# [gmx-users] non isotropic kinetic energy

David van der Spoel spoel at xray.bmc.uu.se
Tue Sep 15 12:28:24 CEST 2009

```herz wrote:
> Hi
>> Have you tested the equipartitioning per atom? This must be correct.
> We have done per atom (here of course only ekin is available). Here the
> average ekin parallel to the interface deviates from the ekin
> perpendicular to the interface (this is the data in the zip file of the
> old mail).
>
> You could use quaternions to do water as rigid body or eule angles or
> some other scheme of your choide, there are many.
> Generally, the EOM of any rigid body can be completely described using
> this view (COM motion+rotation around COM), afaik.
> So we analyzed the rotation around COM and the translational velocity of
> the COM of each water molecule
> (in addition to the per atom calcs). Here the rotational energy is not
> equidistributed (translational is) for interfacial systems.
> The com motion+rotation describtion is a physically valid describtion of
> this kind of system.
> If the constraints are not equivalent then this would be a real problem.
>
> Unless of course, there is some error in my reasoning :)

It is well known that water at a surface is ordered. How do you choose
the waters to analyze? If there is a net ordering in the system due to
external factors your system is not in equilibrium, but rather in a
steady state. However if you have e.g. vacuum-water-vacuum the symmetry
makes that equipartition should hold, provided the averaging is over a
time long enough such that water molecules sample both surfaces.

Of course if you are worried about the constraints you could do a
simulation with flexible water for testing.

>> To make water move as a rigid body one would probably need to
>> determine the force and torque on the center of mass and use that to
>> integrate the equations of motion. A quaternion description of rigid
>> water would do this I presume. Did you analyze the EkRot around the
>> center of mass of the molecule?
>> Whether or not a quaternion is equivalent to a constrained atomic
>> system I do not know, but Berk's answer below seems to indicate it is
>> not.
>>
>
> Alex
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