, represents the attractive term responsible for Van der Waals attraction.

When we want to compute either only the attractive term or only the repulsive term, do we discard $4 \varepsilon$ and the negative sign?

  • $\begingroup$ What do you want to use that term for? I don't think it makes sense to separate the LJ, as it is already an empirical approximation of the sum of many different forces. If you separate the first exponential from the second ... both of them are still not really interpretable $\endgroup$
    – MPIchael
    Sep 18, 2023 at 14:30
  • $\begingroup$ I always thought of it in similar ways like a taylor series. The individual terms of a tailor series are not interpretable in any physical way. $\endgroup$
    – MPIchael
    Sep 18, 2023 at 14:31
  • $\begingroup$ @MPIchael, What do you want to use that term for? I don't think it makes sense to separate the LJ, --- My professor wants me to print the values of those terms on each iteration. That is why... $\endgroup$
    – user366312
    Sep 18, 2023 at 15:13
  • 2
    $\begingroup$ Well in that case I'd include the $4\epsilon$ to conserve the physical units, print the values as requested and foster my hidden disdain for said professor. $\endgroup$
    – MPIchael
    Sep 19, 2023 at 9:56
  • $\begingroup$ Actually, if that's what your professor wants you to do, why don't you ask them whether they want the common factor included or not? $\endgroup$ Sep 19, 2023 at 14:16


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