R. W. Godby

A brief introduction to the ABINIT software package

Abstract 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.

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.

The GW space-time method for the self-energy of large systems

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 Hedins GW approximation. At the heart of the method is a representation of the Green 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.

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 and calculate the effective local potential experienced by electrons in the near-surface region. The relative contribution of exchange proves to be very different for states above the Fermi level. The image-plane position for interacting electrons is 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.

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

We study the behavior 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.

Self-Consistent Calculation of Total Energies of the Electron Gas Using Many-Body Perturbation Theory

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 fulfillment of general conservation rules. These results open further prospects for accurate calculations of ground-state properties circumventing the limitations of standard density-functional theory.

Enhancements to the GW space-time method

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 (1999) 211) 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 Greens function by replacing higher unoccupied eigenstates by free electron states (plane waves). These improvements make the calculation of larger systems (surfaces, clusters, defects etc.) accessible.

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).

Long-wavelength behavior of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems

The polarization dependence of the exchange-correlation (re) energy functional of periodic insulators within Kohn-Sham (KS) density-functional theory requires a O(1/q(2)) divergence in the re kernel for small vectors q. This behavior, exemplified for a one-dimensional model semiconductor, is also observed when an insulator happens to be described asa KS metal, or vice versa. Although it can occur in the exchange-only kernel, it is not found in the usual local, semilocal, or even nonlocal 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.

Electronic Structure of Cubic GaN with Self-Energy Corrections

We present the results 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 quasi-particle 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.