  We theoretically investigate the corrections of exciton binding energy in
monolayer transition metal dichalcogenides (TMDs) due to the exciton-optical
phonon coupling in the Fr$\ddot{o}$hlich interaction model by using the linear
operator combined Lee-Low-Pines variational method. We not only consider the
excitons couple with the intrinsic longitudinal optical (LO) phonon modes, but
also the surface optical phonon modes that induced by the polar substrates
underneath the TMDs. We find that exciton binding energies are corrected in a
large scale due to these exciton-optical phonon couplings. We discuss the
dependences of exciton binding energy on the cut-off wave vector of optical
phonon modes, the polarization parameters of materials and the interlayer
distance between the polar substrates and TMDs. These results provide potential
explanations for the divergence of the exciton binding energy between
experiment and theory in TMDs.
