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.

We present an implementation of the GW approximation for the electronic self-energy within the full-potential linearized augmented-plane-wave (FLAPW) method. The algorithm uses an allelectron mixed product basis for the representation of response matrices and related quantities. This basis is derived from the FLAPW basis and is exact for wave-function products. The correlation part of the self-energy is calculated on the imaginary frequency axis with a subsequent analytic continuation to the real axis. As an alternative we can perform the frequency convolution of the Green function G and the dynamically screened Coulomb interaction W explicitly by a contour integration. The singularity of the bare and screened interaction potentials gives rise to a numerically important self-energy contribution, which we treat analytically to achieve good convergence with respect to the k-point sampling. As numerical realizations of the GW approximation typically suffer from the high computational expense required for the evaluation of the nonlocal and frequencydependent self-energy, we demonstrate how the algorithm can be made very efficient by exploiting spatial and time-reversal symmetry as well as by applying an optimization of the mixed product basis that retains only the numerically important contributions of the electron-electron interaction. This optimization step reduces the basis size without compromising the accuracy and accelerates the code considerably. Furthermore, we demonstrate that one can employ an extrapolar approximation for high-lying states to reduce the number of empty states that must be taken into account explicitly in the construction of the polarization function and the self-energy. We show convergence tests, CPU timings, and results for prototype semiconductors and insulators as well as ferromagnetic nickel.

This paper investigates the influence of the basis set on the GW self-energy correction in the fullpotential linearized augmented-plane-wave (LAPW) approach and similar linearized all-electron methods. A systematic improvement is achieved by including local orbitals that are defined as second and higher energy derivatives of solutions to the radial scalar-relativistic Dirac equation and thus constitute a natural extension of the LAPW basis set. Within this approach linearization errors can be eliminated, and the basis set becomes complete. While the exchange contribution to the self-energy is little affected by the increased basis-set flexibility, the correlation contribution benefits from the better description of the unoccupied states, as do the quasiparticle energies. The resulting band gaps remain relatively unaffected, however; for Si we find an increase of 0.03 eV.

We present a computational scheme to study spin excitations in magnetic materials from first principles. The central quantity is the transverse spin susceptibility, from which the complete excitation spectrum, including single-particle spin-flip Stoner excitations and collective spin-wave modes, can be obtained. The susceptibility is derived from many-body perturbation theory and includes dynamic correlation through a summation over ladder diagrams that describe the coupling of electrons and holes with opposite spins. In contrast to earlier studies, we do not use a model potential with adjustable parameters for the electron-hole interaction but employ the random-phase approximation. To reduce the numerical cost for the calculation of the four-point scattering matrix we perform a projection onto maximally localized Wannier functions, which allows us to truncate the matrix efficiently by exploiting the short spatial range of electronic correlation in the partially filled d or f orbitals. Our implementation is based on the full-potential linearized augmented-plane-wave method. Starting from a ground-state calculation within the local-spin-density approximation ͑LSDA͒, we first analyze the matrix elements of the screened Coulomb potential in the Wannier basis for the 3d transition-metal series. In particular, we discuss the differences between a constrained nonmagnetic and a proper spin-polarized treatment for the ferromagnets Fe, Co, and Ni. The spectrum of single-particle and collective spin excitations in fcc Ni is then studied in detail. The calculated spin-wave dispersion is in good overall agreement with experimental data and contains both an acoustic and an optical branch for intermediate wave vectors along the ͓1 0 0͔ direction. In addition, we find evidence for a similar double-peak structure in the spectral function along the ͓1 1 1͔ direction. To investigate the influence of static correlation we finally consider LSDA+ U as an alternative starting point and show that, together with an improved description of the Fermi surface, it yields a more accurate quantitative value for the spin-wave stiffness constant, which is overestimated in the LSDA.

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.Much of the modern theory of many-body effects in the electronic structure of solids relies on a closed set of coupled integral equations known as Hedin's equations [1], which connect the Green's function G of a system of interacting electrons with the self-energy operator Σ, the polarization propagator P , the dynamically screened Coulomb interaction W , and a vertex function Γ. Simultaneously solving Hedin's equations for a specified external potential in principle yields the exact Green's function and quasiparticle excitation spectrum without the need of actually calculating the many-electron wavefunction. Unfortunately, however, the relation between the quantities is not just purely numerical but involves nontrivial functional derivatives, so that an automated numerical solution is not feasible and approximate functional expressions with simpler dependences have to be considered instead. Most calculations of quasiparticle excitations in real materials employ the GW approximation [1], which uses intermediate operators from the first cycle of an iterative solution of Hedin's equations starting from Hartree theory as a zeroth order approximation. The GW approximation neglects diagrammatic vertex corrections both in the polarization propagator and the selfenergy. Its theoretical foundation lies in the assumption that sufficient convergence has been reached after the initial cycle, but rigorous evidence has so far been prevented by the inherent mathematical difficulties associated with a continuation of the iterative process. Some corroboration stems from the surprisingly good agreement with experimental spectra for a wide range of semiconductors [2,3] and simple metals [4], while more recent studies of transition metals and their oxides highlighted deficiencies in the calculated spectra that clearly indicate a lack of convergence for materials with strong electronic correlation [5]. The GW approximation has since often been reinterpreted as the first order term in an expansion of the exact self-energy in terms of the screened Coulomb interaction, and considerable effort has been spent to include second order contributions. However, such attempts have failed to produce a general improvement in numerical accuracy due to far-reaching cancellation between the additional terms [6]. In this Letter, we return to the original spirit of solving Hedin's equations iteratively and present a scheme that generates progressively accurate functional expressions at arbitrary levels of ...

In the context of photoelectron spectroscopy, the GW approach has developed into the method of choice for computing excitation spectra of weakly correlated bulk systems and their surfaces. To employ the established computational schemes that have been developed for three-dimensional crystals, two-dimensional systems are typically treated in the repeated-slab approach. In this work we critically examine this approach and identify three important aspects for which the treatment of long-range screening in two dimensions differs from the bulk: (1) anisotropy of the macroscopic screening (2) k-point sampling parallel to the surface (3) periodic repetition and slab-slab interaction. For prototypical semiconductor (silicon) and ionic (NaCl) thin films we quantify the individual contributions of points (1) to (3) and develop robust and efficient correction schemes derived from the classic theory of dielectric screening.

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Given the vast range of lithium niobate (LiNbO3) applications, the knowledge about its electronic and optical properties is surprisingly limited. The direct band gap of 3.7 eV for the ferroelectric phase – frequently cited in the literature – is concluded from optical experiments [1]. Recent theoretical investigations [2] show that the electronic band‐structure and optical properties are very sensitive to quasiparticle and electron‐hole attraction effects, which were included using the GW approximation for the electron self‐energy and the Bethe‐Salpeter equation respectively, both based on a model screening function. The calculated fundamental gap was found to be at least 1 eV larger than the experimental value. To resolve this discrepancy we performed first‐principles GW calculations for lithium niobate using the full‐potential linearized augmented plane‐wave (FLAPW) method [3]. Thereby we use the parameter‐free random phase approximation for a realistic description of the nonlocal and energydependent screening. This leads to a band gap of about 4.7 (4.2) eV for ferro(para)‐electric lithium niobate (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)