Statistical Thermodynamics and Rate Theories/Molecular partition functions of polyatomic gases

Rotational partition functions

Rotational partition function of a linear rotor $q_{rot}=\frac{8\pi I{k}_{B}T}{h^2}$

Partition function of a spherical rotor

Rotational partition function of a spherical rotor $q_{rot}=\frac{{\pi }^{1/2}}{\sigma }{\left(\frac{8{\pi }^{2}I{k}_{B}T}{h^2}\right)}^{3/2}$

Partition function of a symmetric top

Rotational partition function of a symmetric rotor $q_{rot}=\frac{{\pi }^{1/2}}{\sigma }\left(\frac{8{\pi }^2{I}_A{k}_{B}T}{h^2}\right){\left(\frac{8{\pi }^2{I}_B{k}_{B}T}{h^2}\right)}^{1/2}$

Rotational partition function of an asymmetric rotor $q_{rot}=\frac{{\pi }^{1/2}}{\sigma }{\left(\frac{8{\pi }^2{I}_A{k}_{B}T}{h^2}\right)}^{1/2}{\left(\frac{8{\pi }^2{I}_B{k}_{B}T}{h^2}\right)}^{1/2}{\left(\frac{8{\pi }^2{I}_C{k}_{B}T}{h^2}\right)}^{1/2}$

Vibrational partition functions

Vibrational partition function of a polyatomic molecule $q_{vib}=\prod _i\frac{1}{1-\text{exp}\left(\frac{-hv}{k_{B}T}\right)}$