Thermodynamic Properties of a Diatomic Molecule Under Effects of Small Oscillations in an Elastic Environment

• Published in: Symmetry (Basel) Vol. 17; no. 7; p. 1038
• Main Authors: Vitória, Ricardo L. L., Pereira, Carlos F. S., Martins, Sergio Murilo da Silva Braga
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 02.07.2025
• Subjects: Analysis; Elastic media; Elastic systems; Electrons; Energy; Energy levels; Free energy; Internal energy; Investigations; Morse potential; Oscillations; Parameter modification; Point defects; Schrodinger equation; Spacetime; Thermodynamic properties; Thermodynamics
• ISSN: 2073-8994; 2073-8994
• DOI: 10.3390/sym17071038

In this paper, we analytically investigate a diatomic molecule subject to the Morse potential under the small oscillations regime, immersed in a medium with a point defect representing impurities or vacancies in an elastic system. Initially, we apply the small oscillations method to the Morse potential to obtain an analogue to the harmonic potential, and then we solve the generalized Schrödinger equation considering the geometric effects of the defect. The solutions obtained for the bound states reveal that the energy levels and the radial stability point of the molecule are modified by the presence of the defect, depending on the parameters associated with the geometry of the medium. In a second step, we analyze the thermodynamic properties of the system in contact with a thermal reservoir at finite temperature. We derive analytical expressions for the internal energy, Helmholtz free energy, entropy, and specific heat, showing that all these quantities are influenced by the presence of the point defect. The results demonstrate how structural defects alter the quantum and thermodynamic behavior of confined molecules, contributing to the understanding of systems in non-trivial elastic media.