# [gmx-users] multicomponent system- units

Elisabeth katesedate at gmail.com
Thu Apr 28 02:06:48 CEST 2011

```Hi Mark,

I am excited to see that there is a solution to my issue. I thought this
problem can not be resolved.

In thermodynamics of polymer solutions, people use some models (equation of
state) in which an interaction parameter K_AB appears which is defined in
terms of interaction energies i.e. 1-K_AB=(E_AB)/(E_AA*E_BB)^0.5. One way to
obtain this parameter is to manipulate this K so that equation of state
predicts say bubble point data or density vs. pressure. In this procedure
they dont look at interaction energies E_BB,...and only K is tuned. (or in
some models they deal with E_ij interaction energies and manipulate so that
some properties are fitted to experimental data).

Now what I am interested in is calculating these interaction energies by MD
and thats why I need to extract pairwise energies per mol. To double check
what I have done with you:

FOr a system having 4 polymer chains and 100 solvent molecules, I defined
two groups in index file: [polymer] with all atoms of polymer chains. and
[solvent] with all atoms of solvent. and use energygrps= polymer
solvent.  Now I have polymer-solvent, polymer-polymer and solvent-solvent
interaction energies (LJ + Coulomb SR for each pair).

As you say to normalize this I have to divide by [(4*Np)*(100*Ns)] where Np
and Ns are number of atoms in polymer chain and solvent molecule.

1- Did I get your instruction correctly?

2- The unit of energies is per atom now? I am confused if its per atom or
molecule?

3- Since the interaction parameter in the model is defined as  1-
K_AB=(E_AB)/(E_AA*E_BB)^0.5 and the ratio of interaction energies appear in
K, is this normalization sufficient? I mean because of ratio of energies it
seems there is no need to convert these normalized values to MOL!

4- Is it possible to achieve energy per MOL for this binary system from
normalized energies?

Best :)

On 12 April 2011 00:10, Mark Abraham <Mark.Abraham at anu.edu.au> wrote:

>  Hello Mark,
>
> trying to validate pairwise energy values (nonbonded) with some other work (
> a thermodynamic model) where they fit these AA AB BB (E_AA, E_AB, E_BB)
> energies so that some phase diagrams are reproduced. The pairwise energies
> defined in the model are in KJ/mol.
>
>
> So how did they compute these interaction energies?
>
> The energy quantity GROMACS reports for a microstate can be best thought of
> as the energy one would have for a mole of such microstates. Alternatively,
> divide by N_A and that's the energy for this microstate - but that's a much
> less convenient number to use.
>
> To obtain a quantity that is independent of the number of particles, you
> have to normalize for the number of interactions of each type. If these are
> all pairwise between atoms in a unary system, then you need to divide by the
> square of the number of atoms. So for the mixed interaction energy of the
> binary system, you divide by the product of the respective numbers of atoms.
>
> You should also verify that these actually are converged observables that
> are independent of the number of particles by simulating replicates from
> different starting configurations, and systems of different sizes.
>
> Mark
>
>
>  Since my energies are not per mol, my results are useless, unfortunately.
> As they depend on number of molecules in the system. To achieve my goal,
> what do you suggest? For a binary system, can I run two separate simulations
> for pure A and B in which case using -nmol gives per mol energies and
> somehow predict AB from them? Does this make sense?
>
> Please guide me, I am stuck on this..
>
> Thanks,
>
> On 9 April 2011 20:56, Mark Abraham <Mark.Abraham at anu.edu.au> wrote:
>
>>  On 8/04/2011 12:18 PM, Elisabeth wrote:
>>
>>> Hello everyone,
>>>
>>> I have encountered a simple problem. For a homogenous system what
>>> g_energy reports is dependent on the system size and one needs to use -nmol
>>> option to divide energies by number of molecules to obtain per mol values.
>>>
>>> I am attempting to extract interaction energies between species in a
>>> three component system. I am puzzled how this can be achieved for such a
>>> system. Say there are 100 solvent, 20 solute A and 10 B molecules.
>>>
>>
>>  You would have to start by defining energy groups that contain relevant
>> sets of molecules (see manual). Even once you've got them, the group-wise
>> energies won't mean much of anything. Every observable is dependent on the
>> configuration microstate, and unless you can estimate the relative
>> population of different microstates to estimate a free energy...
>>
>> Mark
>>  --
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>
>
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