# [gmx-users] Diffusion Coefficient from VAC

Alexandre Suman de Araujo asaraujo at if.sc.usp.br
Thu Feb 23 15:06:24 CET 2006

```Hi Viswanadham

I´ll read the paper you cited and try to modify the box of simulations
and see what happen with the dif. coefficient.
Thank you very much for the help.

Alexandre Suman de Araujo
asaraujo at if.sc.usp.br
UIN: 6194055
IFSC - USP - São Carlos - Brasil

> Hi Alexandre,
> One more suggestion, Try to increase the box size and see its effect
> on diffusion coefficient calculated from MSD. You can see the
> difference(though the difference is very small)., as it is earlier
> cited in many papers by Dr.Spoel's group. Now, your box size looks
> like it is 3.5nm by 3.5nm by 3.5nm, try increasing it andd see its
> effect also (you can play with that).
> You can also see a change in the value of D, depending it on how long
> you run and how the bins are selected too.
>
> Regards,
> -V
>
>
> On 2/23/06, *Viswanadham Sridhara* <muta.mestri at gmail.com
> <mailto:muta.mestri at gmail.com>> wrote:
>
>     Hi,
>     There will be some difference between the value of D calculated
>     from MSD and VACF. I think your procedure is right. You can output
>     it every 200fs if you are doing it by MSD.
>     But do few things, in calculating MSD, do it in bins, like first
>     calculate the diffusion coefficient from MSD using 200-500 ps of
>     the curve, then split it into bins, 200-300ps, 300-400ps, and so
>     on, and finally see whether they are same or not.
>     About VACF, all you need is atmost 1ps of the curve("generally"
>     speaking), and you said you are outputting it every 1fs. so, Thats
>     fine!
>     Go through this journal, which gives field dependence of diffusion
>     coefficient. You are doing it right, as you need a static
>     diffusion coefficient value, (so you can ignore cosine and
>     things). "Analysis of the velocity autocorrelation function of
>     water" Balucani, U. et. al.
>     Thanks,
>
>
>     On 2/23/06, *Alexandre Suman de Araujo* <asaraujo at if.sc.usp.br
>     <mailto:asaraujo at if.sc.usp.br>> wrote:
>
>         Ok, maybe I was not so clear.
>
>         My system is constituted by only one ion and water molecules
>         (1400). I´m
>         trying to calculate de diffusion coefficient of this ion in water.
>
>         Using MSD the value is in relative good agreement with
>         experiment (MSD =
>         1.5x10^-5 cm^2/s, experimental = 1.9 x10^-5 cm^2/s). Using VAC
>         I have
>         the value of D = 0.9 x 10^-5 cm^2/s. The main problem is not
>         the values
>         don´t agree very good with experimental but the values
>         calculated from
>         VAC and MSD be so different, while in some papers that I read
>         they are
>         very near.
>
>         The difference between the simulations I use to calculate MSD
>         and VAC is
>         only the output time, where for MSD I have outputs every 200
>         fs while
>         for the VAC simulations the output is made every 1 fs. The
>         models for
>         the water and ion are the same. The size of the box too.
>
>         I think my problem is in the way I´m integrating the VAC
>         function. I´m
>         doing a simple integration and I believe that there is any
>         details in
>         this calculation that I don´t know.
>
>         You said me something about multiply by cosine of the angular
>         frequency
>         and scaling. Could you detail this procedure for me?
>
>         Thank you very much for your value help.
>
>         Alexandre Suman de Araujo
>         asaraujo at if.sc.usp.br <mailto:asaraujo at if.sc.usp.br>
>         UIN: 6194055
>         IFSC - USP - São Carlos - Brasil
>
>
>
>
>> Can you give me some more details?
>> Are the ions just in bulk water?
>> Or are the ions going from bulk water through some protein
>         and coming
>> to bulk water?
>> If you can explain me the situation, then people here can
>> I recently did some work in these lines too.
>>
>>
>> On 2/23/06, *Alexandre Suman de Araujo* <
>         asaraujo at if.sc.usp.br <mailto:asaraujo at if.sc.usp.br>
>> <mailto: asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>>> wrote:
>>
>>     My calculations is for ions in water and I´m using the
>         mass of the
>>     ions.
>>     My units are correct, a think this is not my problem.
>>     Thank´s
>>
>>     Alexandre Suman de Araujo
>>     asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br><mailto: asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>>
>>     UIN: 6194055
>>     IFSC - USP - São Carlos - Brasil
>>
>>
>>
>>
>>     > IF it is for pure water (bulk), then mass of the water
>         should be
>>     > m=(18e-3)/Ava, where Ava is the Avogadro number.
>>     > KbT/m works out to be 1.3857e+005;
>>     >
>>     > On 2/22/06, * Alexandre Suman de Araujo* <
>         asaraujo at if.sc.usp.br <mailto:asaraujo at if.sc.usp.br>
>>     <mailto:asaraujo at if.sc.usp.br <mailto:asaraujo at if.sc.usp.br>>
>>     > <mailto: asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br> <mailto:asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>>>>
>>     wrote:
>>     >
>>     >     I think the Kubo equation is to use in the
>         non-normalized VAC,
>>     >     since the
>>     >     D = kT/M*integral is for normalized ones.
>>     >
>>     >     Alexandre Suman de Araujo
>>     >     asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br> <mailto:asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>>
>>     <mailto: asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br> <mailto:asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>>>
>>     >     UIN: 6194055
>>     >     IFSC - USP - São Carlos - Brasil
>>     >
>>     >
>>     >
>>     >
>>     >     > Did you try 1/3*your integral
>>     >     >
>>     >     > On 2/22/06, *Alexandre Suman de Araujo* <
>>     asaraujo at if.sc.usp.br <mailto:asaraujo at if.sc.usp.br>
>         <mailto: asaraujo at if.sc.usp.br <mailto:asaraujo at if.sc.usp.br>>
>>     >     <mailto: asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br> <mailto: asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>>>
>>     >     > <mailto: asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>
>>     <mailto: asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>> <mailto: asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>
>>     <mailto:asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>>>>>
>>     >     wrote:
>>     >     >
>>     >     >     Hi Gmxers.
>>     >     >
>>     >     >     I´m trying to calculate coefficient diffusion
>         values for
>>     >     ions in
>>     >     >     water.
>>     >     >
>>     >     >     I made some calculations using MSD and the
>         results
>>     were in good
>>     >     >     agreement with experimental values.
>>     >     >
>>     >     >     The problem is when I try to calculate it
>         from integration
>>     >     of VAC
>>     >     >     function for the ions, like in Rasaiah paper
>         (J. Chem
>>     Phys.
>>     >     101(8)
>>     >     >     6964).
>>     >     >
>>     >     >     I made 40 simulations of 250 ps with 1 fs
>         time step and
>>     >     output of
>>     >     >     velocities every 1 fs. >From these simulations I
>>     calculated the
>>     >     >     normalized VAC function from these 40
>         simulations and
>>     >     calculated the
>>     >     >     mean. This methodology is implemented to have
>         a good
>>     >     statistic and a
>>     >     >     more smooth VAC function (without
>         fluctuations that could
>>     >     make the
>>     >     >     integral diverge). With this VAC function I
>         use this
>>     equation to
>>     >     >     calculate do diffusion coefficient:
>>     >     >
>>     >     >     D = kT/M*Y, where Y is the integral of the
>         VAC function
>>     >     >
>>     >     >     The problem is that the value calculated from
>         VAC does not
>>     >     agree with
>>     >     >     one calculated from MSD.
>>     >     >
>>     >     >     Does anyone knows any trick to perform this
>         kind of
>>     calculation?
>>     >     >     In the
>>     >     >     paper cited above these two values are very
>         near and I´m
>>     >     using the
>>     >     >     same
>>     >     >     methodology.
>>     >     >
>>     >     >     Thank´s!
>>     >     >
>>     >     >     --
>>     >     >     Alexandre Suman de Araujo
>>     >     >     asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br> <mailto:asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>>
>>     <mailto: asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br> <mailto:asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>>>
>>     >     <mailto: asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>
>>     <mailto:asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>> <mailto: asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>
>>     <mailto: asaraujo at if.sc.usp.br
>         <mailto:asaraujo at if.sc.usp.br>>>>
>>     >     >     UIN: 6194055
>>     >     >     IFSC - USP - São Carlos - Brasil
>>     >     >
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