[gmx-users] Gromacs single sum virial calculation for periodic systems

[Julius Schulz]

Hello again,
I’ve put some more thoughts on this subject and I am quite certain that the derivation for the
single sum virial as given in the Gromacs Manual is actually wrong.
The delta_i as defined in equation B.3 should better be called delta_ij, as it depends on both
i and j. But then the step from Eq. B.8 to B.9 breaks down and with it anything that follows.

The correct calculation is given in the thesis by Bekker and as far as I can see, the Gromacs
implementation does exactly what’s given there. I was actually not able to obtain the original
publication in Physics Computing 92, but i guess this is similar to the chapter in the thesis
by Bekker. A similar calculation is also given by Thompson et. al. in J. Chem. Phys, 131, 154107,
2009. I might be nice, to have an easily obtainable citation in the Gromacs Manual as well.

Since in an older thread (https://mailman-1.sys.kth.se/pipermail/gromacs.org_gmx-users/2009-August/044133.html) someone was already confused by this section in the Gromacs manual, it might
be helpul removing/rewriting this section.

The verdict for me is, the knowledge of the positions and total force on each atom is
not enough information to calculate the virial of a periodic system.

Greetings, Julius

> Am 21.07.2015 um 21:51 schrieb Julius Schulz <julius.schulz at fu-berlin.de>:
> 
>> 
>> Am 21.07.2015 um 20:44 schrieb David van der Spoel <spoel at xray.bmc.uu.se>:
>> 
>> On 21/07/15 17:32, Julius Schulz wrote:
>>> Hello,
>>> I am trying to understand, how Gromacs calculates the virial for periodic systems. According to
>>> Eq. B.11 in the Gromacs manual, this should be a function of the total forces of the particles.
>>> However, I don't understand, how delta_i is being calculated.
>>> 
>>> As far as I can see it is basically defined in Eq. B.3. In Eq. B.11 it is used as if it would only
>>> depend on the particle index i, however as defined in Eq. B.3 I would guess it should depend on both
>>> i and j. An older thread on that matter referenced to the thesis of Henk Bekkers
>>> (http://dissertations.ub.rug.nl/faculties/science/1996/h.bekker/, Chapter 2), however there the
>>> second part of the virial is not simply a function of the total force on the individual particles
>>> and the sums runs over all periodic images not over all particles.
>>> 
>>> Maybe someone can help me understanding this? Basically what I am after is, that I have an already
>>> existing (expensive to compute) trajectory with forces for which I would like to obtain the virial.
>>> Is this impossible?
>> Are you aware of the mdrun -rerun option?
> 
> Yes, I know about this option, but actually it is a non-gromacs trajectory (some very expensive
> to calculate ab-initio md trajectories I was given by a colleague). But since I am most familiar
> with Gromacs, I’m using this as a testbed to get my calculation correct.
> 
> Therefore I’m looking for a way to calculate the virial using forces and positions (and velocities)
> alone. The Gromacs Manual is basically the only place I found this single sum virial with pbc, thus
> I was hoping to find an answer on this list. Eq. B.11 at least suggests to me, it should be possible,
> or is this a misinterpretation of mine?
> 
> Thank you, Greetings, Julius
> 
> PS: Actually I think, the problem would even exist if it was a Gromacs trajectory, since I would need
> individual pair forces, which would have to be recalculated during the rerun and this is what’s computionally
> expensive, or am I mistaken? (I need full time resolution, so no frame skipping would be possible)
> 
>>> 
>>> Greetings, Julius
>>> 
>>> ----
>>> Julius Schulz
>>> FU Berlin, Fachbereich Physik,
>>> AG Netz  (room 0.3.30)
>>> Phone (++49|0) 30-838-55279
>>> Arnimallee 14
>>> 14195 Berlin, Germany
>>> 
>>> 
>>> 
>>> 
>>> 
>>> 
>> 
>> 
>> --
>> David van der Spoel, Ph.D., Professor of Biology
>> Dept. of Cell & Molec. Biol., Uppsala University.
>> Box 596, 75124 Uppsala, Sweden. Phone:	+46184714205.
>> spoel at xray.bmc.uu.se    http://folding.bmc.uu.se
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