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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.

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For the calculation of neutral excitations, time-dependent density functional theory (TDDFT) is an exact reformulation of the many-body time-dependent Schrödinger equation, based on the knowledge of the density instead of the many-body wavefunction. The density can be determined in an efficient scheme by solving one-particle noninteracting Schrödinger equations-the Kohn-Sham equations. The complication of the problem is hidden in the-unknown-time-dependent exchange and correlation potential that appears in the Kohn-Sham equations and for which it is essential to find good approximations. Many approximations have been suggested and tested for finite systems, where even the very simple adiabatic local density approximation (ALDA) has often proved to be successful. In the case of solids, ALDA fails to reproduce optical absorption spectra, that are instead well described by solving the Bethe-Salpeter equation of manybody perturbation theory (MBPT). On the other hand, ALDA can lead to excellent results for loss functions (at vanishing and finite momentum transfer). In view of that and thanks to recent successful developments of improved linear response kernels derived from MBPT, TDDFT is today considered a promising alternative to MBPT for the calculation of electronic spectra, even for solids. After reviewing the fundamentals of TDDFT within linear response, we discuss different approaches and a variety of applications to extended systems.

A robust and efficient frequency dependent and non-local exchange-correlation fxc (r, r ′ ; ω) is derived by imposing time-dependent density-functional theory (TDDFT) to reproduce the manybody diagrammatic expansion of the Bethe-Salpeter polarization function. As an illustration, we compute the optical spectra of LiF, SiO2 and diamond and the finite momentum transfer energy-loss spectrum of LiF. The TDDFT results reproduce extremely well the excitonic effects embodied in the Bethe-Salpeter approach, both for strongly bound and resonant excitons. We provide a working expression for fxc that is fast to evaluate and easy to implement.PACS numbers: 71.15.Qe ; Since the 30's, excitons have been ubiquitous in our understanding of the optics of bulk materials, surfaces, nanostructures and organic/bio-molecules [1]. Only recently, however, has the first principle description of excitons in the optical absorption of extended systems been achieved, by solving the Bethe-Salpeter equation (BSE) of Many-Body Perturbation Theory (MBPT) [2]. The solution of the BSE is usually cast into an equivalent Hamiltonian problem whose dimension increases with the number of k-points and number of valence and conduction bands. However, even if the BSE results reproduce well the experimental spectra for semiconductors and insulators, the complexity of the calculations impedes the application of this technique to large systems such as nanostructures and complex surfaces.An alternative approach to the study of correlation in many-body systems is given by density-functional theory, in its static (DFT) [3] and time dependent formulations (TDDFT) [4]. Similar to the paradigm of DFT for ground-state properties, TDDFT has emerged as a very powerful tool for the description of excited states. In principle TDDFT is exact for neutral excited-state properties, and its simplicity relies on the fact that two-point response functions are needed instead of the four-point function of the BSE [1]. TDDFT casts all many-body effects into the dynamical exchange-correlation kernel f xc (r, t, r ′ ; t ′ ) = δv xc (r, t) /δρ (r ′ , t ′ ), where v xc (r, t) is the corresponding time-dependent exchange-correlation potential. It was early recognized [5] that, in extended systems, the standard approximations for v xc -local density (LDA) or generalized gradient (GGA) -that work extremely well for ground state properties, fail to describe, among other effects, the band-gap of insulators and semiconductors and the excitonic effects in the optical and energy-loss spectra [1]. Recently, promising results have been obtained within a polarization dependent functional derived in the framework of current-DFT [6] and within the exact-exchange DFT approach [7]. The calculated optical spectrum of silicon exhibits excitonic effects in qualitative agreement with experiment. However, empirical cutoffs were introduced to construct f xc [8], that somehow account for the screening of the electron-hole interaction. Furthermore, to-date the calculations of the absorption spectra of s...

We show that the electronic and optical properties of silicon nanowires, with different size and orientation, are dominated by important many-body effects. The electronic and excitonic gaps, calculated within first principles, agree with the available experimental data. Huge excitonic effects, which depend strongly on wire orientation and size, characterize the optical spectra. Modeling porous silicon as a collection of interacting nanowires, we find an absorption spectrum which is in very good agreement with experimental measurements only when the electron-hole interaction is included.

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We present an analytical expression for the local-field factor G(q) of the homogeneous electron gas which reproduces recently published quantum Monte Carlo data by Moroni, Ceperley, and Senatore ͓Phys. Rev. Lett. 75, 689 ͑1995͔͒, reflects the theoretically known asymptotic behaviors for both small-and large-q limits, and allows us to express the exchange-correlation kernel K xc analytically in both the direct and reciprocal space. The last property is particularly useful in numerical applications to real solids. ͓S0163-1829͑98͒04823-1͔