[Pw_forum] How to calculate Mean Square Displacement (MSD)

Ari P Seitsonen Ari.P.Seitsonen at iki.fi
Mon Oct 30 10:37:18 CET 2017

Dear All,

   Yes, never fold back when studying the real mean-square displacement; 
like Nicola wrote, your results would depend on the size of the box.

   One issue to consider is whether one should remove the centre-of-mass 
motion, as there is always such in DFT-based simulations (finite basis 
set/grid in the exchange-correlation term, finite convergence toward 
self-consistency, ...), unless it is removed manually (I do not know if 
QE does it automatically). I tend to do it - sometimes the whole set of 
atoms or molecules has travelled a long distance in a single direction. 
Then there is also the question if the temperature during the simulation 
is correct, or whether one should remove the centre-of-mass velocity also 
at each step... Again, I do not know if QE handles this - can some one 
confirm what is done (CPV, PW)?

     Greetings from Sunny Paris,


   Ari Paavo Seitsonen / Ari.P.Seitsonen at iki.fi / http://www.iki.fi/~apsi/
     Ecole Normale Supérieure (ENS), Département de Chimie, Paris
     Mobile (F) : +33 789 37 24 25    (CH) : +41 79 71 90 935

On Mon, 30 Oct 2017, Marzari Nicola wrote:

> You need to be able to follow genuine diffusion - eg a liquid, a superionic, a fast interstitial...
> If you fold, your msd will always tend to a constant (rather than eg a straight line with finite slope, as a function of time).
> Nic
> Sent from a tiny keyboard... Contact info: http://theossrv1.epfl.ch/Main/Contact
> On 30 Oct 2017, at 10:13, Lorenzo Paulatto <paulatz at gmail.com> wrote:
>       On 30/10/17 10:09, Marzari Nicola wrote:
>             ?? For MSD you should not fold back.
>       Re-reading the question i think you are right. But I also think that it
>       should not matter, i.e. that each atom should always stay close to its
>       initial position. If it matters the displacements are too large, maybe
>       the timestep is too large if doing molecular dynamics?
>       cheers
>       --
>       Lorenzo Paulatto - Paris
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