[gmx-users] non isotropic kinetic energy

[Berk Hess]

Equipartitioning only works per degree of freedom, not per atom.

It works for translation and rotation of a water molecule,
but that requires a transformation from atomic to COM trans and rot
coordinates.

The standard Ekin in Gromacs determines translational kinetic energy.
Of the three rotational degrees of freedom of the water molecule
one can put one in the plane of the water molecule and two out of plane.
The one in plane give a "translational atomic" component in plane,
whereas the two out of plane rotations give 2 "translational atomic" components
in the out of plane direction.
Again, this does not violate equipartitioning.
Equipartitioning is per degree of freedom.
If the dof's you constrain happen to be ordered at an interface,
you remove more (or less) degrees of freedom in on direction than in another.

Berk

> Date: Tue, 15 Sep 2009 12:00:23 +0200
> From: alexander.herz at mytum.de
> To: gmx-users at gromacs.org
> Subject: Re: [gmx-users] non isotropic kinetic energy
> 
> 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 :)
> >
> > 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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