Ulf von Barth

Model GW band structure of InAs and GaAs in the wurtzite phase

We report quasiparticle calculations of the newly observed wurtzite polymorph of InAs and GaAs. The calculations are performed in the GW approximation (based on a model dielectric function) using plane waves and pseudopotentials. For comparison we also report the study of the zinc-blende phase within the same approximations. In the InAs compound the In 4d electrons play a very important role: whether they are frozen in the core or not leads either to a correct or a wrong band ordering (negative gap) within the local-density appproximation (LDA). We have calculated the GW band structure in both cases. In the first approach, we have estimated the correction to the pd repulsion calculated within the LDA and included this effect in the calculation of the GW corrections to the LDA spectrum. In the second case, we circumvent the negative gap problem by first using the screened exchange approximation and then calculating the GW corrections starting from the so obtained eigenvalues and eigenfunctions. This approach, that can be thought of as a step towards self-consistency, leads to a more realistic band structure and was also used for GaAs. For both InAs and GaAs in the wurtzite phase we predict an increase of the quasiparticle gap with respect to the zinc-blende polytype.

The effect of the core hole on X-ray emission spectra in simple metals

Shows that one-particle calculations of X-ray spectra with and without the core hole can give drastically different results, indicating a breakdown of one-particle theory. Only emission spectra obtained in the absence of the core hole consistently show a close resemblance to experiment. The authors show, that this fact can be explained by the many-body theory of Nozieres and DeDominicis (1969). They are then able to give the first interpretation of the L2,3 satellite spectrum of sodium.(17 refs)

Conserving approximations in time-dependent density functional theory

In the present work, we propose a theory for obtaining successively better approximations to the linear response functions of time-dependent density or current-density functional theory. The new technique is based on the variational approach to many-body perturbation theory (MBPT) as developed during the sixties and later expanded by us in the mid-nineties. Due to this feature, the resulting response functions obey a large number of conservation laws such as particle and momentum conservation and sum rules. The quality of the obtained results is governed by the physical processes built in through MBPT but also by the choice of variational expressions. We here present several conserving response functions of different sophistication to be used in the calculation of the optical response of solids and nanoscale systems.

Correlation energy functional and potential from time-dependent exact-exchange theory

In this work we studied a new functional for the correlation energy obtained from the exact-exchange (EXX) approximation within time-dependent density functional theory. Correlation energies have been calculated for a number of different atoms showing excellent agreement with results from more sophisticated methods. These results lose little accuracy by approximating the EXX kernel by its static value, a procedure which enormously simplifies the calculations. The correlation potential, obtained by taking the functional derivative with respect to the density, turns out to be remarkably accurate for all atoms studied. This potential has been used to calculate ionization potentials, static polarizabilities, and van der Waals coefficients with results in close agreement with experiment.

Linear density response function within the time-dependent exact-exchange approximation

We have calculated the frequency-dependent exact-exchange (EXX) kernel of time-dependent (TD) density-functional theory employing our recently proposed computational method based on cubic splines. With this kernel we have calculated the linear density response function and obtained static polarizabilites, van der Waals coefficients, and correlation energies for all spherical spin-compensated atoms up to argon. Some discrete excitation energies have also been calculated for Be and Ne. As might be expected, the results of the TDEXX approximation are close to those of TD Hartree-Fock theory. In addition, correlation energies obtained by integrating over the strength of the Coulomb interaction turn out to be highly accurate.

Exact-exchange kernel of time-dependent density functional theory: Frequency dependence and photoabsorption spectra of atoms

In this work we have calculated excitation energies and photoionization cross sections of Be and Ne in the exact-exchange (EXX) approximation of time-dependent density functional theory (TDDFT). The main focus has been on the frequency dependence of the EXX kernel and on how it affects the spectrum as compared to the corresponding adiabatic approximation. We show that for some discrete excitation energies the frequency dependence is essential to reproduce the results of time-dependent Hartree-Fock theory. Unfortunately, we have found that the EXX approximation breaks down completely at higher energies, producing a response function with the wrong analytic structure and making inner-shell excitations disappear from the calculated spectra. We have traced this failure to the existence of vanishing eigenvalues of the Kohn-Sham non-interacting response function. Based on the adiabatic TDDFT formalism we propose a new way of deriving the Fano parameters of autoionizing resonances.

Some open questions in TDDFT: Clues from lattice models and Kadanoff–Baym dynamics

Two aspects of TDDFT, the linear response approach and the adiabatic local density approximation, are examined from the perspective of lattice models. To this end, we review the DFT formulations on the lattice and give a concise presentation of the time-dependent Kadanoff-Baym equations, used to asses the limitations of the adiabatic approximation in TDDFT. We present results for the density response function of the 3D homogeneous Hubbard model, and point out a drawback of the linear response scheme based on the linearized Sham-Schluter equation. We then suggest a prescription on how to amend it. Finally, we analyze the time evolution of the density in a small cubic cluster, and compare exact, adiabatic-TDDFT and Kadanoff-Baym equations densities. Our results show that non-perturbative (in the interaction) adiabatic potentials can perform quite well for slow perturbations but that, for faster external fields, memory effects, as already present in simple many-body approximations, are clearly required

Optimized Gaussian basis sets for Goedecker–Teter–Hutter pseudopotentials

We have optimized the exponents of Gaussian s and p basis functions for the elements H, B–F and Al–Cl using the pseudopotentials of (Goedecker, Teter and Hutter 1996 Phys. Rev. B 54 1703) by minimizing the total energy of dimers. We found that this procedure causes the Gaussians to be somewhat more localized than the usual procedure, where the exponents are optimized for atoms. We further found that three exponents, equal for s and p orbitals, are sufficient to reasonably describe the electronic structure of all elements that we have studied. For Li and Be results are presented for pseudopotentials of (Hartwigsen et al 1998 Phys. Rev. B 58 3641). We expect that our exponents will be useful for density functional theory studies where speed is important.

Towards nonlocal density functionals by explicit modeling of the exchange-correlation hole in inhomogeneous systems

We put forward an approach for the development of a nonlocal density functional by a direct modeling of the shape of exchange-correlation (xc) hole in inhomogeneous systems. The functional is aimed at giving an accurate xc energy and an accurate corresponding xc potential even in difficult near-degeneracy situations such as molecular bond breaking. In particular we demand that: (1) the xc hole properly contains -1 electron, (2) the xc potential has the asymptotic -1/r behavior outside finite systems, and (3) the xc potential has the correct step structure related to the derivative discontinuities of the xc energy functional. None of the currently existing functionals satisfies all these requirements. These demands are achieved by screening the exchange hole in such a way that the pair-correlation function is symmetric and satisfies the sum rule. These two features immediately imply (1) and (2) while the explicit dependence of the exchange hole on the Kohn-Sham orbitals implies (3). Preliminary calculations show an improved physical description of the dissociating hydrogen molecule. Though the total energy is still far from perfect, the binding curve from our nonlocal density functional provides a significant improvement over the local density approximation. DOI: 10.1103/PhysRevA.87.022514 (Less)

Interpretation of high-energy X-ray satellites of L2,3 emission bands of Na, Mg, Al and Si

The high-energy satellite of the L2,3 X-ray emission band in Na, Mg, Al and Si has for a long time been attributed to the decay of an initial state with two holes in the 2p shell. In particular, the satellite threshold has been assigned to an initial (2p2)1D state. It has recently been found that X-ray and Auger data give two different values for the energy of this doubly-ionized state, and attempts have been made to interpret this difference in terms of localized valence states. The authors have re-examined the interpretation of the L2,3, satellite using data on K and L2,3 satellites, Auger and radiative Auger KLL spectra. It is concluded that the L2,3 satellite originates from an initial (2p2)3P state, contrary to previous assumptions.