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We present a first-principles method for the calculation of optical excitations in nanosystems. The method is based on solving the Bethe-Salpeter equation (BSE) for neutral excitations. The electron self-energy is evaluated within the GW…

Materials Science · Physics 2009-11-11 Murilo L. Tiago , James R. Chelikowsky

The Bethe-Salpeter equation (BSE) is the key equation in many-body perturbation theory based on Green's functions to access response properties. Within the $GW$ approximation to the exchange-correlation kernel, the BSE has been successfully…

Chemical Physics · Physics 2023-02-15 Roberto Orlando , Pina Romaniello , Pierre-François Loos

We present an approach to calculate the optical absorption spectra that combines the quasiparticle self-consistent GW method [Phys. Rev. B, 76 165106 (2007)] for the electronic structure with the solution of the ladder approximation to the…

Materials Science · Physics 2018-03-21 Brian Cunningham , Pooya Azarhoosh , Dimitar Pashov , Myrta Gruening , Mark van Schilfgaarde

A time-dependent formulation for electron-hole excitations in extended finite systems, based on the Bethe-Salpeter equation (BSE), is developed using a stochastic wave function approach. The time-dependent formulation builds on the…

Materials Science · Physics 2015-02-11 Eran Rabani , Roi Baer , Daniel Neuhauser

The GW plus Bethe-Salpeter equation (GW-BSE) formalism is a well-established approach for calculating excitation energies and optical spectra of molecules, nanostructures, and crystalline materials. We implement GW-BSE in the CP2K code and…

Computational Physics · Physics 2026-05-29 Maximilian Graml , Jan Wilhelm

The Bethe-Salpeter equation (BSE) is currently the state of the art in the description of neutral electron excitations in both solids and large finite systems. It is capable of accurately treating charge-transfer excitations that present…

The Bethe-Salpeter equation (BSE) formalism is a computationally affordable method for the calculation of accurate optical excitation energies in molecular systems. Similar to the ubiquitous adiabatic approximation of time-dependent…

Chemical Physics · Physics 2020-09-22 Pierre-François Loos , Xavier Blase

The formalism to calculate excited state properties from the $GW$-Bethe-Salpeter equation (BSE) method is introduced, providing convenient access to excited state absorption, excited state circular dichroism, and excited state optical…

Chemical Physics · Physics 2024-12-25 Paula Himmelsbach , Christof Holzer

The Bethe-Salpeter Equation (BSE) is the workhorse method to study excitons in materials. The BSE Hamiltonian size, which depends on how many valence-to-conduction band transitions are considered, needs to be chosen to be sufficiently large…

Materials Science · Physics 2025-10-20 Rafael R. Del Grande , David A. Strubbe

We study the optical absorption spectra of small Ag_n (n=2,4,6,8) clusters using the Bethe-Salpeter equation (BSE) formalism with a Hamiltonian built from GW quasiparticle energies. Calculations are based on an effective core potential…

Materials Science · Physics 2026-01-16 Xavier Blase , Ivan Duchemin

We present an efficient way to solve the Bethe-Salpeter equation (BSE), a model for the computation of absorption spectra in molecules and solids that includes electron-hole excitations. Standard approaches to construct and diagonalize the…

Computational Physics · Physics 2018-02-01 Wei Hu , Meiyue Shao , Andrea Cepellotti , Felipe H. da Jornada , Lin Lin , Kyle Thicke , Chao Yang , Steven G. Louie

The Bethe-Salpeter equation (BSE) is a powerful theoretical approach that is capable to accurately treat electron-hole interactions in materials in an excited state. We developed an ab initio framework based on the BSE to describe a…

Materials Science · Physics 2026-05-19 Nasrin Farahani , Daria Popova-Gorelova

Two self-consistent schemes involving Hedin's $GW$ approximation are studied for a set of sixteen different atoms and small molecules. We compare results from the fully self-consistent $GW$ approximation (SC$GW$) and the quasi-particle…

Materials Science · Physics 2015-06-19 Peter Koval , Dietrich Foerster , Daniel Sánchez-Portal

The combination of the many-body Green's function $GW$ approximation and the Bethe-Salpeter equation (BSE) formalism has shown to be a promising alternative to time-dependent density-functional theory (TD-DFT) for computing vertical…

Chemical Physics · Physics 2020-06-05 Pierre-François Loos , Anthony Scemama , Ivan Duchemin , Denis Jacquemin , Xavier Blase

Computing the $GW$ quasiparticle bandstructure and Bethe-Salpeter Equation (BSE) absorption spectra for materials with spin-orbit coupling has commonly been done by treating $GW$ corrections and spin-orbit coupling as separate perturbations…

A GW-BSE approximation scheme is assessed by applying it to a model of asymmetric two-dimensional (2D) interacting electron system. The model is assumed to have a parabolic band characterized by two independent effective mass parameters. A…

Materials Science · Physics 2026-05-26 Xiaoguang Wu

The self-consistent GW{\Gamma} method satisfies the Ward-Takahashi identity (i.e., the gauge invariance or the local charge continuity) for arbitrary energy ($\omega$) and momentum ($\bf q$) transfers. Its self-consistent first-principles…

Other Condensed Matter · Physics 2016-10-12 Riichi Kuwahara , Yoshifumi Noguchi , Kaoru Ohno

We present theoretical calculations of quasiparticle energies in closed-shell molecules using the GW method. We compare three different approaches: a full-frequency $G_0W_0$ (FF-$G_0W_0$) method with density functional theory (DFT-PBE) used…

Materials Science · Physics 2015-06-22 Johannes Lischner , Sahar Sharifzadeh , Jack Deslippe , Jeffrey B. Neaton , Steven G. Louie

The Bethe-Salpeter equation (BSE) can provide an accurate description of low-energy optical spectra of insulating crystals - even when excitonic effects are important. However, due to high computational costs it is only possible to include…

To study the characteristic features of relativistic bound systems, the Bethe-Salpeter equation (BSE) for two equal mass spin 1/2 particles (like the deuteron) is solved in the cm-frame for a covariant separable interaction kernel. For that…

Nuclear Theory · Physics 2007-05-23 Frieder Kleefeld , Manfred Dillig