Two-component $GW$ calculations: Cubic scaling implementation and comparison of vertex corrected and partially self-consistent $GW$ variants

Abstract

We report an all-electron, atomic orbital (AO) based, two-component (2C) implementation of the $GW$ approximation (GWA) for closed-shell molecules. Our algorithm is based on the space-time formulation of the GWA and uses analytical continuation of the self-energy, and pair-atomic density fitting (PADF) to switch between AO and auxiliary basis. By calculating the dynamical contribution to the $GW$ self-energy at a quasi-one-component level, our 2C $GW$ algorithm is only about a factor of two to three slower than in the scalar relativistic case. Additionally, we present a 2C implementation of the simplest vertex correction to the self-energy, the statically screened $G3W2$ correction. Comparison of first ionization potentials of a set of 67 molecules with heavy elements (a subset of the SOC81 set) calculated with our implementation against results from the WEST code reveals mean absolute deviations of around 70 meV for $G_0{W}_0$@PBE and $G_0{W}_0$@PBE0. These are most likely due to technical differences in both implementations, most notably the use of different basis sets, pseudopotential approximations, different treatment of the frequency dependency of the self-energy and the choice of the 2C-Hamiltonian. Finally, we assess the performance of some (partially self-consistent) variants of the GWA for the calculation of first IPs by comparison to vertical experimental reference values. $G_0{W}_0$PBE0 (25 \% exact exchange) and $G_0{W}_0$BHLYP (50 \% exact exchange) perform best with mean absolute deviations (MAD) of about 200 meV. Eigenvalue-only self-consistent $GW$ (ev$GW$) and quasi-particle self-consistent $GW$ (qs$GW$) significantly overestimate the IPs. Perturbative $G3W2$ corrections improve the agreement with experiment in cases where $G_0{W}_0$ alone underestimates the IPs. With a MAD of only 140 meV, 2C-$G_0{W}_0$PBE0 + $G3W2$ is in best agreement with the experimental reference values.

arXiv commentVersion with recalculated results due to a bug in the code with which the original results where produced

References in corpus (63)

• Quasiparticle Self-Consistent GW Theory
• Resolution-of-identity approach to Hartree-Fock, hybrid density functionals, RPA, MP2, and \textit{GW} with numeric atom-centered orbital basis functions
• All-electron self-consistent GW approximation: Application to Si, MnO, and NiO
• Effect of spin-orbit interaction on the excitonic effects in single-layer, double-layer, and bulk MoS2
• Quasiparticle self-consistent $GW$ method; a basis for the independent-particle approximation
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• Implementation of an all-electron GW approximation based on the PAW method without plasmon pole approximation: application to Si, SiC, AlAs, InAs, NaH and KH
• Quasiparticle and Optical Properties of Rutile and Anatase TiO${}_2$
• Quasiparticle GW calculations for solids, molecules and 2D materials
• Unified description of ground and excited states of finite systems: the self-consistent GW approach
• A Benchmark of GW Methods for Azabenzenes: Is the GW Approximation Good Enough?
• The GW space-time method for the self-energy of large systems
• Cubic scaling $GW$: towards fast quasiparticle calculations
• Self-consistent GW: All-electron implementation with localized basis functions
• Quasi-Particle Self-Consistent $GW$ for Molecules
• Towards GW Calculations on Thousands of Atoms
• Benchmark of GW approaches for the GW100 testset
• Accurate absolute and relative core-level binding energies from $GW$
• Fully self-consistent $GW$ and quasi-particle self-consistent $GW$ for molecules
• An O(N^3) implementation of Hedin's GW approximation for molecules
• Electronic structure of Pu and Am metals by self consistent relativistic GW
• Evaluating the GW Approximation with CCSD(T) for Charged Excitations Across the Oligoacenes
• Equation-of-Motion Coupled-Cluster Theory based on the 4-component Dirac-Coulomb(-Gaunt) Hamiltonian. Energies for single electron detachment, attachment and electronically excited states
• Cubic-scaling all-electron GW calculations with a separable density-fitting space-time approach
• Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms
• 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
• Self-consistent solution of Hedin's equations: semiconductors/insulators
• Spin-dependent Hedin's equations
• Swift $GW$ beyond $10,000$ electrons using fractured stochastic orbitals
• Full-Frequency GW without Frequency
• Accurate optical properties from first principles: a Quasiparticle Self consistent GW plus Bethe-Salpeter Equation approach
• Low-scaling $GW$ with benchmark accuracy and application to phosphorene nanosheets
• Diagrammatic expansion for positive spectral functions beyond GW: Application to vertex corrections in the electron gas
• Linearized self-consistent quasiparticle GW method: Application to semiconductors and simple metals
• Unphysical Discontinuities in GW Methods
• GW100: A Slater Type Orbital Perspective
• Growth optimization and device integration of narrow-bandgap graphene nanoribbons
• Photoluminescent properties of the carbon-dimer defect in hexagonal boron-nitride: a many-body finite-size cluster approach
• Self-consistency in $GW\Gamma$ formalism leading to quasiparticle-quasiparticle couplings
• Exploring the Statically Screened $G3W2$ Correction to the $GW$ Self-Energy: Charged Excitations and Total Energies of Finite Systems
• Dynamical Correction to the Bethe-Salpeter Equation Beyond the Plasmon-Pole Approximation
• Relativistic Self-Consistent $GW$: Exact Two-Component Formalism with One-Electron Approximation for Solids
• Assessment of the GW approximation using Hubbard chains
• A similarity renormalization group approach to Green's function methods
• Dynamically screened vertex correction to $GW$
• Justifying quasiparticle self-consistent schemes via gradient optimization in Luttinger-Ward theory
• Spin-Conserved and Spin-Flip Optical Excitations From the Bethe-Salpeter Equation Formalism
• Optical response and band structure of LiCoO2 including electron-hole interaction effects
• Unphysical Discontinuities, Intruder States and Regularization in $GW$ Methods
• A Finite-field Approach for $GW$ Calculations Beyond the Random Phase Approximation
• One-electron spectra and susceptibilities of 3D electron gas from self-consistent solutions of Hedin's equations
• Towards Pair Atomic Density Fitting for Correlation Energies with Benchmark Accuracy
• Simple eigenvalue-self-consistent $\bar{\Delta }G{W}_0$
• Decomposition and embedding in the stochastic $GW$ self-energy
• Gaussian-Based Quasiparticle Self-Consistent $GW$ for Periodic Systems
• Efficient treatment of molecular excitations in the liquid phase environment via stochastic many-body theory
• Assessment of the second-order statically screened exchange correction to the random phase approximation for correlation energies
• Universal polarization energies for defects in monolayer, surface and bulk hexagonal boron nitride : A finite-size fragments GW approach
• Vertex effects in describing the ionization energies of the first-row transition-metal monoxide molecules
• Practical $GW$ scheme for electronic structure of 3$d$-transition-metal monoxide anions: ScO${}^{-}$, TiO${}^{-}$, CuO${}^{-}$, and ZnO${}^{-}$
• Photoelectron spectra of early $3d$-transition metal dioxide cluster anions from $GW$ calculations

Cited by in corpus (11)

• Accelerating core-level $GW$ calculations by combining the contour deformation approach with the analytic continuation of $W$
• Comparing self-consistent GW and vertex corrected G0W0 (G0W0Γ) accuracy for molecular ionization potentials
• Beyond quasi-particle self-consistent $GW$ for molecules with vertex corrections
• Challenges with relativistic GW calculations in solids and molecules
• Quasiparticle and fully self-consistent GW methods: an unbiased analysis using Gaussian orbitals
• GW with hybrid functionals for large molecular systems
• Joint Approximate Diagonalization approach to Quasiparticle Self-Consistent $GW$ calculations
• Benchmarking the accuracy of the separable resolution of the identity approach for correlated methods in the numeric atom-centered orbitals framework
• Polarizable Continuum Models and Green's Function $\mathbf{GW}$ Formalism: On the Dynamics of the Solvent Electrons
• Efficient $GW$ band structure calculations using Gaussian basis functions and application to atomically thin transition-metal dichalcogenides
• All-electron Quasiparticle Self-consistent GW for Molecules and Periodic Systems within the Numerical Atomic Orbital Framework