Fractional Derivative Models for Energy Levels and Molar Entropy of Diatomic Molecules
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Abstract
This study develops new analytical equations for the energy levels and molar entropy of substances by solving the Schrödinger equation with the Pöschl-Teller potential. While thermodynamics is crucial in fields like agriculture, drug design, and medical research, existing models often use spectroscopic constants but overlook fractional parameters, which limits their accuracy for gaseous diatomic molecules. By integrating fractional parameters alongside spectroscopic constants, this study addresses this limitation and improves precision. The new equations are applied to analyze pure substances, including Br2 (X 1∑g+), Cl2 (X 1∑g+), CO (X 1∑+), and Na2 (X 1∑g+). The mean percentage absolute deviation (MPAD) of the energy levels obtained is 1.4797%, 0.9043%, 0.0898%, and 1.1352%, respectively, compared to Rydberg-Klein-Rees data. For molar entropy, the MPAD values are 0.1381%, 0.1360%, 0.1322%, and 0.6437% relative to data from the National Institute of Standards and Technology (NIST) database. These results indicate a significant improvement in accuracy over existing models and are consistent with the literature on gaseous molecules.
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