Density functional for short-range correlation: Accuracy of the random-phase approximation for isoelectronic energy changes

Yan, Zhihui; Perdew, John P.; Kurth, Stefan

doi:10.1103/physrevb.61.16430

Cited by 156 publications

(178 citation statements)

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“…1 and 2 for recent reviews). One of the advantages of RPA is its good description of dispersion interactions at large separation, [3][4][5] whereas two important disadvantages are its poor description of short-range electron correlations 6 and its slow Gaussian basis convergence. [7][8][9] These two limitations can be overcome by the range-separation approach (see, e.g., Ref.…”

Section: Introductionmentioning

confidence: 99%

Spin-unrestricted random-phase approximation with range separation: Benchmark on atomization energies and reaction barrier heights

Mussard

Reinhardt

Ángyán

et al. 2015

The Journal of Chemical Physics

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We consider several spin-unrestricted random-phase approximation (RPA) variants for calculating correlation energies, with and without range separation, and test them on datasets of atomization energies and reaction barrier heights. We show that range separation greatly improves the accuracy of all RPA variants for these properties. Moreover, we show that a RPA variant with exchange, hereafter referred to as RPAx-SO2, first proposed by Szabo and Ostlund [A. Szabo and N. S. Ostlund, J. Chem. Phys. 67, 4351 (1977)] in a spin-restricted closed-shell formalism, and extended here to a spin-unrestricted formalism, provides on average the most accurate range-separated RPA variant for atomization energies and reaction barrier heights. Since this range-separated RPAx-SO2 method had already been shown to be among the most accurate range-separated RPA variants for weak intermolecular interactions [J. Toulouse, W. Zhu, A. Savin, G. Jansen, and J. G. Ángyán, J. Chem. Phys. 135, 084119 (2011)], this works confirms range-separated RPAx-SO2 as a promising method for general chemical applications.

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Section: Introductionmentioning

confidence: 99%

Spin-unrestricted random-phase approximation with range separation: Benchmark on atomization energies and reaction barrier heights

Mussard

Reinhardt

Ángyán

et al. 2015

The Journal of Chemical Physics

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“…This was later refined by specially constructing also the density-gradient dependent part using additional properties of the short-range behavior of RPA. 140 Here, the short-range correlation energy, E c,sr , comes from a GGA density functional, while the RPA is used only for the long-range part, E c,lr . However, the range separation is accomplished only approximately using E c GGA@RPA and depends on how well this GGA functional describes the short-range part of RPA.…”

Section: Methods Based On the Random-phase Approximationmentioning

confidence: 99%

First-Principles Models for van der Waals Interactions in Molecules and Materials: Concepts, Theory, and Applications

2017

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Noncovalent van der Waals (vdW) or dispersion forces are ubiquitous in nature and influence the structure, stability, dynamics, and function of molecules and materials throughout chemistry, biology, physics, and materials science. These forces are quantum mechanical in origin and arise from electrostatic interactions between fluctuations in the electronic charge density. Here, we explore the conceptual and mathematical ingredients required for an exact treatment of vdW interactions, and present a systematic and unified framework for classifying the current first-principles vdW methods based on the adiabatic-connection fluctuation−dissipation (ACFD) theorem (namely the Rutgers−Chalmers vdW-DF, Vydrov−Van Voorhis (VV), exchange-hole dipole moment (XDM), Tkatchenko−Scheffler (TS), many-body dispersion (MBD), and random-phase approximation (RPA) approaches). Particular attention is paid to the intriguing nature of many-body vdW interactions, whose fundamental relevance has recently been highlighted in several landmark experiments. The performance of these models in predicting binding energetics as well as structural, electronic, and thermodynamic properties is connected with the theoretical concepts and provides a numerical summary of the state-of-the-art in the field. We conclude with a roadmap of the conceptual, methodological, practical, and numerical challenges that remain in obtaining a universally applicable and truly predictive vdW method for realistic molecular systems and materials.

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“…72 and 73, and their overlap matrix are preliminary quantities that, later on, will be modified to the auxiliary basis functions and overlap matrix actually used, see Subsection II C. By acting with the resolution of the identity (6) from the left and with the resolution of the identity (7) from the right in Eq. (5) and by inserting the resolution of the identity (6) into the right hand side of Eq. (5) after the Coulomb kernel, Eq.…”

Section: A Correlation Energy In the Random Phase Approximationmentioning

confidence: 99%

Efficient self-consistent treatment of electron correlation within the random phase approximation

Bleiziffer¹,

Heßelmann²,

Görling³

2013

The Journal of Chemical Physics

101

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A self-consistent Kohn-Sham (KS) method is presented that treats correlation on the basis of the adiabatic-connection dissipation-fluctuation theorem employing the direct random phase approximation (dRPA), i.e., taking into account only the Coulomb kernel while neglecting the exchangecorrelation kernel in the calculation of the Kohn-Sham correlation energy and potential. The method, denoted self-consistent dRPA method, furthermore treats exactly the exchange energy and the local multiplicative KS exchange potential. It uses Gaussian basis sets, is reasonably efficient, exhibiting a scaling of the computational effort with the forth power of the system size, and thus is generally applicable to molecules. The resulting dRPA correlation potentials in contrast to common approximate correlation potentials are in good agreement with exact reference potentials. The negatives of the eigenvalues of the highest occupied molecular orbitals are found to be in good agreement with experimental ionization potentials. Total energies from self-consistent dRPA calculations, as expected, are even poorer than non-self-consistent dRPA total energies and dRPA reaction and non-covalent binding energies do not significantly benefit from self-consistency. On the other hand, energies obtained with a recently introduced adiabatic-connection dissipation-fluctuation approach (EXXRPA+, exact-exchange random phase approximation) that takes into account, besides the Coulomb kernel, also the exact frequency-dependent exchange kernel are significantly improved if evaluated with orbitals obtained from a self-consistent dRPA calculation instead of an exact exchange-only calculation. Total energies, reaction energies, and noncovalent binding energies obtained in this way are of the same quality as those of high-level quantum chemistry methods, like the coupled cluster singles doubles method which is computationally more demanding. © 2013 AIP Publishing LLC.

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Density functional for short-range correlation: Accuracy of the random-phase approximation for isoelectronic energy changes

Cited by 156 publications

References 50 publications

Spin-unrestricted random-phase approximation with range separation: Benchmark on atomization energies and reaction barrier heights

Spin-unrestricted random-phase approximation with range separation: Benchmark on atomization energies and reaction barrier heights

First-Principles Models for van der Waals Interactions in Molecules and Materials: Concepts, Theory, and Applications

Efficient self-consistent treatment of electron correlation within the random phase approximation

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