# [gmx-users] Total potential energy: 1/2 protein-solvent interactions??

David van der Spoel spoel at xray.bmc.uu.se
Thu Mar 6 12:13:19 CET 2008

```Xavier Periole wrote:
>>>> Still, if you want to partition the energy over molecules you have
>>>> to make some kind of division. For instance, if you calculate the
>>>> potential energy for 216 water molecules you will find that is is
>>>> roughly -9000 kJ/mol at room T, and hence you can derive the
>>>> potential energy per molecule to be -42 kJ/mol, which agrees with
>>>> heat of vaporization.
>>> Agreed.
>>>> If you however would do as you suggest, and take one water molecule
>>>> and compute all its intermolecular interactions you would end up
>>>> with an energy of -84 kJ/mol, because all terms are counted double!
>>> There no terms counted 2 times in this calculation!? They become
>>> doubled if
>>> you use this number x 216 H2O to obtain the total potential energy. The
>>> average interaction energy of one molecule with 215 others is still
>>> -84 kJ/mol!
>>> Isn't it?
>>
>> There are no terms calculated double in the MD simulation. But the
>> average interaction energy is indeed -84 kJ/mol.
> That is fine! It is just wrong to use this value to get the total energy
> of the system, because then they are doubled. The factor of two in there
> only because the water molecules are actually identical.
> In the case of the protein-solvent interaction I don't see how you can
> say that the interaction is doubled! There is only one protein!
Look at it this way: the total energy is a double sum over all
particles. For efficiency one only computes half the matrix, i.e.

E = sum_{i=1}^N sum_{j=i+1}^N E_{ij}

however one can also compute it like this:

E = 1/2 sum_{i=1}^N sum_{j=1}^N E_{ij}

Now if you define

E_i = 1/2 sum_{j=1}^N E_{ij}

then you still have

E = sum_{i=1}^N E_i

So that's fine isn't it?
>
>>
>>>> Therefore it is entirely reasonable (though this is not a rigorous
>>>> derivation!) to partition the Protein-Solvent energy equal between
>>>> protein and solvent, in order to get an estimate of the Protein energy.
>>> I totally miss the concept of partitioning the interaction energy
>>> between
>>> two parts into each one!
>>
>> Hm, what can I say?
> Then what is the physical basis of the partitioning of the energy?
> I can understand that for parametrisation and transferability of the
> parameters one often uses this type partitioning. More than that, I don't
> know.
>> We are actually working on testing something like this systematically,
>> i.e. how does the energy of a protein/water system changes with the
> Well, as you increase the system size you'll see the interaction
> energy increasing (if the cutoff follows the increase) bu the actual
> effect on the system should not change: at long distances the forces
> cancel each other on a spherical basis.
> I am missing something?

I think the interaction energy will level off, even without cutoff (i.e.
PME). More later when we've done the work.

>
> XAvier
>>
>>
>> --
>> David van der Spoel, Ph.D.
>> Molec. Biophys. group, Dept. of Cell & Molec. Biol., Uppsala University.
>> Box 596, 75124 Uppsala, Sweden. Phone:    +46184714205. Fax: +4618511755.
>> spoel at xray.bmc.uu.se    spoel at gromacs.org   http://folding.bmc.uu.se
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>
> -----------------------------------------------------
> XAvier Periole - PhD
>
> NMR & Molecular Dynamics Group
> University of Groningen
> The Netherlands
> http://md.chem.rug.nl/~periole
> -----------------------------------------------------
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