# What is the relation between Ea and S in the Lennard-Jones Equation?

Matt Jones jonesmat at ohsu.edu
Wed Jul 29 14:15:41 EST 1998

```In article <35BD3606.407FE3ED at lms.mit.edu> David Green,
dfgreen at lms.mit.edu writes:
>&nbsp;The Lennard-Jones energy is the potential energy of the system, U,
>which is related to H by U=H-pV.&nbsp; As you can see ... it doesn't consider
>entropy ( U in constant volume systems is somewhat analogous to H in constant
>pressure systems).&nbsp; As for how to deal with entropy, I'm not so sure,
>but it depends on how large&nbsp; a system your working with.&nbsp; For
>a really small system in vacuum, you may be able to get away with calculating
>statistical entropy.&nbsp; For larger systems, or anything in solvent,
>this won't work.&nbsp; You might get more help if you describe your application
>a bit more.&nbsp; For example, are you trying to do dynamics?&nbsp; How
>

My system is about as simple as you can get: A point "particle"
representing a ligand, and two "particles" representing two parts of a
protein, one is an "anchor" and is supposed to represent some large mass
in the protein, and the other is a moveable "arm", supposed to represent
the part of the protein that actually binds the ligand. At rest, the arm
sits in the potential well generated between itself and the anchor. When
the ligand is inserted nearby, the arm and the ligand generate an
additional well, with a minimum at some unknown radius to be calculated.
So I used Lennard-Jones as the field equation between all particles, and
solved (by an optimizing algorithm) for the final positions of the
particles that minimized the total system potential energy. The
coefficients of the Lennard-Jones equation (radius and well-depth) and
the separations between particles, were all free parameters. Now I just
want to see if this has taught me anything about whether this
hypothetical binding reaction is enthalpy or entropy driven, so to speak.

Thanks,

Matt

```