Tight binding within the fourth moment approximation: Efficient implementation and application to liquid Ni droplet diffusion on graphene

Application of the fourth moment approximation (FMA) 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, is 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. In this paper we present a sufficiently detailed description of the FMA and its technical implications, containing the essential elements for an efficient implementation in a simulation code. Using a recent, existing FMA-based model for C-Ni systems, we investigated the size dependence of the diffusion of a liquid Ni cluster on a graphene sheet and find a power law dependence of the diffusion constant on the cluster size (number of cluster atoms) with an exponent very close to −2/3, equal to a previously found exponent for the relatively fast diffusion of solid clusters on a substrate with incommensurate lattice matching. The cluster diffusion exponent gives rise to a specific contribution to the cluster growth law, which is due to cluster coalescence. This is confirmed by a simulation for Ni cluster growth on graphene, which shows that cluster coalescence dominates the initial stage of growth, overruling Oswald ripening.