In this paper we formulate the theory of the interaction of a diatomic linear molecule 
in a spatially degenerate state with the non-resonant laser field and of the 
rovibrational dynamics in the presence of the field. We report on ab initio 
calculations employing the double electron attachment intermediate Hamiltonian Fock 
space coupled cluster method restricted to single and double excitations for all 
electronic states of the Rb2 molecule up to 5s+5d dissociation limit of about 26.000 
cm?¹. In order to correctly predict the spectroscopic behavior of Rb2, we have also 
calculated the electric transition dipole moments, non-adiabatic coupling and spin-
orbit coupling matrix elements, and static dipole polarizabilities, using the 
multireference configuration interaction method. When a molecule is exposed to a strong
non-resonant light, its rovibrational levels get hybridized. We study the spectroscopic
signatures of this effect for transitions between the X¹Sg? electronic ground state and
the A¹Su? and b³?u excited state manifold. The latter is characterized by strong 
perturbations due to the spin-orbit interaction. We find that for non-resonant field 
strengths of the order 10? W/cm², the spin-orbit interaction and coupling to the non-
resonant field become comparable. The non-resonant field can then be used to control 
the singlet-triplet character of a rovibrational level.