Accurate ground state- and quasiparticle energies: beyond the RPA and GW methods with adiabatic exchange-correlation kernels

Abstract

We review the theory and application of adiabatic exchange-correlation (xc-) kernels for ab initio calculations of ground state energies and quasiparticle excitations within the frameworks of the adiabatic connection fluctuation dissipation theorem and Hedin's equations, respectively. Various different xc-kernels, which are all rooted in the homogeneous electron gas, are introduced but hereafter we focus on the specific class of renormalized adiabatic kernels, in particular the rALDA and rAPBE. The kernels drastically improve the description of short-range correlations as compared to the random phase approximation (RPA), resulting in significantly better correlation energies. This effect greatly reduces the reliance on error cancellations, which is essential in RPA, and systematically improves covalent bond energies while preserving the good performance of the RPA for dispersive interactions. For quasiparticle energies, the xc-kernels account for vertex corrections that are missing in the GW self-energy. In this context, we show that the short-range correlations mainly correct the absolute band positions while the band gap is less affected in agreement with the known good performance of GW for the latter. The renormalized xc-kernels offer a rigorous extension of the RPA and GW methods with clear improvements in terms of accuracy at little extra computational cost.

arXiv commentReview article. 53 pages-

References in corpus (45)

• Van der Waals Density Functional for General Geometries
• The GW method
• The Computational 2D Materials Database: High-Throughput Modeling and Discovery of Atomically Thin Crystals
• Quasiparticle Self-Consistent GW Theory
• W4 theory for computational thermochemistry: in pursuit of confident sub-kJ/mol predictions
• Random-phase approximation and its applications in computational chemistry and materials science
• SCAN+rVV10: A promising van der Waals density functional
• First-principles GW calculations for fullerenes, porphyrins, phtalocyanine, and other molecules of interest for organic photovoltaic applications
• Screening and Many-Body Effects in Two-Dimensional Crystals: Monolayer MoS${}_2$
• Combining GW calculations with exact-exchange density-functional theory: An analysis of valence-band photoemission for compound semiconductors
• Fully selfconsistent GW calculations for molecules
• Conserving GW scheme for nonequilibrium quantum transport in molecular contacts
• Beyond the Random Phase Approximation for the Electron Correlation Energy: The Importance of Single Excitations
• Kadanoff-Baym approach to quantum transport through interacting nanoscale systems: From the transient to the steady-state regime
• Quasiparticle GW calculations for solids, molecules and 2D materials
• Describing static correlation in bond dissociation by Kohn-Sham density functional theory
• Dispersive and Covalent Interactions Between Graphene and Metal Surfaces from the Random Phase Approximation
• First-Principle Description of Correlation Effects in Layered Materials
• Bootstrap approximation for the exchange-correlation kernel of time-dependent density functional theory
• Benchmark tests of a strongly constrained semilocal functional with a long-range dispersion correction
• Linear density response function in the projector-augmented wave method: Applications to solids, surfaces, and interfaces
• Assessment of correlation energies based on the random-phase approximation
• The random phase approximation applied to solids, molecules, and graphene-metal interfaces: From weak to strong binding regimes
• Analytical expressions for the local-field factor G(q) and the exchange-correlation kernel K_{xc}(r) of the homogeneous electron gas
• Correlation energy expressions from the adiabatic-connection fluctuation-dissipation theorem approach
• The long-wavelength behaviour of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems
• Efficient many-body calculations of 2D materials using exact limits for the screened potential: Band gaps of MoS${}_2$, hBN, and phosphorene
• Phase transformation in Si from semiconducting diamond to metallic beta-Sn phase in QMC and DFT under hydrostatic and anisotropic stress
• Optical spectra of solids obtained by time-dependent density-functional theory with the jellium-with-gap model exchange-correlation kernel
• Extending the random-phase approximation for electronic correlation energies: The renormalized adiabatic local density approximation
• Adiabatic-connection fluctuation-dissipation DFT for the structural properties of solids-the renormalized ALDA and electron gas kernels
• Accurate Ground State Energies of Solids and Molecules from Time Dependent Density Functional Theory
• Simple dynamic exchange-correlation kernel of the uniform electron gas
• Beyond the random phase approximation: Improved description of short range correlation by a renormalized adiabatic local density approximation
• Simple vertex correction improves GW band energies of bulk and two-dimensional crystals
• Correlation energy within exact-exchange ACFD theory: systematic development and simple approximations
• Beyond the random phase approximation with a local exchange vertex
• Static correlation beyond the random phase approximation: Dissociating H2 with the Bethe-Salpeter equation and time-dependent GW
• Assessing the performance of the Random Phase Approximation for exchange and superexchange coupling constants in magnetic crystalline solids
• Adiabatic-Connection-Fluctuation-Dissipation approach to the long-range behavior of the exchange-correlation energy at metal surfaces: A numerical study for jellium slabs
• Efficient calculation of van der Waals dispersion coefficients with time-dependent density functional theory in real time: application to polycyclic aromatic hydrocarbons
• Exchange-correlation kernels for excited states in solids
• Hubbard-$U$ corrected Hamiltonians for non-self-consistent random-phase approximation total-energy calculations: A study of ZnS, TiO${}_2$, and NiO
• Simple model of the static exchange-correlation kernel of a uniform electron gas with long-range electron-electron interaction
• Metal-insulator transition in disordered systems from the one-body density matrix

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