Molecules with two electronic energy levels: coupling between the molecules in the solid state via the optical and acoustic phonon branches

In the adiabatic approximation the values of the spring constants of the springs contained in a molecule depend on its electronic state. We consider molecules with two electronic energy levels separated by Δ. For a crystal of such molecules, the phonon branches depend therefore on the electronic states of the molecules. One can ask if that dependence does not introduce a coupling between the molecules via the optical and the acoustic branches. It is known that for a one-dimensional chain of N identical diatomic molecules there are two phonon branches, an optical branch and an acoustic one. In this study we introduce in the hamiltonian of the chain two assumptions: (i) each molecule has two electronic energy levels separated by Δ and the spring constant of the spring contained in the molecule has a value which depends on its electronic state; (ii) the spring constant of the spring which links two molecules nearest neighbours has a value which depends on the electronic states of both molecules linked. One can show that phonons create on each molecule a field-like which favours the excited level and create between two molecules nearest neighbours an exchange-like interaction which can be ferro-like, antiferro-like and which can be equal to zero. For some values of T and Δ, the chain can display a first-order phase transition with the presence of a thermal hysteresis loop. The phase transition takes place between the phase where all the molecules are in the fundamental level and that where they are in the excited one. The parameters of the model can be expressed in function of the applied pressure and of the volume of the crystal.