Nonlocal energy-optimized kernel: Recovering second-order exchange in the homogeneous electron gas

Bates, Jefferson E.; Laricchia, Savio; Ruzsinszky, Adrienn

doi:10.1103/physrevb.93.045119

Cited by 36 publications

(76 citation statements)

References 63 publications

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“…where the effective interaction W 2,α (iω) = αηκ α (iω) −2 η T is more strongly screened than the RPA effective interaction W 1,α (iω) defined in eq (10).W 2 , the coupling-strength average of W 2,α , 42 can be integrated analytically: 25,38,46…”

Section: Rpa Renormalization With Axkmentioning

confidence: 99%

Performance and Scope of Perturbative Corrections to Random-Phase Approximation Energies

Chen

Agee

Furche

2018

J. Chem. Theory Comput.

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It has been suspected since the early days of the random-phase approximation (RPA) that corrections to RPA correlation energies result mostly from short-range correlation effects and are thus amenable to perturbation theory. Here we test this hypothesis by analyzing formal and numerical results for the most common beyond-RPA perturbative corrections, including the bare second-order exchange (SOX), secondorder screened exchange (SOSEX), and approximate exchange kernel (AXK) methods.Our analysis is facilitated by efficient and robust algorithms based on the resolutionof-the-identity (RI) approximation and numerical frequency integration, which enable benchmark beyond-RPA calculations on medium-and large-size molecules with sizeindependent accuracy. The AXK method systematically improves upon RPA, SOX, and SOSEX for reaction barrier heights, reaction energies, and noncovalent interaction This document is the unedited Author's version of a Submitted Work that was subsequently accepted for publication in energies of main-group compounds. The improved accuracy of AXK compared with SOX and SOSEX is attributed to stronger screening of bare SOX in AXK. For reactions involving transition-metal compounds, particularly 3d transition metal dimers, the AXK correction is too small and can even have the wrong sign. These observations are rationalized by a measureᾱ of the effective coupling strength for beyond-RPA correlation. When the effective coupling strength increases beyond a criticalᾱ value of approximately 0.5, the RPA errors increase rapidly, and perturbative corrections become unreliable. Thus, perturbation theory can systematically correct RPA, but only for systems and properties qualitatively well captured by RPA, as indicated by small α values.

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Section: Rpa Renormalization With Axkmentioning

confidence: 99%

Performance and Scope of Perturbative Corrections to Random-Phase Approximation Energies

Chen

Agee

Furche

2018

J. Chem. Theory Comput.

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“…58 This kernel (which can be applied to an arbitrary non-uniform system) is based on exact constraints and on the concept of the uniform electron gas;…”

Section: Methodology a The Neo-i Kernelmentioning

confidence: 99%

“…The problem is that this kernel (as introduced in Ref. 58) produces an unwanted long-ranged exchange kernel in the tail of the electron density of a jellium surface (Z σ → 1 and k F σ → 0) where the RPA should be recovered as discussed in Ref. 35.…”

Section: B Neo-ii Kernelmentioning

confidence: 99%

“…Beyond the jellium model, recent calculations showed a remarkably accuracy of the RPA for various properties (including the surface energy) of real materials [49][50][51][52][53][54][55] . To account for this missing short-range part of the RPA correlation energy in the uniform electron gas and inhomogeneous systems, we rely on (for the jellium surface) a nonlocal energy-optimized (NEO) model kernel 56,57 which has been introduced and tested recently 58 . This kernel is designed to satisfy exact constraints utilizing the iso-orbital Z indicator, a meta-GGA ingredient.…”

Section: Introductionmentioning

confidence: 99%

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Kernel-corrected random-phase approximation for the uniform electron gas and jellium surface energy

2016

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We introduce and test a nonlocal energy-optimized model kernel (NEO) within the adiabatic connection fluctuation-dissipation (ACFD) density-functional theory for the jellium surface and uniform electron gas, as benchmarks for simple metallic systems. Our model kernel is short-ranged for the uniform electron gas paradigm system, and one-electron self-correlation free. One-electron self-interaction freedom is provided by an iso-orbital indicator. We show how several versions of the NEO kernel perform for the uniform electron gas and jellium surface energies, and in addition we explain the underlying physics of self-interaction-free exchange-only kernels for exponentially decaying surface densities.

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“…However the absence of an exchange-correlation (xc) kernel in RPA leads to an inaccurate description of short-range correlation. [69][70][71][72] Beyond-RPA (bRPA) methods including an approximate exchange-correlation kernel from time dependent DFT 45,46,[72][73][74] (TDDFT) correct this deficiency of RPA while preserving the accurate description of long-range interactions.…”

Section: Introductionmentioning

confidence: 99%

Rocksalt or cesium chloride: Investigating the relative stability of the cesium halide structures with random phase approximation based methods

2018

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The ground state structural and energetic properties for rocksalt and cesium chloride phases of the cesium halides were explored using the Random Phase Approximation (RPA) and beyond-RPA methods to benchmark the non-empirical SCAN meta-GGA and its empirical dispersion corrections. The importance of non-additivity and higher-order multipole moments of dispersion in these systems is discussed. RPA generally predicts the equilibrium volume for these halides within 2.4% of the experimental value, while beyond-RPA methods utilizing the renormalized adiabatic LDA (rALDA) exchange-correlation kernel are typically within 1.8%. The zero-point vibrational energy is small and shows that the stability of these halides is purely due to electronic correlation effects. The rAPBE kernel as a correction to RPA overestimates the equilibrium volume and could not predict the correct phase ordering in the case of cesium chloride, while the rALDA kernel consistently predicted results in agreement with the experiment for all of the halides. However, due to its reasonable accuracy with lower computational cost, SCAN+rVV10 proved to be a good alternative to the RPA-like methods for describing the properties of these ionic solids.Alkali halides provide a useful benchmark for new theoretical methods to test their performance in predicting equilibrium and non-equilibrium properties of ionic solids 1-7 . Among the alkali halides, cesium halides are of particular interest in terms of their phase stability and have been studied both experimentally as well as theoretically 3,8-12 . CsF is experimentally stable in the B1 structure, while the Cl, Br, and I materials exist experimentally in the B2 structure. In Strukturbericht notation, B1 corresponds to the rocksalt (NaCl) phase, whereas B2 refers to the CsCl phase 13 . This difference in phase preference for the cesium halides can only be understood through the inclusion of dispersion interactions 3,8-12 .The unexpected stability of an ionic B2 phase was explained by London 8 through the presence of relatively large van der Waals interactions between the heavy Cs + cation and the heavier halide anions (Cl − , Br − , and I − ). Since dispersion effects are proportional to the polarizability and number of electrons in the anion, they are expected to become more important as one moves down the halide column. Furthermore, the coordination number of Cs in the B2 phase is higher than that in the B1 phase so there are locally more halide anions with which to interact. Dispersion is a pure quantum mechanical effect due to instantaneous or induced electronic multipole moments and is therefore difficult to capture with classical models 14 . The simplest treatment of the dispersion interaction is modeled by simple pairwiseadditive interactions between atoms, but this type of approximation completely ignores any nonadditive, nonlocal, and collective many-body effects 14,15 , which can be important in cases where screening effects modify electron-electron interactions.Rather than rely on classical models, ab...

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Nonlocal energy-optimized kernel: Recovering second-order exchange in the homogeneous electron gas

Cited by 36 publications

References 63 publications

Performance and Scope of Perturbative Corrections to Random-Phase Approximation Energies

Performance and Scope of Perturbative Corrections to Random-Phase Approximation Energies

Kernel-corrected random-phase approximation for the uniform electron gas and jellium surface energy

Rocksalt or cesium chloride: Investigating the relative stability of the cesium halide structures with random phase approximation based methods

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