In this article we discuss the Slater-Koster (SK) tight-binding (TB) method from the perspective of our own developments and applications to this method. We first present an account of our work in constructing TB Hamiltonians and applying them to a variety of calculations which require an accurate representation of the electronic energy bands and density of states. In the second part of the article we present the Naval Research Laboratory TB method, wherein we demonstrate that this elaborate scheme can accurately account for both the band structure and total energy of a given system. The SK parameters generated by this method are transferable to other structures and provide the means for performing computationally demanding calculations of fairly large systems. These calculations, including molecular dynamics, are of comparable accuracy to first-principles calculations and three orders of magnitude faster. Contents 1. Introduction 414 2. Formalism of the tight-binding method 415 3. Fitting of band structures 417 3.1. Single-element materials 418 3.2. Binary compounds 419 3.3. Ternary compounds 420 3.4. High-temperature superconductors 421 4. The NRL tight-binding method 422 4.1. The tight-binding parameters-elemental systems 423 4.2. The tight-binding parameters-multi-component systems 425 5. Equation of state 426 6. Elastic constants 427 7. Phonon frequencies 428 8. Vacancies 430

The authors examine the interlayer surface relaxations and surface energies for the low-index faces of fcc Ni, Pd, Rh, Pt, Au, and 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 ϫ 1 (011) missing row reconstruction for these metals. The TB method predicts that, in agreement with experiment, Au and Pt undergo this reconstruction, while Ni, Pd, and Rh do not, but predicts the Ir ground state structure to be unreconstructed 1 ϫ 1, opposite to experiment. The interatomic relaxations of the (011) missing row structure for Pt, Au, and 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.

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