Generalized Gradient Corrections Research Articles

HYDROGEN ADSORPTION ON THE (100) SURFACES OF RHODIUM, PALLADIUM AND SILVER

The adsorption of atomic hydrogen on the (100) surfaces of face-centered-cubic rhodium, palladium and silver has been studied using ab-initio density-functional calculations (including generalized gradient corrections). At the example of Rh(100) we present detailed investigations of the influence of the nonlocal corrections to the exchange-correlation functional on the stable geometries and the energies of adsorption. We also study the influence of the adsorbate on the relaxation of the substrate. Chemical trends are studied along the series Rh–Pd–Ag.

Geometry effects on the electronic properties of YBa2Cu3O7

We have performed electronic structure calculations for the high T c compound YBa2Cu3O7 with a 3% reduced unit-cell volume. The effect on band structure and Fermi surface is investigated. The predominant features are van Hoove singularities at the Fermi level. Keeping the experimental lattice parameters, nearly the same effects occur when replacing the local-density approximation by a generalized gradient correction scheme.

The influence of generalized gradient corrections on the structural and electronic properties of tellurium

The structural and electronic properties of trigonal tellurium have been investigated by the total energy-pseudopotential method within the local density approximation (LDA), without and including generalized gradient corrections (GGC). We find that the LDA causes an overbinding that is equivalent to a fictitious positive pressure, while the inclusion of gradient corrections tends to overcorrect and have the effect of adding a negative pressure to the system. Our results obtained within GGC are in good agreement with experiment showing systematic improvement over LDA. In order to apply hydrostatic pressure we used the Cleveland-Wentzcovitch Lagrangian that optimizes the cell dimensions under compression by attributing a fictitious mass to the unit cell. It is seen that although this method is more efficient than the traditional exhaustive search of each lattice parameter, but it has some shortcomings in providing accurate hydrostatic pressure in anisotropic systems.

Theoretical investigations of structural and vibronic properties of YBa 2Cu 3O 7 by first-principles atomic-force calculations

We have determined the force-free geometry and the dynamical matrix for the five Raman-active A 1 g modes in YBa 2Cu 3O 7 by full-potential LAPW atomic-force calculations. Treating exchange and correlation effects by LDA leads to phonon frequencies in rather good agreement with experimental values. However, they are significantly improved by employing generalized gradient corrections to the local exchange-correlation potential.

Gradient-corrected correlation with nearly exact Kohn-Sham exchange: Calculations for Si and Ge

We have constructed a pseudopotential that reduces the errors inherent in ordinary pseudopotentials when used together with nonlocal exchange potentials. Using the very accurate approximation of Krieger, Li, and Iafrate to the exact Kohn-Sham exchange potential together with correlation in the local-density approximation (LDA) both with and without the generalized gradient correction of Perdew and Wang, we calculated the electronic and physical properties of Si and Ge. The gradient corrections result in a large reduction of the indirect energy gaps, worsening agreement with experiment. They also reduce the total energy of both of the atoms and both of the crystals, resulting in increases of the Si and Ge cohesive energies which improve their agreement with experiment. In addition we have studied the effect of adding gradient corrections when the valence electrons see a Hartree-Fock potential from the core electrons and LDA exchange and correlation among themselves.

Structure and properties of cobalt clusters up to the tetramer: A density-functional study

All-electron calculations have been performed on cobalt clusters up to the tetramer using the local and generalized gradient correction spin density formalisms. These clusters present an abundance of low-lying states. In the case of ${\mathrm{Co}}_{4}$, we have found that two and three-dimensional structures are energetically very close. Symmetric structures exhibit high degeneracy. Jahn-Teller deformations have hence been investigated and have been found to play an important role in such transition-metal clusters. General trends in the magnetic moment per atom and in the attachment energy have been elucidated.

First Principles Calculations to Describe Zirconia Pseudopolymorphs

ABSTRACTThe structural and electronic properties of four different structures of zirconia (ZrO2) are studied using ab initio total energy calculations. The calculations are made in the framework of density functional (DFT) and pseudopotential theory. We compare results given within the LDA (Local Density Approximation) and including Generalized Gradient Corrections (GGCs) in the Perdew Wang and Perdew Becke formalisms. We present results for pure and defective zirconia (oxygen vacancies and Zr substitution by Fe) showing the effects of such point defects on tne relative structural stabilities of the different pseudopolymorphs.

Design of an exchange functional with correct asymptotics

Knowledge of asymptotic conditions on exchange allows for a better design of exchange energy expressions in density functional theory. By working inside an exchange-only framework, the fulfillment of such conditions by some of the most widely used exchange functionals is discussed. In turn, we propose a model expression which partially meets the energetics and asymptotics of both the exchange energy density and potential. Improvement upon the local spin density approximation without the use of generalized gradient corrections is also presented. Hartree-Fock orbitals are employed to build electron densities. © 1997 John Wiley & Sons, Inc.

Theoretical investigations of the elastic constants in Laves phases

The bulk modulus B and the tetragonal shear modulus C′ of the C15 Laves phases AAl2, A = Ca, Sc, Y, La and Gd and ZrB2, B = V, Cr, Fe, Co, Zn and Mo; the C14 Laves phases ZrMn2, ZrAl2, ZrCr2, TiCr2, NbCr2 and TaFe2 and the metals forming these Laves phases are studied theoretically by ab-initio density functional band structure calculations. Additionally, the Poisson ratios, the Young moduli, for cubic systems C11 and C12 and for the hexagonal phases C11 + C12, C13 and C33 are calculated and compared with the experimental data. We also compare the results of B obtained from the augmented spherical wave method using the local density and atomic sphere approximations and the full potential linear muf-fin-tin orbitals procedure with and without the generalized gradient correction for the crystal potential. All procedures give the right trend in B and the differences between experiment and theory are less than 15% for systems without a transition element and up to 25% for systems with a transition metal component. The correlation between B and the electron density ϱI in the interstitial region of the crystal found by Moruzzi et al. for metals can be extended to B for the Laves phases and allows rules of mixture for B. For C′ and the other elastic constants, the agreement between experiment and theory is similar for the non-transition metals but less satisfactory for the transition metals and the Laves phases with a transition metal component.

The energetics of adsorption of HCOOH on the MgO(100) surface

Ab initio calculations based on density functional theory and the pseudopotential method have been used to investigate the adsorption of HCOOH (formic acid) on the flat non-defective MgO(100) surface. The aims of the work are to find the energetically most favorable adsorbed configurations, and to determine whether dissociative adsorption is favorable. The calculations are performed in slab geometry using periodic boundary conditions. They are fully converged with respect to the size of the plane-wave basis set, and full relaxation of all atoms in the system is performed throughout. Results obtained both with the local density approximation and including generalized gradient corrections are presented. It is found that the most stable configuration is dissociative, with the formate ion symmetrically attached via its oxygen atoms to two surface Mg ions. This configuration is more stable than the most stable molecular configuration by ∼0.3 eV. The energy barrier separating molecular and dissociated adsorbed configurations is small, so that spontaneous dissociation would occur under all conditions of interest. The relations between our findings and previous experimental and theoretical results are discussed.

Calculation of positron states and annihilation in solids: A density-gradient-correction scheme.

The generalized gradient correction method for positron-electron correlation effects in solids [B. Barbiellini et al., Phys. Rev. B 51, 7341 (1995)] is applied in several test cases. The positron lifetime, energetics, and momentum distribution of the annihilating electron-positron pairs are considered. The comparison with experiments shows systematic improvement in the predictive power of the theory compared to the local-density approximation results for positron states and annihilation characteristics. \textcopyright{} 1996 The American Physical Society.

Generalized gradient correction for exchange: Deduction from the oscillator model.

We propose two simple, first-principles generalized gradient corrections for exchange, which are exact for the one- and two-electron oscillator and for the weakly perturbed electron gas in second order of the gradient and which are very close to Becke's empirical correction. Also, the procedure is given for fulfilling additional exact constraints. The result is tested for the exchange energy of atoms and some exactly solved one- and two-electron problems in the external potentials -Z/r and 1/2${\mathrm{\ensuremath{\omega}}}^{2}$${\mathit{r}}^{2}$ for a wide range of the parameters Z and \ensuremath{\omega}. \textcopyright{} 1996 The American Physical Society.

Theoretical investigation of the high-pressure crystal structures of Ce and Th.

The high-pressure crystal structures of Ce and Th are studied theoretically by means of a full potential linear muffin-tin orbital technique, where the generalized gradient correction to density-functional theory has been implemented. A crystallographic phase transition from fcc to bct is found for u-Ce at about 10 GPa, in good agreement with experiment. The calculated pressure dependence of the crystallographic c/a ratio (of the bct structure) is in good agreement with experiment. For n-Ce a subsequent transition to the hcp crystal structure is predicted at about 1600 GPa. For Th a continuous transformation from fcc to bct at 45 GPa is found, confirming recent experimental findings. Also for this material the calculated pressure dependence of the crystallographic c/a ratio (of the bct structure) is in good agreement with experiment. For Th we also predict a transformation to the hcp crystal structure at even higher pressures. The metals Ce (Z= 58) and Th (Z= 90) are located at the beginning of the 4f (lanthanides) and the Sf (actinides) transition-metal series, respectively. Ce is the first lanthanide metal that has an appreciable occupation of the 4f states, and is a known subject for controversy. Primarily the debate concerns the localized versus itinerant character of the 4f electron. The electronic structure of Ce has been reported earlier. As regards the 5f population at ambient conditions, calculations show that the actinide metal Th has a smaller f occupation than ct Ce Se-ver.al recent investigations of these two metals, both experimental as well as theoretical, have been motivated by their crystallographic phase transitions under compression. In the lanthanide series localized 4f states are progressively being filled and their inhuence on the chemical bonding is negligible. In the actinide series, however, the earlier metals have delocalized 5f electrons that contribute to the chemical bonding. The increasing 5f occupation as a function of atomic number results in increasingly distorted (complex) crystal structures. This is understood from the increased contribution to the bonding from the narrow 5f bands. ' Particularly interesting in the present context is the occurrence of the bct (c/a =0.825) structure at ambient conditions for Pa (Z=91). The increased 5f occupation in Pa, in comparison to Th, results in a bonding which favorizes the bct crystal structure over the fcc structure (which is found in Th at ambient pressure). The effect of pressure upon an itinerant 5f metal is first a lowering of the energy of the 5f bands relative to the other valence states and second a broadening of the Sf band as well as a broadening of the other bands. The relative lowering of the Sf states results in an increased Sf population. Therefore, in view of the known crystal structure of Pa (bct), it is not surprising to find a pressure-induced onset of a bct crystal structure in Th. Since u-Ce from certain aspects can be regarded as an analog element to Th, a similar behavior (stabilization of the bct structure) of Ce under pressure is not surprising either. However, for Ce, in contrast to Th, there is an intermediate bodycentered-monoclinic (bcm) phase found experimentally in the interval 6— 12 GPa. This bcm structure can be seen as a small distortion of the bct crystal structure, and can therefore be, approximately, described as a bct structure. In fact both the bcm and the bct phases of Ce at moderate compressions can be viewed as more or less distorted fcc structures. We note here that the experimental structure is not quite clear for Ce since it has been reported that an orthorhombic n-U type of structure is stabilized, instead of the bcm structure. In the present report we take the view point that the bcm and the u-U structures are very close in energy and that the u-U

Bulk and surface magnetism and interplanar spacings in Gd from first-principles calculations.

The magnetic ground state of bulk Gd and surface Gd is investigated by means of first-principles calculations based on the local-spin-density approximation. Good agreement between theory and experiment is found for all calculated bulk properties only if we treat the 4f states as core electrons. For the bulk calculations we also studied the effect of the generalized gradient correction to the potential, and also here good agreement between theory and experiment was found only when we treated the 4f states as core electrons. At compressed volumes we predict that bulk Gd should become antiferromagnetic. Our calculations reproduce the experimentally determined ferromagnetic alignment between the surface and subsurface layers of Gd (0001), as well as a \ensuremath{\sim}0.13 \AA{} inward relaxation of the surface layer.

The influence of generalized gradient corrections to the LDA on predictions of structural phase stability: the Peierls distortion in As and Sb

The crystal structure and phase stability of the group-V elements As and Sb has been investigated by total-energy calculations within the local-density approximation (LDA), without and including generalized gradient corrections (GGC). We show that, contrary to the case of the group-VI elements Se and Te, where the LDA predicts crystal structures with a much smaller difference between the short intra-chain bonds and the long inter-chain bonds than is observed, for As and Sb the LDA leads to equilibrium structures in reasonable, or even good, agreement with experiment and describes the pressure-induced phase transition to a simple cubic structure in Sb (but not in As) very well. The GGC corrections show a tendency to overshoot and do not improve agreement with experiment. In both cases the main effect of the GGC is to add an isotropic pressure to the system, while the local electronic and bonding properties at constant volume remain unchanged.

Theory of the crystal structures of selenium and tellurium: The effect of generalized-gradient corrections to the local-density approximation.

The crystal structure and phase stability of selenium and tellurium have been investigated by total-energy calculations within the local-density approximation (LDA), without and including generalized-gradient corrections (GGC). We find that the LDA underestimates the equilibrium volume by as much as 15% and predicts a crystal structure that is much more isotropic than observed: the nearest-neighbor distances in the helical chains are increased, but the interchain distances are reduced. Adding generalized-gradient corrections to the LDA results in a crystal structure, equilibrium volume, and binding energy in better agreement with experiment. We show that the effect of the GGC's is to add a uniform internal pressure to the system, the local bonding properties at constant volume, however, are unchanged.

The energetics and dynamics of H 2 dissociation on Al(110)

We present a modeling of the sticking dynamics of H 2 on Al(110). The modeling is based on an ab initio calculation of the H 2/Al(110) potential energy surface. The calculation is done both within the local density approximation (LDA) and using non-local corrections via the generalized gradient correction (GGA). We find that the GGA increases the barrier for dissociation substantially, and that the inclusion of gradient corrections greatly influences the dissociation dynamics. The dissociation dynamics is simulated by first doing a full quantum mechanical calculation of the dynamics in two of the six H 2 coordinates, the distance of the molecule from the surface and the intra-molecular bond length. The other four degrees of freedom are then included using the hole model. This implies that these coordinates are treated classically, and in the sudden approximation. Test calculations in three dimensions, where full quantum calculations are feasible, show the hole model to work well for the onset of sticking. Finally, the full six-dimensional sticking calculations are compared to the results of molecular beam experiments, both for pure and seeded beams.

Spectroscopic constants of diatomic molecules computed correcting Hartree-Fock or general-valence-bond potential-energy curves with correlation-energy functionals.

The Kohn-Sham energy with exact exchange [using the exact Hartree-Fock (HF) exchange but an approximate correlation-energy functional] may be computed very accurately by adding the correlation obtained from the HF density to the total HF energy. Three density functionals are used: local spin density (LSD), LSD with self-interaction correction, and LSD with generalized gradient correction. This scheme has been extended (Lie-Clementi, Colle-Salvetti, and Moscardo--San-Fabian) to be used with general-valence-bond (GVB) energies and wave functions, so that the extra correlation included in the GVB energy is not counted again. The effect of all these approximate correlations on HF or GVB spectroscopic constants (${\mathit{R}}_{\mathit{e}}$,${\mathrm{\ensuremath{\omega}}}_{\mathit{e}}$, and ${\mathit{D}}_{\mathit{e}}$) is studied. Approximate relations showing how correlation affects them are derived, and may be summarized as follows: (1) the effect on ${\mathit{R}}_{\mathit{e}}$ and ${\mathrm{\ensuremath{\omega}}}_{\mathit{e}}$ depends only on the correlation derivative at ${\mathit{R}}_{\mathit{e}}$, and (2) the effect on ${\mathit{D}}_{\mathit{e}}$ depends mainly on the correlation difference between quasidissociated and equilibrium geometries. A consequence is that all the correlation corrections tested here give larger ${\mathrm{\ensuremath{\omega}}}_{\mathit{e}}$ and ${\mathit{D}}_{\mathit{e}}$ and shorter ${\mathit{R}}_{\mathit{e}}$ than the uncorrected HF or GVB values. This trend is correct for ${\mathit{D}}_{\mathit{e}}$ for both HF and GVB. For ${\mathit{R}}_{\mathit{e}}$ and ${\mathrm{\ensuremath{\omega}}}_{\mathit{e}}$, it is correct in most cases for GVB, but it often fails for the HF cases. A comparison is made with Kohn-Sham calculations with both exchange and correlation approximated. As a final conclusion, it is found that, within the present scheme, a qualitatively correct HF or GVB potential-energy curve, together with a correlation-energy approximation with correct dissociation behavior, is crucial for obtaining good estimates of spectroscopic constants.

Simplified self-interaction correction applied to the energy bands of neon and sodium chloride

The local-density approximation (LDA) for the exchange-correlation potential underestimates the fundamental energy gaps of insulators by about 40%. When a simplified self-interaction correction (SSIC) is applied to the band structures of Ne and NaCl, vast improvements over LDA are found in the gaps, with little change in the valence-band widths or conduction-band structures. Because it is applied directly to the Bloch orbital representation, SSIC is very easy to incorporate into LDA computer codes. Results are also reported using the Langreth-Mehl (LM) generalized gradient correction to LDA. The LM potential, which we regard as a close approximation to the exact Kohn-Sham potential, yields band structures very close to those of LDA.