【分享】MSDs计算无误注意事项

[LAMMPS]

General remarks:
1) If simulations are performed under PBCs the trajectory must be
properly
unfolded (revert PBCs) before any further calculation may be done.
2) Statistics is considerably improved if multiple time origins are
taken into
account.

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"Long" time:
There seems to be some agreement that at least several hundred
picoseconds are
necessary to obtain meaningful results. The simulation time depends,
of course,
also on the ensemble size (single molecules naturally need longer
simulation
times).

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Non-linearity:
1) One cause may be insufficient statistics at long time. In that
case a
weighted linear fit may be helpful using the standard deviation as
the
weights.
2) Another problem may arise from translational and/or rotational
movement of
the total system.

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Error estimation:
1) The covariance matrix may be derived from the slope which yields a
measure
of the error bar.
2) Another method seems to be to plot ln(MSD) vs ln(t). The slope
should be
close to 1.
3) I found the paper from G. C. Lie and E. Clementi [Phys. Rev. A, 33
(1986),
2679] very usful to interpret statical and dynamical properties in
solution.
These authors calculate the MSD for a water simulation separately
for H's
and O's. At short time (a few picoseconds) both MSDs develop into
a straight
line but different slope. However, since water must move as a
single
entity, the curves must have the same slope after some time.