Fundamental View on the Calculation of Internal Partition Functions Using Occupational Probabilities

TL;DR

This paper establishes fundamental rules for calculating internal partition functions using occupational probabilities, highlighting common violations in literature and proposing a solution to ensure accurate and consistent calculations.

Contribution

It introduces a set of fundamental rules for calculating internal partition functions with occupational probabilities and provides a method to ensure these rules are followed.

Findings

Violations of fundamental rules lead to inaccuracies in IPF calculations

Proposed solution improves the consistency of occupational probability methods

Sample calculations demonstrate the significance of adhering to the rules

Abstract

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.