[gmx-users] multicomponent system- units

Mark Abraham Mark.Abraham at anu.edu.au
Thu Apr 28 04:01:53 CEST 2011

```On 4/28/2011 10:06 AM, Elisabeth wrote:
> 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.

Ok - but the important point (as I said before) is how those energies
are defined. Without knowing that, you've no idea what you're trying to
reproduce from the GROMACS numbers.

> 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?

Yes, that's the sense of my suggestion.

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

The energy of each inter-atom interaction is measured in... drumroll...
kJ/mol. That number is the energy that a mole of such interactions would
have. Adding them up and dividing by the number of interactions doesn't
change anything, except the awkwardness of articulating what the system
now is.

>
> 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!

Maybe. Look up the definitions of those energy quantities. Don't
randomly invent "MOL" as nomenclature... I don't know whether your
emphasis is supposed to differentiate from "mol", nor whether you intend
"mole" or "molecule". Use abbreviations for brevity, but not so as to
impede clarity :-)

Mark

> 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
> <mailto:Mark.Abraham at anu.edu.au>> wrote:
>
>>     Hello Mark,
>>
>>     groups. I am 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
>>     <mailto: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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