  The dynamics of dissipative soft-sphere gases obeys Newton's equation of
motion which are commonly solved numerically by (force-based) Molecular
Dynamics schemes. With the assumption of instantaneous, pairwise collisions,
the simulation can be accelerated considerably using event-driven Molecular
Dynamics, where the coefficient of restitution is derived from the interaction
force between particles. Recently it was shown, however, that this approach may
fail dramatically, that is, the obtained trajectories deviate significantly
from the ones predicted by Newton's equations. In this paper, we generalize the
concept of the coefficient of restitution and derive a numerical scheme which,
in the case of dilute systems and frictionless interaction, allows us to
perform highly efficient event-driven Molecular Dynamics simulations even for
non-instantaneous collisions. We show that the particle trajectories predicted
by the new scheme agree perfectly with the corresponding (force-based)
Molecular Dynamics, except for a short transient period whose duration
corresponds to the duration of the contact. Thus, the new algorithm solves
Newton's equations of motion like force-based MD while preserving the
advantages of event-driven simulations.
