Ising model for low-spin high-spin transitions in molecular compounds; within and beyond the mean-field approximation

Abstract

Abstract Some transition-metal containing molecules can undergo a spin transition (ST) between a low-spin (LS) and a high-spin (HS) state. The main goal of this paper has been to explore the theoretical status of the equation proposed by Slichter and Drickamer, giving the free energy of an assembly of ST molecules. The parameters of this equation are the enthalpy variation, ΔH, the entropy variation, ΔS, accompanying the LS⇆HS reaction, and an enthalpy term accounting for intermolecular interactions, T. First, a ST molecule has been described by a two-level system, and the ST problem at the microscopic scale has been formulated in the form of an Ising Hamiltonian. Then, the free energy of an assembly of such molecules has been calculated, using the mean-field approximation, which has led to the equation of Slichter and Drickamer. This approach has allowed us to relate the ΔH, ΔS, and T parameters of the thermodynamical equation to molecular (microscopic) data. In particular, T has been found to be equal to 2NzJ; N is Avogadro's number, z is the number of nearest neighbors of a molecule, and J is given by [ (E LH +E HL 2− (E LL +E HH 2 ]/2 ; ELL, EHH, ELH, and EHL are the possible values for the energy of a pair of nearest neighbor ST molecules; ELL stands when the two molecules are in the LS state, EHH when they are in the HS state, ELH and EHL when one of the molecules is in the LS state and the other in the HS state. In the mean-field approach the LS and HS molecules are randomly distributed within the crystal lattice, which is a questionable approximation when T is large. Therefor, we have explored what happens beyond the mean-field approximation, when the ST molecules are no longer randomly distributed, using Monte Carlo simulations. Two main results have emerged, namely: the occurrence of a thermal hysteresis is less probable in the non-random-distribution model, and the like-spin molecules tend to assemble in like-spin clusters. These clusters must be viewed in terms of high probability and not of static distribution. Our findings have been discussed at the light of the previous theoretical approaches and of the experimental data.