R. W. Godby, G. A. Benesh, R. Haydock and V. Heine

*Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, UK*

*Physical Review B 32 655 (1985)*

We have calculated self-consistently the electronic structure of a model of a
c(2×2) oxygen overlayer on the nickel (001) surface using the linearized
augmented-plane-wave method, obtaining good agreement with the experimentally
measured electronic excitation spectra. Our purpose has been to analyze the
charge density, wave functions, bond orders, local densities of states, and
energy levels to obtain a picture of the bonding between the oxygen and the
nickel surface. We find that the oxygen 2p
states hybridize more strongly with the nickel
4s4p bands than with the 3d
bands, and we demonstrate that the optimal local orbitals for the oxygen nucleus
which span the resulting 2p-like bands
centered at E_{F}-5.5
eV resemble large oxygen 2p orbitals.
Bond orders exhibit the bonding nature of these states and the existence of
antibonding states above E_{F}.

PACS Numbers: 68.20.+t, 73.20.Hb, 73.30.+y, 68.30.+z

Keywords: DFT

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R. W. Godby

*Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, UK*

*Physical Review B 32 5432 (1985)*

Calculations of the electron density in oxygen overlayers on a nickel (001) surface show a ‘‘ball-and-stick’’ model to be inappropriate in understanding the small work-function increase measured on chemisorption. The form of the charge transfer and the effective surface dipole layer is explained in terms of the very large 2p-like oxygen orbitals that span the O 2p–like bands.

PACS Numbers: 73.30.+y, 73.20.Hb

Keywords: DFT

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R. W. Godby

*Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, UK*

*Physical Review B 32 7641 (1985)*

From calculations of the electronic structure of c(2×2) and p(1×1) overlayers of oxygen atoms on the nickel (001) surface, we demonstrate the closed-shell nature of the oxygen-oxygen repulsion that prevents the formation of the p(1×1) structure. The closed shells consist of the large oxygen p orbitals that span the oxygen 2p-like bands. The widths of these bands and the changes in the density of states upon chemisorption show quantitatively that this effectively direct adsorbate-adsorbate interaction is dominant.

PACS Numbers: 68.20.+t, 73.20.-r

Keywords: DFT

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R.W. Godby^{1} and N. Garcia^{2}

^{1}AT&T Bell Laboratories, Murray Hill, NJ 07974, USA^{
2}IBM Zurich Research Laboratory, 8803 Rüschlikon, Switzerland

*Surf. Sci. 163 L681 (1985) (Letters)*

Self-consistent calculations of the charge density of the c(2×2) phase of oxygen
on nickel (001) (i) give a helium scattering potential which in excellent
agreement with the shape, height and width of that obtained by Rieder by fitting
his atom-surface scattering data: (ii) justify the use of a hard-wall fit
because of a 4.2 Å^{−1} average softness parameter; and (iii) rule out
superposition of atomic or ionic charge densities for this and similar systems.

Keywords: DFT

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R.W. Godby^{1}, M. Schlüter^{1} and L.J.
Sham^{2}

^{1 }*AT&T Bell Laboratories, Murray Hill,
NJ 07974
*

*Physical Review Letters 56 2415 (1986)*

We obtain an accurate density-functional exchange-correlation
potential, *V*_{xc} (**r**), for silicon, from
calculations of the self-energy Σ(**r**,**r'**,*ω*).
No local-density approximation (LDA) is used for *V*_{xc}.
The band structure with this *V*_{xc} is in remarkably
close agreement with that obtained with the LDA, while both differ
significantly from the quasiparticle spectrum of Σ.
The 50% band-gap error found in LDA calculations is therefore
not caused by the LDA but by the discontinuity, Δ,
in the exact *V*_{xc} on addition of an electron.

PACS Numbers: 71.45.Gm, 71.25.Rk

Keywords: GW DFT

See also: Paper 6, Paper 7, Paper 8 and Paper 9

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R.W. Godby^{1}, M. Schlüter^{1} and L.J.
Sham^{2}

^{1 }*AT&T Bell Laboratories, Murray Hill,
NJ 07974
*

*Proceedings of the 18th International Conference on the Physics of
Semiconductors (Stockholm, 1986), World Scientific Publishing, Singapore, 1987
*

We obtain accurate density-functional-theory exchange-correlation potentials, *V*_{xc} (**r**),
and their gap-discontinuities Δ, for Si, GaAs and diamond by using an exact
relationship between *V*_{xc} and the self-energy Σ(**r**,**r'**,*ω*).
In each case about 80% of the LDA band-gap error is attributable to Δ and not to
the LDA itself. We also discuss the forms of *V*_{xc} and Σ
in real space.

Keywords: GW DFT

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R.W. Godby^{1}, M. Schlüter^{1} and L.J.
Sham^{2}

^{1 }*AT&T Bell Laboratories, Murray Hill,
NJ 07974
*

*Physical Review B Rapid Communications 35 4170 (1987)*

We calculate the quasiparticle band structures of GaAs and AlAs and compare them with previous experimental assignments. Generally good agreement is obtained, except for the L conduction-band minimum in AlAs, which is found to be 0.8±0.2 eV above the X minimum rather than 0.3 eV as found in the literature. A new interpretation of the experimental data is therefore proposed.

Keywords: GW DFT

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R.W. Godby^{1}, M. Schlüter^{1} and L.J.
Sham^{2}

^{1 }*AT&T Bell Laboratories, Murray Hill,
NJ 07974
*

*Physical Review B 36 6497 (1987) *

We examine the trends in the self-energy operators of Si, diamond, GaAs, and
AlAs, and in their corresponding exchange-correlation potentials
V_{xc} and their
discontinuities Δ. The potentials are
calculated from the self-energies, thus avoiding use of a local-density
approximation (LDA). In each case about 80% of the LDA band-gap error is also
present for the true density-functional theory eigenvalue difference derived
from V_{xc} and so is caused by
Δ. The self-energies themselves,
calculated in the Hedin-Lundqvist GW
approximation, reproduce the experimental quasiparticle energies accurately, and
are also shown to be well modeled by a simple functional form in real space.

Keywords: GW DFT

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R.W. Godby^{1}, M. Schlüter^{2} and L.J.
Sham^{3}

^{1 }*AT&T Bell Laboratories, Murray Hill,
NJ 07974 and Cavendish Laboratory, University of Cambridge, Madingley
Rd., Cambridge CB3 0HE, United Kingdom
*

*Physical Review B 37 10159 (1988)*

We show how the density-functional (DFT) exchange-correlation
potential *V*_{xc} (**r**) of a semiconductor
is calculated from the self-energy operator Σ(**r**,**r'**,*ω*),
and how Σ is obtained using the one-particle
Green's function and the screened Coulomb interaction (the *GW*
approximation). We discuss the nature of *V*_{xc}
and the self-energy in real space, and investigate features and
trends found in Si, GaAs, AlAs and diamond. In each case the calculated
quasiparticle band structure is in good agreement with experiment,
while the DFT band structure is surprisingly similar to that with
the common local-density approximation (LDA); in particular, about
80% of the severe LDA band-gap error is shown to be inherent in
DFT calculations, being accounted for by the discontinuity Δ in *V*_{xc }on addition of an electron. The
relationship of the calculated *V*_{xc}to the LDA
and its extensions is also examined.

PACS Numbers: 71.45.Gm, 71.25.Rk

Keywords: GW DFT

See also: Paper 5, Paper 6, Paper 7 and Paper 8

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R.W. Godby and R.J. Needs

*Cavendish Laboratory, University of Cambridge, Madingley Rd.,
Cambridge CB3 0HE, United Kingdom*

*Physical Review Letters 62 1169 (1989)*

We investigate the pressure-induced metal-insulator transition
of silicon in the diamond structure. Quasiparticle theory (QPT)
calculations are performed within the *GW* approximation,
and Kohn-Sham theory (KST) results are obtained by using an exchange-correlation
potential derived from the *GW* self-energy operator, not
using the common local-density approximation (LDA). In both KST
and the LDA metallization occurs at a much larger volume than
in QPT. These results suggest that the metallization point and
Fermi surface of the Kohn-Sham electrons are *not* necessarily
those of the real system.

PACS Numbers: 71.30.+h, 71.25.Rk, 71.45.Gm

Keywords: GW DFT

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R.W. Godby^{1}, L.J. Sham^{1} and M. Schlüter^{2}

^{1 }*Department of Physics, University of California
at San Diego, La Jolla, California 92093
*

*Physical Review Letters 65 2083 (1988)*

Commenting on a recent paper by Das *et al.*, we show how
the discontinuity Δ in the exchange-correlation
potential on addition of an electron will, in general, cause the
*p*- and *n*-type Schottky barrier heights at a metal-semiconductor
interface (and the band offsets at a semiconductor heterojunction)
to be different in exact Kohn-Sham density-functional theory from
the correct quasiparticle values. The error is accommodated by
a long-distance variation in the exchange-correlation potential
which accompanies the variation in the electrostatic potential.

PACS Numbers: 73.20.At, 73.40.Ns

Keywords: GW DFT

See also: Paper 26

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R.W. Godby and R.J. Needs

*Cavendish Laboratory, University of Cambridge, Madingley Rd.,
Cambridge CB3 0HE, United Kingdom*

*Physica Scripta T31 227 (1990) *

By calculating an exchange-correlation potential from the
self-energy operator, we show that interpretation of the one-electron band
structure appearing in density-functional theory (DFT) calculations as
quasiparticle energies is seriously invalid. For example, the well-known error
in the minimum band gap of semiconductors and insulators is not caused by the
use of the local density approximation (LDA), but is inherent to DFT.
Furthermore, the metal-insulator transition undergone when a semiconductor is
compressed is not described correctly within DFT, showing that the DFT Fermi
surface is not necessarily that of the real system. However, excited state
properties can be calculated correctly, by using computational many-body theory.
The *GW* approximation for the self-energy operator gives quasiparticle
energies in excellent agreement with experiment. It may also be used to obtain
the one-particle Green's function, from which other properties of the system may
be found.

Keywords: GW DFT

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R.W. Godby, R.J. Needs and M.C. Payne

*Cavendish Laboratory, University of Cambridge, Madingley Rd.,
Cambridge CB3 0HE, United Kingdom*

*Physics World, October 1990, p.39*

Imagine a physics laboratory in which it is possible to examine the smallest details of a solid, seeing not just the positions of atoms but also the electron density and even the individual electronic wavefunctions; to apply pressures to solids hundreds of times greater than previously possible; to measure forces on individual atoms; and even to hold selected atoms in place while moving others to investigate the interatomic forces which determine the structure of the solid. In fact, starting only from the elements of quantum mechanics, supercomputers allow powerful experiments to be performed on solids in just such an imaginary ‘laboratory’. Here atoms may be manipulated at will, and the behaviour of their electrons, which governs the electronic and optical properties of the solid and the forces which hold it together, measured in great detail. The insights gained can then be used to build a new understanding of physical processes.

Keywords: GW DFT

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K. Karlsson^{1},
R.J. Needs* ^{2}*, A. Qteish

^{1}Dept. of Physics, Chalmers University of
Technoligy, Goteborg, Sweden

^{2}Cavendish Laboratory, University of Cambridge, Madingley Rd.,
Cambridge CB3 0HE, United Kingdom

*J. Phys. Cond. Matt. (Letters) 2 5265 (1990)*

The
electronic structure at the interface between bulk GaAs(001) and short-period
superlattices of (AlAs)_{n}(GaAs)_{m} has been calculated using
ab initio pseudopotential techniques. The results show that the valence band
offsets at such interfaces are very similar to those obtained experimentally for
random alloy systems, but superior transport properties are anticipated for the
ordered systems.

Keywords: DFT

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B. Farid, R.W. Godby and R.J. Needs

*Cavendish Laboratory, University of Cambridge, Madingley Rd., Cambridge CB3
0HE, United Kingdom*

*Proceedings of the 20th International Conference on the Physics of
Semiconductors (Thessaloniki, 1990), World Scientific Publishing, Singapore,
1990*

We outline our strategy to tackle the problem of total-energy
calculations for real semiconductors and insulators including many-body effects.
In our treatment we use the total-energy expression of Galitskii and Migdal
within the framework of Hedin’s *GW* approximation for the self-energy
operator. While numerical evaluation of this expression for real materials might
seem impracticable, we show how it can simply be transformed into a form whose
elements can be evaluated. We also presents some computational results for bulk
silicon.

Keywords: GW DFT

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J.P.A. Charlesworth, A. Oschlies, R.W. Godby, R.J. Needs and L.J. Sham

Progress with treating many-body effects in solids using
the *GW* formulation of the self-energy operator is illustrated using three
examples: (i) Many-body effects in a Al/GaAs Schottky barrier; (ii) Band-gap
narrowing in doped semiconductors; (iii) Many-body effects in the momentum
densities of semiconductors.

Keywords: GW DFT

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B. Farid and R.W. Godby

*Cavendish Laboratory, University of Cambridge, Madingley Rd.,
Cambridge CB3 0HE, United Kingdom*

*Physical Review B 43 14248 (1991)*

We comment on the controversies that seem to exist about the experimental value of the cohesive energy for silicon. We argue that this can be safely taken to be 4.62±0.08 eV/atom. We conclude that, whereas in the case of diamond the cohesive energy predicted by recent variational quantum Monte Carlo pseudopotential calculation is in excellent agreement with experiment, for silicon there remains a discrepancy of 0.19 eV/atom. To clarify these points, we mention briefly some fundamental principles of the measurement of cohesive energies and explain how they can be obtained from the thermodynamic tables.

Keywords: DFT

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R.W. Godby

*Cavendish Laboratory, University of Cambridge, Madingley Rd.,
Cambridge CB3 0HE, United Kingdom*

*Chapter in "Unoccupied electronic states" (Topics in Applied
Physics, Vol. 69), ed. J.E. Inglesfield and J. Fuggle, Springer, 1992*

In this chapter theories of the effects of the electron-electron interaction on optical and electronic properties of solids are described, with particular focus on the new first-principles approaches to many-body phenomena.

Keywords: GW DFT

Book from Springer

Chapter from Springer

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A. Oschlies, R.W. Godby and R.J. Needs

*Cavendish Laboratory, University of Cambridge, Madingley Rd.,
Cambridge CB3 0HE, United Kingdom*

*Physical Review B Rapid Communications 45 13741 (1992)*

We calculate the band-gap narrowing in silicon caused by the introduction of additional electrons, using a first-principles self-energy approach within the GW approximation. We include full local-field effects and the nonlocal and energy-dependent dielectric function of the intrinsic material. We also analyze our calculations to test the approximations normally used in simple models of this effect: local-field effects are found to be unimportant, but the inclusion of the energy dependence of the dielectric response of the intrinsic material, which is normally neglected in model calculations, is found to be crucial at high carrier concentrations.

Keywords: GW DFT

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W. Knorr and R.W. Godby

*Cavendish Laboratory, University of Cambridge, Madingley Rd.,
Cambridge CB3 0HE, United Kingdom*

*Physical Review Letters 68 639 (1992)*

Using the Diffusion Quantum Monte Carlo method, we calculate the
ground-state density and energy, and the quasiparticle band gap,
of a model semiconductor. The exchange-correlation potential of
density-functional theory (DFT), *V*_{xc} (**r**),
is obtained using optimisation techniques. From this we calculate
the DFT functionals *E*_{xc} and *T*_{s} and the DFT band gap for various
external potentials and compare the results with the local-density
approximation (LDA). Whereas energies are found to be very accurate
in the LDA, and the density reasonably good, we find large differences
in the shape of *V*_{xc} (**r**).

PACS Numbers: 71.10.+x, 71.45.Gm

Keywords: DFT

See also: Paper 30

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J.P.A. Charlesworth, R.W. Godby, R.J. Needs and L.J. Sham

*Materials Science and Engineering (B) 14 262 (1992)*

We present the results of recent research on the electronic structure of Schottky barriers. This is in two parts: (i) ab initio calculations of the equilibrium geometry and electronic structure of a GaAs(110)-A1 Schottky barrier, and (ii) a discussion of the significance of Schottky barrier heights calculated in exact density functional theory

Keywords: GW DFT

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M. Palummo, L. Reining, R.W. Godby and C.M. Bertoni

*Proceedings of the 21st International Conference on the Physics of
Semiconductors (Beijing, 1992)*

We present the results of a density-functional calculation on
gallium nitride in the zinc blende phase and compare band structure and
ground-state properties with the results obtained for the wurtzite structure.
The use of norm-conserving pseudopotentials requires a large plane-wave basis
set (100 Ryd cutoff) for a converged calculation. In addition, we determine the
self-energy corrections to the quasiparticle energies in the *GW* scheme. A
comparison with other calculations and existing experimental data is also given.

Keywords: GW

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J.P.A. Charlesworth, R.W. Godby and R.J. Needs

*Cavendish Laboratory, University of Cambridge, Madingley Rd.,
Cambridge CB3 0HE, United Kingdom*

*Physical Review Letters 70 1685 (1993)*

We calculate the quasiparticle electronic structure of a Al/GaAs(110)
Schottky barrier as a function of distance from the interface,
using the *GW* self-energy operator. The GaAs band gap is
significantly narrowed near the metal, although the classical
picture of image-potential narrowing is subject to large quantum
corrections. The nature of these corrections is explored further
using model calculations.

PACS Numbers: 73.30.+y, 73.40.Ns, 71.10.+x

Keywords: GW

See also: Paper 49 Paper 59 Paper 64

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A. Natori and R.W. Godby

*Cavendish Laboratory, University of Cambridge,
Madingley Rd., Cambridge CB3 0HE, United Kingdom*

*Physical Review B 47 15816 (1993)*

Surface diffusion of an adatom on a vicinal surface is investigated, using site-dependent hopping rates based on a model surface-potential profile of a regularly stepped surface. We solved analytically the coupled rate equations for the occupation probability of an adatom at a sufficiently long time, in analogy to the tight-binding theory of electronic structure. From this, the general relation between the hopping rates and the diffusion coefficient is derived. Formulas of both surface diffusion coefficients, parallel and perpendicular to a step edge direction, are obtained as functions of related atomic hopping rates at a terrace site, an upper edge site, and a lower edge site and of the step spacing. The fundamental mechanism determining the crucial role of step arrays on surface diffusion is clarified. No difference was found between step-up diffusion and step-down diffusion, even in the absence of inversion symmetry on the surface-potential profile. With Monte Carlo simulation, the effect of kink sites on surface diffusion is studied. Kinks greatly suppress the parallel diffusion coefficient, while they suppress only weakly the perpendicular diffusion coefficient.

PACS Numbers: 68.35.Fx

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R.J. Needs, J.P.A. Charlesworth and R.W. Godby

*Cavendish Laboratory, University of Cambridge,
Madingley Rd., Cambridge CB3 0HE, United Kingdom*

*Europhysics Letters 25
31 (1994)*

The relaxed atomic structures, energies, and Schottky barrier heights of six translation states of the Al-GaAs(110) interface are calculated using a first-principles pseudopotential technique. The Schottky barrier height varies by 0.7 eV depending on the translation state, even though the energies of the structures are very similar. The lowest-energy translation state, which has not been considered in any previous studies, is the only one which allows every interface atom to participate in bonding across the interface. For each of the unrelaxed interface structures the Fermi level is pinned very close to the local charge neutrality level.

PACS Numbers: 73.30.+y, 73.40.Ns, 71.10.-w

Keywords: GW DFT

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R.W. Godby^{1} and L.J. Sham^{2}

^{1 }*Cavendish Laboratory, University of Cambridge,
Madingley Rd., Cambridge CB3 0HE, United Kingdom
*

*Physical Review B 49 1849 (1994)*

We investigate the exact Kohn-Sham exchange-correlation potential at semiconductor interfaces, including Schottky barriers, heterojunctions and semiconductor surfaces. By considering the electron density at the interface, we deduce the way in which the exact exchange-correlation potential differs from its bulk counterpart. The potential has a slow spatial variation related to the discontinuity, Δ, that occurs on addition of an electron to the bulk semiconductor. This variation, which corresponds to an ultra-non-local "vertex correction" in the Kohn-Sham formulation of the dielectric response of the semiconductor, results in correction terms for Schottky barrier heights and band offsets calculated using Kohn-Sham orbital energies. The effect is exhibited numerically for a model semiconductor.

PACS Numbers: 73.20.At, 73.40.Ns, 71.45.Gm

Keywords: GW DFT

See also: Paper 11

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R. Del Sole^{1}, Lucia Reining^{2} and R.W. Godby^{3}

^{1 }*Departimento di Fisica, Università di Roma
"Tor Vergata", Viale della Ricerca Scientifica 1, I-00173
Roma, Italy
*

*Physical Review B 49 8024 (1994)*

The widely used *GW* approximation for the self-energy of
a system of interacting electron may, in principle, be improved
using an approximate vertex correction Γ. We estimate Γ
using the local-density approximation. We report the results of
a comparable series of *GW* calculations for the band structure
of silicon, in which such a vertex correction is (i) excluded
entirely, (ii) included only in the screened Coulomb interaction
*W*, and (iii) included in both *W* and the expression
for the self-energy. We also discuss the symmetry properties of
the exact vertex correction and how they may be retained in further
improvements.

Keywords: GW

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N.E. Maddocks, R.W. Godby and R.J. Needs

*Cavendish Laboratory, University of Cambridge, Madingley Rd.,
Cambridge CB3 0HE, United Kingdom*

*Physical Review B (Rapid Communications) 49 8502 (1994)*

We present results from *ab initio* calculations of the full
inverse dielectric matrix of beryllium, from which we obtain the
dynamic scattering cross section. This is shown to be in excellent
agreement with recent inelastic X-ray scattering experiments,
both in overall shape and in precise details of the fine structure.
As the calculations have been performed entirely within the random-phase
approximation, this presents conclusive evidence that band-structure
effects are responsible for the observed structure.

Keywords: GW DFT

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M. Palummo^{1}, L. Reining^{2}, R.W. Godby^{3},
C.M. Bertoni^{1} and N. Börnsen^{2}

^{1} *Departimento di Fisica, Università di Roma
"Tor Vergata", Viale della Ricerca Scientifica 1, I-00173
Roma, Italy
*

*Europhysics Letters 26 607 (1994)*

We present the result of a calculation for the bulk electronic
structure of gallium nitride in the zincblende phase. We determine
the equilibrium lattice constant, the cohesive energy and the
bulk modulus in the Density Functional approach within the Local
Density Approximation (DFT-LDA). The one-particle eigenvalues
of the DFT Kohn-Sham equation do in principle not agree with the
experimental band structure. Therefore, we calculate the quasiparticle
energies by including self-energy corrections to the DFT-LDA exchange-correlation
potential, with the *GW* approximation for the electron self-energy.
We use norm-conserving pseudopotentials and a large plane-wave
basis set (100 Ry cut-off) for a converged calculation in the
DFT-LDA. The LDA band gap turns out to be very sensitive to the
crystal volume. We find that *GW* corrections to the LDA
band gap are significant. A detailed comparison with other DFT-LDA
results and approximate *GW* calculations and with existing
experimental data is given.

PACS Numbers: 71.25T

Keywords: GW DFT

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W. Knorr and R.W. Godby

*Cavendish Laboratory, University of Cambridge, Madingley Rd.,
Cambridge CB3 0HE, United Kingdom*

*Physical Review B 50 1779 (1994)*

We use Diffusion Quantum Monte Carlo (DQMC) techniques to obtain accurate estimates of the components of the Kohn-Sham effective potential of density-functional theory (DFT) for a model semiconductor, and the corresponding components of the energy functional, by determining the local potential which, when filled with non-interacting electrons, reproduces the DQMC electron density. The results are compared with the widely-used local-density approximation (LDA). There is a large deviation in the exchange-correlation potential, a slight deviation in the electron density, but a very small deviation in the total energy and its components. We also use DQMC techniques to calculate the quasiparticle band gap, and hence the discontinuity Δ in the exchange-correlation potential on addition of an electron.

PACS Numbers: 71.10.+x, 71.45.Gm

Keywords: DFT

See also: Paper 20

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