How can the singularity of force and the nonconservation of energy be eliminated simultaneously?

For potentials like airebo and tersoff, the original cut-off radius for C-C covalent bond (Rmin=1.7A, Rmax=2.0A) leads to a sudden rise in the bond force
when the bond is stretched to a length near breaking. To solve this problem, Rmin=Rmax=2.0A has also been widely adopted.
However, another problem arises. The potential energy of the C-C bond will suddenly change to zero instead of gradually going to zero at Rmax resulting
in the nonconservation of etotal. Especially when I performed an impact simulations of graphene under nve, the nonconservation of the etotal impedes my analysis.
I believe this is not an accident. So, can you give me some advice?
Best regards.

Something on this topic should be discussed in this paper


It is always not a good idea to change potential parameters including the cutoffs. Changing the inner and outer cutoffs to the same value is even worse.