Self-consistent random phase approximation and optimized hybrid functionals for solids

Abstract

The random phase approximation (RPA) and the $GW$ approximation share the same total energy functional but RPA is defined on a restricted domain of Green's functions determined by a local Kohn-Sham (KS) potential. In this work, we perform self-consistent RPA calculations by optimizing the local KS potential through the optimized effective potential equation. We study a number of solids (C, Si, BN, LiF, MgO, TiO${}_2$), and find in all cases a lowering of the total energy with respect to non-self-consistent RPA. We then propose a variational approach to optimize parameter-dependent hybrid functionals based on the minimization of the RPA total energy with respect to the fraction of exact exchange used to generate the input KS orbitals. We show that this scheme leads to hybrid functionals with a KS band structure in close agreement with RPA, and with lattice constants of similar accuracy as within RPA. Finally, we evaluate $G_0{W}_0$ gaps using RPA and hybrid KS potentials as starting points. Special attention is given to TiO${}_2$, which exhibits a strong starting-point dependence.

16 pages, 10 figures

References in corpus (36)

• Advanced capabilities for materials modelling with Quantum ESPRESSO
• Optimized norm-conserving Vanderbilt pseudopotentials
• Yambo: an \textit{ab initio} tool for excited state calculations
• Quasiparticle Self-Consistent GW Theory
• Random-phase approximation and its applications in computational chemistry and materials science
• Many-body perturbation theory calculations using the yambo code
• More-Realistic Band Gaps from Meta-Generalized Gradient Approximations: Only in a Generalized Kohn-Sham Scheme
• 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
• Fully self-consistent GW calculations for atoms and molecules
• Efficient and accurate calculation of exact exchange and RPA correlation energies in the Adiabatic-Connection Fluctuation-Dissipation theory
• Bond Breaking and Bond Formation: How Electron Correlation is Captured in Many-Body Perturbation Theory and Density-Functional Theory
• Electronic structure of Pu and Am metals by self consistent relativistic GW
• Electronic structure of Na, K, Si, and LiF from self-consistent solution of Hedin's equations including vertex corrections
• Beyond the quasiparticle approximation: Fully self-consistent $GW$ calculations
• GW quasiparticle bandgaps of anatase TiO2 starting from DFT+U
• The correlation potential in density functional theory at the GW-level: spherical atoms
• Discontinuities of the exchange-correlation kernel and charge-transfer excitations in time-dependent density functional theory
• Correlation potentials for molecular bond dissociation within the self-consistent random phase approximation
• Correlation energy functional and potential from time-dependent exact-exchange theory
• Static correlation and electron localization in molecular dimers from the self-consistent RPA and GW approximation
• Analytic Interatomic Forces in the Random Phase Approximation
• Precise response functions in all-electron methods: Application to the optimized-effective-potential approach
• Kohn-Sham band gaps and potentials of solids from the optimised effective potential method within the random phase approximation
• Exact-exchange kernel of time-dependent density functional theory: Frequency dependence and photoabsorption spectra of atoms
• Zero-point Renormalization of the Band Gap of Semiconductors and Insulators Using the PAW Method
• Beyond the random phase approximation with a local exchange vertex
• Derivative discontinuity and exchange-correlation potential of meta-GGAs in density-functional theory
• Efficient and accurate description of adsorption in zeolites
• Electronic structure of TiSe${}_2$ from a quasi-self-consistent G${}_0$W${}_0$ approach
• Random phase approximation with exchange for an accurate description of crystalline polymorphism
• Optimized effective potentials from the random-phase approximation: Accuracy of the quasiparticle approximation
• Ground state properties of 3d metals from self-consistent GW approach
• Plane wave basis set correction methods for RPA correlation energies
• High-pressure II-III phase transition in solid hydrogen: Insights from state-of-the-art ab initio calculations
• Assessing many-body methods on the potential energy surface of the (H${}_2$)${}_2$ hydrogen dimer