Singles correlation energy contributions in solids

Abstract

The random phase approximation to the correlation energy often yields highly accurate results for condensed matter systems. However, ways how to improve its accuracy are being sought and here we explore the relevance of singles contributions for prototypical solid state systems. We set out with a derivation of the random phase approximation using the adiabatic connection and fluctuation dissipation theorem, but contrary to the most commonly used derivation, the density is allowed to vary along the coupling constant integral. This yields results closely paralleling standard perturbation theory. We re-derive the standard singles of Görling-Levy perturbation theory [Görling and Levy, Phys. Rev. A {\bf 50}, 196 (1994)], highlight the analogy of our expression to the renormalized singles introduced by Ren and coworkers [Ren, Tkatchenko, Rinke, and Scheffler, Phys. Rev. Lett. {\bf 106}, 153003 (2011)], and introduce a new approximation for the singles using the density matrix in the random phase approximation. We discuss the physical relevance and importance of singles alongside illustrative examples of simple weakly bonded systems, including rare gas solids (Ne, Ar, Xe), ice, adsorption of water on NaCl, and solid benzene. The effect of singles on covalently and metallically bonded systems is also discussed.

References in corpus (10)

• Nonlocal van der Waals density functional: The simpler the better
• Van der Waals bonding in layered compounds from advanced first-principles calculations
• Perspective: Advances and challenges in treating van der Waals dispersion forces in density functional theory
• Predictive GW calculations using plane waves and pseudopotentials
• The random phase approximation applied to solids, molecules, and graphene-metal interfaces: From weak to strong binding regimes
• Range-separated density-functional theory with random phase approximation: detailed formalism and illustrative applications
• Linear density response function within the time-dependent exact-exchange approximation
• The random phase approximation applied to ice
• Kohn-Sham band gaps and potentials of solids from the optimised effective potential method within the random phase approximation
• Cubic-scaling algorithm and self-consistent field for the random-phase approximation with second-order screened exchange

Cited by in corpus (18)

• On the physisorption of water on graphene: Sub-chemical accuracy from many-body electronic structure methods
• Coupled cluster theory in materials science
• Correlation energy for the homogeneous electron gas: exact Bethe-Salpeter solution and new approximate evaluation
• Properties of the water to boron nitride interaction: from zero to two dimensions with benchmark accuracy
• Analytic Interatomic Forces in the Random Phase Approximation
• Lattice energies of molecular solids from the random phase approximation with singles corrections
• Cerium Oxides without $U$: The Role of Many-Electron Correlation
• Efficient and accurate description of adsorption in zeolites
• RPA natural orbitals and their application to post-Hartree-Fock electronic structure methods
• Random Phase Approximation Applied to Many-Body Noncovalent Systems
• Random-Phase Approximation in Many-Body Noncovalent Systems: Methane in a Dodecahedral Water Cage
• Assessment of random-phase approximation and second order Møller-Plesset perturbation theory for many-body interactions in solid ethane, ethylene, and acetylene
• Plane wave basis set correction methods for RPA correlation energies
• Phase Stability of the Argon Crystal: A First-Principles Study Based on Random Phase Approximation plus Renormalized Single Excitation Corrections
• Binding energies of molecular solids from fragment and periodic approaches
• An accurate and efficient framework for modelling the surface chemistry of ionic materials
• Understanding the wetting of transition metal dichalcogenides from an ab initio perspective
• Regularized Perturbation Theory for Ab initio Solids