Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green’s-function equations, starting with a one-electron propagator and considering the electron-hole Green’s function for the response. Key ingredients are the electron’s self-energy S and the electron-hole interaction. A good approximation for S is obtained with Hedin’s GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of S. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green’s functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green’s functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.

/pdf/electronic-excitations-density-functional-versus-many-body-2tgqd9dfpy.pdf

Electronic excitations: density-functional versus many-body Green's-function approaches

During the past decade, computer simulations based on a quantum-mechanical description of the interactions between electrons and between electrons and atomic nuclei have developed an increasingly important impact on solid-state physics and chemistry and on materials science—promoting not only a deeper understanding, but also the possibility to contribute significantly to materials design for future technologies. This development is based on two important columns: (i) The improved description of electronic many-body effects within density-functional theory (DFT) and the upcoming post-DFT methods. (ii) The implementation of the new functionals and many-body techniques within highly efficient, stable, and versatile computer codes, which allow to exploit the potential of modern computer architectures. In this review, I discuss the implementation of various DFT functionals [local-density approximation (LDA), generalized gradient approximation (GGA), meta-GGA, hybrid functional mixing DFT, and exact (Hartree-Fock) exchange] and post-DFT approaches [DFT + U for strong electronic correlations in narrow bands, many-body perturbation theory (GW) for quasiparticle spectra, dynamical correlation effects via the adiabatic-connection fluctuation-dissipation theorem (AC-FDT)] in the Vienna ab initio simulation package VASP. VASP is a plane-wave all-electron code using the projector-augmented wave method to describe the electron-core interaction. The code uses fast iterative techniques for the diagonalization of the DFT Hamiltonian and allows to perform total-energy calculations and structural optimizations for systems with thousands of atoms and ab initio molecular dynamics simulations for ensembles with a few hundred atoms extending over several tens of ps. Applications in many different areas (structure and phase stability, mechanical and dynamical properties, liquids, glasses and quasicrystals, magnetism and magnetic nanostructures, semiconductors and insulators, surfaces, interfaces and thin films, chemical reactions, and catalysis) are reviewed. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2008

Ab-initio simulations of materials using VASP: Density-functional theory and beyond.

The science of the total environment

Point defects and impurities strongly affect the physical properties of materials and have a decisive impact on their performance in applications. First-principles calculations have emerged as a powerful approach that complements experiments and can serve as a predictive tool in the identification and characterization of defects. The theoretical modeling of point defects in crystalline materials by means of electronic-structure calculations, with an emphasis on approaches based on density functional theory (DFT), is reviewed. A general thermodynamic formalism is laid down to investigate the physical properties of point defects independent of the materials class (semiconductors, insulators, and metals), indicating how the relevant thermodynamic quantities, such as formation energy, entropy, and excess volume, can be obtained from electronic structure calculations. Practical aspects such as the supercell approach and efficient strategies to extrapolate to the isolated-defect or dilute limit are discussed. Recent advances in tractable approximations to the exchange-correlation functional ($\mathrm{DFT}+U$, hybrid functionals) and approaches beyond DFT are highlighted. These advances have largely removed the long-standing uncertainty of defect formation energies in semiconductors and insulators due to the failure of standard DFT to reproduce band gaps. Two case studies illustrate how such calculations provide new insight into the physics and role of point defects in real materials.

First-principles calculations for point defects in solids

Graphene has been hailed as a wonderful material in electronics, and recently, it is the rising star in photonics, as well. The wonderful optical properties of graphene afford multiple functions of signal emitting, transmitting, modulating, and detection to be realized in one material. In this paper, the latest progress in graphene photonics, plasmonics, and broadband optoelectronic devices is reviewed. Particular emphasis is placed on the ability to integrate graphene photonics onto the silicon platform to afford broadband operation in light routing and amplification, which involves components like polarizer, modulator, and photodetector. Other functions like saturable absorber and optical limiter are also reviewed.

Graphene photonics, plasmonics, and broadband optoelectronic devices.

Exact solutions are presented to the steady-state coupled-mode equations that govern the nonlinear parametric interaction of a central-frequency wave with a pair of upshifted and downshifted sidebands in isotropic single-mode optical fibers. This solution accounts for pump depletion as well for as a possible phase mismatch among the waves. The existence is predicted of eigensolutions propagating unchanged along the fiber, which may be either spatially stable or spatially unstable, depending on the total power and the propagation-constant mismatch. The presence of spatially unstable eigensolutions dramatically affects the power exchange among the three waves. The physical implications of this instability for the frequency-conversion process, as well as its potential application to all-optical switching, are discussed.

Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects

Homologous classes of polycyclic aromatic hydrocarbons (PAHs) in their crystalline state are among the most promising materials for organic opto-electronics. Following previous works on oligoacenes we present a systematic comparative study of the electronic, optical, and transport properties of oligoacenes, phenacenes, circumacenes, and oligorylenes. Using density functional theory (DFT) and time-dependent DFT we computed: (i) electron affinities and first ionization energies; (ii) quasiparticle correction to the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap; (iii) molecular reorganization energies and (iv) electronic absorption spectra of neutral and ±1 charged systems. The excitonic effects are estimated by comparing the optical gap and the quasiparticle corrected HOMO–LUMO energy gap. For each molecular property computed, general trends as a function of molecular size and charge state are discussed. Overall, we find that circumacenes have the best transport properties, displaying a steeper decrease of the molecular reorganization energy at increasing sizes, while oligorylenes are much more efficient in absorbing low-energy photons in comparison to the other classes.

Electronic and optical properties of families of polycyclic aromatic hydrocarbons: A systematic (time-dependent) density functional theory study

We present a model for the dielectric function of semiconductors. It has been tested successfully for Si, Ge, GaAs, and ZnSe. In conjunction with the single plasmon-pole approximation it yields plasmon-energy dispersions in fair agreement with experiments. It allows one, moreover, to deduce an analytical expression for the Coulomb-hole part of the static self-energy operator.

Model dielectric function for semiconductors.

An efficient method for calculating quasiparticle energies in semiconductors

We present a systematic theoretical study of the five smallest oligoacenes (naphthalene, anthracene, tetracene, pentacene, and hexacene) in their anionic, neutral, cationic, and dicationic charge states. We used density functional theory (DFT) to obtain the ground-state optimised geometries, and time-dependent DFT (TD-DFT) to evaluate the electronic absorption spectra. Total-energy differences enabled us to evaluate the electron affinities and first and second ionisation energies, the quasiparticle correction to the HOMO–LUMO energy gap and an estimate of the excitonic effects in the neutral molecules. Electronic absorption spectra have been computed by combining two different implementations of TD-DFT: the frequency–space method to study general trends as a function of charge-state and molecular size for the lowest-lying in-plane long-polarised and short-polarised π → π∗ electronic transitions, and the real-time propagation scheme to obtain the whole photo-absorption cross-section up to the far-UV. Doubly ionised PAHs are found to display strong electronic transitions of π → π∗ character in the near-IR, visible, and near-UV spectral ranges, like their singly charged counterparts. While, as expected, the broad plasmon-like structure with its maximum at about 17–18 eV is relatively insensitive to the charge-state of the molecule, a systematic decrease with increasing positive charge of the absorption cross-section between ∼6 and ∼12 eV is observed for each member of the class.

Giancarlo Cappellini

Papers

Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects

Electronic and optical properties of families of polycyclic aromatic hydrocarbons: A systematic (time-dependent) density functional theory study

Model dielectric function for semiconductors.

An efficient method for calculating quasiparticle energies in semiconductors

Time-dependent density functional study of the electronic spectra of oligoacenes in the charge states −1, 0, +1, and +2