Elimination of unoccupied state summations in it 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

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)

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

Crowding Out Voluntary Contributions to Public Goods

We test the null hypothesis that involuntary transfers for the provision of a public good will completely crowd out voluntary transfers against the warm-glow hypothesis that crowding-out will be incomplete because individuals care about giving. Our design differs from the related design used by Andreoni in considering two levels of the involuntary transfer and a wider range of contribution possibilities, and in mixing groups every period instead of every four periods. We analyse the data with careful attention to boundary effects. We retain the null hypothesis of complete crowding-out in two of three pairwise comparisions, but reject it in favour of incomplete crowding-out in the comparison most closely akin to Andreoni's design. Thus we confirm the existence of incomplete crowding-out in some environments, but suggest that the warm-glow hypothesis is inadequate in explaining it.

Crowding Out Voluntary Contributions to Public Goods

We test the null hypothesis that involuntary transfers for the provision of a public good will completely crowd out voluntary transfers against the warm-glow hypothesis that crowding-out will be incomplete because individuals care about giving. Our design differs from the related design used by Andreoni in considering two levels of the involuntary transfer and a wider range of contribution possibilities, and in mixing groups every period instead of every four periods. We analyse the data with careful attention to boundary effects. We retain the null hypothesis of complete crowding-out in two of three pairwise comparisions, but reject it in favour of incomplete crowding-out in the comparison most closely akin to Andreoni’s design. Thus we confirm the existence of incomplete crowding-out in some environments, but suggest that the warm-glow hypothesis is inadequate in explaining it.

Hartree-Fock theory of a current-carrying electron gas

State-of-the-art simulation tools for nonequilibrium quantum transport systems typically take the current-carrier occupations to be described in terms of equilibrium distribution functions characterized by two different electrochemical potentials, while for the description of electronic exchange and correlation, the local density approximation (LDA) to density functional theory 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 nonequilibrium 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 since it is not captured by the commonly used functionals. 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

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

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.Comment: 11 pages, 1 Fig

Band structures of rare gas solids within the GW approximation

Band structures for solid rare gases (Ne, Ar) have been calculated using the GW approximation. All electron and pseudopotential ab initio calculations were performed using Gaussian orbital basis sets and the dependence of particle-hole gaps and electron affinities on basis set and treatment of core electrons is investigated. All electron GW calculations have a smaller particle-hole gap than pseudopotential GW calculations by up to 0.2 eV. Quasiparticle electron and hole excitation energies, valence band widths and electron affinities are generally in very good agreement with those derived from optical absorption and photoemission measurements.Comment: 7 pages 1 figur

Efficient total energy calculations from self-energy models

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