  In this paper, we explore the dynamics of a Hamiltonian system after a double
van der Waals potential energy surface degenerates into a single well. The
energy of the system is increased from the bottom of the potential well up to
the dissociation energy, which occurs when the system becomes open. In
particular, we study the bifurcations of the basic families of periodic orbits
of this system as the energy increases using Lagrangian descriptors and
Poincar\'e maps. We investigate the capability of Lagrangian descriptors to
find periodic orbits of bifurcating families for the case of resonant,
saddle-node and pitchfork bifurcations.
