arXiv subjects

R. W. Godby

Publications and source records attributed to R. W. Godby.

49 records · Page 3Linked to original sources

arXiv1998

Spectra and total energies from self-consistent many-body perturbation theory

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 GWGamma 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.

cond-mat.mtrl-sci↗

arXiv1998

Elimination of unoccupied state summations in ab-initio self-energy calculations for large supercells

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.

cond-mat↗

arXiv1998

The charge density of semiconductors in the GW approximation

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 a very well justified.

cond-mat↗

arXiv1997

Dynamic image potential at an Al(111) surface

We evaluate the electronic self-energy Sigma(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.

cond-mat.mtrl-sci↗

arXiv1997

Assessment of the GW approximation using Hubbard chains

We investigate the performance of the GW approximation by comparison to 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 examined, and we show how a proper treatment can improve computational implementations of many-body perturbation 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.

cond-mat.mtrl-sci↗

arXiv1997

Influence of Dynamics on Magic Numbers for Silicon Clusters

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 Si4 and Si6 and destroys that of Si7.

physics.atm-clus↗

arXiv1997

Systematic vertex corrections through iterative solution of Hedin's equations beyond the GW approximation

We present a general procedure for obtaining progressively more 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.

cond-mat.mtrl-sci↗

arXiv1997

Density-relaxation part of the self energy

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).

cond-mat.mtrl-sci↗

arXiv1997

Density-functional theory and the v-representability problem for model strongly correlated electron systems

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.

cond-mat.str-el↗

arXiv1997

Supercell technique for total-energy calculations of finite charged and polar systems

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.

cond-mat.mtrl-sci↗

arXiv1997

The long-wavelength behaviour of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems

The polarization-dependence of the exchange-correlation (XC) energy functional of periodic insulators within Kohn-Sham (KS) density-functional theory requires a ${\cal O} (1/q^2)$ 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.

cond-mat.mtrl-sci↗

arXiv1996

Density Functional Theory of Polar Insulators

We examine the density-functional theory of macroscopic insulators, obtained in the large-cluster limit or under periodic boundary conditions. For polar crystals, we find that the two procedures are not equivalent. In a large-cluster case, the exact exchange-correlation potential acquires a homogeneous ``electric field'' which is absent from the usual local approximations, 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 incorrect even if the exact functional is used.

cond-mat.mtrl-sci↗

arXiv1995

Density-Polarization Functional Theory of the response of a periodic insulating solid to an electric field.

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 {\em 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.

mtrl-th↗