  We demonstrate how dynamic Stark control (DSC) can be achieved on molecular
photodissociation in the dipole limit, using single-cycle (FWHM) laser pulses
in the terahertz (THz) regime. As the laser-molecule interaction follows the
instantaneous electric field through the permanent dipoles, the molecular
potentials dynamically oscillate and so does the crossings between them. In
this paper, we consider rotating-vibrating diatomic molecules (2D description)
and reveal the interplay between the dissociating wave packet and the
dynamically fluctuating crossing seam located in the configuration space of the
molecules spanned by the R vibrational and $\theta$ rotational coordinates. Our
showcase example is the widely studied lithium-fluoride (LiF) molecule for
which the two lowest $\Sigma$ states are nonadiabatically coupled at an avoided
crossing (AC), furthermore a low-lying pure repulsive $\Pi$ state is
energetically close. Optical pumping of the system in the ground state thus
results in two dissociation channels: one indirect route via the AC in the
ground $\Sigma$ state and one direct path in the $\Pi$ state. We show that
applying THz control pulses with specific time delays relative to the pumping,
can significantly alter the population dynamics, as well as, the kinetic energy
and angular distribution of the photofragments.
