Exploring the Statically Screened $G3W2$ Correction to the $GW$ Self-Energy: Charged Excitations and Total Energies of Finite Systems

Abstract

Electron correlation in finite and extended systems is often described in an effective single-particle framework within the $GW$ approximation. Here, we use the statically screened second-order exchange contribution to the self-energy ($G3W2$) to calculate a perturbative correction to the $GW$ self-energy. We use this correction to calculate total correlation energies of atoms, relative energies, as well as charged excitations of a wide range of molecular systems. We show that the second-order correction improves correlation energies with respect to the RPA and also improves relative energies for many, but not all considered systems. While the full $G3W2$ contribution does not give consistent improvements over $GW$, taking the average of $GW$ and $GW+G3W2$ generally gives excellent results. Improvements over quasiparticle self-consistent $GW$, which we show to give very accurate charged excitations in small and medium molecules by itself, are only minor. $G_0{W}_0$ quasiparticle energies evaluated with eigenvalue and orbitals from range-separated hybrids, however, are tremendously improved upon: The second-order corrected $G_0{W}_0$ outperforms all existing $GW$ methods for the systems considered herein and also does not come with substantially increased computational cost compared to $G_0{W}_0$ for systems with up to 100 atoms.

Revised version as accepted by Physical review B (Phys. Rev. B 2022, 105, 125121, 10.1103/PhysRevB.105.125121) Compared to our first submission, a programming mistake in our first implementation has been corrected leading to different (better) results

References in corpus (51)

• Phonons in single and few-layer MoS2 and WS2
• Towards standard methods for benchmark quality ab initio thermochemistry --- W1 and W2 theory
• Quasiparticle Self-Consistent GW Theory
• Random-phase approximation and its applications in computational chemistry and materials science
• Assessment of W1 and W2 theories for the computation of electron affinities, ionization potentials, heats of formation, and proton affinities
• Quasiparticle self-consistent $GW$ method; a basis for the independent-particle approximation
• The GW compendium: A practical guide to theoretical photoemission spectroscopy
• Van der Waals forces in density functional theory: perturbational long-range electron interaction corrections
• The Ground State Correlation Energy of the Random Phase Approximation from a Ring Coupled Cluster Doubles Approach
• Quasiparticle spectra from a non-empirical optimally-tuned range-separated hybrid density functional
• Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation
• Quasiparticle and Optical Properties of Rutile and Anatase TiO${}_2$
• Bootstrap approximation for the exchange-correlation kernel of time-dependent density functional theory
• Long-range-corrected hybrids including RPA correlation
• Bound excitons in time-dependent density-functional-theory: optical and energy-loss spectra
• Cubic scaling $GW$: towards fast quasiparticle calculations
• Assessment of correlation energies based on the random-phase approximation
• Many-body perturbation theory using the density-functional concept: beyond the GW approximation
• Benchmark of GW approaches for the GW100 testset
• Range-separated density-functional theory with random phase approximation applied to noncovalent intermolecular interactions
• Correlation energy expressions from the adiabatic-connection fluctuation-dissipation theorem approach
• Range-separated density-functional theory with random phase approximation: detailed formalism and illustrative applications
• Particle-particle and quasiparticle random phase approximations: Connections to coupled cluster theory
• Electronic structure of Na, K, Si, and LiF from self-consistent solution of Hedin's equations including vertex corrections
• Closed-shell ring coupled cluster doubles theory with range separation applied on weak intermolecular interactions
• Random-phase-approximation-based correlation energy functionals: Benchmark results for atoms
• Low-order Scaling $G_0{W}_0$ by Pair Atomic Density Fitting
• Systematic vertex corrections through iterative solution of Hedin's equations beyond the GW approximation
• Self-consistent solution of Hedin's equations: semiconductors/insulators
• Accurate optical properties from first principles: a Quasiparticle Self consistent GW plus Bethe-Salpeter Equation approach
• Strong renormalization of the electronic band gap due to lattice polarization in the GW formalism
• Diagrammatic expansion for positive spectral functions beyond GW: Application to vertex corrections in the electron gas
• Accurate ground state- and quasiparticle energies: beyond the RPA and GW methods with adiabatic exchange-correlation kernels
• Ab-initio prediction of the electronic and optical excitations in polythiophene: isolated chains versus bulk polymer
• Kohn-Sham band gaps and potentials of solids from the optimised effective potential method within the random phase approximation
• GW100: A Slater Type Orbital Perspective
• Simple vertex correction improves GW band energies of bulk and two-dimensional crystals
• Non conventional screening of the Coulomb interaction in low dimensional and finite size system
• Vertex corrections to the polarizability do not improve the GW approximation for the ionization potential of molecules
• Lowering of the complexity of quantum chemistry methods by choice of representation
• Dynamically screened vertex correction to $GW$
• Justifying quasiparticle self-consistent schemes via gradient optimization in Luttinger-Ward theory
• Role of non-locality in exchange-correlation for magnetic 2D van der Waals materials
• Full versus quasi-particle self consistency in vertex corrected GW approaches
• Vertex corrections for positive-definite spectral functions of simple metals
• On the duality of ring and ladder diagrams and its importance for many-electron perturbation theories
• One-electron spectra and susceptibilities of 3D electron gas from self-consistent solutions of Hedin's equations
• Electronic structure of TiSe${}_2$ from a quasi-self-consistent G${}_0$W${}_0$ approach
• Electronic structure of LaNiO${}_2$ and CaCuO${}_2$ from self consistent vertex corrected GW approach
• Electronic structure of van der Waals ferromagnet CrI${}_3$ from self consistent vertex corrected GW approaches
• Optimized effective potentials from the random-phase approximation: Accuracy of the quasiparticle approximation

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