Estudo Geralhttps://estudogeral.sib.uc.ptThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 03 Aug 2020 21:29:35 GMT2020-08-03T21:29:35Z50211Self-compression of metallic clusters under surface tensionhttp://hdl.handle.net/10316/41590Title: Self-compression of metallic clusters under surface tension
Authors: Perdew, John P.; Brajczewska, Marta; Fiolhais, Carlos
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/10316/415901993-01-01T00:00:00ZCompression of metallic clusters in the stabilized jellium modelhttp://hdl.handle.net/10316/41572Title: Compression of metallic clusters in the stabilized jellium model
Authors: Brajczewska, Marta; Fiolhais, Carlos; Vieira, Armando; Perdew, John P.
Sat, 01 Jan 1994 00:00:00 GMThttp://hdl.handle.net/10316/415721994-01-01T00:00:00ZSelf-expansion and compression of charged clusters of stabilized jelliumhttp://hdl.handle.net/10316/12366Title: Self-expansion and compression of charged clusters of stabilized jellium
Authors: Vieira, Armando; Fiolhais, Carlos; Brajczewska, Marta; Perdew, John P.
Abstract: In a positively charged metallic cluster, surface tension tends to enhance the ionic density with respect to its bulk value, while surface-charge repulsion tends to reduce it. Using the stabilized jellium model, we examine the self-expansion and compression of positively charged clusters of simply metals. Quantal results from the Kohn-Sham equations using the local density approximation are compared with continuous results from the liquid drop model. The positive background is constrained to a spherical shape. Numerical results for the equilibrium radius and the elastic stiffness are presented for singly and doubly positively charged aluminum, sodium, and cesium clusters of 1-20 atoms. Self-expansion occurs for small charged clusters of sodium and cesium, but not of aluminum. The effect of the expansion or compression on the ionization energies is analyzed. For Al6, we also consider net charges greater than 2+. The results of the stabilized jellium model for self-compression are compared with those of other models, including the SAPS (spherical averaged pseudopotential model)
Mon, 01 Jan 1996 00:00:00 GMThttp://hdl.handle.net/10316/123661996-01-01T00:00:00ZEnergetics of small clusters of stabilized jellium : continuum and shell-structure effectshttp://hdl.handle.net/10316/41772Title: Energetics of small clusters of stabilized jellium : continuum and shell-structure effects
Authors: Brajczewska, Marta; Fiolhais, Carlos; Perdew, John P.
Fri, 01 Jan 1993 00:00:00 GMThttp://hdl.handle.net/10316/417721993-01-01T00:00:00ZNonempirical density functionals investigated for jellium: Spin polarized surfaces, spherical clusters, and bulk linear responsehttp://hdl.handle.net/10316/12356Title: Nonempirical density functionals investigated for jellium: Spin polarized surfaces, spherical clusters, and bulk linear response
Authors: Tao, Jianmin; Perdew, John P.; Almeida, Luís Miguel; Fiolhais, Carlos; Kümmel, Stephan
Abstract: Jellium, a simple model of metals, is a standard testing ground for density functionals both for bulk and for surface properties. Earlier tests show that the Tao–Perdew–Staroverov–Scuseria (TPSS) nonempirical metageneralized gradient approximation (meta-GGA) for the exchange-correlation energy yields more accurate surface energies than the local spin density (LSD) approximation for spin-unpolarized jellium. In this study, work functions and surface energies of a jellium metal in the presence of “internal” and external magnetic fields are calculated with LSD, Perdew–Burke–Ernzerhof (PBE) GGA, and TPSS meta-GGA and its predecessor, the nearly nonempirical Perdew–Kurth–Zupan–Blaha meta-GGA, using self-consistent LSD orbitals and densities. The results show that (i) For normal bulk densities, the surface correlation energy is the same in TPSS as in PBE, as it should be since TPSS strives to represent a self-correlation correction to PBE; (ii) Normal surface density profiles can be scaled uniformly to the low-density or strong-interaction limit, and TPSS provides an estimate for that limit that is consistent with (but probably more accurate than) other estimates; (iii) For both normal and low densities, TPSS provides the same description of surface magnetism as PBE, suggesting that these approximations may be generally equivalent for magnetism. The energies of jellium spheres with up to 106 electrons are calculated using density functionals and compared to those obtained with diffusion quantum Monte Carlo data, including our estimate for the fixed-node correction. Typically, while PBE energies are too low for spheres with more than about two electrons, LSD and TPSS are accurate there. We confirm that curvature energies are lower in PBE and TPSS than in LSD. Finally, we calculate the linear response of bulk jellium using these density functionals and find that not only LSD but also PBE GGA and TPSS meta-GGA yield a linear response in good agreement with that of the quantum Monte Carlo method, for wave vectors of the perturbing external potential up to twice the Fermi wave vector
Thu, 05 Jun 2008 00:00:00 GMThttp://hdl.handle.net/10316/123562008-06-05T00:00:00ZReply to “Comment on ‘Energy and pressure versus volume: Equations of state motivated by the stabilized jellium model”http://hdl.handle.net/10316/40616Title: Reply to “Comment on ‘Energy and pressure versus volume: Equations of state motivated by the stabilized jellium model”
Authors: Alchagirov, Alim B.; Perdew, John P.; Boetteger, Jonathan C.; Albers, R. C.; Fiolhais, Carlos
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10316/406162003-01-01T00:00:00ZTests of a density-based local pseudopotential for sixteen simple metalshttp://hdl.handle.net/10316/12363Title: Tests of a density-based local pseudopotential for sixteen simple metals
Authors: Pollack, L.; Perdew, John P.; He, Jingsong; Marques, M.; Nogueira, Fernando; Fiolhais, Carlos
Abstract: A comprehensive study of the lattice dynamics, elastic moduli, and liquid metal resistivities for 16 simple metals in the bcc and fcc crystal structures is made using a density-based local pseudopotential. The phonon frequencies exhibit excellent agreement with both experiment and nonlocal pseudopotential theory. The bulk modulus is evaluated by the long wave and homogeneous deformation methods, which agree after a correction is applied to the former. Calculated bulk and Voigt shear moduli are insensitive to crystal structure, and long-wavelength soft modes are found in certain cases. Resistivity calculations confirm that electrons scatter off the whole Kohn-Sham potential, including its exchange-correlation part as well as its Hartree part. All of these results are found in second-order pseudopotential perturbation theory. However, the effect of a nonperturbative treatment on the calculated lattice constant is not negligible, showing that higher-order contributions have been subsumed into the pseudopotential by construction. For bcc sodium, the band structures of local and nonlocal pseudopotentials are found to be almost identical
Wed, 01 Jan 1997 00:00:00 GMThttp://hdl.handle.net/10316/123631997-01-01T00:00:00ZDensity-functional versus wave-function methods: Toward a benchmark for the jellium surface energyhttp://hdl.handle.net/10316/12367Title: Density-functional versus wave-function methods: Toward a benchmark for the jellium surface energy
Authors: Yan, Zidan; Perdew, John P.; Kurth, Stefan; Fiolhais, Carlos; Almeida, Luís
Abstract: For the surface energy of jellium at alkali-metal densities, the local-density approximation (LDA) and more advanced density-functional methods disagree strongly with the wave-function-based Fermi hypernetted-chain and diffusion Monte Carlo methods. We present a wave-vector interpolation correction to the generalized gradient approximation which gives jellium surface energies consistent with two other estimates based on advanced density functionals. LDA makes compensating errors at intermediate and small wave vectors. Studies of small jellium clusters also support the density-functional estimate for the jellium surface energy
Sat, 15 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10316/123672000-01-15T00:00:00ZEnergy and pressure versus volume: Equations of state motivated by the stabilized jellium modelhttp://hdl.handle.net/10316/12337Title: Energy and pressure versus volume: Equations of state motivated by the stabilized jellium model
Authors: Alchagirov, Alim B.; Perdew, John P.; Boettger, Jonathan C.; Albers, R. C.; Fiolhais, Carlos
Abstract: Explicit functions are widely used to interpolate, extrapolate, and differentiate theoretical or experimental data on the equation of state (EOS) of a solid. We present two EOS functions which are theoretically motivated. The simplest realistic model for a simple metal, the stabilized jellium (SJ) or structureless pseudopotential model, is the paradigm for our SJEOS. A simple metal with exponentially overlapped ion cores is the paradigm for an augmented version (ASJEOS) of the SJEOS. For the three solids tested (Al, Li, Mo), the ASJEOS matches all-electron calculations better than prior equations of state. Like most of the prior EOS’s, the ASJEOS predicts pressure P as a function of compressed volume v from only a few equilibrium inputs: the volume v0, the bulk modulus B0, and its pressure derivative B1. Under expansion, the cohesive energy serves as another input. A further advantage of the new equation of state is that these equilibrium properties other than v0 may be found by linear fitting methods. The SJEOS can be used to correct B0 and the EOS found from an approximate density functional, if the corresponding error in v0 is known. We also (a) estimate the typically small contribution of phonon zero-point vibration to the EOS, (b) find that the physical hardness Bv does not maximize at equilibrium, and (c) show that the “ideal metal” of Shore and Rose is the zero-valence limit of stabilized jellium
Mon, 01 Jan 2001 00:00:00 GMThttp://hdl.handle.net/10316/123372001-01-01T00:00:00ZIonization energy and electron affinity of a metal cluster in the stabilized jellium model: Size effect and charging limithttp://hdl.handle.net/10316/12365Title: Ionization energy and electron affinity of a metal cluster in the stabilized jellium model: Size effect and charging limit
Authors: Seidl, Michael F; Perdew, John P.; Brajczewska, Marta; Fiolhais, Carlos
Abstract: We report the first reliable theoretical calculation of the quantum size correction c which yields the asymptotic ionization energy I(R) = W + ((1/2) + c)/R + O(R–2) of a simple-metal cluster of radius R. Restricted-variational electronic density profiles are used to evaluate two sets of expressions for the bulk work function W and quantum size correction c: the Koopmans expressions, and the more accurate and profile-insensitive Delta SCF expressions. We find c [approximate] –0.08 for stabilized (as for ordinary) jellium, and thus for real simple metals. We present parameters from which the density profiles may be reconstructed for a wide range of cluster sizes, including the planar surface. We also discuss how many excess electrons can be bound by a neutral cluster of given size. Within a continuum picture, the criterion for total-energy stability of a negatively charged cluster is less stringent than that for existence of a self-consistent solution
Fri, 15 May 1998 00:00:00 GMThttp://hdl.handle.net/10316/123651998-05-15T00:00:00ZMetal-cluster ionization energy: A profile-insensitive exact expression for the size effecthttp://hdl.handle.net/10316/12352Title: Metal-cluster ionization energy: A profile-insensitive exact expression for the size effect
Authors: Seidl, Michael F; Perdew, John P.; Brajczewska, Marta; Fiolhais, Carlos
Abstract: The ionization energy of a large spherical metal cluster of radius R is I(R)=W+(+c)/R, where W is the bulk work function and c≈-0.1 is a material-dependent quantum correction to the electrostatic size effect. We present 'Koopmans' and 'displaced-profile change-in-self-consistent-field' expressions for W and c within the ordinary and stabilized-jellium models. These expressions are shown to be exact and equivalent when the exact density profile of a large neutral cluster is employed; these equivalences generalize the Budd-Vannimenus theorem. With an approximate profile obtained from a restricted variational calculation, the 'displaced-profile' expressions are the more accurate ones. This profile insensitivity is important, because it is not practical to extract c from solutions of the Kohn-Sham equations for small metal clusters
Thu, 15 May 1997 00:00:00 GMThttp://hdl.handle.net/10316/123521997-05-15T00:00:00ZFormation energies of metallic voids, edges, and steps: Generalized liquid-drop modelhttp://hdl.handle.net/10316/12331Title: Formation energies of metallic voids, edges, and steps: Generalized liquid-drop model
Authors: Perdew, John P.; Ziesche, Paul; Fiolhais, Carlos
Abstract: The void formation energy is the work needed to create the curved surface of a void. For a spherical hole in a homogeneous metal (jellium or stabilized jellium), the void formation energy is calculated for large radii from the liquid-drop model (surface plus curvature terms), and for small radii from perturbation theory. A Padé approximation is proposed to link these limits. For radii greater than or equal to that of a single atom or monovacancy, the liquid-drop model is found to be usefully accurate. Moreover, the predicted monovacancy formation energies for stabilized jellium agree reasonably well with those measured for simple metals. These results suggest a generalized liquid-drop model of possible high accuracy and explanatory value for the energetics of stable metal surfaces curved on the atomic scale (crystal faces, edges, corners, etc.). The bending energy per unit length for an edge at angle θ is estimated to be γ(π-θ)/4, where γ is the intrinsic curvature energy. The step energy is estimated as (n-2+π/2)σd, where σ is the intrinsic surface energy, n≥1 is the number of atomic layers at the step, and d is the layer height
Tue, 15 Jun 1993 00:00:00 GMThttp://hdl.handle.net/10316/123311993-06-15T00:00:00ZEnergies of curved metallic surfaces from the stabilized-jellium modelhttp://hdl.handle.net/10316/12339Title: Energies of curved metallic surfaces from the stabilized-jellium model
Authors: Fiolhais, Carlos; Perdew, John P.
Abstract: In the liquid-drop model, the total energy of a system is expanded as a sum of volume, surface, and curvature terms. We derive an expression for the curvature energy of a metal in terms of the electron-density profile for a planar surface, and show that the resulting values agree with the fits of calculated or measured total energies to the liquid-drop expansion. In particular, this expansion accurately describes the formation energies of microscopic voids (including monovacancies) in metals. In our calculations, the curvature energy is determined by the bulk density. It is nearly the same for restricted trial density profiles as for self-consistent Kohn-Sham profiles, for the fourth-order gradient expansion as for the exact kinetic energy, and for jellium as for stabilized jellium. We also report Kohn-Sham results for the surface energy and work function. The stabilized-jellium model, while retaining the simplicity and nonempirical character of jellium, gives a significantly more realistic description of the simple metals, especially those with high bulk densities
Sun, 15 Mar 1992 00:00:00 GMThttp://hdl.handle.net/10316/123391992-03-15T00:00:00ZDominant density parameters and local pseudopotentials for simple metalshttp://hdl.handle.net/10316/12330Title: Dominant density parameters and local pseudopotentials for simple metals
Authors: Fiolhais, Carlos; Perdew, John P.; Armster, Sean Q.; MacLaren, James M.; Brajczewska, Marta
Abstract: The properties of the simple metals are controlled largely by three density parameters: the equilibrium average valence electron density 3/4πrs3, the valence z, and the density on the surface of the Wigner-Seitz cell, represented here by the equilibrium number Nint of valence electrons in the interstitial region. To demonstrate this fact, and as a refinement of the ‘‘stabilized jellium’’ or ‘‘structureless pseudopotential’’ model, we propose a structured local electron-ion pseudopotential w(r) which depends upon either rs and z (‘‘universal’’ choice for Nint), or rs, z, and Nint for each metal (‘‘individual’’ potential). Calculated binding energies, bulk moduli, and pressure derivatives of bulk moduli, evaluated in second-order perturbation theory, are in good agreement with experiment for 16 simple metals, and the bulk moduli are somewhat better than those calculated from first-principles nonlocal norm-conserving pseudopotentials. Structural energy differences agree with those from a nonlocal pseudopotential calculation for Na, Mg, and Al, but not for Ca and Sr. Our local pseudopotential w(r) is analytic for all r, and displays an exponential decay of the core repulsion as r→∞. The decay length agrees with that of the highest atomic core orbital of s or p symmetry, corroborating the physical picture behind this ‘‘evanescent core’’ form. The Fourier transform or form factor w(Q) is also analytic, and decays rapidly as Q→∞; its first and only zero Q0 is close to conventional or empirical values. In comparison with nonlocal pseudopotentials, local ones have the advantages of computational simplicity, physical transparency, and suitability for tests of density functional approximations against more-exact many-body methods
Sun, 01 Jan 1995 00:00:00 GMThttp://hdl.handle.net/10316/123301995-01-01T00:00:00ZTrends in the properties and structures of the simple metals from a universal local pseudopotentialhttp://hdl.handle.net/10316/12360Title: Trends in the properties and structures of the simple metals from a universal local pseudopotential
Authors: Nogueira, Fernando; Fiolhais, Carlos; Perdew, John P.
Abstract: The properties of simple metals are fixed primarily by the equilibrium average valence-electron density parameter rs, and secondarily by the valence z. The simplest level of theory that can account quantitatively for these trends invokes a “universal” local electron-ion pseudopotential, defined for each pair (rs,z) and treated as a second-order perturbation. We construct this pseudopotential from two conditions: (1) The total energy should minimize at the equilibrium Wigner-Seitz radius z1/3rs. (2) The bulk modulus should equal the realistic rs-dependent prediction of the stabilized jellium model with effective valence z*=1. These conditions can be satisfied by an analytic local pseudopotential depending upon two parameters other than z; we show that the choice of the two-parameter form (evanescent core vs Heine-Abarenkov) is not important. Our universal local pseudopotential is applied to calculate realistic bulk binding energies, pressure derivatives of bulk moduli, Voigt shear moduli, and interstitial electron numbers, revealing their trends as functions of rs and z. Equilibrium crystal structures are mapped in the rs-z plane, where the Hume-Rothery rules for substitutional alloys are manifest. The effect of pressure on crystal structure is also examined
Fri, 15 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10316/123601999-01-15T00:00:00ZSpherical voids in the stabilized jellium model: Rigorous theorems and Padé representation of the void-formation energyhttp://hdl.handle.net/10316/12333Title: Spherical voids in the stabilized jellium model: Rigorous theorems and Padé representation of the void-formation energy
Authors: Ziesche, Paul; Perdew, John P.; Fiolhais, Carlos
Abstract: We consider the energy needed to form a spherical hole or void in a simple metal, modeled as ordinary jellium or stabilized jellium. (Only the latter model correctly predicts positive formation energies for voids in high-density metals.) First we present two Hellmann-Feynman theorems for the void-formation energy 4πR2σRv(n¯) as a function of the void radius R and the positive-background density n¯, which may be used to check the self-consistency of numerical calculations. They are special cases of more-general relationships for partially emptied or partially stabilized voids. The difference between these two theorems has an analog for spherical clusters. Next we link the small-R expansion of the void surface energy (from perturbation theory) with the large-R expansion (from the liquid drop model) by means of a Padé approximant without adjustable parameters. For a range of sizes (including the monovacancy and its ‘‘antiparticle,’’ the atom), we compare void formation energies and cohesive energies calculated by the liquid drop expansion (sum of volume, surface, and curvature energy terms), by the Padé form, and by self-consistent Kohn-Sham calculations within the local-density approximation, against experimental values. Thus we confirm that the domain of validity of the liquid drop model extends down almost to the atomic scale of sizes. From the Padé formula, we estimate the next term of the liquid drop expansion beyond the curvature energy term. The Padé form suggests a ‘‘generalized liquid drop model,’’ which we use to estimate the edge and step-formation energies on an Al (111) surface
Tue, 15 Mar 1994 00:00:00 GMThttp://hdl.handle.net/10316/123331994-03-15T00:00:00ZStructural phase transitions in Na, Mg and Al crystals: dominant role of the valence in local pseudopotential theoryhttp://hdl.handle.net/10316/4533Title: Structural phase transitions in Na, Mg and Al crystals: dominant role of the valence in local pseudopotential theory
Authors: Perdew, John P.; Nogueira, Fernando; Fiolhais, Carlos
Abstract: Within a perturbative treatment of realistic local electron-ion pseudopotentials for the simple metals, we study structural phase transitions under pressure in Na and other monovalent metals, Mg and other divalent metals, and Al and other trivalent metals. For the "good local pseudopotential" metals Na, Mg, and Al, our results are in reasonable agreement with experiment. The sequence of predicted transitions between crystal structures, and the volume compression ratios V/V0 at which these transitions are predicted, are determined largely by the valence z. The valence z also determines the dependence of the total energy upon the tetragonal c/a ratio along the Bain path from bcc to fcc. This path shows the divalent metals unstable in both fcc and bcc structures, and the trivalent metals unstable in bcc.
Sat, 01 Jan 2000 00:00:00 GMThttp://hdl.handle.net/10316/45332000-01-01T00:00:00ZTransferability of a local pseudopotential based on solid-state electron densityhttp://hdl.handle.net/10316/12358Title: Transferability of a local pseudopotential based on solid-state electron density
Authors: Nogueira, Fernando; Fiolhais, Carlos; He, Jingsong; Perdew, John P.; Rubio, Angel
Abstract: Local electron - ion pseudopotentials fitted to dominant density parameters of the solid state (valence, equilibrium average electron density and interstitial electron density) have been constructed and tested for sixteen simple metals. Calculated solid-state properties present little evidence of the need for pseudopotential non-locality, but this need is increasingly evident as the pseudopotentials are transferred further from their solid-state origins. Transferability is high for Na, useful for ten other simple metals (K, Rb, Cs, Mg, Al, Ga, In, Tl, Sn, and Pb), and poor for Li, Be, Ca, Sr and Ba. In the bulk solid, we define a predictor of transferability and check the convergence of second-order pseudopotential perturbation theory for bcc Na. For six-atom octahedral clusters, we find that the pseudopotential correctly predicts self-compressions or self-expansions of bond length with respect to the bulk for Li, Na, Mg, and Al, in comparison with all-electron results; dimers of these elements are also considered. For the free atom, we examine the bulk cohesive energy (which straddles the atomic and solid-state limits), the atomic excitation energies and the atomic density. For the cohesive energy, we also present the results of the simpler stabilized jellium and universal-binding-energy-curve models. The needed non-locality or angular-momentum dependence of the pseudopotential has the conventional character, and is most strongly evident in the excitation energies
Mon, 01 Jan 1996 00:00:00 GMThttp://hdl.handle.net/10316/123581996-01-01T00:00:00ZA new pseudopotential for simple metalshttp://hdl.handle.net/10316/41557Title: A new pseudopotential for simple metals
Authors: Fiolhais, Carlos; Brajcewska, Marta; Fiolhais, Manuel; Perdew, John P.; Armster, S. Q.
Sat, 01 Jan 1994 00:00:00 GMThttp://hdl.handle.net/10316/415571994-01-01T00:00:00ZSurface and curvature energies from jellium spheres: Density functional hierarchy and quantum Monte Carlohttp://hdl.handle.net/10316/12342Title: Surface and curvature energies from jellium spheres: Density functional hierarchy and quantum Monte Carlo
Authors: Almeida, L. M.; Perdew, John P.; Fiolhais, Carlos
Abstract: We consider spherical jellium clusters with up to 200 electrons as a testing ground for density functional approximations to the exchange-correlation energy of a many-electron ground state. As nearly-exact standards, we employ Hartree–Fock energies at the exchange-only level and the diffusion Monte Carlo (DMC) energies of Sottile and Ballone (2001) at the correlated level. The density functionals tested are the local spin density (LSD), generalized gradient (GGA), and meta-generalized gradient (meta-GGA) approximations; the latter gives the most accurate results. By fitting the deviation from the LSD energy of closed-shell clusters to the predictions of the liquid drop model, we extract the exchange-correlation surface energies and curvature energies of a semi-infinite jellium from the energies of finite clusters. For the density functionals, the surface energies so extracted agree closely with those calculated directly for a single planar surface. But for the diffusion Monte Carlo method, the surface energies so extracted are considerably lower (and we suspect more accurate) than those extrapolated by Acioli and Ceperley (1996) from their DMC supercell calculations. The errors of the LSD, GGA, and meta-GGA surface and curvature energies are estimated, and are found to be consistently small for both properties only at the meta-GGA level. These errors are qualitatively related to relative performances of the various density functionals for the calculation of atomization energies: the proper self-interaction correction to the LSD for a one-electron atom is in the curvature energy (as it is in meta-GGA), not in the surface energy (as it is in GGA). Additionally, a formula is given for the interpolation and extrapolation of the surface energy σxc as a function of the bulk density parameter rs
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10316/123422002-01-01T00:00:00ZAtoms, molecules, solids and surfaces: Applications of the generalized gradient approximation for exchange and correlationhttp://hdl.handle.net/10316/2535Title: Atoms, molecules, solids and surfaces: Applications of the generalized gradient approximation for exchange and correlation
Authors: Perdew, John P.; Chevary, J A.; Vosko, S. H.; Jackson, Koblar A.; Pederson, Mark; Singh, D. J.; Fiolhais, Carlos
Abstract: Generalized gradient approximations (GGA’s) seek to improve upon the accuracy of the local-spin-density (LSD) approximation in electronic-structure calculations. Perdew and Wang have developed a GGA based on real-space cutoff of the spurious long-range components of the second-order gradient expansion for the exchange-correlation hole. We have found that this density functional performs well in numerical tests for a variety of systems: (1) Total energies of 30 atoms are highly accurate. (2) Ionization energies and electron affinities are improved in a statistical sense, although significant interconfigurational and interterm errors remain. (3) Accurate atomization energies are found for seven hydrocarbon molecules, with a rms error per bond of 0.1 eV, compared with 0.7 eV for the LSD approximation and 2.4 eV for the Hartree-Fock approximation. (4) For atoms and molecules, there is a cancellation of error between density functionals for exchange and correlation, which is most striking whenever the Hartree-Fock result is furthest from experiment. (5) The surprising LSD underestimation of the lattice constants of Li and Na by 3–4 % is corrected, and the magnetic ground state of solid Fe is restored. (6) The work function, surface energy (neglecting the long-range contribution), and curvature energy of a metallic surface are all slightly reduced in comparison with LSD. Taking account of the positive long-range contribution, we find surface and curvature energies in good agreement with experimental or exact values. Finally, a way is found to visualize and understand the nonlocality of exchange and correlation, its origins, and its physical effects.
Tue, 01 Sep 1992 00:00:00 GMThttp://hdl.handle.net/10316/25351992-09-01T00:00:00Z