  We propose a theoretical scheme for coupling a nanomechanical resonator to a
single diatomic molecule via microwave cavity mode of a driven LC resonator. We
describe the diatomic molecule by a Morse potential and find the corresponding
equations of motion of the hybrid system by using Fokker-Planck formalism.
Analytical expressions for the effective frequency and the effective damping of
the nanomechanical resonator are obtained. We analyze the ground state cooling
of the nanomechanical resonator in presence of the diatomic molecule. The
results confirm that presence of the molecule improves the cooling process of
the mechanical resonator. Finally, the effect of molecule's parameters on the
cooling mechanism is studied.
