  We study a general problem of the
translational/rotational/vibrational/electronic dynamics of a diatomic molecule
exposed to an interaction with an arbitrary external electromagnetic field. The
theory developed in this paper is relevant to a variety of specific
applications. Such as, alignment or orientation of molecules by lasers,
trapping of ultracold molecules in optical traps, molecular optics and
interferometry, rovibrational spectroscopy of molecules in the presence of
intense laser light, or generation of high order harmonics from molecules.
Starting from the first quantum mechanical principles, we derive an appropriate
molecular Hamiltonian suitable for description of the center of mass,
rotational, vibrational and electronic molecular motions driven by the field
within the electric dipole approximation. Consequently, the concept of the
Born-Oppenheimer separation between the electronic and the nuclear degrees of
freedom in the presence of an electromagnetic field is introduced. Special
cases of the dc/ac field limits are then discussed separately. Finally, we
consider a perturbative regime of a weak dc/ac field, and obtain simple
analytic formulas for the associated Born-Oppenheimer
translational/rotational/vibrational molecular Hamiltonian.
