Energy eigenvalue and thermodynamic properties for Deng-Fan screening potential

This research aims to study energy eigenvalues and thermodynamic properties associated with the screening Deng-Fan potential in diatomic molecules. For this authors developed a theoretical model for energy eigenvalues and investigated the nature of energy eigenvalues for H2, Cl2, and HCl, considering screening parameters and bond dissociation energy. The study involves detailed exploration, numerical simulations, and analysis to understand the relationship between screening parameters and energy levels. The bond dissociation energy affects the energy levels, providing insights into bond formation and breaking processes. The thermodynamic properties, partition function decreases exponentially within 0.005 screening range for H2, Cl2, and HCl. Entropy drops exponentially due to screening, Cl2 has higher entropy due to electron density and screening effects. Mean free energy stays constant, Cl2 is higher due to electron density and screening. Specific heat capacity is zero, indicating electrons lack measurable heat capacity unlike macroscopic objects. The findings are expected to contribute significantly to molecular physics and quantum mechanics, enhancing our understanding of molecular bonding and reactivity with potential applications in diverse physical systems and technologies.