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The second self-diffusion and viscosity virial coefficients of the Lennard-Jones (LJ) fluid were calculated by a detailed evaluation of the velocity and shear-stress autocorrelation functions using equilibrium molecular dynamics simulations at low and moderate densities. Accurate calculation of these coefficients requires corresponding transport coefficient values with low degrees of uncertainty. These were obtained via very long simulations by increasing the number of particles and by using the knowledge of correlation functions in the Green-Kubo method in conjunction with their corresponding generalized Einstein relations. The values of the self-diffusion and shear viscosity coefficients have been evaluated for systems with reduced densities between 0.0005 and 0.05 and reduced temperatures from 0.7 to 30.0. This provides a new insight into the transport coefficients beyond what can be offered by the Rainwater-Friend theory, which has not been developed for the self-diffusion coefficient.

Anti-Mackay icosahedral clusters of composition Ag 32 M 13 , where M is either Cu,Ni, or Co, have been recently shown to possess special structural stability both by calculations and experiments. These nanoalloys assume a core-shell arrangement, with an icosahedral core of 13 M atoms surrounded by an Ag shell of anti-Mackay structure. In this paper we study the melting of these three nanoalloys, showing that, despite the close similarity of the structures, melting takes place through quite different mechanisms. In particular, we find that Ag 32 Co 13 and Ag 32 Ni 13 present a premelting phenomenon which involves only the shell of the cluster while the core melts at higher temperatures, in agreement with previous calculations. On the contrary, in Ag 32 Cu 13 , melting occurs through stages that involve the shell and the core at the same time. These findings are rationalized in terms of the different features of the energy landscape of these nanoalloys. Our simulations, in which special care has been devoted to avoid non-ergodicity problems, show also that the particles keep their core-shell structures even in the liquid phase, indicating an incomplete miscibility of Ag with Ni, Co or Cu at the nanoscale up to quite high temperatures.We start off our results on investigation into the melting mechanism of anti-Mackay nanoalloys with presenting caloric curves.Since the total potential energy of the cluster is written, within the Gupta model, by a sum of individual atomic energies, it is possible to associate energies to the core and to the shell separately, by summing atomic energies on core and shell atoms 1-33 | 7