A laser scheme using a periodically changing frequency is used to induce oscillations of the internuclear motion, which are quantum analogs of classical vibrations in diatomic molecules. This is what we call the periodic laser adiabatic manipulation of the bond, or p-LAMB scheme. In p-LAMB, the carrier frequency of the laser must vary periodically from the blue to the red of a photodissociation band and backwards, following for instance a cosine-dependent frequency of period τ(c). In the adiabatic regime the dynamics is fully time-reversible. The amplitude of the internuclear oscillation is controlled by the pulse frequency ω(t), while τ(c) determines the duration (or period) of the bond oscillation. In the presence of efficient dipole coupling, the bandwidth of the pulse is the main constraint to the maximum bond stretch that can be obtained. Before the onset of the adiabatic regime the dynamics are more complex, showing dispersion of the vibrational wave packet and anharmonic deformation of the bond. However, the nonadiabatic effects are mostly canceled and full revivals are observed at certain multiples of τ(c).