Subject: Re: CCL:MD/MM combination

From: Konrad Hinsen <[email-masked]>
Date: Wed, 6 Nov 96 10:08:38 +0100

> Let's consider the following example:
> We have a rather flexible molecule which has functional groups allowing the
> formation of hydrogen bonds. Now we put it in a box of water molecules and
> calculate the potential energy of the system with a forcefield. If we do an MD
> calculation with a fixed geometry of the molecule (just the solvent is moving)
> we'll get an ensemble and we can average the potential energy.

Sure, but I don't see what this "averaged potential energy" is good
for. It is not a well-defined thermodynamic quantity.

> Question 2:
> If I calculate all internal forces on the atoms of the molecule and average all
> forces excerted by the solvent on the molecule, I'll get the gradient on that
> potential energy surface mentioned above. (Right?)

Not quite. What you described above is the calculation of some energy
for isolated configurations, not a surface. The average force is (by
definition) the gradient of the potential of mean force, which is a
well-defined thermodynamic quantity.

> Question 3:
> As far as I understood the Thermodynamic Integration method and related
> methods, the free energy difference can be calculated by defining a reaction
> coordinate  and integrating over the averaged forces along that reaction
> coordinate.

Right, and that will give you the profile of the potential of mean force
along the reaction coordinate.

> I'm not quite clear, where this deviates from the aproach above. If I asume the

The difference is that you have to calculate a whole path between two
configurations, whereas your original idea was to calculate something for
only the two end points. A separate calculation of the two end points
means that you have an unknown additive constant for *each* of them, 
and hence no information about the difference in free energy. By calculating
the path you end up with only *one* unknown additive constant, and you
can evaluate the energy.

-- 
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Konrad Hinsen                          | E-Mail: [email-masked]
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