[gmx-users] non isotropic kinetic energy

[Berk Hess]

Equipartitioning still holds.
The issue here is that constraints remove degrees of freedom.
If you remove a degree of freedom, there is not potential or kinetic energy
anymore in that generalized coordinate.
This does not introduce any problems with ensembles or something like that.

I did not have time yet to implement pull code with pbc.
I will do it this week.

Berk

> Date: Mon, 14 Sep 2009 16:08:55 +0200
> From: alexander.herz at mytum.de
> To: gmx-users at gromacs.org
> Subject: Re: [gmx-users] non isotropic kinetic energy
> 
> Hm,
> 
> apparently there are constraint algorithms which don't change the ensemble
> (e.g. http://www.informaworld.com/smpp/content~db=all~content=a750934359).
> The equipartition theorem requires that the energy depends on
> no other powers of v but v^2
> (http://www.whfreeman.com/modphysics/PDF/8-2c.pdf)
>  which should be the case for the md systems including constraints
> (lj pot and estatic only depend on the particles' positions). So as far
> as I can see the
> equipartition theorem should hold in td equilibrum for these systems. So
> the constraints
> might modify the ensemble which could lead to all kinds of trouble?
> 
> The water molecules at the interface are oriented but taking the above
> paragraph into
> account this shouldn't cause any trouble.
> 
> By the way,
> did you find a chance to look at the pulling problem we discussed before
> last week?
> 
> Thx,
> Alex
> 
> 
> Berk Hess schrieb:
> > I have been looking at very similar things recently.
> >
> > Your result could actually be correct.
> > If the water orders at the interface you should have a difference
> > in Ekin components, since the constraints, which remove kinetic energy
> > are not ordered isotropically in space.
> > You should be able to quantify this by looking at the order of the water
> > normal.
> >
> > Berk
> >
> > > Date: Thu, 10 Sep 2009 18:11:16 +0200
> > > From: alexander.herz at mytum.de
> > > To: gmx-users at gromacs.org; felix.sedlmeier at ph.tum.de
> > > Subject: Re: [gmx-users] non isotropic kinetic energy
> > > CC:
> > >
> > > Hi,
> > >
> > > we took a couple of days to reexamine this and try out a couple of
> > things:
> > >
> > > -On small interfacial systems (ca. 2k spc/e water molecules sandwiched
> > > by vacuum)
> > > the difference between ekin_x/y and ekin_z is 20 to 60kJ/mol depending
> > > on the specific system/settings
> > > (e.g. see attached file of averaged ekin (x/y/z) over time).
> > > -On larger interfacial systems the difference grows (up to several
> > > 100kJ/mol for ca. 32k spc/e water).
> > >
> > > The following settings make no difference (so the error persists even if
> > > we change the setting):
> > > -thermostat (we tryed nose-hoover, berendsen and no thermostat)
> > > -estatics (cut-off instead of pme)
> > > -type of constraint algo for water (so lincs, shake or settle, we
> > > modified the spc/e water molec definition to change this)
> > > -changing system size so that the box length is equal in all 3 dim (as
> > > said, magnifies problem)
> > > -rotating system (error rotates with system)
> > > -use smaller time step of 1fs (no difference)
> > >
> > > We ran a simulation with flexible water (so bonds instead of
> > > constraints) , here the error vanishes!
> > > Also, we ran similar sims with amber, where the error does not appear at
> > > all (for constraint water).
> > >
> > > We found out about this problem while doing surface tension/contact
> > > angle calculations.
> > > The surf tens calced via virial differs from the surf tens calculated
> > > via pressure tensor (unless one corrects
> > > for the anisotropic kinetic energy). A simple way to see the deficit is
> > > trying to calc the average pressure tensor from the average virial
> > > tensor (using the simple def from the gromacs manual
> > P_ij=2/V(Ekin-Vir_ij):
> > > a) assuming equidistributed kinetic energy (ekin/3 per dim)
> > > b) using the anisotropic ekin which can be extracted from a trr with a
> > > tool (source attached) if velocities have been written to the trr.
> > >
> > > All this appears to hint at a problem with the constraints for the
> > > waters and might also hint at an incorrect ensemble as a consequence.
> > >
> > > Alex
> > >
> > > sample input file (several variants of this file have been used):
> > >
> > > title = pure water
> > > cpp = /usr/bin/cpp
> > > integrator = md
> > > nsteps = 2500000
> > > nstlist = 50
> > > nstxout = 1000
> > > nstvout = 1000
> > > nstlog = 1000
> > > dt = 0.002
> > > nstcomm = 200
> > > comm-mode = linear
> > > constraints = h-bonds
> > > nstenergy = 100
> > > ns_type = grid
> > > coulombtype = pme
> > > fourierspacing = 0.12
> > > pme_order = 4
> > > rlist = 0.9
> > > rvdw = 0.9
> > > rcoulomb = 0.9
> > > tcoupl = Berendsen
> > > tc_grps = SOL
> > > energygrps = SOL
> > > tau_t = 0.4
> > > ref_t = 300
> > >
> > >
> > >
> > > David van der Spoel schrieb:
> > > > aherz wrote:
> > > >> Hi,
> > > >>
> > > >> we're running simulations of a water slab sandwiched by vacuum
> > (ca. 2k
> > > >> waters, 3x3x12 nm^3 box) in NVT
> > > >> and look at the pressure tensor. We are surprised to find that the
> > > >> kinetic energy is equivalent (within statistical uncertainty) for
> > x and
> > > >> y dim(parallel to the interface) but not in z dim. This appears to
> > > >> violate the equipartition theorem?
> > > >>
> > > >> This is gromacs 3.0 and 4.0 using berendsen thermostat.
> > > >
> > > > First, try it with a real thermostat, second please report some
> > numbers.
> > > >
> > > >>
> > > >> Alex
> > > >> _______________________________________________
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> > >
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