Energy Conservation


I’m new to molecular dynamics, and per my textbook, it says that molecular dynamics cannot be run using a Lennard-Jones truncated potential because energy conservation will be violated whenever atoms cross over the cutoff. “…as the potential changes discontinuously at Rc, a truncated potential is not particularly suitable for a Molecular Dynamics simulation.”

I get that shifting the potential won’t change the calculated force because the force is the derivative of the potential, but why doesn’t the current way that LAMMPS is setup lead to the violation of energy conservation?



If you have a large system, with 1000s of atoms, then
at any step many pairs of atoms are going outside the
cutoff, many are moving inside. On aggregate there
is very little variation in the energy. If the system is
stable, that continues every step. So that overall
the energy of 1000s of atoms is “conserved” in the
sense there are just tiny variations around a mean.
If you shift the potential the variations get smaller,
but nothing really changes. So often people don’t worry
about shifting an LJ potential. The shift at 2.5 sigma

is very small anyway.