Re-examining traditional and rotational canonical partition functions for undergraduate physical chemistry: Exact and insightful views

This study explores the canonical partition function of both translational and rotational motion quantum mechanically and in the semi-classical limit (high temperature limit) at all conditions, including all temperatures. The treatment of physical chemistry textbooks of the translational and rotational partition functions is commented on. Exact quantum mechanical closed-form expressions, which are not available in any physical chemistry textbook, or the in literature for that matter, are reported for both types of partition functions at a wide range of temperatures and conditions are derived.