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Q_{vib}(T) = e^{- \frac{E_{ZP}}{k_B T}} \prod_j \frac{1}{ 1 - e^{-\frac{ h c \tilde{\nu}_j}{k_B T}} }
</math>
It is convenient to define a characteristic vibrational temperature
:<math> \Theta_{i,vib} = \frac{h \nu_i}{k_B} </math>
where <math> \nu </math> is experimentally determined for each vibrational mode by taking a spectrum or by calculation. By taking the zero point energy as the reference point to which other energies are measured, the expression for the partition function becomes
<math> Q_{vib}(T) = \prod_{i=1}^f \frac{1}{1-e^{-\Theta_{vib,i}/T}} </math>
== References ==
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