Interlayer surface relaxations and energies of fcc metal surfaces by a tight-binding method

The authors examine the interlayer surface relaxations and surface energies for the low-index faces of fcc $\mathrm{Ni}$, $\mathrm{Pd}$, $\mathrm{Rh}$, $\mathrm{Pt}$, $\mathrm{Au}$, and $\mathrm{Ir}$ using the Naval Research Laboratory (NRL) tight-binding (TB) method. We compare the TB calculations, utilizing self-consistent charge transfer, with experimental measurements, density functional theory (DFT) calculations, and semiempirical methods. We find that for these metals the NRL-TB method largely reproduces the trends with respect to the exposed face and periodic table position obtained in DFT calculations and experimental measurements. We find that the inclusion of self-consistency in the TB surface calculations is essential for obtaining this agreement, as the TB calculations without it predict large first interlayer expansions for many of these surfaces. We also examine the energetics and relaxations of the $2\ifmmode\times\else\texttimes\fi{}1$ (011) missing row reconstruction for these metals. The TB method predicts that, in agreement with experiment, $\mathrm{Au}$ and $\mathrm{Pt}$ undergo this reconstruction, while $\mathrm{Ni}$, $\mathrm{Pd}$, and $\mathrm{Rh}$ do not, but predicts the $\mathrm{Ir}$ ground state structure to be unreconstructed $1\ifmmode\times\else\texttimes\fi{}1$, opposite to experiment. The interatomic relaxations of the (011) missing row structure for $\mathrm{Pt}$, $\mathrm{Au}$, and $\mathrm{Ir}$ are in good agreement with DFT calculations and experiment. Finally, we analyze the bonding characteristics of these metals using a decomposition of the TB total energy over neighboring atoms and angular momentum character.