Dear Lammps-users,

Thanks for the help from Axel and Steve, i searched some paper about the

statistic error of molecular dynamics, and when i increase the simulation

length from 150 ps to 1ns and 2 ns, the divergence from the use of different

random number seed can be reduced, but for the slight difference from the

use of different number of cores, it didn't work. But, it's fair enough to

take these slight difference as statistic errors. Anyway, thanks for the

help!!!

i don't think you found a paper with good advice to assess statistical

uncertainty, and i don't think that your rationalization is good.

first off, you seem to be overlooking three major things:

1) how much are your results impacted by the equilibration process?

are there any artifacts (e.g. phonons) that remain in your system

after equilibration, that may affect your production data?

2) how much are your results impacted by your method of postprocessing the data?

3) how much are your results impacted by other simulation settings,

e.g. the method and settings to adjust temperature? length of time

step? cutoffs? neighbor list updates?

then, rather than just making your simulation longer and taking what

you see as remaining divergence on good faith (which is not a good

idea in science), you should look for a more systematic approach. one

of them is to analyze your simulation data in chunks. the smaller the

chunks, the better you can assess impact of equilibration (or lack of

it) and the better you can see, if there are low frequency effects. in

the most rigorous of these approaches, you first divide your

simulation data in halves and analyze each half separately and look at

the differences. then you take quarters, eighths and so on until each

chunk is too small and the result too noisy. with this approach, you

can actually quantify the

the statistical variation and extrapolate to an actual statistical

uncertainty, and with those numbers, you can apply a dependable error

bar to each data point of your determined IR spectra.

furthermore, you seem to be ignoring, that the intensities your are

looking at have no real meaning in the first place. they do not take

into account that for either IR or Raman spectroscopy not all

potential vibrational modes are allowed and that the intensity is

determined by the transition moment integrals, i.e. the reaction of

the wavefunction to the dipole operator (IR) or electronic

polarizability (Raman).

...and it doesn't stop there, there are also empirical corrections

that take into account the current temperature of your material and

technically, you should be looking at the (total?) dipole moment

instead of velocities. all of that affects your intensities, but not

the frequencies. those are primarily affected by the accuracy and

applicability of the empirical potential that you are using.

so, if you want to sort this out properly (and i recommend to do and

practice this, as this kind of statistically error assessment should

be done for almost all simulation data where a quantitative result is

desired), you still have to some work and some thinking ahead of you.

axel.