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

Rotational partition functions

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

Partition function of a spherical rotor

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

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 $q_{vib}=\prod _{i}{\frac {1}{1-{\textrm {exp}}\left({\frac {-hv}{k_{B}T}}\right)}}$