Connections and performances of Green's function methods for charged and neutral excitations

Abstract

In recent years, Green's function methods have garnered considerable interest due to their ability to target both charged and neutral excitations. Among them, the well-established $GW$ approximation provides accurate ionization potentials and electron affinities and can be extended to neutral excitations using the Bethe-Salpeter equation (BSE) formalism. Here, we investigate the connections between various Green's function methods and evaluate their performance for charged and neutral excitations. Comparisons with other widely-known second-order wave function methods are also reported. Additionally, we calculate the singlet-triplet gap of cycl[3,3,3]azine, a model molecular emitter for thermally activated delayed fluorescence, which has the particularity of having an inverted gap thanks to a substantial contribution from the double excitations. We demonstrate that, within the $GW$ approximation, a second-order BSE kernel with dynamical correction is required to predict this distinctive characteristic.

arXiv comment18 pages, 1 figure

References in corpus (93)

• The GW method
• Quasiparticle Self-Consistent GW Theory
• Ab initio calculation of excitonic effects in the optical spectra of semiconductors
• Random-phase approximation and its applications in computational chemistry and materials science
• All-electron self-consistent GW approximation: Application to Si, MnO, and NiO
• Quasiparticle self-consistent $GW$ method; a basis for the independent-particle approximation
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• A Mountaineering Strategy to Excited States: Highly-Accurate Reference Energies and Benchmarks
• Fully selfconsistent GW calculations for molecules
• Perspectives on double-excitations in TDDFT
• Unified description of ground and excited states of finite systems: the self-consistent GW approach
• The Bethe-Salpeter Equation Formalism: From Physics to Chemistry
• Charge-transfer excitations in molecular donor-acceptor complexes within the many-body Bethe-Salpeter approach
• First-principles GW calculations for DNA and RNA nucleobases
• Levels of self-consistency in the GW approximation
• Cubic scaling $GW$: towards fast quasiparticle calculations
• Self-consistent GW: All-electron implementation with localized basis functions
• Quasi-Particle Self-Consistent $GW$ for Molecules
• QUESTDB: a database of highly-accurate excitation energies for the electronic structure community
• Towards GW Calculations on Thousands of Atoms
• Ab-initio calculation of the electronic and optical excitations in polythiophene: effects of intra- and interchain screening
• Reference Energies for Intramolecular Charge-Transfer Excitations
• Benchmark of GW approaches for the GW100 testset
• Fully self-consistent GW calculations for atoms and molecules
• Accurate absolute and relative core-level binding energies from $GW$
• Fully self-consistent $GW$ and quasi-particle self-consistent $GW$ for molecules
• The description of strong correlation within self-consistent Green's function second-order perturbation theory
• Electronic structure and magnetic properties of correlated metals: A local self-consistent perturbation scheme
• Particle-particle and quasiparticle random phase approximations: Connections to coupled cluster theory
• LDA++ approach to electronic structure of magnets: correlation effects in iron
• An O(N^3) implementation of Hedin's GW approximation for molecules
• Dynamical excitonic effects in metals and semiconductors
• Exchange-Correlation Energy from Pairing Matrix Fluctuation and the Particle-Particle Random Phase Approximation
• An assessment of the low-lying excitation energies and triplet instabilities of organic molecules with an ab initio Bethe-Salpeter equation approach
• Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory
• Beyond the GW approximation: combining correlation channels
• Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes
• Beyond the quasiparticle approximation: Fully self-consistent $GW$ calculations
• Cubic-scaling all-electron GW calculations with a separable density-fitting space-time approach
• On The Relation Between Equation-of-Motion Coupled-Cluster Theory and the GW Approximation
• Second-order Green's function perturbation theory for periodic systems
• All-electron GW calculation for molecules: Ionization energy and electron affinity of conjugated molecules
• Systematic vertex corrections through iterative solution of Hedin's equations beyond the GW approximation
• On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime
• Full-Frequency GW without Frequency
• Accurate optical properties from first principles: a Quasiparticle Self consistent GW plus Bethe-Salpeter Equation approach
• Ab Initio Bethe-Salpeter Equation Approach to Neutral Excitations in Molecules with Numeric Atom-Centered Orbitals
• Equivalence of Particle-Particle Random Phase Approximation Correlation Energy and Ladder-Coupled-Cluster-Double
• Separable Resolution-of-the-Identity with All-Electron Gaussian Bases: Application to Cubic-scaling RPA
• Vertex corrections in localized and extended systems
• Electron-magnon scattering in elementary ferromagnets from first principles: lifetime broadening and band anomalies
• Unphysical Discontinuities in GW Methods
• Redshift of excitons in carbon nanotubes caused by the environment polarizability
• Green functions and self-consistency: insights from the spherium model
• Vertex corrections to the polarizability do not improve the GW approximation for the ionization potential of molecules
• Exact relationships between the GW approximation and equation-of-motion coupled-cluster theories through the quasi-boson formalism
• Is ADC(3) as Accurate as CC3 for Valence and Rydberg Transition Energies?
• Fractional charge and spin errors in self-consistent Green's function theory
• Self-consistency in $GW\Gamma$ formalism leading to quasiparticle-quasiparticle couplings
• Local Hamiltonians for quantitative Green's function embedding methods
• Exploring the Statically Screened $G3W2$ Correction to the $GW$ Self-Energy: Charged Excitations and Total Energies of Finite Systems
• Renormalized Singles Green's Function in the T-Matrix Approximation for Accurate Quasiparticle Energy Calculation
• Dynamical Correction to the Bethe-Salpeter Equation Beyond the Plasmon-Pole Approximation
• A Density-Based Basis-Set Incompleteness Correction for GW Methods
• Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel
• Full-frequency dynamical Bethe-Salpeter equation without frequency and a study of double excitations
• Pros and Cons of the Bethe-Salpeter Formalism for Ground-State Energies
• A similarity renormalization group approach to Green's function methods
• Dynamically screened vertex correction to $GW$
• Spin-Conserved and Spin-Flip Optical Excitations From the Bethe-Salpeter Equation Formalism
• Iterative subspace algorithms for finite-temperature solution of Dyson equation
• A 'moment-conserving' reformulation of GW theory
• Stochastic many-body perturbation theory for Moiré states in twisted bilayer phosphorene
• Evaluation of two-particle properties within finite-temperature self-consistent one-particle Green's function methods: theory and application to GW and GF2
• Helium atom excitations by the GW and Bethe-Salpeter many-body formalism
• Connections between many-body perturbation and coupled-cluster theories
• Unphysical Discontinuities, Intruder States and Regularization in $GW$ Methods
• Potential energy surfaces without unphysical discontinuities: the Coulomb-hole plus screened exchange approach
• A wave function perspective and efficient truncation of renormalised second-order perturbation theory
• Static and Dynamic Bethe-Salpeter Equations in the $T$-Matrix Approximation
• Scrutinizing $GW$-based methods using the Hubbard dimer
• Dynamical Kernels for Optical Excitations
• Comparing many-body approaches against the helium atom exact solution
• Efficient excitations and spectra within a perturbative renormalization approach
• Decomposition and embedding in the stochastic $GW$ self-energy
• Efficient treatment of molecular excitations in the liquid phase environment via stochastic many-body theory
• A route to improving RPA excitation energies through its connection to equation-of-motion coupled cluster theory
• Vertex effects in describing the ionization energies of the first-row transition-metal monoxide molecules
• Combining Renormalized Singles $GW$ Methods with the Bethe-Salpeter Equation for Accurate Neutral Excitation Energies
• Renormalized Singles with Correlation in $GW$ Green's Function Theory for Accurate Quasiparticle Energies
• Ground-state correlation energy of beryllium dimer by the Bethe-Salpeter equation
• Improved quasiparticle self-consistent electronic band structure and excitons in $\beta$-LiGaO${}_2$
• Hydrogen molecule spectrum by many-body GW and Bethe-Salpeter equation

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• Can $GW$ Handle Multireference Systems?
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