# [gmx-users] Re: PMF from pull code, unexpected results

Michael Brunsteiner mbx0009 at yahoo.com
Wed Feb 23 23:16:07 CET 2011

```chris.neale at utoronto.ca wrote:

> Looking at http://www.brunsteiner.net/tbut-pmf.gif you seem to be getting
>exactly what I would
> expect. The difference is the entropy term. Note that the spherical shell
>increases volume as r
> increases for pulldim YYY but this effect is absent for pulldim NNY. This is
>why you can correct
> as per an RDF.

The "entropy term" (Eqn 6.1 in the manual) has already been the source
of some confusion in this list ...

If you make a "Gedankenexperiment" and consider the PMF between two atoms in
vacuum

that interact ONLY through a simple radial, for example a LJ, potential, and
then calculate the PMF

using the pull-code ...  if you don't do umbrella sampling + WHAM but instead
use constraints

(pull = constraint) you can do the calculation in your head, to find that the
resulting PMF

is, of course, nothing else but the original LJ potential. And you will get the
SAME result
if you do this calculation in one or in three dimensions (pulldim NNY or pulldim
YYY)
so where does the entropy and the correction term in eqn 6 come in here??

In Section 6.1 of the manual it says: "But when calculating a PMF between two
solutes in a
solvent, for the purpose of simulating without solvent, the entropic
contribution should be removed."
I find this a bit confusing, first ... "simulating without solvent" ... why
would that be
my (or anybodies) purpose? and second:

according to eqn 6.1 this "entropic contribution" is: PMF(r) = - (nc-1)kBT
log(r)

for this to make sense r would have to be dimensionless wouldn't it?
I could divide r by the distance at which i arbitrarily chose my PMF to vanish,
call it r_c, which would have the advantage that then the correction is zero at
this
distance ... but then this is just wild guess of mine ... anyway, that would
mean

that, if I call the PMF coming out of mdrun/g_wham PMF_wham,
then the "true" PMF is: PMF(z) = PMF_wham (z) + (nc-1)kBT log(z/r_c)
(the plus comes from the double minus, as in: "removing" something thats
negative)

is that correct? ... and if so, why does it, seemingly, not apply in the above
Gedankenexperiment?

Yours truly (and maybe some other people) would really appreciate if somebody in
the know
would clarify that!