&60; p&62; Abstract&60;/p&62; &60; p&62; We report on the calculations of the cohesive energy, melting temperature and vacancy formation energy for Au nanocrystals with different size supported on and embedded in SiO&60; sub&62; 2&60;/sub&62;. The calculations are performed crossing our previous data on the surface free energy of the supported and embedded nanocrystals with the theoretical surface-area-difference model developed by WH Qi for the description of the size-dependent thermodynamics properties of low-dimensional solid-state systems. Such calculations are employed as a function of the nanocrystals size and surface energy. For nanocrystals supported on SiO&60; sub&62; 2&60;/sub&62;, as results of the calculations, we obtain, for a fixed nanocrystal size, an almost constant cohesive energy, melting temperature and vacancy formation energy as …