Sodium gold structure in which sodium (Na) undergoes bonding with gold (Au), due to many special features in material science and nanotechnology. Disodium gold structure \((Na_{2}Au)\) can catalyze the chemical reaction, particularly in organic syntheses. The fabrication of gold nanoparticles is concerned with electronics and sensor applications. It is still being researched because of its electrical conductivity properties in energy storage systems. In this paper, we calculate the complex relation between a network of topological indices and the Gibbi’s energy. Using a curve-fitting model, we predict and interpret the Gibbi’s energy, a key thermodynamic parameter dictating stability and reactivity for disodium gold structure, taking into consideration several topological indices. Curves fitted in MATLAB were based on rationality, linearity, and non-linearity using several methods. Using a systematic correlation, we find patterns and relationships between the Gibbs energy and topological descriptors such as the fourth and fifth Zagreb index, Randic, and the atom bond connectivity. In particular, Gibbs energy shows nonlinear dependencies on a number of topological indices, pointing to the complexity of the molecular interactions in disodium gold networks. These findings have enhanced not only the theoretical understanding of topological indices but also provided tools of practical use in predicting thermodynamic behaviors of molecular systems.
