We're using lammps to study the uranium properties and we've found good results at the moment concerning these properties that are in good agreement with the literature. Now we'd like to calculate the error on our quantities.

I've checked a lot on books and papers and so on and have not found no one error on thereotical calculation of elastic constants, BM and so on may you suggest something or it's our trouble on errors out of standard procedures?

I'll assume by error you mean some measure of uncertainty. The two
main sources of uncertainty in MD simulations are from the interatomic
potential and from thermal fluctuations. The former can not really be
measured in the simulation, but can be inferred by comparison with
more accurate calculations, such as DFT. The latter is fairly straight
forward and is well covered in text books on molecular simulation such
as the one by Frenkel and Smit. Essentially it boils down to dividing
the equilibrated portion of the simulation into N statistically
independent blocks and calculating sigma, the standard deviation of
the block averages. The uncertainty in the overall average is then
sigma/sqrt(N). If you are only interested in T=0 properties, then
there is no uncertainty due to thermal fluctuations; it's really all
down to the interatomic potential. Then there are quantum effects....

Indeed I was interested in uncertainties thx for your reply Aidan now I need to study cause we're interested not only in T=0 simulation but you're mail it's a good start for our job,