GW method and Bethe–Salpeter equation for calculating electronic excitations

Abstract

The introduction of GW approximation to the electron's self‐energy by Hedin in the 1960s, where G and W denote the one‐particle Green's function and the screened Coulomb interaction, respectively, facilitates the computation of quasiparticle energies through Dyson's equation. GW method can also help us determine the electron–hole interaction, which is a functional derivative of self‐energy with respect to one‐particle Green's function, with excellent accuracy, and its combination with Bethe–Salpeter equation, which is derived from two‐particle Green's function, is a powerful tool to study electronic excitations and optical absorption. Thanks to the development of methodology and softwares during the last 30 years, the capability of GW method and Bethe–Salpeter equation to deal with real systems is elevated substantially, while they also exhibit many advantages over other first‐principles methods in band structures, ionization potentials, electron affinities, optical spectra, and so on. They have been successfully applied in the excited states of various systems, including crystals, metals, nanomaterials, chemical and biological systems, and so on. WIREs Comput Mol Sci 2016, 6:532–550. doi: 10.1002/wcms.1265 This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Theoretical and Physical Chemistry > Spectroscopy

Dimension-dependent band alignment and excitonic effects in graphitic carbon nitride: a many-body perturbation and time-dependent density functional theory study

“…26, where the used starting point for the G 0 W 0 calculation was the LDA eigenvalues and eigenfunctions. Recently, it has become well-known that the starting point of G 0 W 0 may affect the results, 37 and so we attribute the discrepancy in the monolayer band gap to the different starting points in the G 0 W 0 calculation.…”

Low-cost alternatives to the Bethe-Salpeter equation: Towards simple hybrid functionals for excitonic effects in solids

“…The standard method to describe the excitons-coupled and correlated electron-hole quasiparticles (QPs)-is through a Green's-function-based approach known as the Bethe-Salpeter equation (BSE) [1][2][3]. For extended systems, the BSE is the most accurate method to calculate optical properties [4][5][6], but this accuracy tends to come with a rather high computational cost.…”

Many-body perturbation theory calculations using the yambo code

“…The GW-BSE approach has been implemented in a number of free and commercially available codes [2][3][4][5][6][7][8] and applied to a wide range of materials (we cited works where the GW-BSE approach is coded in plane-waves, for a recent and more comprehensive review, see Ref. 9). Nonetheless, the complexity and relatively poor scaling of the GW-BSE method, and often of its implementation, constitutes a barrier towards its application to realistic systems of large size or to physical phenomena that lie outside the scope of most state-of-the-art approaches.…”