Vibrational partition function
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The vibrational partition function traditionally refers to the component of the canonical partition function resulting from the vibrational degrees of freedom of a system. The vibrational partition function is only well-defined in model systems where the vibrational motion is relatively uncoupled with the system's other degrees of freedom.
[edit] Approximations
[edit] Quantum Harmonic Oscillator
The most common approximation to the vibrational partition function uses a model in which the vibrational eigenmodes or vibrational normal modes of the system are considered to be a set of uncoupled quantum harmonic oscillators. It is a first order approximation to the partition function which allows one to calculate the contribution of the vibrational degree of freedom of molecules towards thermodyanmic variables. A quantum harmonic oscillator has an energy spectrum characterized by:
where j is an index representing the vibrational mode, and i is the quantum number for each energy level of the jth vibrational mode. The vibrational partition function is then calculated as:
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