A Quick Trip through Some Partition Functions

A QUICK TRIP THROUGH SOME PARTITION FUNCTIONS 

In calculations of statistical mechanics, it is only the two-body correlations which are important, although there may be many particles that have an influence upon a particular particle. The reason for this is simply that the forces acting upon a body from multiple directions are additive in a vector sense. Since the force is the divergence of potential energy, the calculated potential energies generated from the particles are also additive at each point in space. Or for forces, F, and potential energies, u. 

Therefore, since Ps are real they must be of the form 

The normaUzing factor Q is referred to as the partition function. Further arguments relating these relationships to thermodynamics by analogy reveals that fi = —kT (or RT on a per mole basis). 

Partition functions in generd can usually be separated into separate multiplicative parts, such as rotational, vibrational, electronic and translational. For the following discussions, the internal portions, that is vibrational and electronic, are being ignored and the molecules in question are assumed to be spherically symmetrical, or nearly so, so the rotational portion is also ignored. 

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