Materials with spin-crossover (SCO) properties hold great potentials in information storage and therefore have received a lot of concerns in the recent decades. The hysteresis phenomena accompanying SCO is attributed to the intermolecular cooperativi
ty whose underlying mechanism may have a vibronic origin. In this work, a new vibronic Ising-like model in which the elastic coupling between SCO centers is included by considering harmonic stretching and bending (SAB) interactions is proposed and solved by Monte Carlo simulations. The key parameters in the new model, $k_1$ and $k_2$, corresponding to the elastic constant of the stretching and bending mode, respectively, can be directly related to the macroscopic bulk and shear modulus of the material in study, which can be readily estimated either based on experimental measurements or first-principles calculations. The convergence issue in the MC simulations of the thermal hysteresis has been carefully checked, and it was found that the stable hysteresis loop can be more readily obtained when using the SAB model compared to that using the Wajnflasz-Pick model. Using realistic parameters estimated based on first-principles calculations of a specific polymeric coordination SCO compound, [Fe(pz)Pt(CN)$_4$]$cdot$2H$_2$O, temperature-induced hysteresis and pressure effects on SCO phenomena are simulated successfully.
