It is studied the atom-phonon coupling model introduced recently for spin-conversion phenomenon High-spin (HS) ↔ Lowspin (LS). The originality of this model, performed on a linear chain of atoms, is that the interaction between two molecules is harmonic and the value of the elastic force constant values of the spring linking two atoms depends on their electronic states. In this model a Zeeman-like and an exchange-like interactions appear naturally. In this contribution we reproduce the sigmoïdale behaviour in the HS→LS relaxation at low temperatures as obtained experimentally as well as the Light Induced Thermal Hysteresis (LITH).