We discuss the effects of a static long-range contribution Ϫ␣/q 2 to the exchange-correlation kernel f xc (q) of time-dependent density functional theory. We show that the optical absorption spectrum of solids exhibiting a strong continuum excitonic effect is considerably improved with respect to calculations where the adiabatic local-density approximation is used. We discuss the limitations of this simple approach, and in particular that the same improvement cannot be found for the whole spectral range including the valence plasmons and bound excitons. On the other hand, we also show that within the range of validity of the method, the parameter ␣ depends linearly on the inverse of the dielectric constant, and we demonstrate that this fact can be used to predict continuum excitonic effects in semiconductors. Results are shown for the real and imaginary part of the dielectric function of Si, GaAs, AlAs, diamond, MgO, SiC and Ge, and for the loss function of Si.

We have established and implemented a fully ab initio method which allows one to calculate optical absorption spectra, including excitonic effects, without solving the cumbersome Bethe-Salpeter equation, but obtaining results of the same precision. This breakthrough has been achieved in the framework of time-dependent density-functional theory, using new exchange-correlation kernels f(xc) that are free of any empirical parameter. We show that the same excitonic effects in the optical spectra can be reproduced through different f(xc)'s, ranging from frequency-dependent ones to a static one, by varying the kernel's spatial degrees of freedom. This indicates that the key quantity is not f(xc), but f(xc) combined with a response function. We present results for the optical absorption of bulk Si and SiC in good agreement with experiment, almost indistinguishable from those of the Bethe-Salpeter approach.

The experimental valence band photoemission spectrum of semiconductors exhibits multiple satellites that cannot be described by the GW approximation for the self-energy in the framework of many-body perturbation theory. Taking silicon as a prototypical example, we compare experimental high energy photoemission spectra with GW calculations and analyze the origin of the GW failure. We then propose an approximation to the functional differential equation that determines the exact one-body Green's function, whose solution has an exponential form. This yields a calculated spectrum, including cross sections, secondary electrons, and an estimate for extrinsic and interference effects, in excellent agreement with experiment. Our result can be recast as a dynamical vertex correction beyond GW, giving hints for further developments.Photoemission is a prominent tool to access information about electronic structure and excitations in materials. Modern synchrotron sources can provide detailed insight, thanks to their high intensity and broad photon energy range. But the interpretation of the experimental data is far from obvious, and theory is an essential complementary tool. However, ab initio calculations typically focus on bulk bandstructure [1, 2]; thus surface effects are ignored, and satellites are not included. The latter are a pure many-body effect due to coupling to excitations of the material. Such many-body effects are contained in approaches developed for correlated materials [3,4] however, these are usually based on models with short-range interactions, whereas satellites such as plasmons involve long-range effects. Plasmon satellites have been extensively studied in core-level experiments [5]. There they can be described by a theoretical model where a single dispersionless fermion couples to bosons. The resulting exact Green's function has an exponential form given by the so-called cumulant expansion (CE). A Taylor expansion of the exponential leads to a well defined quasi-particle (QP) peak followed by a decaying series of plasmon satellites at energy differences given by the plasmon energy, consistent with experimental observations [6][7][8][9][10]. In the valence region, plasmon satellites are much less studied, though ab initio approaches can provide a good starting point. At high photoelectron energies the photoemission spectrum is approximately proportional to the intrinsic spectral function A(ω) = −(1/π)Im G(ω), where G is the one-particle Green's function. The latter is typically calculated using the widely used GW approximation (GWA) [7,11,12]. In principle, the GWA contains correlations effects beyond the quasiparticle approximation. However, these additional features are rarely calculated due to computational complexity and, more importantly, the serious discrepancies between GWA and experiment (see e.g. [13][14][15][16]). The CE has also been used for the homogeneous electron gas [17] and simple metals [14,15], yielding an improved description of satellites over GW. Silicon [16] and graphite [18] ...

We have measured a strictly linear π plasmon dispersion along the axis of individualized single wall carbon nanotubes, which is completely different from plasmon dispersions of graphite or bundled single wall carbon nanotubes. Comparative ab initio studies on graphene based systems allow us to reproduce the different dispersions. This suggests that individualized nanotubes provide viable experimental access to collective electronic excitations of graphene, and it validates the use of graphene to understand electronic excitations of carbon nanotubes. In particular, the calculations reveal that local field effects (LFE) cause a mixing of electronic transitions, including the 'Dirac cone', resulting in the observed linear dispersion. PACS numbers: 73.20.Mf,78.20.Bh Single-wall carbon nanotubes (SWNT) and its parent compound graphene are archetypes of low dimensional systems with strongly anisotropic and unique electronic properties which make them interesting for both fundamental research and as building blocks in nanoelectronic applications [1]. Their electronic bandstructure is frequently studied. In graphene, the linear band dispersion at the Fermi level, the 'Dirac cone', leads to unique characteristics in nanoelectronic devices [2]. One can expect a strong analogy between graphene and isolated SWNT for excitations along the sheet and along the tube axis, respectively. Within the zone-folding model, i.e. neglecting curvature effects, the graphene bandstructure is sliced along parallel lines when the sheet is rolled up into a cylinder. The result are characteristic van Hove singularities (VHS) in the density of states (DOS) [3]. Bulk (i.e. bundled) SWNT show an optical absorption peak at ∼ 4.5 eV due to transitions of the π electrons [4]. In vertically aligned SWNT (VA-SWNT) one finds the same peak position for onaxis polarization and an additional peak for perpendicular polarization at ∼ 5.2 eV [5]. Further information can be obtained from collective electronic excitations (plasmons) beyond the optical limit [6] (i.e. momentum transfer q > 0). Angle resolved electron energy loss spectroscopy (EELS) assesses the detailed plasmon dispersion [7,8], but it is so far missing for freestanding isolated sp 2 carbon systems. Models based on the homogeneous electron gas [9], or the tight-binding scheme [10,11] have been used to describe these excitations. The former are however bound to metallic systems. The latter have provided valuable insight and predictions for the properties of isolated sheets, tubes, and assemblies of these objects; in particular, they have predicted an almost linear plasmon dispersion for isolated systems. However, the tight binding results neglect screening beyond the π bands, and they depend on parameters that hide the underlying complexity. No realistic parameter-free calculations have been performed to predict the plasmon dispersion in these systems, nor has its origin been analyzed. Instead, ab initio spectroscopy calculations have dealt with absorption spectra (q → 0) for SWNT [12,13,14],...

We present a theoretical investigation of electronic and optical properties of free-base porphyrins based on density functional theory and many-body perturbation theory. The electronic levels of free-base porphine (H(2)P) and its phenyl derivative, free-base tetraphenylporphyrin (H(2)TPP) are calculated using the ab initio GW approximation for the self-energy. The approach is found to yield results that compare favorably with the available photoemission spectra. The excitonic nature of the optical peaks is revealed by solving the Bethe-Salpeter equation, which provides an accurate description of the experimental absorption spectra. The lowest triplet transition energies are in good agreement with the measured values.

Low-dimensional materials differ from their bulk counterparts in many respects. In particular, the screening of the Coulomb interaction is strongly reduced, which can have important consequences such as the significant increase of exciton binding energies. In bulk materials the binding energy is used as an indicator in optical spectra to distinguish different kinds of excitons, but this is not possible in low-dimensional materials, where the binding energy is large and comparable in size for excitons of very different localization. Here we demonstrate that the exciton band structure, which can be accessed experimentally, instead provides a powerful way to identify the exciton character. By comparing the ab initio solution of the many-body Bethe-Salpeter equation for graphane and single-layer hexagonal boron nitride, we draw a general picture of the exciton dispersion in two-dimensional materials, highlighting the different role played by the exchange electron-hole interaction and by the electronic band structure. Our interpretation is substantiated by a prediction for phosphorene.

We propose an alternative formulation of many-body perturbation theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, which leads to excellent optical absorption and energy-loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-dependent density-functional theory. Numerical results for the band gap of bulk silicon and solid argon illustrate corrections beyond the GW approximation for the self-energy.

Time-dependent density-functional theory (TDDFT) is widely used in the study of linear response properties of finite systems. However, there are difficulties in properly describing excited states, which have double- and higher-excitation characters, which are particularly important in molecules with an open-shell ground state. These states would be described if the exact TDDFT kernel were used; however, within the adiabatic approximation to the exchange-correlation (xc) kernel, the calculated excitation energies have a strict single-excitation character and are fewer than the real ones. A frequency-dependent xc kernel could create extra poles in the response function, which would describe states with a multiple-excitation character. We introduce a frequency-dependent xc kernel, which can reproduce, within TDDFT, double excitations in finite systems. In order to achieve this, we use the Bethe-Salpeter equation with a dynamically screened Coulomb interaction W(omega), which can describe these excitations, and from this we obtain the xc kernel. Using a two-electron model system, we show that the frequency dependence of W does indeed introduce the double excitations that are instead absent in any static approximation of the electron-hole screening.