Vibrational partition function: Difference between revisions

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<math>Q_{vib}(T) =\prod_j{\sum_n{e^{-\frac{E_{j,n}}{k_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 j'th mode when it has vibrational quantum number <math> n= 0, 1, 2, \ldots </math>. For an isolated molecule of ''n'', atoms, the number of [[Molecular vibration|vibrational modes]] (i.e. values of j) equalsis 3''n'' − 5 orfor linear molecules and 3''n'' − 6 dependent upon whether the molecule isfor non-linear or nonlinear respectivelyones.<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==