Martin M. Rieger^{1,3}, L. Steinbeck^{2}, I.D.
White^{1}, H.N. Rojas^{1,4} and R.W. Godby^{2}

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

Computer Physics Communications **117** 211-228 (1999)

We present a detailed account of the *GW* space-time method. The method
increases the size of systems whose electronic structure can be studied with a
computational implementation of Hedin's *GW* approximation. At the heart of the
method is a representation of the Green's function *G* and the screened Coulomb
interaction *W* in the real-space and imaginary-time domain, which allows a more
efficient computation of the self-energy approximation Σ = *iGW*. For
intermediate steps we freely change between representations in real and reciprocal
space on the one hand, and imaginary time and imaginary energy on the other, using fast
Fourier transforms. The power of the method is demonstrated using the example of Si
with artificially increased unit cell sizes.

PACS Numbers: 71.15.Th,71.20.-b,79.60.Jv

Keywords: GW

Preprint from arXiv.org

Paper from
ScienceDirect

See also: Paper 34, Paper 53, Paper 72

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

Arno Schindlmayr^{1}, Thomas J. Pollehn^{1} and R.W.
Godby^{2}

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

Physical Review B **58** 12684-90 (1998)

With the aim of identifying universal trends, we compare fully self-consistent
electronic spectra and total energies obtained from the *GW*approximation with
those from an extended *GW*Γ scheme that includes a nontrivial vertex
function and the fundamentally distinct Bethe-Goldstone approach based on the
*T*-matrix. The self-consistent Green's function *G*, as derived from Dyson's
equation, is used not only in the self-energy but also to construct the screened
interaction *W* for a model system. For all approximations we observe a similar
deterioration of the spectrum, which is not removed by vertex corrections. In
particular, satellite peaks are systematically broadened and move closer to the
chemical potential. The corresponding total energies are universally raised,
independent of the system parameters. Our results therefore suggest that any
improvement in total energy due to self-consistency, such as for the electron gas in
the *GW* approximation, may be fortuitous.

PACS numbers: 71.10.-w, 71.45.Gm, 71.15.Nc

Keywords: GW

Preprint from arXiv.org

Paper from PRB

See also: Paper 32, Paper 41, Paper 46

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

L. Steinbeck^{1}, A. Rubio^{2}, L. Reining^{3}, M.
Torrent^{3}, I.D. White^{4} and R.W. Godby^{1}

^{1}*Department of Physics, University of York, Heslington, York YO10 5DD,
UK
^{2}Departamento Fisica Teorica, Universidad de Valladolid, E-47011 Valladolid,
Spain
^{3}Laboratoire des Solides Irradiés, URA 1380 CNCRS-CEA/DTA/DECM, Ecole
Polytechnique, Palaiseau, F-91128, France*

Computer Physics Communications **125** 105-118 (2000)

We describe the following new features which significantly enhance the power of the
recently developed real-space imaginary-time *GW* scheme (Rieger *et al.*,
Comp. Phys. Commun. **117** 211 (1999)) for the calculation of self-energies and
related quantities of solids: (i) to fit the smoothly decaying time/energy tails of the
dynamically screened Coulomb interaction and other quantities to model functions,
treating only the remaining time/energy region close to zero numerically and performing
the Fourier transformation from time to energy and vice versa by a combination of
analytic integration of the tails and Gauss-Legendre quadrature of the remaining part
and (ii) to accelerate the convergence of the band sum in the calculation of the
Green's function by replacing higher unoccupied eigenstates by free electron states
(plane waves).

PACS numbers: 71.15.Th, 71.20.-b, 79.60.Jv

Keywords: GW

Preprint from arXiv.org

Paper from
ScienceDirect

See also: Paper 34, Paper 53, Paper 72

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

P. García-González and R.W. Godby

Department of Physics, University of York, Heslington, York YO10 5DD, UK

Physical Review B **63** 075112 (2001) (4 pages)

The performance of many-body perturbation theory for calculating ground-state
properties is investigated. We present fully numerical results for the electron gas in
three and two dimensions in the framework of the *GW* approximation. The overall
agreement with very accurate Monte Carlo data is excellent, even for those ranges of
densities for which the *GW* approach is often supposed to be unsuitable. The
latter seems to be due to the fulfilment of general conservation rules. These results
open further prospects for accurate calculations of ground-state properties
circumventing the limitations of standard density functional theory.

PACS numbers: 71.10.-w, 71.10.Ca

Keywords: GW

Preprint from arXiv.org

Paper from PRB

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

Paula Sánchez-Friera and R.W. Godby

Department of Physics, University of York, Heslington, York YO10 5DD, UK

Physical Review Letters **85** 5611-5614 (2000)

We propose a new method for calculating total energies of systems of interacting electrons, which requires little more computational resources than standard density-functional theories. The total energy is calculated within the framework of many-body perturbation theory by using an efficient model of the self-energy, that nevertheless retains the main features of the exact operator. The method shows promising performance when tested against quantum Monte Carlo results for the linear response of the homogeneous electron gas and structural properties of bulk silicon.

PACS numbers: 71.15.Nc, 71.45.Gm, 71.15.Mb

Keywords: GW

**Reprint**

Preprint from arXiv.org

Paper from PRL

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

(review in a special CCP3 issue of Computer Physics Communications)

P. García-González and R.W. Godby

Department of Physics, University of York, Heslington, York YO10 5DD, UK

Computer Physics Communications **137** 108-122 (2001)

The many-body *GW* approximation has become the most popular method in *ab
initio* calculations of excited-state properties in real materials. *GW*
overcomes many of the limitations of traditional density functional theories to predict
one-electron excitation spectra for a wide variety of materials. In this article we
review some applications of *GW* to real surfaces, from calculations of surface
band structures in semiconductors to estimations of the lifetimes of surface states in
metals.

PACS numbers: 31.15.Ar, 31.15.Lc, 73.20.At, 73.20.+y

Keywords: GW

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

Arno Schindlmayr^{1}, P. García-González^{2} and R.W.
Godby^{3}

^{1}*Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6,
14195 Berlin-Dahlem, Germany*

Physical Review B **64** 235106 (2001) (6 pages)

There is increasing interest in many-body perturbation theory as a practical tool
for the calculation of ground-state properties. As a consequence, unambiguous sum rules
such as the conservation of particle number under the influence of the Coulomb
interaction have acquired an importance that did not exist for calculations of
excited-state properties. In this paper we obtain a rigorous, simple relation whose
fulfilment guarantees particle-number conservation in a given diagrammatic self-energy
approximation. Hedin's *G*_{0}*W*_{0} approximation does not
satisfy this relation and hence violates the particle-number sum rule. Very precise
calculations for the homogeneous electron gas and a model inhomogeneous electron system
allow the extent of the non-conservation to be estimated.

PACS numbers: 71.45.Gm, 71.15.Qe

Keywords: GW

Preprint from arXiv.org Paper from PRB

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

P. García-González^{1} and R.W. Godby^{2}

^{1}*Departamento de Física Fundamental, Universidad Nacional de
Educación a Distancia, Apartado 60141, 28080 Madrid, Spain*

Physical Review Letters **88** 056406 (2002) (4 pages)

We present *GW* many-body results for ground-state properties of two simple but
very distinct families of inhomogenous systems in which traditional implementations of
density-functional theory (DFT) fail drastically. The *GW* approach gives
notably better results than the well-known random-phase approximation, at a similar
computational cost. These results establish *GW* as an superior alternative
to standard DFT schemes without the expensive numerical effort required by quantum
Monte Carlo simulations.

PACS numbers: 71.15.Nc, 71.15.Mb, 71.45.Gm

Keywords: GW DFT

**Reprint**

Preprint from
arXiv.org

Paper from PRL

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

G. Fratesi^{1}, G. P. Brivio^{1}, P. Rinke^{2} and R. W.
Godby^{2}

^{1}*INFM and Dipartimento di Scienza dei Materiali, Università di
Milano-Bicocca, via Cozzi 53, 20125 Milano, Italy*

Physical Review B **68** 195404 (2003) (5 pages)

The electronic properties of a semi-infinite metal surface without a bulk gap are
studied by a formalism able to account for the continuous spectrum of the system. The
density of states at the surface is calculated within the *GW* approximation of
many-body perturbation theory. We demonstrate the presence of an unoccupied surface
resonance peaked at the position of the first image state. The resonance encompasses
the whole Rydberg series of image states and cannot be resolved into individual peaks.
Its origin is the shift in spectral weight when many-body correlations are taken into
account.

PACS number: 73.20.At

Keywords: GW

**Reprint**

Preprint from
arXiv.org

Paper from PRB

See also:Paper 23 Paper 49 Paper 64

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

Silvana Botti, Francesco Sottile, Nathalie Vast, Valerio Olevano, and Lucia
Reining

*Laboratiores des Solides Irradiés, CNRS-CEA, École Polytechnique,
F-91128 Palaiseau, France
* Hans-Christian Weißker

Angel Rubio

Physical Review B **69** 155112 (2004) (14 pages)

We discuss the effects of a static long-range contribution
-*α*/*q*^{2} to the exchange-correlation kernel
*f*_{xc} of time-dependent density functional theory. We show that the
optical absorption spectrum of solids exhibiting a strong continuum exciton effect is
considerably improved with respect to calculations where the adiabatic local density
approximation is used. We discuss the limitations of this simple approach, and in
particular why the same improvement cannot be found for the whole spectral range
including the valence plasmons and bound excitons. On the other hand, we also show that
within the range of validity of the method, the parameter depends linearly on the
inverse of the dielectric constant, and we demonstrate that this fact can be used to
predict continuum excitonic effects in semiconductors. Results are shown for the real
and imaginary part of the dielectric function of Si, GaAs, AlAs, diamond, MgO and SiC,
and for the loss function of Si.

PACS numbers: 71.10.-w, 78.20.Bh, 71.35.-y, 71.15.Qe

Keywords: DFT

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

P. Bokes and R. W. Godby

Department of Physics, University of York, Heslington, York YO10 5DD, United Kingdom

*Physical Review B 68 125414 (2003) (5 pages)*

We develop a theoretical framework for describing steady-state quantum transport phenomena, based on the general maximum-entropy principle of nonequilibrium statistical mechanics. The general form of the many-body density matrix is derived, which contains the invariant part of the current operator that guarantees the nonequilibrium and steady-state character of the ensemble. Several examples of the theory are given, demonstrating the relationship of the present treatment to the widely used scattering-state occupation schemes at the level of the self-consistent single-particle approximation. The latter schemes are shown not to maximize the entropy, except in certain limits.

PACS numbers: 73.23.Ad, 05.60.Gg, 05.30.Ch

Keywords: Transport

**Reprint of
paper
Reprint of
Erratum**

Preprint from arXiv.org

Paper from PRB

Erratum from PRB

See also: Paper 66,Paper 69, Paper 70, Paper 71

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

R. W. Godby^{1} and P. García-González^{2}

^{1}*Department of Physics, University of York, Heslington, York YO10 5DD,
United Kingdom*

Chapter in “*A Primer in Density Functional Theory*” (Lecture Notes
in Physics vol. 620), ed. Carlos Fiolhais, Fernando Nogueira and M. A. L. Marques,
Springer (Heidelberg), 2003.

Keywords: GW DFT

Book from Springer

Chapter from Springer

Preprint

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

Kris Delaney^{1}, P. García-González^{2}, Angel
Rubio^{3}, Patrick Rinke^{4}, and R. W. Godby^{1}

^{1}*Department of Physics, University of York, Heslington, York YO10 5DD,
United Kingdom*

Physical Review Letters **93** 249701 (2004) (1 page)

PACS Numbers: 71.15.Qe, 71.10.-w

Keywords: GW

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

Patrick Rinke^{1}, Kris Delaney^{1}, P.
García-González^{2} and R. W. Godby^{1}

^{1}*Department of Physics, University of York, Heslington, York YO10 5DD,
United Kingdom*

Physical Review A **70** 063201 (2004) (5 pages)

The existence of image states in small clusters is shown for the first time, using
an *ab initio* many-body approach. We present image state energies and
wavefunctions for spherical jellium clusters up to 186 atoms, calculated in the
*GW* approximation, which by construction contains the dynamic long-range
correlation effects that give rise to image effects. In addition we find that image
states are also subject to quantum confinement. To extrapolate our investigations to
clusters in the mesoscopic size range we propose a semi-classical model potential,
which we test against our full *ab initio* results.

PACS Numbers: 36.40.Cg, 73.20.At, 73.22.Dj

Keywords: GW

**Reprint**

Preprint from arXiv.org

Paper from PRA

See also: Paper 23, Paper 49, Paper 59

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

J. Jung^{1}, P. García-González^{2}, J.E.
Alvarellos^{2} and R. W. Godby^{3}

^{1}*Departamento de Física Fundamental, Universidad Nacional de
Educación a Distancia, Apartado 60141, E-28080 Madrid, Spain*

Physical Review A **69** 052501 (2004) (7 pages)

The complex nature of electron-electron correlations is made manifest in the very simple but non-trivial problem of two electrons confined within a sphere. The description of highly non-local correlation and self-interaction effects by widely used local and semi-local exchange-correlation energy density functionals is shown to be unsatisfactory in most cases. Even the best such functionals exhibit significant errors in the Kohn-Sham potentials and density profiles.

PACS Numbers: 31.15.Ew, 31.25.-v, 71.15.Mb

Keywords: DFT

**Reprint**

Preprint from arXiv.org

Paper from PRA

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

P. Bokes^{1,2} and R. W. Godby^{1}

^{1}*Department of Physics, University of York, Heslington, York YO10 5DD,
United Kingdom*

Physical Review B **69** 245420 (2004) (8 pages)

We revisit the expression for the conductance of a general nanostructure -- such as
a quantum point contact -- as obtained from the linear response theory. We show that
the conductance represents the strength of the Drude singularity in the conductivity
*σ*(**k**,**k**';*i*ω→0). Using the equation of
continuity for electric charge we obtain a formula for conductance in terms of
polarization of the system. This identification can be used for direct calculation of
the conductance for systems of interest even at the *ab-initio* level. In
particular, we show that one can evaluate the conductance from calculations for a
finite system without the need for special "transport" boundary conditions.

PACS numbers: 73.23.-b, 73.63.-b, 05.60.Gg

Keywords: Transport

**Reprint**

Preprint from arXiv.org

Paper from PRB

See also: Paper 61, Paper 69, Paper 70, Paper 71

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

J. Jung^{1}, P. García-González^{2}, J.F.
Dobson^{3} and R. W. Godby^{4}

^{1}*Departamento de Física Fundamental, Universidad Nacional de
Educación a Distancia, Apartado 60141, E-28080 Madrid, Spain*

Phys. Rev. B **70** 205107 (2004) (11 pages)

The performance of the adiabatic-connection fluctuation-dissipation theorem (ACFDT)
is discussed through the implementation of a non-local energy optimized
exchange-correlation kernel to account for short range correlation effects. Whereas
*total* electron correlation energies are rather sensitive to the details of the
kernel, any physically well motivated approximation describes binding energies
(including surface energies) within the same level of accuracy.

PACS numbers: 71.10.-w, 71.15.Mb, 71.15.Nc, 71.45.Gm

Keywords: DFT

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

Xavier Gonze, Gian-Marco Rignanese, Matthieu Verstraete, Jean-Michel Betiken, Yann Pouillon, Razvan Caracas, Francois Jollet, Marc Torrent, Glues Zerah, Masayoshi Mikami, Philippe Ghosez, Marek Veithen, Jean-Yves Raty, Valerio Olevano, Fabien Bruneval, Lucia Reining, Rex Godby, Giovanni Onida, D. R. Hamann and Douglas C. Allan

Zeitschrift für Kristallographie **220** 558–562 (2005)
(Special issue on Computational Crystallography)

A brief introduction to the ABINIT software package is given. Available under a Free software license, it allows to compute directly a large set of properties useful for solid state studies, including structural and elastic properties, prediction of phase (meta)stability or instability, specific heat and free energy, spectroscopic and vibrational properties. These are described, and corresponding applications are presented. The emphasis is also laid on its ease of use and extensive documentation, allowing newcomers to quickly step in.

Keywords: GW

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

H. Mera^{1}, P.
Bokes^{2} and R.W. Godby^{1}

^{1}*Department of Physics, University of York, Heslington, York YO10 5DD,
United Kingdom*

Physical Review B **72** 085311 (2005) (6 pages)

*Ab-initio* simulations of
quantum transport commonly focus on a central region which is considered to be
connected to infinite, periodic leads through which the current flows. The
electronic structure of these distant leads is normally obtained from an
*equilibrium* calculation, ignoring the self-consistent response of the leads to
the current. We examine the consequences of this, and show that the electrostatic
potential, Δ*φ*, is effectively being approximated by the difference
between electrochemical potentials, Δ*μ*, and that this approximation is
incompatible with asymptotic charge neutrality. In a test calculation for a simple
metal-vacuum-metal junction, we find large errors in the non-equilibrium properties
calculated with this approximation, in the limit of small vacuum gaps. We provide a
simple scheme by which these errors may be corrected.

PACS numbers: 05.60.Gg, 73.40.-c, 41.20

Keywords: Transport

**Reprint**

Preprint from arXiv.org

Paper from PRB

See also:Paper 61,Paper 66, Paper 70, Paper 71

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

P. Bokes^{1,2,} H.
Mera^{2}, and R.W. Godby^{2}

^{1}*Department of Physics, Faculty of Electrical Engineering and
Information Technology, Slovak Technical University, Ilkovičova 3, 812 19
Bratislava, Slovak Republic*

Physical Review B **72** 165425 (2005) (10 pages)

Presently, the main methods for describing a non-equilibrium charge-transporting steady state are based on time-evolving it from the initial zero-current situation. An alternative class of theories would give the statistical non-equilibrium density operator from principles of statistical mechanics, in a spirit close to Gibbs ensembles for equilibrium systems, leading to a variational principle for the non-equilibrium steady state. We discuss the existing attempts to achieve this using the maximum entropy principle based on constraining the average current. We show that the current-constrained theories result in a zero induced drop in electrostatic potential, so that such ensembles cannot correspond to the time-evolved density matrix, unless left- and right-going scattering states are mutually incoherent.

PACS numbers: 73.63.-b, 73.23.Ad, 05.60.Gg

Keywords: Transport

**Reprint**

Preprint from arXiv.org

Paper from
PRB

See also: Paper 61,Paper 66, Paper 69, Paper 71

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

P. Bokes^{1}, J.
Jung^{2,3} and R. W. Godby^{3}

^{1}*Department of Physics, Faculty of Electrical Engineering and
Information Technology, Slovak Technical University, Ilkovičova 3, 812 19
Bratislava, Slovak Republic*

arXiv.org cond-mat/0604317

Note: the results in this paper were subsequently published as part of Paper 76: see below

We obtain the conductance of a system of electrons connected to leads, within time-dependent density-functional theory, using a direct relation between the conductance and the density response function. Corrections to the non-interacting conductance appear as a consequence of the functional form of the exchange-correlation kernel at small frequencies and wavevectors. The simple adiabatic local-density approximation and non-local density-terms in the kernel both give rise to significant corrections in general. In the homogeneous electron gas, the former correction remains significant, and leads to a failure of linear-response theory for densities below a critical value.

PACS numbers: 73.63.-b, 71.15.Mb, 73.40.Jn, 05.60.Gg

Keywords: Transport

See also: Paper 61,Paper 66, Paper 69, Paper 70

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

Christoph Freysoldt^{1}, Philipp Eggert^{1}, Patrick
Rinke^{1}, Arno Schindlmayr^{1,2}, R.W. Godby^{3} and Matthias
Scheffler^{1}

^{1}*Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6,
14195 Berlin, Germany*

^{2}*Institut für Festkörperforschung, Forschungszentrum
Jülich, 52425 Jülich, Germany*

^{3}*Department of Physics, University of York, Heslington, York YO10 5DD,
United Kingdom*

Computer Physics Communications, **176** 1-13 (2007)

Excited-state calculations, notably for quasiparticle band structures, are nowadays
routinely performed within the *GW* approximation for the electronic self-energy.
Nevertheless, certain numerical approximations and simplifications are still employed
in practice to make the computations feasible. An important aspect for periodic systems
is the proper treatment of the singularity of the screened Coulomb interaction in
reciprocal space, which results from the slow 1/*r* decay in real space. This must
be done without introducing artificial interactions between the quasiparticles and
their periodic images in repeated cells, which occur when integrals of the screened
Coulomb interaction are discretised in reciprocal space. An adequate treatment of both
aspects is crucial for a numerically stable computation of the self-energy. In this
article we build on existing schemes for isotropic screening and present an extension
for anisotropic systems. We also show how the contributions to the dielectric function
arising from the non-local part of the pseudopotentials can be computed efficiently.
These improvements are crucial for obtaining a fast convergence with respect to the
number of points used for the Brillouin zone integration and prove to be essential to
make *GW* calculations for strongly anisotropic systems, such as slabs or
multilayers, efficient.

PACS numbers: 71.15.Qe, 71.45.Gm

Keywords: GW

Preprint from arXiv.org

Paper from ScienceDirect

See also: Paper 34, Paper 51, Paper 53

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

H. Mera^{1,2}, P.
Bokes^{3} and R. W. Godby^{2}

^{1}*Department of Physics, University of York, Heslington, York YO10 5DD,
United Kingdom*

Physical Review B **76** 125319 (2007) (5 pages)

State-of-the-art simulation tools for non-equilibrium quantum transport systems
typically take the current-carrier occupations to be described in terms of equilibrium
distribution functions characterised by two different electro-chemical potentials,
while for the description of electronic exchange and correlation, the local density
approximation (LDA) to density functional theory (DFT) is generally used. However this
involves an inconsistency because the LDA is based on the homogeneous electron gas in
equilibrium, while the system is not in equilibrium and may be far from it. In this
paper we analyze this inconsistency by studying the interplay between non-equilibrium
occupancies obtained from a maximum entropy approach and the Hartree-Fock exchange
energy, single-particle spectrum and exchange hole, for the case of a two-dimensional
homogeneous electron gas. The current-dependence of the local exchange potential is
also discussed.

It is found that the single-particle spectrum and exchange hole have a significant
dependence on the current which has not been taken into account in practical
calculations. The exchange energy and the local exchange potential, however, are shown
to change very little with respect to their equilibrium counterparts. The weak
dependence of these quantities on the current is explained in terms of the symmetries
of the exchange hole.

PACS numbers: 71.10.-w, 71.10.Ca, 71.70.Gm, 73.23.-b

Keywords: Transport

**Reprint**

Preprint from arXiv.org

Preprint from PRB

See also:Paper 61,Paper 66, Paper 69, Paper 70

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

W.
Nelson^{1}*, P. Bokes^{2}, Patrick Rinke^{3} and R.W.
Godby^{1}

^{1}Department of Physics,
University of York, Heslington, York YO10 5DD, United Kingdom and European Theoretical
Spectroscopy Facility^{2}Department of Physics,
Faculty of Electrical Engineering and Information Technology, Slovak University of
Technology, Ilkovičova 3, 841 04
Bratislava, Slovak Republic and European Theoretical Spectroscopy
Facility^{3}Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany and European Theoretical
Spectroscopy Facility

*Present address: Department of Physics, King's College, London, Strand, London WC2R
2LS, United Kingdom

Physical Review A **75** 032505 (2007) (4 pages)

Atomic
hydrogen provides a unique test case for computational electronic structure methods,
since its electronic excitation energies are known analytically. With only one
electron, hydrogen contains no electronic correlation and is therefore particularly
susceptible to spurious self-interaction errors introduced by certain computational
methods. In this paper we focus on many-body perturbation-theory (MBPT) in Hedin's
*GW* approximation. While the Hartree-Fock and the exact MBPT self-energy are free
of self-interaction, the correlation part of the *GW* self-energy does not have
this property. Here we use atomic hydrogen as a benchmark system for *GW* and show
that the self-interaction part of the *GW* self-energy, while non-zero, is small.
The effect of calculating the *GW* self-energy from exact wavefunctions and
eigenvalues, as distinct from those from the local-density approximation, is also
illuminating.

PACS numbers: 31.25Jf, 31.15 Lc, 31.15 Ar

Keywords: GW

**Reprint**

Preprint from arXiv.org

Paper from
PRA

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

Andrew J.
Morris^{1}, Martin Stankovski^{1}, Kris T. Delaney^{2}, Patrick
Rinke^{3}, P.
García-González^{4} and R.W.
Godby^{1}

^{1}Department of
Physics, University of York, Heslington, York YO10 5DD, United Kingdom^{
2}Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL
61801, USA

^{3}Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195
Berlin-Dahlem, Germany^{4}Departmento de Física Fundamental, U.N.E.D., Apartado 60141,
E-28080 Madrid, Spain

*Physical Review* *B
76 155106 (2007) (9 pages)*

Within
many-body perturbation theory we apply vertex corrections to various closed-shell atoms
and to jellium, using a local approximation for the vertex consistent with starting the
many-body perturbation theory from a DFT-LDA Green’s function. The vertex appears
in two places – in the screened Coulomb interaction, *W*, and in the
self-energy, Σ – and we obtain a systematic discrimination of these two
effects by turning the vertex in Σ on and off. We also make comparisons to
standard *GW* results within the usual random-phase approximation (RPA), which
omits the vertex from both. When a vertex is included for closed-shell atoms, both
ground-state and excited-state properties demonstrate only limited improvements over
standard *GW*. For jellium we observe marked improvement in the quasiparticle band
width when the vertex is included only in *W*, whereas turning on the vertex in
Σ leads to an unphysical quasiparticle dispersion and work function. A simple
analysis suggests why implementation of the vertex only in *W* is a valid way to
improve quasiparticle energy calculations, while the vertex in Σ is unphysical,
and points the way to development of improved vertices for *ab initio* electronic
structure calculations.

PACS numbers: 71.45.Gm, 31.25.Eb, 31.25.Jf, 71.10.Ca

Keywords: GW

**Reprint**

Preprint from arXiv.org

Paper from
PRB

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

P. Bokes^{1,2}, J. Jung^{3,1} and R.W.
Godby^{1}

^{1}Department of
Physics, University of York, Heslington, York YO10 5DD, United
Kingdom^{} ^{2}Department of Physics,
Faculty of Electrical Engineering and Information Technology, Slovak University of
Technology, Ilkovičova 3, 841 04
Bratislava, Slovak Republic

^{3}Physics Division, National Center for Theoretical Sciences, P.O. Box 2-131,
Hsinchu, Taiwan

*Physical Review* *B
76 125433 (2007) (8 pages)*

We derive an expression for the 4-point conductance of a general quantum junction in terms of the density response function. Our formulation allows us to show that the 4-point conductance of an interacting electronic system possessing either a geometrical constriction and/or an opaque barrier becomes identical to the macroscopically measurable 2-point conductance. Within time-dependent density-functional theory the formulation leads to a direct identification of the functional form of the exchange-correlation kernel that is important for the conductance. We demonstrate the practical implementation of our formula for a metal-vacuum-metal interface.

PACS numbers: 73.63.-b, 71.15.Mb, 73.40.Jn, 05.60.Gg

Keywords: Transport

**Reprint**

Preprint from arXiv.org

Paper from PRB

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

J. Jung^{1,2},P. Bokes^{2,3} and R.W.
Godby^{3}

^{1}Physics
Division, National Center for Theoretical Sciences, P.O. Box 2-131, Hsinchu,
Taiwan^{} ^{2}Department of Physics,
Faculty of Electrical Engineering and Information Technology, Slovak University of
Technology, Ilkovičova 3, 841 04
Bratislava, Slovak Republic^{
3}Department of Physics, University of York, Heslington, York YO10 5DD, United
Kingdom

Physical Review Letters **98** 259701 (2007)

We comment on the treatment of the electronic viscosity in the
paper "*Dynamical corrections to the DFT-LDA electron conductance in nanoscale
systems*", Na Sai, Michael Zwolak, Giovanni Vignale and Massimiliano Di Ventra,
Phys. Rev. Lett. **94** 186810 (2005), using calculations for a model
metal-vacuum-metal system.

PACS numbers: 73.63.Nm, 68.37.Ef, 71.15.Mb, 73.40.Jn

Keywords: Transport

**Reprint**

Preprint from arXiv.org

Paper from PRL

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

P. Bokes^{1,2}, F. Corsetti^{1} and R.W.
Godby^{1}

^{1}Department
of Physics, University of York, Heslington, York YO10 5DD, United
Kingdom^{2}*Department of Physics, Faculty of Electrical Engineering and Information
Technology, Slovak University of Technology, Ilkovičova 3, 841 04 Bratislava, Slovak Republic*

Physical Review Letters **101** 046402 (2008) (4
pages).

We introduce the construction of a orthogonal wavepacket basis set, using the concept of stroboscopic time propagation, tailored to the efficient description of non-equilibrium extended electronic systems. Thanks to three desirable properties of this basis, significant insight is provided into non-equilibrium processes (both time-dependent and steady-state), and reliable physical estimates of various many-electron quantities such as density, current and spin polarization can be obtained. The use of this novel tool is demonstrated for time-dependent switching-on of the bias in quantum transport, and new results are obtained for current-induced spin accumulation at the edge of a 2D doped semiconductor caused by edge-induced spin-orbit interaction.

PACS numbers: 71.15.-m, 72.10.Bg, 72.25.-b, 73.63.-b

Keywords: Transport DFT

**Reprint**

Preprint from arXiv.org

Paper from PRL

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

Matthieu J. Verstraete* ^{1,3}*, P. Bokes

^{1}Department
of Physics, University of York, Heslington, York YO10 5DD, United
Kingdom^{2}*Department of Physics, Faculty of Electrical Engineering and Information
Technology, Slovak University of Technology, Ilkovičova 3, 841 04 Bratislava, Slovak Republic
^{3}European Theoretical Spectroscopy Facility (ETSF)*

Journal of Chemical Physics **130** 124715 (2009) (8
pages)

A method for the calculation of the conductance of nanoscale electrical junctions is extended to ab-initio electronic structure methods and applied to realistic models of metallic wires and break-junctions of sodium and gold. The method is systematically controllable and convergeable, and can be straightforwardly extended to include more complex processes and interactions. Important issues about the order in which are taken both the thermodynamic and the static (small field) limits are clarified, and characterized further through comparisons to model systems.

PACS numbers: 73.63.Rt, 71.15.-m

Keywords: Transport GW

**Reprint**

Preprint from arXiv.org

Paper from JCP

See also: Paper 76

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list

L. K. Dash^{1,2}, H. Ness^{1,2} and R. W.
Godby^{1,2}

^{1}Department
of Physics, University of York, Heslington, York YO10 5DD, United
Kingdom^{2}*European Theoretical Spectroscopy Facility (ETSF)*

Journal of Chemical Physics **132** 104113 (2010) (20
pages)

We consider the interaction between electrons and molecular vibrations in the context of electronic transport in nanoscale devices. We present a method based on non-equilibrium Green’s functions to calculate both equilibrium and non-equilibrium electronic properties of a single-molecule junction in the presence of electron-vibron interactions. We apply our method to a model system consisting of a single electronic level coupled to a single vibration mode in the molecule, which is in contact with two electron reservoirs. Higher-order diagrams beyond the usual self-consistent Born approximation (SCBA) are included in the calculations. In this paper we consider the effects of the double-exchange diagram and the diagram in which the vibron propagator is renormalized by one electron-hole bubble. We study in detail the effects of the first- and second-order diagrams on the spectral functions for a large set of parameters and for different transport regimes (resonant and off-resonant cases), both at equilibrium and in the presence of a finite applied bias. We also study the linear response (linear conductance) of the nanojunction for all the different regimes. We find that it is indeed necessary to go beyond the SCBA in order to obtain correct results for a wide range of parameters.

PACS numbers: 71.38.-k, 73.40.Gk, 85.65.+h, 73.63.-b

Keywords: Transport

**Reprint**

Preprint from arXiv.org

Paper from JCP

Use your browser's *Back* button to return, or click
here to jump to top of main publications
list