Where does the factor of 4 come from in the Lennard-Jones potential?

1 Answer
Alan P.
Mar 27, 2015

An attempt to answer this question depends upon how far back we need to go in the underlying concepts.

Remember that (at least in some sense) the the L-J potential equation is empirical (It is inexact mathematical model that approximates real inter-particle interaction.)

If you are willing to accept the L-J model in the form:
#V_(LJ) = epsilon [ (r_(min)/r)^12 - 2(r_(min)/r)^6]#

then the alternate form:
#V_(LJ) = 4 epsilon [(sigma/r)^12 -(sigma/r)^6]#
(which contains the #4#, I assume you referred to)

follows arithmetically from the substitution:
#r_(min) = 2^(1/6) sigma#

As I said, I'm not sure how far back I need to go and I am assuming you are familiar with the basic parameters of this model.

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