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

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

*Europhysics Letters 27 681 (1994)
*

We present *ab initio* calculations of the dynamic scattering cross-section of aluminium, including local-field effects. The fine structure is in excellent agreement with recent inelastic X-ray scattering experiments, and arises from bandstructure effects, in contrast to recent theoretical suggestions. The calculated cross-section exhibits definite anisotropy, especially at higher momentum transfers.

PACS Numbers: 61.45G, 78.70C

Keywords: DFT

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C. Verdozzi^{1,2}, R.W. Godby^{1} and S. Holloway^{2}

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

^{2} *Surface Science Research Centre, University of Liverpool, PO Box 147, Liverpool L69 3BX, United Kingdom*

*Physical Review Letters 74 2327 (1995)
*

We evaluate several approximations for the self-energy operator and dielectric function of systems of interacting electrons using a two-dimensional Hubbard cluster for which the self-energy, dielectric function and one-particle Green's function may be calculated exactly. The results show the *GW* approximation (in the form in which it is commonly used in ab initio calculations for real materials) to be relatively successful in establishing the main features of the spectrum, even when the electron-electron interaction is not weak. It is also clear that improving the *G* and *W* used in this approximation without including vertex corrections in the self-energy does not lead to major improvements. The implications for *ab initio* calculations are considered.

PACS Numbers: 71.10.+x, 71.45.Gm

Keywords: GW

See also: Paper 41 , Paper 46 , Paper 52

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

*Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, U.K.
*

*Physical Review B 51 1527 (1995)
*

We investigate the band-gap narrowing in silicon caused by the introduction of additional electron carriers together with a neutralising uniform positive background charge. The local density approximation (LDA) is shown to be inadequate for calculating the band-gap narrowing. Using a first-principles technique and the *GW* approximation for the self-energy operator, we show that the change in the screening of the electron-electron interaction is the dominant effect. By employing the non-local inhomogeneous and energy-dependent dielectric function of the intrinsic material we obtain significant corrections at high doping densities to previous model theories which use the simple static dielectric constant. While the inclusion of local-field effects is shown to give a negligible contribution, it is the energy-dependence of the dielectric function that gives the main improvement. The inclusion in the screened Coulomb interaction of the "true" wavefunctions (calculated using the LDA) which we assume the additional carriers to occupy is found to have no significant effect compared with the results obtained from a calculation using plane-wave functions. This is due to the fact that the changes in the electron-electron interaction occur predominantly at long wavelengths, so that the microscopic details of the wavefunctions are unimportant.

PACS Numbers: 71.25.Rk, 71.45.Gm

Keywords: GW DFT

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H.N. Rojas, R.W. Godby and R.J. Needs

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

*Physical Review Letters 74 1827 (1995)
*

We present a new method for efficient, accurate calculations of many-body properties of periodic systems. The main features are (i) use of a real-space/imaginary-time representation; (ii) avoidance of any model form for the screened interaction *W*; (ii) exact separation of *W* and the self-energy Σ into short- and long-ranged parts; (iv) the use of novel analytical continuation techniques in the energy domain. The computer time scales approximately linearly with system size. We give results for jellium and silicon, including the spectral function of silicon obtained from the Dyson equation.

PACS Numbers: 71.10.+x, 71.45.Gm, 71.25.Cx, 71.25.Rk

Keywords: GW

See also: Paper 51 , Paper 53 , Paper 72

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Z. Dadachanji^{1}, R.W. Godby^{1}, R.J. Needs^{1} and P.B. Littlewood^{2}

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

^{2 }*AT&T Bell Laboratories, Murray Hill, NJ 07974, USA*

*Physical Review B 52 16204-7 (1995)
*

First-principles calculations of the dielectric matrix of the key structural element of the copper-oxide superconductors show a weakly-damped resonance at 3.5 eV which contains most of the oscillator strength in charge-transfer excitations. Such excitations have been proposed as a mediating boson for superconductive pairing. Although this mode is a well-developed and robust excitation, we find its energy to be too large to give high superconducting transition temperatures.

PACS Numbers: 74.65.+n, 71.45.Gm

Keywords: GW

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X. Gonze^{1}, P. Ghosez^{1} and R.W. Godby^{2}

^{1 }*Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
*

*Physical Review Letters 74 4035 (1995)
*

The response of an infinite, periodic, insulating, solid to an infinitesimally small electric field is investigated in the framework of Density Functional Theory. We find that the applied perturbing potential is not a unique functional of the periodic density change: it depends also on the change in the macroscopic *polarization*. Moreover, the dependence of the exchange-correlation energy on polarization induces an exchange-correlation electric field. These effects are exhibited for a model semiconductor. We also show that the scissor-operator technique is an approximate way of bypassing this polarization dependence.

PACS Numbers: 71.10.+x; 77.20.+y; 78.20.Bh

Keywords: DFT GW

See also: Paper 39 , Paper 42 , Paper 44

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Arno Schindlmayr and R.W. Godby

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

*Physical Review B 51 10427 (1995)
*

Inspired by earlier work on the band-gap problem in insulators, we reexamine the treatment of strongly correlated Hubbard-type models within density-functional theory. In contrast to previous studies, the density is fully parametrized by occupation numbers *and* overlap of orbitals centered at neighboring atomic sites, as is the local potential by the hopping matrix. This corresponds to a good formal agreement between density-functional theory in real space and second quantization. It is shown that density-functional theory is formally applicable to such systems and the theoretical framework is provided. The question of noninteracting *v*-representability is studied numerically for finite one-dimensional clusters, for which exact results are available, and qualitatively for infinite systems. This leads to the conclusion that the electron density corresponding to interacting systems of the type studied here is in fact *not* noninteracting *v*-representable because the Kohn-Sham electrons are unable to reproduce the correlation-induced localization correctly.

PACS Numbers: 71.10.+x, 71.45.Gm

Keywords: GW DFT

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Giovanni Onida^{1}, Lucia Reining^{1}, R.W. Godby^{2}, R. Del Sole^{3} and Wanda Andreoni^{4}

^{1} *Laboratoire des Solides Irradiés, URA 1380 CNRS - CEA/DTA/DECM, Ecole Polytechnique, F-91128 Palaiseau, France
*

*Physical Review Letters 75 818 (1995)
*

We report the first *ab-initio* quasiparticle calculation in a real cluster, Na_{4}, within Hedin's *GW* approximation for the valence electron self-energy. Our approach avoids the summations over empty states, and also eliminates the problem of residual interactions between the periodic images. Self-energy corrections open the LDA gap by more than 2 eV; finite-size effects on screening are shown to play an important role. The absorption spectrum calculated by including excitonic effects using our *ab-initio* screened interaction gives a good account of the experimental photodepletion data.

Keywords: GW

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X. Gonze^{1}, P. Ghosez^{1} and R.W. Godby^{2}

^{1 }*Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
*

*Physical Review Letters 78 294 (1997)
*

We examine the density-functional theory of macroscopic insulators, obtained either from the large-size limit of a cluster, or by imposing periodic boundary conditions. For *polar* crystals, we find that these two procedures describe distinct physics. In the large-cluster case, a homogeneous exchange-correlation electric field appears, and the Kohn-Sham electronic system becomes metallic. With periodic boundary conditions, such a field is forbidden, and the polarization deduced from Kohn-Sham wavefunctions is generally incorrect. The latter effect is exhibited for a model insulator.

PACS Numbers: 71.15.Mb; 71.10.-w; 77.22.Ej

Keywords: GW DFT

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Paper from PRL

See also: Paper 36 , Paper 42 , Paper 44

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Lucia Reining^{1}, Giovanni Onida^{1,2} and R.W. Godby^{3}

^{1 }*Laboratoire des Solides Irradiés, URA 1380 CNRS - CEA/DTA/DECM, Ecole Polytechnique, F-91128 Palaiseau, France
*

*Physical Review B (Rapid Communications) 56 R4301 (1997)
*

We present a new method for the computation of self-energy corrections in large supercells. It eliminates the explicit summation over unoccupied states, and uses an iterative scheme based on an expansion of the Green's function around a set of reference energies. This improves the scaling of the computational time from the fourth to the third power of the number of atoms for both the inverse dielectric matrix and the self-energy, yielding improved efficiency for 8 or more silicon atoms per unit cell.

PACS Numbers: 71.10.-w, 71.15.Ap, 71.45.Gm, 71.20.Mq

Keywords: GW

Preprint from arXiv server

Paper from PRB

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