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

Abstract

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 ⌺ and the electron-hole interaction. A good approximation for ⌺ 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 ⌺. 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. CONTENTS

Plasmonics in atomically thin materials

“…Plasmons in metal clusters of atomic dimensions have been examined and optically characterized for a long time [54], and they have even been used as a toolbox to test the ability of different first-principles computational methods to simulate optical and electron-based spectroscopic measurements [55]. In a separate effort, atomic self-assembly has been used to produce monoatomic gold wires [56], which were later shown to sustain extremely confined plasmons [57].…”

Stretching of BDT-gold molecular junctions: thiol or thiolate termination?

“…This limits its ability to predict the energy level alignment, when compared to experiments, which often leads to overestimated values for G. 47,48 A rigorous way to include such non-local correlation effects is by using many-body perturbation theory, for example the GW approximation constructed on top of DFT. [49][50][51] In the last few years, this approach has been used for evaluating level alignments, [52][53][54][55][56][57] in general with good success. The drawback of the GW scheme is the fact that it is highly computationally demanding, which limits the system size that can be tackled.…”

Exciton Radiative Lifetimes in Two-Dimensional Transition Metal Dichalcogenides

“…18,20−22 First-principles calculations combining density functional theory (DFT) and many-body perturbation theory are ideally suited to study excited state dynamics in layered 2D-TMDs. 25,26 These approaches can accurately predict excited state properties in the energy domain such as band gaps, exciton energies, and absorption/loss spectra, 26,27 and there is significant promise to extend these methods to study excited state processes in the time domain. 28−30 In this work, we compute intrinsic exciton radiative lifetimes in layered 2D-TMDs from first principles.…”