Spin-Conserved and Spin-Flip Optical Excitations From the Bethe-Salpeter Equation Formalism

Abstract

Like adiabatic time-dependent density-functional theory (TD-DFT), the Bethe-Salpeter equation (BSE) formalism of many-body perturbation theory, in its static approximation, is "blind" to double (and higher) excitations, which are ubiquitous, for example, in conjugated molecules like polyenes. Here, we apply the spin-flip \textit{ansatz} (which considers the lowest triplet state as the reference configuration instead of the singlet ground state) to the BSE formalism in order to access, in particular, double excitations. The present scheme is based on a spin-unrestricted version of the $GW$ approximation employed to compute the charged excitations and screened Coulomb potential required for the BSE calculations. Dynamical corrections to the static BSE optical excitations are taken into account via an unrestricted generalization of our recently developed (renormalized) perturbative treatment. The performance of the present spin-flip BSE formalism is illustrated by computing excited-state energies of the beryllium atom, the hydrogen molecule at various bond lengths, and cyclobutadiene in its rectangular and square-planar geometries.

arXiv comment14 pages, 3 figures and 3 tables

References in corpus (41)

• Quasiparticle Self-Consistent GW Theory
• Ab initio calculation of excitonic effects in the optical spectra of semiconductors
• All-electron self-consistent GW approximation: Application to Si, MnO, and NiO
• Fundamental gaps of finite systems from the eigenvalues of a generalized Kohn-Sham method
• 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
• Quasiparticle spectra from a non-empirical optimally-tuned range-separated hybrid density functional
• Fractional spins and static correlation error in density functional theory
• Perspectives on double-excitations in TDDFT
• A Mountaineering Strategy to Excited States: Highly-Accurate Energies and Benchmarks for Medium Size Molecules
• Benchmarking TD-DFT and Wave Function Methods for Oscillator Strengths and Excited-State Dipole Moments
• The Bethe-Salpeter Equation Formalism: From Physics to Chemistry
• Reference Energies for Double Excitations
• The Quest For Highly Accurate Excitation Energies: A Computational Perspective
• 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
• QUESTDB: a database of highly-accurate excitation energies for the electronic structure community
• Ab-initio calculation of the electronic and optical excitations in polythiophene: effects of intra- and interchain screening
• Conserving approximations in time-dependent quantum transport: Initial correlations and memory effects
• An assessment of the low-lying excitation energies and triplet instabilities of organic molecules with an ab initio Bethe-Salpeter equation approach
• A Mountaineering Strategy to Excited States: Highly-Accurate Energies and Benchmarks for Exotic Molecules and Radicals
• Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory
• Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes
• Assessment of Dressed Time-Dependent Density-Functional Theory for the Low-Lying Valence States of 28 Organic Chromophores
• All-electron GW calculation for molecules: Ionization energy and electron affinity of conjugated molecules
• 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
• A Mountaineering Strategy to Excited States: Highly-Accurate Oscillator Strengths and Dipole Moments of Small Molecules
• Unphysical Discontinuities in GW Methods
• Green functions and self-consistency: insights from the spherium model
• A Density-Based Basis-Set Incompleteness Correction for GW Methods
• Dynamical Correction to the Bethe-Salpeter Equation Beyond the Plasmon-Pole Approximation
• Range-separated time-dependent density-functional theory with a frequency-dependent second-order Bethe-Salpeter correlation kernel
• Kadanoff-Baym approach to double-excitations in finite systems
• Pros and Cons of the Bethe-Salpeter Formalism for Ground-State Energies
• Potential energy surfaces without unphysical discontinuities: the Coulomb-hole plus screened exchange approach
• Dynamical Kernels for Optical Excitations
• A formally exact one-frequency-only Bethe-Salpeter-like equation. Similarities and differences between GW +BSE and self-consistent RPA
• Hydrogen molecule spectrum by many-body GW and Bethe-Salpeter equation

Cited by in corpus (16)

• Connections and performances of Green's function methods for charged and neutral excitations
• Reference Energies for Valence Ionizations and Satellite Transitions
• Connections between many-body perturbation and coupled-cluster theories
• Static and Dynamic Bethe-Salpeter Equations in the $T$-Matrix Approximation
• Two-component $GW$ calculations: Cubic scaling implementation and comparison of vertex corrected and partially self-consistent $GW$ variants
• The three channels of many-body perturbation theory: $GW$, particle-particle, and electron-hole $T$-matrix self-energies
• Scrutinizing $GW$-based methods using the Hubbard dimer
• Can $GW$ Handle Multireference Systems?
• Combining Renormalized Singles $GW$ Methods with the Bethe-Salpeter Equation for Accurate Neutral Excitation Energies
• Combining Localized Orbital Scaling Correction and Bethe-Salpeter Equation for Accurate Excitation Energies
• Anomalous propagators and the particle-particle channel: Bethe-Salpeter equation
• Energy-Specific Bethe-Salpeter Equation Implementation for Efficient Optical Spectrum Calculations
• Excited State Properties from the Bethe--Salpeter Equation: State-to-State Transitions and Spin-Orbit Coupling
• Complex Absorbing Potential Green's Function Methods for Resonances
• Computation of the expectation value of the spin operator ${\hat{S}}^2$ for the Spin-Flip Bethe-Salpeter Equation
• LibppRPA: An Open-Source Library for Particle-Particle Random Phase Approximation