From: Josh Vermaas (
Date: Mon Feb 03 2014 - 19:04:56 CST

Hi Juita,

If your MD engine wraps, and enough particles go from one side of the
periodic boundary to the other, your diffusion constants will be way
off. Over the short term, the diffusion constant should be too high, as
particles appear to teleport across periodic boundaries despite not
moving very far along your real coordinate system (they are "wrapped"
into the periodic image nearest to the origin). Over the longer term,
with wrapping turned on, the maximum displacement any particle could
experience is proportional to the box-size, so your diffusion constant
will approach zero as time progresses. This should be easy to check, as
then your MSD would no longer increase linearly with time, but rather
plateau at some value. This is something you'll need to look into more
deeply, and perhaps do a test with a simpler system that you know the
answer to in order to track down what exactly is happening, as I suspect
DFTB is doing something you aren't expecting it to.

Good luck!

On 02/03/2014 06:49 PM, . Juita wrote:
> Dear Josh,
> I am so sorry for late reply. I think that I missed your email.
> Thank you so much for your information.
> Yes, so far I know, diffusion coefficients are normally reported from QM molecular dynamics studies.
> You are right about long simulations. I am still continuing running the simulation until ns level. However, I think there is something wrong with the calculation which is not caused by long simulations as the self-diffusion coefficient values are 2 orders of magnitude lower.
> - I have double checked the units for both space and time and they are right. The trajectories are in Angstrom. I specified the timestep as 1 femtosecond and MD restart frequency is 100 so that the time between frame is 100 fs.
> - Yes, this is a periodic system. I am wondering if wrapping means the coordinates outside the specified box size. If there is a wrapping, do you think the diffusion constants can be far away (2 orders of magnitude difference) from the correct value?
> Thank you so much for your assistance.
> Best regards,
> Juita
> ________________________________________
> From: Josh Vermaas <>
> Sent: 31 January 2014 01:12
> To: . Juita;
> Subject: Re: vmd-l: self-diffusion coefficient from RMSD
> Hi Juita,
> Are diffusion constants usually reported from QM studies? In my
> experience, short simulations (<1ns) tend to be in the regime where
> things are settling down and the Einstein relation gives nonsensical
> answers (atoms haven't had the time to change directions enough for it
> to be a good random walker yet). Some other possible explanations:
> -Trajectory spit out by DFTB may not be in the units you or VMD expect
> (No idea if this is true, but just looking at the docs quickly, DFTB
> uses Bohr instead of Angstrom internally, so make sure you check the
> units for both space and time!).
> -Is this a periodic system? If so, have you checked wrapping? There
> should be no wrapping.
> Your shortcut should in principle work, but it never hurts to check an
> alternative formulation for determining diffusion, and keep in mind that
> computational diffusion constants do not perfectly agree with literature
> values in general (although 2 orders of magnitude is a bit extreme).
> Good luck!
> -Josh Vermaas
> On 01/30/2014 03:21 AM, . Juita wrote:
>> Dear VMD users,
>> I am doing calculation of self-diffusion coefficient from the trajectories data obtained from DFTB+ simulation. I am wondering whether I do the correct calculation. I utilise VMD to calculate and plot the RMSD, then squared it to get the plot of MSD (mean square displacement). The self-diffusion coefficient is estimated from the slope of MSD vs time plot using Einstein relation. However, I get the value 100 times less compared to the literature value. I would appreciate any assistance for this problem.
>> Thank you so much for your assistance.
>> Best regards,
>> Juita