The Bethe-Salpeter Equation Formalism: From Physics to Chemistry

Abstract

The Bethe-Salpeter equation (BSE) formalism is steadily asserting itself as a new efficient and accurate tool in the ensemble of computational methods available to chemists in order to predict optical excitations in molecular systems. In particular, the combination of the so-called $GW$ approximation, giving access to reliable ionization energies and electron affinities, and the BSE formalism, able to model UV/Vis spectra, has shown to provide accurate singlet excitation energies with a typical error of $0.1$--$0.3$ eV. With a similar computational cost as time-dependent density-functional theory (TD-DFT), BSE is able to provide an accuracy on par with the most accurate global and range-separated hybrid functionals without the unsettling choice of the exchange-correlation functional, resolving further known issues (\textit{e.g.}, charge-transfer excitations). In this \textit{Perspective} article, we provide a historical overview of BSE, with a particular focus on its condensed-matter roots. We also propose a critical review of its strengths and weaknesses in different chemical situations.

13 pages, 3 figures, Perspective review article

References in corpus (13)

• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• Impact of the electron-electron correlation on phonon dispersions: failure of LDA and GGA functionals in graphene and graphite
• Cubic scaling $GW$: towards fast quasiparticle calculations
• Quasi-Particle Self-Consistent $GW$ for Molecules
• Towards GW Calculations on Thousands of Atoms
• Correlation energy expressions from the adiabatic-connection fluctuation-dissipation theorem approach
• Electron-Phonon Coupling from $\text{Ab Initio}$ Linear-Response Theory within the $GW$ Method: Correlation-Enhanced Interactions and Superconductivity in Ba${}_{1-x}$K${}_x$BiO${}_3$
• Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory
• Static correlation and electron localization in molecular dimers from the self-consistent RPA and GW approximation
• Separable Resolution-of-the-Identity with All-Electron Gaussian Bases: Application to Cubic-scaling RPA
• A finite field approach to solving the Bethe Salpeter equation
• Correlated electron-hole mechanism for molecular doping in organic semiconductors
• Correlation energy within exact-exchange ACFD theory: systematic development and simple approximations

Cited by in corpus (49)

• QUESTDB: a database of highly-accurate excitation energies for the electronic structure community
• Assessing the Performances of CASPT2 and NEVPT2 for Vertical Excitation Energies
• Low-scaling $GW$ with benchmark accuracy and application to phosphorene nanosheets
• Connections and performances of Green's function methods for charged and neutral excitations
• Full-frequency dynamical Bethe-Salpeter equation without frequency and a study of double excitations
• A Mountaineering Strategy to Excited States: Revising Reference Values with EOM-CC4
• A similarity renormalization group approach to Green's function methods
• Connections between many-body perturbation and coupled-cluster theories
• Unphysical Discontinuities, Intruder States and Regularization in $GW$ Methods
• Reference Energies for Cyclobutadiene: Automerization and Excited States
• Reference CC3 Excitation Energies for Organic Chromophores: Benchmarking TD-DFT, BSE/$GW$ and Wave Function Methods
• Static and Dynamic Bethe-Salpeter Equations in the $T$-Matrix Approximation
• State-Specific Coupled-Cluster Methods for Excited States
• Scrutinizing $GW$-based methods using the Hubbard dimer
• Spin-orbit torque in single-molecule junctions from ab initio
• Low-scaling GW algorithm applied to twisted transition-metal dichalcogenide heterobilayers
• Reference Vertical Excitation Energies for Transition Metal Compounds
• Multiorbital exciton formation in an organic semiconductor
• Can $GW$ Handle Multireference Systems?
• Bethe Salpeter Equation Spectra for Very Large Systems
• Unified Deep Learning Framework for Many-Body Quantum Chemistry via Green's Functions
• Combining Renormalized Singles $GW$ Methods with the Bethe-Salpeter Equation for Accurate Neutral Excitation Energies
• Neutral electronic excitations and derivative discontinuities: An extended $N$-centered ensemble density functional theory perspective
• Combining Localized Orbital Scaling Correction and Bethe-Salpeter Equation for Accurate Excitation Energies
• Anomalous propagators and the particle-particle channel: Bethe-Salpeter equation
• Excitons in twisted AA' hexagonal boron nitride bilayers
• A Guide to Molecular Properties from the Bethe-Salpeter Equation
• Probing excitons with time-resolved momentum microscopy
• Optimized Attenuated Interaction: Enabling Stochastic Bethe-Salpeter Spectra for Large Systems
• Comparative Study of Covalent and van der Waals CdS Quantum Dot Assemblies from Many-Body Perturbation Theory
• Accurate and Efficient Prediction of Double Excitation Energies Using the Particle-Particle Random Phase Approximation
• Fully Analytic Nuclear Gradients for the Bethe--Salpeter Equation
• Energy-Specific Bethe-Salpeter Equation Implementation for Efficient Optical Spectrum Calculations
• Analytic $G_0{W}_0$ gradients based on a double-similarity transformation equation-of-motion coupled-cluster treatment
• Linear and Nonlinear Optical Properties of Molecules from Real-Time Propagation Based on the Bethe-Salpeter Equation
• Excited State Properties from the Bethe--Salpeter Equation: State-to-State Transitions and Spin-Orbit Coupling
• Role of defects in atom probe analysis of sol-gel silica
• Shifting sands of hardware and software in exascale quantum mechanical simulations
• First-principles computational methods for quantum defects in two-dimensional materials: A perspective
• Variational formulation of dynamical electronic response functions in presence of nonlocal exchange interactions
• How to choose efficiently the size of the Bethe-Salpeter Equation Hamiltonian for accurate exciton calculations on supercells
• Deep-learning atomistic semi-empirical pseudopotential model for nanomaterials
• Excited-State Response Theory Within the Context of the Coupled-Cluster Formalism
• Optical spectra of small silver clusters with the Bethe-Salpeter formalism: a Reassessment
• A Kernel-based Machine Learning Approach to Computing Quasiparticle Energies within Many-Body Green's Functions Theory
• Efficient $GW$ band structure calculations using Gaussian basis functions and application to atomically thin transition-metal dichalcogenides
• Observing the spatial and temporal evolution of exciton wave functions
• LibppRPA: An Open-Source Library for Particle-Particle Random Phase Approximation
• Optical excitations in nanographenes from the Bethe-Salpeter equation and time-dependent density functional theory: absorption spectra and spatial descriptors