Fundamental view on the calculation of internal partition functions using occupational probabilities

From first principles, the author gathers a few general rules that need to be abided by in the calculation of the internal partition functions (IPFs) of individual molecules. These rules are violated in many schemes in the literature where occupational probabilities are used including those using the Planck–Larkin partition function (PLPF) within the chemical picture. Considering these rules is useful from conceptual and practical points of view. A solution is introduced to assure fulfilling the above mentioned rules when using occupational probabilities. Sample calculations are performed showing quantitative significance of inaccuracies caused by dishonoring such rules.

► General requirements that need to be abided by in the calculation of internal partition functions are derived and presented.
► These requirements are violated in many schemes in the literature where occupational probabilities are used.
► Using Planck–Larkin partition function within the chemical picture does not satisfy these requirements.
► A solution is introduced to assure fulfilling the above mentioned rules when using occupational probabilities.
► Sample calculations are performed showing quantitative significance of inaccuracies caused by dishonoring such rules.