Atomic and electronic structure of ${\mathrm{MoS}}_2$ nanoparticles

Using density-functional theory (DFT) we present a detailed theoretical study of ${\mathrm{MoS}}_2$ nanoparticles. We focus on the edge structures, and a number of different edge terminations are investigated. Several, but not all, of these configurations have one-dimensional metallic states localized at the edges. The electronic structure of the edge states is studied and we discuss their influence on the chemical properties of the edges. In particular, we study the reactivity towards hydrogen and show that hydrogen may form stable chemical bonds with both the two low-Miller indexed edges of ${\mathrm{MoS}}_2.$ A model for calculating Gibbs free energy of the edges in terms of the DFT energies is also presented. This model allows us to determine the stable edge structure in thermodynamic equilibrium under different conditions. We find that both the insulating and metallic edges may be stable depending on the temperature and the composition of the gas phase. Using the Tersoff-Hamann formalism, scanning-tunneling microscopy (STM) images of the edges are simulated for direct comparison with recent STM experiments. In this way we identify the experimentally observed edge structure.