Thomas J. Pollehn*, Arno Schindlmayr* and R.W. Godby**

**Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge CB3 0HE, United Kingdom
**Department of Physics, University of York, Heslington, York YO1 5DD, United Kingdom*

*Journal of Physics: Condensed Matter 10 1273-1283 (1998)*

We investigate the performance of the *GW* approximation by comparison with exact results for small model systems. The role of the chemical potentials in Dyson's equation as well as the consequences of numerical resonance broadening are reexamined, and we show how a proper treatment can improve computational implementations of many-body theory in general. *GW* and exchange-only calculations are performed over a wide range of fractional band fillings and correlation strengths. We thus identify the physical situations where these schemes are applicable.

PACS Numbers: 71.10.Fd, 71.15.-m, 71.45.Gm

Keywords: GW DFT

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See also: Paper 32, Paper 46, Paper 52

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X. Gonze*, P. Ghosez* and R.W. Godby**

**Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
**Department of Physics, University of York, Heslington, York YO1 5DD, U.K.*

*Physical Review Letters 78 2029 (1997)*

We comment on a recent paper by R. Resta [Phys. Rev. Lett. **77** 2265 (1996)] by noting that an exchange-correlation electric field exists even in the case of exchange-only density-functional theory.

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

Keywords: GW DFT

See also: Paper 36, Paper 39, Paper 44

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I.V. Abarenkov^{1}, V.L. Bulatov^{2}, R.W. Godby^{3}, V. Heine^{4}, M.C. Payne^{4}, P.A. Souchko^{1}, A.V. Titov^{5} and I.I. Tupitsyn^{1}

^{1} *St. Petersburg State University, St. Petersburg, Russia
*

*Physical Review B 56 1743 (1997)*

The present paper proposes a method for electronic structure calculations on a type of system which cannot be handled by present methods. It considers a system where a multi-determinant wave function is essential for an atom or a small cluster of atoms embedded in a large system, normally a solid, which can be treated by density-functional methods such as the LDA. A suitable example is a transition metal atom in a semiconductor or MgO host. In this method the embedding potential for the cluster is generated from an LDA calculation but applied in a multiconfiguration calculation. The method and the concept of the embedding potential are validated by application to a simple system of a cluster Li_{2}Mg_{2} of four pseudoatoms.

Keywords: DFT

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P. Ghosez*, X. Gonze* and R.W. Godby**

**Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
**Department of Physics, University of York, Heslington, York YO1 5DD, U.K.*

*Physical Review B 56 12811-12817 (1997)*

The polarization-dependence of the exchange-correlation (XC) energy functional of periodic insulators within Kohn-Sham (KS) density-functional theory requires a O(1/*q*^{2}) divergence in the XC kernel for small vectors **q**. This behaviour, exemplified for a one-dimensional model semiconductor, is also observed when an insulator happens to be described as a KS metal, or vice-versa. Although it can occur in the exchange-only kernel, it is not found in the usual local, semi-local or even non-local approximations to KS theory. We also show that the test-charge and electronic definitions of the macroscopic dielectric constant differ from one another in exact KS theory, but are equivalent in the above-mentioned approximations.

PACS Numbers: 71.10.+x, 77.22.Ej

Keywords: GW DFT

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See also: Paper 36, Paper 39, Paper 42

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M.R. Jarvis^{1}, I.D. White^{1}, R.W. Godby^{2} and M.C. Payne^{1}

^{1} Theory of Condensed Matter Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, United Kingdom

^{2} Department of Physics, University of York, Heslington, York YO1 5DD, United Kingdom

*Physical Review B 56 14972-8 (1997)*

**Abstract:** We study the behaviour of total-energy supercell calculations for dipolar molecules and charged clusters. Using a cutoff Coulomb interaction within the framework of a plane-wave basis set formalism, with all other aspects of the method (pseudopotentials, basis set, exchange-correlation functional) unchanged, we are able to assess directly the interaction effects present in the supercell technique. We find that the supercell method gives structures and energies in almost total agreement with the results of calculations for finite systems, even for molecules with large dipole moments. We also show that the performance of finite-grid calculations can be improved by allowing a degree of aliasing in the Hartree energy, and by using a reciprocal space definition of the cutoff Coulomb interaction.

PACS numbers: 71.15.-m, 31.15.Ew, 71.15.Ap, 31.15.Qg

Keywords: DFT

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Arno Schindlmayr^{1} and R.W. Godby^{2}

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

^{2} *Department of Physics, University of York, Heslington, York YO1 5DD, United Kingdom*

*Physical Review Letters 80 1702 (1998)*

We present a general procedure for obtaining progressively accurate functional expressions for the electron self-energy by iterative solution of Hedin's coupled equations. The iterative process starting from Hartree theory, which gives rise to the *GW* approximation, is continued further, and an explicit formula for the vertex function from the second full cycle is given. Calculated excitation energies for a Hubbard Hamiltonian demonstrate the convergence of the iterative process and provide further strong justification for the *GW* approximation.

PACS numbers: 71.15.-m, 71.20.-b, 71.45.Gm

Keywords: GW

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See also: Paper 32, Paper 41, Paper 52

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R.W. Godby^{1} and I.D. White^{2}

^{1} *Department of Physics, University of York, Heslington, York YO1 5DD, United Kingdom*

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

*Physical Review Letters 80 3161 (1998)*

A comment is made on the large-cluster limit of the self-energy correction for the quasiparticle energy gap in silicon clusters presented by Serdar Ogut, James R. Chelikowsky and Steven G. Louie in Phys. Rev. Lett. **79**, 1770 (1997).

PACS numbers: 78.66.Db, 61.46.+w , 71.35.Cc, 73.20.Dx

Keywords: GW DFT

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A.R. Porter and R.W. Godby

*Department of Physics, University of York, Heslington, York YO1 5DD, United Kingdom*

*arXiv: physics/9711005*

We present the results of over 90 tight-binding molecular-dynamics simulations of collisions between three- and five-atom silicon clusters, at a system temperature of 2000K. Much the most likely products are found to be two 'magic' four-atom clusters. We show that previous studies, which focused on the equilibrium binding energies of clusters of different sizes, are of limited relevance, and introduce a new effective binding energy which incorporates the highly anharmonic dynamics of the clusters. The inclusion of dynamics enhances the magic nature of both Si_{4} and Si_{6} and destroys that of Si_{7}.

PACS Numbers: 36.40.Sx, 36.40.Qv, 36.40.Jn, 82.20.Wt

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I.D. White^{1}, R.W. Godby^{2}, M.M. Rieger^{1} and R.J. Needs^{1}

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

^{2} *Department of Physics, University of York, Heslington, York YO1 5DD, United Kingdom*

*Physical Review Letters 80 4265-8 (1998)*

We evaluate the electronic self-energy Σ(*E*) at an Al(111) surface using the *GW* space-time method. This self-energy automatically includes the image potential *V*_{im} not present in any local-density approximation for exchange and correlation. We solve the energy-dependent quasiparticle equations to obtain surface state wavefunctions, and calculate the effective local potential experienced by electrons in the near-surface region. We find that *V*_{im} for unoccupied states is due to correlation (not exchange). The image-plane position for interacting electrons is considerably closer to the surface than for the purely electrostatic effects felt by test charges, and, like its classical counterpart, is drawn inwards by the effects of atomic structure.

PACS Numbers: 73.30.-r, 71.15.-m

Keywords: GW DFT

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See also:Paper 23Paper 59Paper 64

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Martin M. Rieger^{1} and R.W. Godby^{2}

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

^{2} *Department of Physics, University of York, Heslington, York YO1 5DD, United Kingdom*

*Physical Review B 58 1343 (1998)*

We present a method to calculate the electronic charge density of periodic solids in the *GW* approximation, using the space-time method. We investigate for the examples of silicon and germanium to what extent the *GW* approximation is charge-conserving and how the charge density compares with experimental values. We find that the *GW* charge density is close to experiment and charge is practically conserved. We also discuss how using a Hartree potential consistent with the level of approximation affects the quasi-particle energies and find that the common simplification of using the LDA Hartree potential is very well justified.

PACS Numbers: 71.20.Mq, 71.15.Th

Keywords: GW DFT

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