MSD vs Green-Kubo ionic conductivity in ionic liquids

GROMACS version: 2020.2
GROMACS modification: No

Hello,

I am studying a ionic liquid system, namely TFSI-/DAMAH+
I have found the topology from Ligpargen. while DAMAH+ came with the right +1 charge, I had to remove the H atom from TFSI in order to get the right -1 charge. This is a pure ionic liquid, no solvent.

My boxes are generated with Packmol. I have 150 pairs of molecules.
I have performed an energy minimization + nvt/npt equilibration following MDtutorials. Temperature, potential and density have converged, and I want to calculate the ionic conductivity. I use both the MSD and Green-Kubo methods, and the experimental value is 0.45 S/m at 300K and 1 bar:

  • MSD method is not very sensitive to parameters change (dt, nstvout) but gives me a results 3/4 times lower
  • Green Kubo depends strongly on nstvout and one can have very different results. From literature I have found that one should use dt~1/2 fs and nsvtout~20/10 respectively.

I would like to ask you if I have any clear mistake to my method or if there is a fundamental difference between the two methods.

The script that I use for the postprocessing is shown below.
######################################################################################################
(echo 0; echo q) | gmx make_ndx -f mdsim.gro -o index.ndx
(echo 2; echo q) | gmx make_ndx -f mdsim.gro -o index2.ndx
(echo 3; echo q) | gmx make_ndx -f mdsim.gro -o index3.ndx

(echo 0; echo q) | gmx msd -f mdsim.xtc -n index.ndx -s mdsim.tpr -mol -o msd.xvg
(echo 2; echo q) | gmx msd -f mdsim.xtc -n index2.ndx -s mdsim.tpr -mol -o msd2.xvg
(echo 3; echo q) | gmx msd -f mdsim.xtc -n index3.ndx -s mdsim.tpr -mol -o msd3.xvg

(echo 0; echo q) | gmx velacc -f mdsim.trr -s mdsim.tpr -n index.ndx -o vac.xvg -nonormalize -fitfn aexp
(echo 2; echo q) | gmx velacc -f mdsim.trr -s mdsim.tpr -n index2.ndx -o vac2.xvg -nonormalize -fitfn aexp
(echo 3; echo q) | gmx velacc -f mdsim.trr -s mdsim.tpr -n index3.ndx -o vac3.xvg -nonormalize -fitfn aexp

gmx analyze -f vac.xvg -integrate yes &> ivac
gmx analyze -f vac2.xvg -integrate yes &> ivac2
gmx analyze -f vac3.xvg -integrate yes &> ivac3

######################################################################################################
NOTES:
1.With the Green-Kubo method I calculate the non normalized VACF using the velacc command and after that I integrate the VACF and I multiply by (1/(3N)) to obtain the diffusion constant.
2.After obtaining the diffusion constant I calculate the conductivity using the Nerst-Einstein equation

Unfortunately I cannot attach the input files because I am a new user in the forum.
If you need any extra information about the simulation please let me now.

Thank you very much,