The tetragonal structure of terephthalic acid involves a specific arrangement of molecules that enhances its physical and chemical properties. The molecular design, characterised by its planar geometry and hydrogen bonding capabilities, contributes to its significance in industrial applications, particularly in the synthesis of polymers like PET. \((TI_{4}Te_{3}Pb)\) is a complex compound with a layered structure that presents unique electronic and thermal properties, making it a subject of interest in materials science, especially in the field of Optics and thermal power. \((TI_{4}Te_{3}Pb)\) typically crystallises in a layered structure, often classified under the tetragonal crystal systems, depending on specific conditions and compositions. This article looks at the relationship between several indices and the Gibbs energy (GE) of a chemical structure. In this work, indices are computed in order to model the structural and electrical characteristics of \((TI_{4}Te_{3}Pb)\) . We have calculated the different degree-based topological indices. We use Excel to create numerical tables, Maple software to compute the topological indices and maple software to create graphics. In MATLAB, curves fitting by Gibbs energy are accomplished through many techniques based on rationality, linearity, nonlinearity and polynomial. However, I have experience fitting curves between indices and Gibbs energy using the rational model.
