Connections between many-body perturbation and coupled-cluster theories

Abstract

Here, we build on the works of Scuseria (et al.) http://dx.doi.org/10.1063/1.3043729 and Berkelbach https://doi.org/10.1063/1.5032314 to show connections between the Bethe-Salpeter equation (BSE) formalism combined with the $GW$ approximation from many-body perturbation theory and coupled-cluster (CC) theory at the ground- and excited-state levels. In particular, we show how to recast the $GW$ and Bethe-Salpeter equations as non-linear CC-like equations. Similitudes between BSE@$GW$ and the similarity-transformed equation-of-motion CC method introduced by Nooijen are also put forward. The present work allows to easily transfer key developments and general knowledge gathered in CC theory to many-body perturbation theory. In particular, it may provide a path for the computation of ground- and excited-state properties (such as nuclear gradients) within the $GW$ and BSE frameworks.

arXiv comment6 pages

References in corpus (55)

• The GW method
• Quasiparticle Self-Consistent GW Theory
• 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
• The Ground State Correlation Energy of the Random Phase Approximation from a Ring Coupled Cluster Doubles Approach
• Impact of the electron-electron correlation on phonon dispersions: failure of LDA and GGA functionals in graphene and graphite
• 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
• Quasi-Particle Self-Consistent $GW$ for Molecules
• Reference Energies for Intramolecular Charge-Transfer Excitations
• Ab-initio calculation of the electronic and optical excitations in polythiophene: effects of intra- and interchain screening
• Correlation-enhanced electron-phonon coupling: Applications of GW and screened hybrid functional to bismuthates, chloronitrides, and other high Tc superconductors
• 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${}_3$
• Correlation energy expressions from the adiabatic-connection fluctuation-dissipation theorem approach
• The description of strong correlation within self-consistent Green's function second-order perturbation theory
• Excited-state Forces within a First-principles Green's Function Formalism
• Particle-particle and quasiparticle random phase approximations: Connections to coupled cluster theory
• An assessment of the low-lying excitation energies and triplet instabilities of organic molecules with an ab initio Bethe-Salpeter equation approach
• Electron-phonon coupling in the C60 fullerene within the many-body GW approach
• Beyond the GW approximation: combining correlation channels
• Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes
• 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
• All-electron GW calculation for molecules: Ionization energy and electron affinity of conjugated molecules
• Low-order Scaling $G_0{W}_0$ by Pair Atomic Density Fitting
• Correlation energy for the homogeneous electron gas: exact Bethe-Salpeter solution and new approximate evaluation
• Correlation effects on electron-phonon coupling in semiconductors: many-body theory along thermal lines
• Excited States via Coupled Cluster Theory without Equation-of-Motion Methods: Seeking Higher Roots with Application to Doubly Excited States and Double Core Hole States
• Full-Frequency GW without Frequency
• Excited States From State Specific Orbital Optimized Pair Coupled Cluster
• Equivalence of Particle-Particle Random Phase Approximation Correlation Energy and Ladder-Coupled-Cluster-Double
• Ab Initio Bethe-Salpeter Equation Approach to Neutral Excitations in Molecules with Numeric Atom-Centered Orbitals
• Separable Resolution-of-the-Identity with All-Electron Gaussian Bases: Application to Cubic-scaling RPA
• Variational coupled cluster for ground and excited states
• Green functions and self-consistency: insights from the spherium model
• Local Hamiltonians for quantitative Green's function embedding methods
• 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
• 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
• Random-phase approximation excitation energies from approximate equation-of-motion ring coupled-cluster doubles
• Spin-Conserved and Spin-Flip Optical Excitations From the Bethe-Salpeter Equation Formalism
• Unphysical Discontinuities, Intruder States and Regularization in $GW$ Methods
• Potential energy surfaces without unphysical discontinuities: the Coulomb-hole plus screened exchange approach
• Static and Dynamic Bethe-Salpeter Equations in the $T$-Matrix Approximation
• Dynamical Kernels for Optical Excitations
• Scrutinizing $GW$-based methods using the Hubbard dimer
• The many-body Green function of degenerate systems
• A route to improving RPA excitation energies through its connection to equation-of-motion coupled cluster theory
• Ground-state correlation energy of beryllium dimer by the Bethe-Salpeter equation
• Hydrogen molecule spectrum by many-body GW and Bethe-Salpeter equation
• Ensemble Green's function theory for interacting electrons with degenerate ground states

Cited by in corpus (15)

• Connections and performances of Green's function methods for charged and neutral excitations
• Exact relationships between the GW approximation and equation-of-motion coupled-cluster theories through the quasi-boson formalism
• Comparing self-consistent GW and vertex corrected G0W0 (G0W0Γ) accuracy for molecular ionization potentials
• Reference Energies for Valence Ionizations and Satellite Transitions
• A 'moment-conserving' reformulation of GW theory
• Challenges with relativistic GW calculations in solids and molecules
• Quasiparticle and fully self-consistent GW methods: an unbiased analysis using Gaussian orbitals
• Fully Analytic Nuclear Gradients for the Bethe--Salpeter Equation
• Finite-size Effects in periodic EOM-CCSD for Ionization Energies and Electron Affinities: Convergence Rate and Extrapolation to the Thermodynamic Limit
• Generalized many-body perturbation theory for the electron correlation energy: multi-reference random phase approximation via diagrammatic resummation
• Joint Approximate Diagonalization approach to Quasiparticle Self-Consistent $GW$ calculations
• Analytic $G_0{W}_0$ gradients based on a double-similarity transformation equation-of-motion coupled-cluster treatment
• Diagrammatic theory of the irreducible coupled-cluster self-energy
• Uncovering relationships between the electronic self-energy and coupled-cluster doubles theory
• Optical excitations in nanographenes from the Bethe-Salpeter equation and time-dependent density functional theory: absorption spectra and spatial descriptors