Determination of Thermodynamic Properties via Partition Function Approaches Derived from the Non-Relativistic Schrödinger Equation

Abstract

A critical challenge in molecular thermodynamics is accurately predicting how variations in dimensionless potential parameters influence macroscopic properties such as magnetisation, specific heat capacity, and molecular vibrational entropy. Traditional approaches often fail to fully capture these dependencies, limiting their predictive accuracy. In this study, we address this gap by developing a rigorous framework based on partition function formulations derived directly from the non-relativistic Schrödinger equation. Our main aim is to investigate the impact of dimensionless potential parameters (  and ) and the temperature parameter (β) on energy spectrum and key thermodynamic and magnetic properties. We systematically compute the energy spectrum for a wide range of potential parameter values and analyse their effects on magnetisation, magnetic susceptibility, internal energy, free energy, entropy, and specific heat capacity. The findings reveal that energy spectrum exhibit strong dependence on these parameters, with ​ generally reducing energy levels while ​ enhances them. Magnetisation typically decreases with ​ but increases with ​ and higher temperatures, while magnetic susceptibility shows complex patterns of enhancement and suppression. Vibrational thermodynamic properties, including internal energy and free energy, also display significant variations tied to the interplay of potential parameters. This study provides a robust, first-principles-based method for understanding and predicting how microscopic potential parameters govern macroscopic thermodynamic behaviour, advancing the fundamental knowledge and practical capabilities of molecular thermodynamics