# [gmx-users] compressibility tensor components, pressure coupling anisotropic PR, triclinic systems

Berk Hess gmx3 at hotmail.com
Sun Mar 22 12:07:18 CET 2009

```Hi,

1)
The "compressibility" or elastic tensor is a full tensor.
You only mention the three eigenvectors and eigenvalues,
but there are off-diagonal components.
I would assume all the eigenvalues are very close.
As a rough guess I would just use the same value for all diagonal
and off-diagonal components.

2)
PR bij itself is not unstable, only for equilibration it might problematic.
But for a crystal the frequency PR barostat should not be close
to an eigenfrequency of the crystal.
Using Berendsen avoids these issues.

Your mdrun errors seem simply to be due to a slightly too small box,
make it a bit bigger.
Also for crystals you might need shifted LJ potentials (I assume you
use PME for electrostatics).

Berk

Date: Sat, 21 Mar 2009 04:21:00 -0700
From: lastexile7gr at yahoo.de
Subject: RE: [gmx-users] compressibility tensor components,	pressure coupling anisotropic PR, triclinic systems
To: gmx-users at gromacs.org

Hello,

thank you Mr Berk for your answers once again. Taking them as feedback and judging from my simulations, two more questions arise.
I would be more than grateful if you could answer me the following:

1)you refer to an initial guess for the compressibility tensor of gromacs. As it was refered to a previous post, the best thing someone can have as an input is the linear compressibility, which as far as I know is a vector and not a tensor. I have found it as scalar modulus too. Taking it as a vector and consulting the book:
Physical properties of crystals by J.F.Nye, I get this equation for beta:

β= (s11+s12+s13)l1**2 + (s12+s22+s23)l2**2 + (s13+s23+s33)l3**2

with l1, l2, l3 the unit axis vectors and sxx the compliance tensor components.

Now, judging from the above, the xy compressibility tensor component in your
implementation in gromacs, should be something like the resultant of the components of beta in l1 and l2 direction (or if you prefer in x and y)?

2)You mention than if I have a liquid then PR anisotropic pressure coupling should be avoided because the box should deform a lot. No objection to this. My question though is:

If I start from the crystal structure with anisotropic pressure coupling and want to melt it, how I should be able to conduct such an md knowing that the melt after a while should crash. I have to mention that It crashed either if I have an anisotropic melt md simulation or if I started from a crystal and melt that crystal. The message I get is:
Not all bonded interactions have been properly assigned to the domain decomposition cells
or
Fatal error:
The X-size of the box (1.808111) times the triclinic skew factor (0.989963) is smaller than the number of DD cells (2) times
the smallest allowed cell size
(0.895000)

The independent simulations (anisotropic crystal, isotropic melt) face no problem.

Thank you in advance,
Nikos

--- Berk Hess <gmx3 at hotmail.com> schrieb am Do, 19.3.2009:
Von: Berk Hess <gmx3 at hotmail.com>
Betreff: RE: [gmx-users] compressibility tensor components, pressure coupling anisotropic PR, triclinic systems
An: "Discussion list for GROMACS users" <gmx-users at gromacs.org>
Datum: Donnerstag, 19. März 2009, 12:43

Hi,

You will have to come up yourself with a reasonable guess.
If you have a hard crystal, I guess it would be close to the diagonal values.

Note that with PR coupling tau_p has to be large enough, something like 10 ps.
(note that in Gromacs 4.0 a bug has been corrected which scaled tau_p by 16.6
in version 3.3 and before)

But for equilibration I would start with Berendsen.

Berk

Date: Thu, 19 Mar 2009 04:30:44
-0700
From: lastexile7gr at yahoo.de
Subject: RE: [gmx-users] compressibility tensor components, pressure coupling anisotropic PR, triclinic systems
To: gmx-users at gromacs.org
Hello,

I do have a crystal system.. You refer to an initial guess. So if I understand correctly, it is a trial and error, if I do not have any data, this is what I can make out of. The part of the shear stress you are reffering I think that it is from experimental values?

Now you say that : compressibility (real)  =  tau_p*compressibility (gromacs) ?

If this is the case I do not think that the units coincide.
(ps/bar) =? (1/bar)

I think that what you mean has to do with equation 3.36 in the manual, where with these components the W is calculated.

Forgive my ignorance in the issue.

Thank you,
Nikos

--- Berk Hess <gmx3 at hotmail.com> schrieb am Do, 19.3.2009:
Von: Berk Hess
<gmx3 at hotmail.com>
Betreff: RE: [gmx-users] compressibility tensor components, pressure coupling anisotropic PR, triclinic systems
An: "Discussion list for GROMACS users" <gmx-users at gromacs.org>
Datum: Donnerstag, 19. März 2009, 10:23

Hi,

If you have a liquid system (no off-diagonal elasticity), you should not use full anistropic pressure coupling.
If you have a solid system (for instance a crystal), you will have an elastic shear stress response
and you can determine and use off-diagonal compressibility values.

You need the compressibility values to set the time scale of the pressure coupling.
The compressibility does not affect any thermodynamic quantity, only the dynamics.
The compressibility always occurs as a product with 1/tau_p.
If you want to determine them from a simulation, you need a reasonable initial guess
for the compressibility and you can use a large tau_p to be on the
safe side
with the actual coupling time.

Berk

Date: Wed, 18 Mar 2009 16:02:38 -0700
From: lastexile7gr at yahoo.de
To: gmx-users at gromacs.org
Subject: [gmx-users] compressibility tensor components, pressure coupling anisotropic PR, triclinic systems
Hello,

Searching first the gromacs mailing list I could not find an answer to the problem I face.

I would like to know the vaules I have to give to the mdp file where it asks for compressibility.
I have to conduct an NPT simulation using barostat Parrinello-Rahman. My pressure coupling should be anisotropic. The values I have given up to now are:
tau_p                    = 1.0
compressibility          = 4.5e-5 4.5e-5 4.5e-5 4.5e-5 4.5e-5
4.5e-5
ref_p                    = 1.0 1.0 1.0 0.0 0.0 0.0

when I try to calculate the elastic constants I get reasonable values for the diagonal elements, yet not good for the off-diagonal. The system I have is a monoclinic one, so giving zeros to xy,xz,yz components is not an option.
An experimental linear compressibility value I have found out is very close to the value above, so this is why I think I get good values in the diagonal elements.

I have found out many different questions, including one about monoclinic systems. In one of them someone was wondering why he had to put as input the compressibility values, while he is supposed to calculate them from the simulation. As far as the monoclinic system is concerned the question had to to with the components in gromacs derived from the linear experimental values... There was no answer
to that.

I have tried some different values myself, for the off - diagonal components and I get either a crash of my simulation of different results for the elastic constants. Is there an algorithm which clearly can point me to the right direction on how to derive the right values?

Thank you in advance,
Nikos

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