Ising-like model with molecular vibrations

6 Ising-like model with molecular vibrations 

The inclusion of molecular vibrations will effect the partition function which, in addition to the electronic contribution, will contain the vibration part [28]. Each molecule is assumed to behave as a set of (3 - 6) independent harmonic oscillators with the fundamental frequencies vf so that the vibration partition functions are 

Then the partition function associated with one molecule is constructed from the respective electronic and vibration increments as 

Here the electronic energy of the LS state is taken as the energy origin  

For the system of equivalent but distinguishable particles (as in the solid state) the total partition function of a canonical system for one mole of particles becomes 

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