Energy level and thermal agitation

Normally, calculating partition functions requires the use of energy levels compatible with, on the one hand, results of quantum mechanics, and on the other hand, summations of relation [6.3]. However, the calculation can be simplified in two extreme cases. 

Let us denote sq and as the two first energy levels that correspond to one degree of freedom. If the difference between these two levels is very large with regard to thermal agitation, i.e. the product kgJ, therefore if  

The partition function corresponding to this degree of freedom is reduced to the first term of equation [6.1], i.e.  

If we choose the first level, i.e. sq=0 as the origin of the energies of this degree of freedom, then the partition function simply becomes  

This degree of freedom is said to be non-excited. This is found to be so for electronic and nuclear degrees of freedom. 

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