# [gmx-users] No convergence in Diffusion Coefficient

Igor Leontyev ileontyev at ucdavis.edu
Tue Jun 29 05:50:47 CEST 2010

```See the table bellow, there is no convergence of the Self-Diffusion
Coefficient (Dself) over the trajectory length. Dself is obtained for NPT
box of 1024 SPC/E water molecules by the Einstein's relation (via RMSD). In
Gromacs Manual or Alien&Tildesley's book I didn't find issues related to the
problem. Is there any idea why I can not achieve the convergence?

Description:
To figure out what the trajectory length is needed for an accurate
simulation of the self-diffusion coefficient I performed the following test.
Split the continuous 10ns long trajectory on parts and calculated Dself for
each of the parts, e.g. the splitting on N parts gives N values of Dself
obtained on trjlenth=10ns/N trajectory part. For the variety of N values we
can calculate the average <Dself> and dispersion Disper. The converged
trajectory length is found as the trjlenth value at which the dispersion is
sufficiently small and <Dself> equal to the value obtained for the whole
10ns trajectory. But it turned out that Dself does not converge (See the
columns 3 and 4 in the Table).

Just for the comparison I carried out the same test for the Dielectric
Constant Eps (See the columns 5 and 6 in the Table) and the converged
trajectory length is about 2.5-5ns which correlates with the length reported
in the literature.

------------------------------------------------------------
trjlenth       N      <Dself>   Disper       <Eps>  Disper
ps               1e-5 cm^2/s
------------------------------------------------------------
10000.0       1      2.6305        0              72.0       0
5000.0         2      2.4591    .0929           71.9      1.1
2500.0         4      2.4554    .0291           71.6      4.7
1250.0         8      2.4816    .0618           71.1      5.2
625.0         16      2.4848    .0786           70.6      7.5
312.5         32      2.4993    .0848           67.7      9.4
156.2         64      2.5128    .1082           63.3    11.6
78.1         128      2.4993    .1119           56.3    14.1
39.0         256      2.5072    .1303           43.6    14.9
19.5         512      2.5133    .1713           31.0    12.4
9.7         1030      2.5449    .2128           19.6      8.0
4.8         2083      2.6318    .2373           12.0      4.9

```

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