# [lammps-users] compute msd -A question about mean square dispalcement

Hi ,
i am willing to compute self diffusion coefficient. So i use compute msd. My question is that in the manual it says that the slope of the a figure msd vs time is proportional to self diffusion coefficient but it doesn’t define to which is it proportional. Which equation should i use in order to compute self diff coeff? I mean ok ,einstein relation is known but there is a lim inside it. What it is the best solution to follow? i have at the moment: MSD-time. Shall i only divide by the number of particles or something else?

Jim

Dear Jim,
You are right you have to use Einstein relation for computing the self diffusion coefficient from MSD vs time plot. Generally slope of this curve at long time ( time -> infinite) gives the diffusion coefficient (however there is a constant in expression which depends on the dimensionality of the problem). Please have a look at the following page,

http://www.matdl.org/matdlwiki/index.php/softmatter:Mean_Squared_Displacement

For more details you can refer to this paper (however it specifically talks about the self diffusion in granular flows, but it will give a fair idea about how to extract this from the MSD vs time curve or from velocity autocorrelation function (VACF)).

Self Diffusion in granular flows, C.S. Campbell, JFM 1997, vol. 348, pp 85-101.

Hope this help.

Regards,
Vidya

2010/4/26 Jim Jim <drazentl@…8…>

Any MD text book will cover this. The formula
is D = MSD/2dt where t is time and d = dimensionality.
Hence MSD/t is the slope.

Steve

2010/4/26 Jim Jim <[email protected]...>: