Vibrational partition function: Difference between revisions

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For a system (such as a molecule or solid) with uncoupled vibrational modes the vibrational partition function is defined by

<math display="block">Q_\text{vib}(T) = \prod_j{\sum_n{e^{-\frac{E_{j,n}}{k_\text{B} T}}}} </math>

where <math> T </math> is the [[Thermodynamic temperature|absolute temperature]] of the system, <math> k_B </math> is the [[Boltzmann constant]], and <math> E_{j,n} </math> is the energy of the ''j''-th mode when it has vibrational quantum number <math> n = 0, 1, 2, \ldots </math>. For an isolated molecule of ''nN'' atoms, the number of [[Molecular vibration|vibrational modes]] (i.e. values of ''j'') is 3''nN'' − 5 for linear molecules and 3''nN'' − 6 for non-linear ones.<ref name="Herzberg">G. Herzberg, ''Infrared and Raman Spectra'', Van Nostrand Reinhold, 1945</ref> In crystals, the vibrational normal modes are commonly known as [[phonon]]s.

==Approximations==