Application of the fourth-moment approximation to the local density of states within a tight binding description to build a reactive, interatomic interaction potential for use in large scale molecular simulations, was a logical and significant step forward to improve the second moment approximation, standing at the basis of several, widely used (semi-)empirical interatomic interaction models. A detailed description of the fourth-moment approximation and its technical implications were presented, containing the essential elements for efficient implementation in a simulation code. Using a recent, existing fourth-moment approximation-based model for C-Ni systems, the size dependence of the diffusion of a liquid Ni cluster on a graphene sheet was investigated and a power law dependence of the diffusion constant on the cluster size (number of cluster atoms) was found, with an exponent which very close to -2/3; equal to the previously found exponent for the relatively fast diffusion of solid clusters on a substrate with incommensurate lattice matching. The cluster diffusion exponent gave rise to a specific contribution to the cluster growth law, which was due to cluster coalescence. This was confirmed by a simulation for Ni cluster growth on graphene, which showed that cluster coalescence dominates the initial stage of growth, overruling Oswald ripening.

Tight Binding Within the Fourth Moment Approximation: Efficient Implementation and Application to Liquid Ni Droplet Diffusion on Graphene. Los, J.H., Bichara, C., Pellenq, R.J.M.: Physical Review B, 2011, 84[8], 085455