Vibrational partition function
= Vibrational partition function
{title2=$q_{\rm vib}$}
A <vibrational partition function> sums over molecular vibrational <energy levels>. A single <quantum harmonic oscillator>, with energies measured relative to its ground level and vibrational temperature $\theta_v=h\nu/k$, has $q_{\rm vib}=(1-e^{-\theta_v/T})^{-1}$. Retaining its absolute <zero-point energy> multiplies this by $e^{-\theta_v/(2T)}$. That factor shifts the <internal energy> but contributes no <entropy>.