Computation of vibrational partition function: a comparative analysis between Poisson summation and classical limit

The computation of partition function (Z) is the bedrock of the study of statistical mechanics as it plays a significant role in the thermodynamic properties (TP) where microscopic properties are connected to macroscopic properties. Several studies have reported TP via the Z using one of the classical limit approach or Poisson summation formula. No study however justifies the agreement or discrepancy between the methods. This study therefore, investigates the two methods for theoretical determination of the vibrational partition function by considering the energy levels of Tietz molecular potential. The first approach employs Poisson summation method with a defined energy levels of the Tietz molecular potential while the second approach adopts the utilization of the classical limit approach with the same energy levels of the Tietz molecular potential. By comparing the results of the two approaches, our result reveals discrepancy between the analytic equations for Z. However, the numerical results obtained for the thermal properties of NaBr and CuCl molecules showed a perfect agreement between the two approaches and the experimental data with the results from classical limit approach closer to the experimental data. This study therefore, provides guidelines for choosing the appropriate approach based on the characteristics of the system under study for theoretical research.