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WIREs Comput Mol Sci
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GW method and Bethe–Salpeter equation for calculating electronic excitations

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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
Schematic representation illustrating how the self‐energy ∑ and one‐particle Green's function G can be determined using Hedin's equations and Dyson's equation iteratively.
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Theoretical and Physical Chemistry > Spectroscopy
Electronic Structure Theory > Ab Initio Electronic Structure Methods

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