Analytic $G_0{W}_0$ gradients based on a double-similarity transformation equation-of-motion coupled-cluster treatment

Abstract

The accurate prediction of ionization potentials (IPs) is central to understanding molecular reactivity, redox behavior, and spectroscopic properties. While vertical IPs can be accessed directly from electronic excitations at fixed nuclear geometries, the computation of adiabatic IPs requires nuclear gradients of the ionized states, posing a major theoretical and computational challenge, especially within correlated frameworks. Among the most promising approaches for IP calculations is the many-body Green's function $GW$ method, which provides a balanced compromise between accuracy and computational efficiency. Furthermore, it is applicable to both finite and extended systems. Recent work has established formal connections between $GW$ and coupled-cluster doubles (CCD) theory, leading to the first derivation of analytic $GW$ nuclear gradients via a unitary CCD framework. In this work, we present an alternative, fully analytic formulation of $GW$ nuclear gradients based on a modified version of the traditional equation-of-motion CCD formalism, enabling the inclusion of missing correlation effects in the traditional CCD methods.

27 pages

References in corpus (52)

• The GW method
• Quasiparticle Self-Consistent GW Theory
• 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
• Self-energy-functional approach to systems of correlated electrons
• 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
• Levels of self-consistency in the GW approximation
• Quasi-Particle Self-Consistent $GW$ for Molecules
• Breaking the theoretical scaling limit for predicting quasi-particle energies: The stochastic GW approach
• Towards GW Calculations on Thousands of Atoms
• 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 $GW$
• 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${}_3$
• Excited-state Forces within a First-principles Green's Function Formalism
• Particle-particle and quasiparticle random phase approximations: Connections to coupled cluster theory
• Electron-phonon coupling in the C60 fullerene within the many-body GW approach
• 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 effects on electron-phonon coupling in semiconductors: many-body theory along thermal lines
• Full-Frequency GW without Frequency
• Low-scaling $GW$ with benchmark accuracy and application to phosphorene nanosheets
• 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
• Connections and performances of Green's function methods for charged and neutral excitations
• Vertex corrections to the polarizability do not improve the GW approximation for the ionization potential of molecules
• Exploring approximations to the GW self-energy ionic gradients
• Exact relationships between the GW approximation and equation-of-motion coupled-cluster theories through the quasi-boson formalism
• Minimax Isometry Method: A compressive sensing approach for Matsubara summation in many-body perturbation theory
• GW approximation with self-screening correction
• A Density-Based Basis-Set Incompleteness Correction for GW Methods
• Accelerating core-level $GW$ calculations by combining the contour deformation approach with the analytic continuation of $W$
• Reference Energies for Valence Ionizations and Satellite Transitions
• Random-phase approximation excitation energies from approximate equation-of-motion ring coupled-cluster doubles
• A similarity renormalization group approach to Green's function methods
• The correlation energy functional within the GW-RPA approximation: exact forms, approximate forms and challenges
• Connections between many-body perturbation and coupled-cluster theories
• The QUEST Database of Highly-Accurate Excitation Energies
• Electron-phonon coupling from GW perturbation theory: Practical workflow combining BerkeleyGW, ABINIT, and EPW
• A route to improving RPA excitation energies through its connection to equation-of-motion coupled cluster theory
• Anomalous propagators and the particle-particle channel: Hedin's equations
• $GW$ self-screening error and its correction using a local density functional
• Finite-size Effects in periodic EOM-CCSD for Ionization Energies and Electron Affinities: Convergence Rate and Extrapolation to the Thermodynamic Limit
• Fully Analytic Nuclear Gradients for the Bethe--Salpeter Equation

Cited by in corpus (1)

• Optical excitations in nanographenes from the Bethe-Salpeter equation and time-dependent density functional theory: absorption spectra and spatial descriptors