For a simple dissociation equilibrium
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the equilibrium constant Kp at temperature T can be written in terms of partial pressures p or densities n in the form given by Equation 6 of Tatum (1966)
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where m is the reduced mass of AB, k the Boltzmann constant, h the Planck constant, QA, QB, QAB the internal partition functions of the species, and D0 the dissociation energy of AB. This equation derives from a more general expression of Kp (T) for a chemical reaction that is demonstrated in all physicalchemistry textbooks treating statistical thermodynamics (see for example Atkins 1990). Partition functions are weighted Boltzmann factors
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with ϵn corresponding to the energy of the eigenstates of degeneracy gn. Provided all the eigenvalues are known, Q values can be calculated exactly. Derivations and calculations of the partition functions can be found in textbooks or in reviews relating to astrophysics.