The interaction between excited N-2 molecules and dimers at a stabilized ZnSe(100) surface has been studied theoretically. The dimerization at the surface is treated as the one-dimensional lattice distortion, the so-called Peierls transition, and the stability of the dimerization interacting with the excited N-2 molecules is evaluated within the mean field approximation. When the orbital energy in the N-2 molecule gets close to the chemical potential of the one-dimensional electron gas, the dimerization is not a preferable state, consistent with the N-2 adsorption and dissociation mechanism on a ZnSe surface we proposed using the cluster model (T. Nakao, T. Uenoyama, Jpn. J. Phys., 32 ( 1993) 660).