We design a density-functional-theory (DFT) exchange-correlation functional that enables an accurate treatment of systems with electronic surfaces. Surface-specific approximations for both exchange and correlation energies are developed. A subsystem functional approach is then used: an interpolation index combines the surface functional with a functional for interior regions. When the local density approximation is used in the interior, the result is a straightforward functional for use in self-consistent DFT. The functional is validated for two metals (Al, Pt) and one semiconductor (Si) by calculations of (i) established bulk properties (lattice constants and bulk moduli) and (ii) a property where surface effects exist (the vacancy formation energy). Good and coherent results indicate that this functional may serve well as a universal first choice for solid-state systems and that yet improved functionals can be constructed by this approach

Density functional theory (DFT) methods for calculating the quantum mechanical ground states of condensed matter systems are now a common and significant component of materials research. The growing importance of DFT reflects the development of sufficiently accurate functionals, efficient algorithms and continuing improvements in computing capabilities. As the materials problems to which DFT is applied have become large and complex, so have the sets of calculations necessary for investigating a given problem. Highly versatile, powerful codes exist to serve the practitioner, but designing useful simulations is a complicated task, involving intricate manipulation of many variables, with many pitfalls for the unwary and the inexperienced. We discuss several of the most important issues that go into designing a meaningful DFT calculation. We emphasize the necessity of investigating these issues and reporting the critical details.

We show that the AM05 functional ͓Armiento and Mattsson, Phys. Rev. B 72, 085108 ͑2005͔͒ has the same excellent performance for solids as the hybrid density functionals tested in Paier et al. ͓J. Chem. Phys. 124, 154709 ͑2006͒; 125, 249901 ͑2006͔͒. This confirms the original finding that AM05 performs exceptionally well for solids and surfaces. Hartree-Fock hybrid calculations are typically an order of magnitude slower than local or semilocal density functionals such as AM05, which is of a regular semilocal generalized gradient approximation form. The performance of AM05 is on average found to be superior to selecting the best of local density approximation and PBE for each solid. By comparing data from several different electronic-structure codes, we have determined that the numerical errors in this study are equal to or smaller than the corresponding experimental uncertainties.

The uniform electron gas, the traditional starting point for density-based manybody theories of inhomogeneous systems, is inappropriate near electronic edges. In its place we put forward the appropriate concept of the edge electron gas.Since the work of Thomas and Fermi (TF) [1] through the earliest papers on density functional theory (DFT) [2] up to ongoing work involving density gradients [3], the uniform electron gas has been the starting point of density-based approximate theories of inhomogeneous systems. However, real physical systems have electronic edge regions where effective single particle wave functions evolve from oscillatory to evanescent, and where clearly approximations starting from a uniform electron gas are ill-founded.The edge surface S, for a given system, may be precisely defined bywhere v ef f (r) is the exact self-consistent potential of the Kohn-Sham (KS) equations [2] and µ is the chemical potential, half-way between the highest occupied and the lowest unoccupied KS orbital energies (In what follows we take µ = 0). Outside of S all occupied KS orbitals decay exponentially (See Fig. 1). Much interesting science involves precisely such edge regions (See Fig. 1), such as ionization energies of the outermost electrons, molecular binding, surface energies etc. For these regions, in place of the uniform electron gas, we discuss in this paper the new concept of the edge electron gas, which is valid in the edge region near S [4].The edge gas concept is based on the principle of "nearsightedness" put forward in [5]: The local electronic structure near a point r, while strictly speaking requiring a knowledge of the density n(r ′ ), or equivalently of the effective potential v ef f (r ′ ), everywhere, in fact is largely determined by v ef f (r ′ ) for r ′ near r. Nearsightedness applies just as much to the edge region as to the interior region far inside S.This principle has been applied to the density n(r) and to the one particle density matrix [5]. In the present paper we also apply it to the exchange energy E x as follows: We writewhere R −1 x (r), the inverse radius of the exchange hole, is defined byand n x (r; r ′ ) is the exchange hole density which satisfies n x (r; r ′ )dr ′ = −1. FIG. 1. Interior and Edge regions of a bounded system. S is the nominal dividing surface (--).S (---)is the physical dividing surface withl = γl. l is defind in Eq. (6) and 1 < γ < 3.For a consideration of the electronic structure at a point r near S we first drop a perpendicular to the nearest point r e on S, take r e as origin of coordinates and the z-axis through r (See Fig. 1.); thus r = (0, 0, z). Near r e we have, up to first order in (x, y, z),This leads to the concept of the Airy gas (AG), the simplest version of the edge gas (Fig. 2a). The AG is a principal subject of this paper. Of course only the properties of the AG near the edge at z = 0 are of physical interest.FIG. 2. a) The Airy gas: a strictly linear v ef f , with a hard wall at the distant point L. b) The edge gas: a typical v ef f (z) near th...

We have revealed, and resolved, an apparent inability of density functional theory, within the local density and generalized gradient approximations, to describe vacancies in Al accurately and consistently. The shortcoming is due to electron correlation effects near electronic edges and we show how to correct for them. We find that the divacancy in Al is energetically unstable and we show that anharmonic atomic vibrations explain the non-Arrhenius temperature dependence of the vacancy concentration.

We use bosonization methods to calculate the exact finite-temperature single-electron Green's function of a spinful Luttinger liquid confined by open boundaries. The corresponding local spectral density is constructed and analyzed in detail. The interplay between boundary, finite-size, and thermal effects are shown to dramatically influence the low-energy properties of the system. In particular, the well-known zero-temperature critical behavior in the bulk always crosses over to a boundary dominated regime in the vicinity of the Fermi level. Thermal fluctuations cause an enhanced depletion of spectral weight for small energies , with the spectral density scaling as 2 for much less than the temperature. Consequences for photoemission experiments are discussed.

The predictive power of first-principles calculations of vacancy formation energies in metals ͑Pt, Pd, Mo͒ is improved by adding a correction for the intrinsic surface error in current implementations of density functional theory. The derived correction is given as a function of electron density; it can be explicitly applied to a wide range of systems. Density functional theory, contrary to claims in previous work, underestimates the vacancy formation energy when structural relaxation is included. This is the case whether using the local density-or the generalized gradient approximation for the exchange-correlation energy. With corrections for the intrinsic surface error we reach excellent agreement between calculated values using the two exchange-correlation functionals. Our final values for the three vacancy formation energies are 1.16, 1.70, and 2.98 eV for Pt, Pd, and Mo, respectively. The numbers are in good agreement with experimental data. We also calculate the barrier for vacancy diffusion in Pt to 1.43 eV.

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