We have investigated the effect of the competition between the electron-electron and elec-tron-phonon interactions on the ground state of MX complex and its third-harmonic generation (THG). On the basis of Hubbard model, the Hartree-Fock(HF) approximation is valid in studying the system when the strength of electron-electron interaction U is less then 2t0(t0is the hopping between M dz2 and X Pz orbitals). As a result, we discover that (i) With U increasing, the system changes from charge density wave (CDW) to spin density wave(SDW). (ii )This phase transition takes place at U～1.2t0 and is a first-order one. (iii) At the critical point, the band gap reaches minimum, thus a large THG is obtained. Based on these results, some proposal is put forward to search for nonlinear optical materials.