<p>The thermodynamic and vibrational behavior of nanoparticles is known to exhibit unusual size dependent properties. We present the results of a theoretical model for the cohesive energy, melting temperature and Debye temperature of silver (Ag) and gold (Au) nanoparticles, developed and analyzed using computer simulations in MATLAB, and validated against experimental data and other theoretical predictions. The results indicate that nanoparticles have lower cohesive energies because of the surface atoms that dominate, resulting in lower melting and Debye temperatures with decreasing particle size. The cohesive energy of Ag nanoparticles decreases from ~ 285 kJ/mol in the bulk to ~ 230 kJ/mol at 5 nm, accompanied by a corresponding decrease in the melting temperature from 1235 K to ~ 700 K, Debye temperature from 230 K to ~ 100 K. The cohesive energy of Au nanoparticles lowers from ~ 368 kJ/mol for bulk to ~ 300 kJ/mol for 5 nm, and the melting temperature and Debye temperature drop from 1337 and 415K, respectively, to around ~ 600K and ~ 200K simultaneously. The experimentally observed and theoretically predicted size dependent trends in these properties are consistent with these trends showing that these properties are intertwined by the atomic bonding strength and vibrational dynamics. All three properties are higher for Au due to stronger metallic bonding. These results offer valuable insights for the design and optimization of metallic nanoparticles in therapeutic cargo delivery, as well as for catalysis, thermal management, and advanced material processing.</p>