The coalescence process of two nanoparticles to yield a core-shell structure is analyzed by a well-tempered metadynamics procedure. This methodology has been shown to be useful in understanding the present phenomenon in terms of two collective variables: the distance between the center of mass of the coalescing particles and the gyration radius of the resulting core element. The free-energy contour plots clearly show that the coalescence process involves the deformation of the core material, which is manifested in the residence of the system in regions with a larger gyration radius. Results from molecular dynamics for the same system were found helpful to reach the definition of this second collective variable. The advantages and limitations of the latter approach are discussed.