An embedding scheme for the Dirac equation

An embedding scheme is developed for the Dirac Hamiltonian H. Dividing space into regions I and II separated by surface S, an expression is derived for the expectation value of H which makes explicit reference to a trial function defined in I alone, with all details of region II replaced by an effective potential acting on S and which is related to the Green function of region II. Stationary solutions provide approximations to the eigenstates of H within I. The Green function for the embedded Hamiltonian is equal to the Green function for the entire system in region I. Application of the method is illustrated for the problem of a hydrogen atom in a spherical cavity and an Au(001)/Ag/Au(001) sandwich structure using basis sets that satisfy kinetic balance.Comment: 16 pages, 5 figure

Dynamic image potential at an Al(111) surface

We evaluate the electronic self-energy Sigma(E) at an Al(111) surface using the GW space-time method. This self-energy automatically includes the image potential V-im not present in any local-density approximation for exchange and correlation. We solve the energy-dependent quasiparticle equations and calculate the effective local potential experienced by electrons in the near-surface region. The relative contribution of exchange proves to be very different for states above the Fermi level. The image-plane position for interacting electrons is closer to the surface than for the purely electrostatic effects felt by test charges, and, like its classical counterpart, is drawn inwards by the effects of atomic structure

Core reconstruction in pseudopotential calculations

A new method is presented for obtaining all-electron results from a pseudopotential calculation. This is achieved by carrying out a localised calculation in the region of an atomic nucleus using the embedding potential method of Inglesfield [J.Phys. C {\bf 14}, 3795 (1981)]. In this method the core region is \emph{reconstructed}, and none of the simplifying approximations (such as spherical symmetry of the charge density/potential or frozen core electrons) that previous solutions to this problem have required are made. The embedding method requires an accurate real space Green function, and an analysis of the errors introduced in constructing this from a set of numerical eigenstates is given. Results are presented for an all-electron reconstruction of bulk aluminium, for both the charge density and the density of states.Comment: 14 pages, 5 figure

Accurate structure factors from pseudopotential methods

Highly accurate experimental structure factors of silicon are available in the literature, and these provide the ideal test for any \emph{ab initio} method for the construction of the all-electron charge density. In a recent paper [J. R. Trail and D. M. Bird, Phys. Rev. B {\bf 60}, 7863 (1999)] a method has been developed for obtaining an accurate all-electron charge density from a first principles pseudopotential calculation by reconstructing the core region of an atom of choice. Here this method is applied to bulk silicon, and structure factors are derived and compared with experimental and Full-potential Linear Augmented Plane Wave results (FLAPW). We also compare with the result of assuming the core region is spherically symmetric, and with the result of constructing a charge density from the pseudo-valence density + frozen core electrons. Neither of these approximations provide accurate charge densities. The aspherical reconstruction is found to be as accurate as FLAPW results, and reproduces the residual error between the FLAPW and experimental results.Comment: 6 Pages, 3 figure

Resonant Lifetime of Core-Excited Organic Adsorbates from First Principles

We investigate by first-principles simulations the resonant electron-transfer lifetime from the excited state of an organic adsorbate to a semiconductor surface, namely isonicotinic acid on rutile TiO$_2$(110). The molecule-substrate interaction is described using density functional theory, while the effect of a truly semi-infinite substrate is taken into account by Green's function techniques. Excitonic effects due to the presence of core-excited atoms in the molecule are shown to be instrumental to understand the electron-transfer times measured using the so-called core-hole-clock technique. In particular, for the isonicotinic acid on TiO$_2$(110), we find that the charge injection from the LUMO is quenched since this state lies within the substrate band gap. We compute the resonant charge-transfer times from LUMO+1 and LUMO+2, and systematically investigate the dependence of the elastic lifetimes of these states on the alignment among adsorbate and substrate states.Comment: 24 pages, 6 figures, to appear in Journal of Physical Chemistry

Theory of inelastic lifetimes of surface-state electrons and holes at metal surfaces

After the early suggestion by John Pendry to probe unoccupied bands at surfaces through the time reversal of the photoemission process, the inverse-photoemission technique yielded the first conclusive experimental evidence for the existence of image-potential bound states at metal surfaces and has led over the last two decades to an active area of research in condensed-matter and surface physics. Here we describe the current status of the many-body theory of inelastic lifetimes of these image-potential states and also the Shockley surface states that exist near the Fermi level in the projected bulk band gap of simple and noble metals. New calculations of the self-energy and lifetime of surface states on Au surfaces are presented as well, by using the $GW\Gamma$ approximation of many-body theory.Comment: 17 pages, 7 figures, to appear in J Phys-Condens Ma