We report self-consistent ab initio calculations of structural and electronic properties for the B-and Mg-terminated MgB2 (0001) surfaces. We employ ultra-soft pseudopotentials and plane wave basis sets within the generalized gradient approximation. The surface relaxations are found to be small for both B-and Mg-terminated surfaces. For the B-terminated surface, both B σ and π surface bands appear, while only one B π surface band exists near the Fermi level for the Mgterminated surface. The superconductivity of the MgB2 surfaces is discussed. The work function is predicted to be 5.95 and 4.25 eV for the B-and Mg-terminated surfaces respectively. The simulated scanning tunneling microscopy images of the surfaces are not sensitive to the sign and value of the bias voltages, but depend strongly on the tip-sample distance. An image reversal is predicted for the Mg-terminated surface.The surprising discovery [1] of superconductivity at 39K in MgB 2 has attracted great scientific interest. The isotope effect experiments [2,3] indicate that MgB 2 may be a BCS phonon-mediated superconductor, with Tc above the commonly accepted limits for phononassisted superconductivity. Band structure calculations [4,5] show that the Mg donates substantially its 3s electrons to the B layer, and that the Fermi surface is derived mainly from B orbitals with two-dimensional character. The superconductivity is believed to be due to the strong coupling of the holes of the B σ bands to the in-plane B phonon lattice vibrations (E 2g modes) [4].Being a simple, low-cost and high-performance binary intermetallic compound, MgB 2 is a very promising candidate for superconducting device as well as large-scale applications. Experimentally, scanning tunneling spectroscopy measurements of the surface of superconducting MgB 2 have been reported [6,7], and the high-quality caxis-oriented epitaxial MgB 2 thin films have been grown successfully on Al 2 O 3 substrates by using a pulsed laser deposition technique [8]. However, there has not been a theoretical study for the MgB 2 surfaces so far. In this Letter, we report a first-principles study of MgB 2 (0001) surfaces. Both B-and Mg-terminated surfaces are investigated. We show that while the relaxations of the * Corresponding author. E-mail: jlyang@ustc.edu.cn surface layers are small for both surfaces, their electronic structures are quite different.Our calculations were carried out within the generalized gradient approximation (GGA) [9] using ultrasoft pseudopotentials and plane wave basis sets [10,11]. A 1 × 1 × 15 supercell geometry was used to model the surfaces in which there are 15 atomic layers and 15 layers of vacuum (hereafter, 15-layer slab model) . The plane wave cutoff is 257.2 eV for structural optimizations and 321.5 eV for static electronic structure calculations. Brillouin zone integrations were performed on a grid of 13 × 13 × 1 Monkhorst-Pack [12] special points. During the structural optimizations, we fixed the central 3 atomic layers in the bulk configuration and allowed all other at...