Showing papers by "Alex Zunger published in 1981"

Self-interaction correction to density-functional approximations for many-electron systems

Abstract: The exact density functional for the ground-state energy is strictly self-interaction-free (i.e., orbitals demonstrably do not self-interact), but many approximations to it, including the local-spin-density (LSD) approximation for exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem. Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD and show that it properly conserves the number content of the exchange-correlation hole, while substantially improving the description of its shape. We apply this method to a number of physical problems, where the uncorrected LSD approach produces systematic errors. We find systematic improvements, qualitative as well as quantitative, from this simple correction. Benefits of SIC in atomic calculations include (i) improved values for the total energy and for the separate exchange and correlation pieces of it, (ii) accurate binding energies of negative ions, which are wrongly unstable in LSD, (iii) more accurate electron densities, (iv) orbital eigenvalues that closely approximate physical removal energies, including relaxation, and (v) correct longrange behavior of the potential and density. It appears that SIC can also remedy the LSD underestimate of the band gaps in insulators (as shown by numerical calculations for the rare-gas solids and CuCl), and the LSD overestimate of the cohesive energies of transition metals. The LSD spin splitting in atomic Ni and $s\ensuremath{-}d$ interconfigurational energies of transition elements are almost unchanged by SIC. We also discuss the admissibility of fractional occupation numbers, and present a parametrization of the electron-gas correlation energy at any density, based on the recent results of Ceperley and Alder.

Density-functional theory of the correlation energy in atoms and ions: A simple analytic model and a challenge

Abstract: A simple and accurate analytic model is derived for the correlation energy of any atom or ion within three densityfunctional approximations based on the uniform electron gas: the local-spin-density approximation (LSD), the selfinteraction corrected (SIC) version of LSD, and the antiparallel-spin LSD of Stoll et al. The last two approximations give good results for the correlation energies of neutral atoms, in contrast to LSD which overestimates these energies by a factor of 2. However, all three approximations show an incorrect $\mathrm{ln}Z$ leading behavior when the nuclear charge $Z$ tends to infinity at fixed electron number $N$. It is hard to see how any a priori electron-gas approximation can reproduce the exact leading behavior, which is constant or linear in $Z$ according to the value of $N$.

Al on GaAs(110) interface: Possibility of adatom cluster formation

Abstract: A reexamination of the experimental data and previous electronic-structure calculations on the prototype Schottky system Al/GaAs(110), together with new calculations, indicates that at low coverages and temperatures neither a covalent bond nor a metallic bond is likely to be formed between Al and the substrate. Instead, the predominant species is likely to be Al clusters which interact only weakly and largely nondirectionally with the substrate. In contrast with all previous theoretical models which assume an epitaxially ordered array of chemisorption bonds even at submonolayer coverage, it then appears that the formation of a Schottky barrier as well as other physical and chemical characteristics of the interface (e.g., core level and exciton shifts, valence-band photoemission spectra, gap states, surface atomic relaxation) are not explainable in terms of strong and ordered chemisorption bonds. This weakly interacting cluster model leads to several interesting predictions regarding the atomic structure and spectroscopy of this metal-semiconductor interface at the initial stages of its formation. The properties of the interface at higher temperatures (i.e., after annealing) are discussed in terms of an Al-Ga exchange reaction.

Quasi bands in Green's-function defect models

Abstract: A basic difficulty in applying the Green s-function formalism to deep defects in solids is discussed. A cure is provided. It is shown that the conventional Green s-function formalism as applied to point-defect problems is derivable by requiring a dual representation of the defect wave functions both in terms of an expression in \"local\" basis functions and, independentIy, in terms of the eigenfunctions of the host-crysta1 Hamiltonian. It is then shown that this dual representation leads to a fundamental limitation of the method. In contrast to what may have been thought, the defect Green's-function (DGF) method does not become increasingly effective as the defect-induced potential perturbation becomes more localized in coordinate space. In fact, a consequence of this dual representation is that for impurities which are chemically mismatched to the host-crystal atoms a computationally intractable and physically undesirable enormous number of host-crystal eigenfunctions (10 —10 ) is needed to obtain even modestly accurate defect wave functions, energies, and chemical trends. A new, formally exact approach (the \"quasi-bandstructure representation\") is presented. This approach overcomes' the'difficulties underlying the dual representation in a simple way. It is based on redefining the zero-order basis set and expanding the defect wave functions in terms of such \"quasi band wave functions\" rather than by pure host wave functions. The former diagonalize the (finite) matrix of the host-crystal Hamiltonian and include aspects of both host and defect orbitals but need not form eigenstates to the host-crystal Hamiltonian operator. We illustrate this exact method for two analytically solvable models: a parabolic defect potential as well as a transition-atom impurity in a silicon free-electron host crystal. A comparison with the results of the conventional DGF calculation is given. Finally, the method is illustrated for a fully self-consistent calculation for substitutional Cu in silicon using nonlocal pseudopotentials.

Initial stage of formation of a metal‐semiconductor interface: Al on GaAs(110)

Abstract: A re‐examination of the experimental data and previous electronic structure calculations on the prototype system Al/GaAs(110), together with new calculations and models, indicates that at low coverages and temperatures neither a covalent bond nor a metallic bond is formed between Al and the substrate. Instead, the predominant species is likely to be Al clusters which interact only weakly with the substrate.

Phenomenology of the Crystal Structures of Transition-Metal-Atom Binary Compounds

Abstract: One of the most successful approaches to the phenomenology of binary AB systems has been the description of various observables S„~''(Z~ Zs) in terms of a function S~~(R,~,R, ) of a. linear dual coordinate system R, = if(Z~ N~) -f(Zs, Ns) i and R,\" =g(Z~, N~) +g(Z~, Ns). Here Z and N are, respectively, the atomic number and the number of all (s, p, d) valence electrons of atom u, and f and g„aresome suitably chosen elementary atomic scales (electronegativity, ionic radii, orbital radii, etc.). Common to all such approaches is the recognition that since S»'\"'(Z„,Z~) mirrors the twodimensional structure of the periodic table, f„ and g should contain variations both in rows and columns of the periodic table. Recently, Machlin and Loh' (ML) have suggested that atom ic number--independent elementary scales f~ =N„nad g~ =N~/2 (i.e., constant within columns) can be used to predict the crystal structures of the 91 inter-transition-metal-atom (TM) binary compounds (i.e. , 16% of the total data base' ). I comment here on an elementary flaw in ML's work. Since in the ML approach A, and A, do not depend on Z„,Zs (viz. core size and structure) but only on the column numbers X„andA~, the model predicts that all n,.~n,. compounds formed between an atom A from column i and an atom B from column j (a maximum of 9 for TM-TM compounds) will have an identical crystal structure. In their plot, ' however, these equivalent n,. n,. points which should correspond to a single (R, ~, R, ~s) value were \"slightly displaced. . . for the sake of cia,rity. '\" It is ea, sy to see that their reported structural separation depends almost entirely on this arbitrary displacement. This is seen in the lower half of Fig. 1 which depicts the observed crystal structure of 95 TM-TM compounds' as a matrix S(N„,Ns). If the ML notion is correct, all crystal structures appearing in any of the 3x 3 squares (constant R, \"s, R, ~s) should be identical. Shading each square for which this condition is not met, one clearly observes that the number of unsuccessful predictions (total shaded a.rea) is overwhelming. This predictive power, approximately equal to a random guess, becomes even worse if only the number of d electrons N \" is used (upper half of Fig. 1), or if compounds between a TM and a simple atom are considered (20% reliability of the modunt 6 7 8 9 10 I~I II I~l A Re FeOs RuCo Ir RhNi Pt PdcuAg Au 0 :.gj:,:Q .0,:Q:..:Q::+:',Q.:Sc :e::~~::::, :::::e::::O::p: Y

Pseudopotential and all‐electron atomic core size scales

Abstract: It has been previously shown by Politzer, Parr, and Boyd that the radius rm at which atomic radial charge densities 4rr2P(r) have their outer minimum constitutes a chemically meaningful quantum mechanical core radius It is shown here that {rm} correlates linearly with the position r(0)nd of the outer node in the l = 0 valence orbital and also with the l = 0 classical crossing point rl = 0 of the recently developed a priori density‐functional atomic pseudopotential The universality of these definitions of the quantum core size is indicated in view of these surprising correlations (AIP)