Considerations of Level Spacing

The spacing between vibrational energy levels cannot be ignored for calculations of qvib at room temperature. For a single harmonic vibration, the energy levels are given by 

for detail, see a statistical mechanics text. For a general N-atomic molecule, there are (3N — 6) normal vibrations j (3N — 5) for a linear molecule) and the corresponding vibrational partition function is 

The formulae for the partition function of a molecule in the rigid-rotor-harmonic-oscillator approximation are summarized in Table 4.1. 

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