  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 cooperativity 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.
