Energy conservation: lj/smooth vs. lj/cut


I have read a number of posts related to this topic, but I haven’t found anything as specific as what I mention here.

In the documentation for lj/smooth there is a cautionary note indicating that force smoothing results in discontinuities in the energy. This make sense. However, not having a smoothing function (e.g. lj/cut) also results in a discontinuity (in the force) since as the energy goes to zero the derivative of energy with respect to distance goes to infinity. As a result, as two atoms/particles cross the cutoff, they experience an artificially high repulsive force that imparts extra kinetic energy to the system resulting in an increase in temperature as can be confirmed with an NVE simulation.

Is this discontinuity resulting from a hard cutoff less of a concern than the discontinuity that results from using a switching function? If so, why?

Kind regards,

Yesterday I had a conversation with Axel on a similar point. He noted that energy discontinuities don’t affect the results of MD simulations, only minimization and diagnostics. Force discontinuities, on the other hand, cause serious issues with the realism of simulations. For the standard lj/cut potential, this is avoided by applying the cutoff either at the minimum (r_{cut}=2^{1/6}\sigma) or at a much larger value where the force discontinuity is small, like 3\sigma. It seems that lj/smooth wants to guarantee a smooth force through both cutoffs, which can be useful in some situations.

In fact, because of that, I would expect a better energy conservation from lj/smooth than from lj/cut, but not as good at lj/long with pppm/disp or ewald/disp with the proper settings. I think the comment in the documentation is a bit misleading.