Sodium atoms and clusters on graphite by density functional theory

Sodium atoms and clusters $(Nl~5)$ on graphite (0001) are studied using density functional theory, pseudopotentials and periodic boundary conditions. A single Na atom is observed to bind at a hollow site 2.45 \AA{} above the surface with an adsorption energy of 0.51 eV. The small diffusion barrier of 0.06 eV indicates a flat potential energy surface. Increased Na coverage results in a weak adsorbate-substrate interaction, which is evident in the larger separation from the surface in the cases of ${\mathrm{Na}}_{3},$ ${\mathrm{Na}}_{4},$ ${\mathrm{Na}}_{5},$ and the $(2\ifmmode\times\else\texttimes\fi{}2)$ Na overlayer. The binding is weak for ${\mathrm{Na}}_{2},$ which has a full valence electron shell. The presence of substrate modifies the structures of ${\mathrm{Na}}_{3},$ ${\mathrm{Na}}_{4},$ and ${\mathrm{Na}}_{5}$ significantly, and both ${\mathrm{Na}}_{4}$ and ${\mathrm{Na}}_{5}$ are distorted from planarity. The calculated formation energies suggest that clustering of atoms is energetically favorable, and that the open shell clusters (e.g., ${\mathrm{Na}}_{3}$ and ${\mathrm{Na}}_{5})$ can be more abundant on graphite than in the gas phase. Analysis of the lateral charge density distributions of Na and ${\mathrm{Na}}_{3}$ shows a charge transfer of $\ensuremath{\sim}0.5$ electrons in both cases.