Random-phase approximation and its applications in computational chemistry and materials science

Ren, Xinguo; Rinke, Patrick; Joas, Christian; Scheffler, Matthias

doi:10.1007/s10853-012-6570-4

Cited by 556 publications

(629 citation statements)

References 202 publications

(485 reference statements)

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“…al 32 , but underbinds compared to experiment 31 . Such underbinding using EXX+RPA method is generally found for other molecules as well 18 . Figure 2 and Table III show the calculated formation energies per oxygen atom.…”

Section: Resultsmentioning

confidence: 80%

“…For example, graphite 21 , which has vdW interlayer coupling, graphene adsorbed on metal surfaces 22 , which have mixed vdW and covalent bonds, and the S22 molecule set 18 , which consists of molecules containing hydrogen bonds, dispersion bonds and mixed bonds, are all significantly improved with RPA compared to PBE xc-functional. On the other hand, it is reported that RPA does slightly worse than PBE in reproducing the atomization energies of molecules, for example the G2-I set 18 , and the cohesive energies for 24 representative solids 12 , which consists of ionic crystal, semiconductors and metals, even though the lattice constants and bulk moduli of these solids calculated with RPA agree better with experiments than PBE.…”

Section: Introductionmentioning

confidence: 94%

“…EXX is free of self-interaction error, while the RPA correlation energy takes into account dynamic electronic screening and is fully non-local. EXX+RPA has been shown to systematically improve lattice constants 12 , atomization/cohesive energies 13,14 , adsorption energies [15][16][17] and reaction barriers 18 for a wide range of systems that have ionic, covalent and van der Waals (vdW) interactions. In particular, by summing up the ring diagrams in many body perturbation theory, RPA takes into account the long range density fluctuations and is especially suitable for vdW bonded systems 19,20 .…”

Section: Introductionmentioning

confidence: 99%

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Formation energies of group I and II metal oxides using random phase approximation

2013

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The enthalpy of formation for 23 metal oxides, which include group I and II as well as two transition metals (Ti and Ru), are calculated using random phase approximation (RPA). Compared to PBE xc-functional, RPA reduces the mean absolute error (MAE) per oxygen from 0.44 eV to 0.15 eV. The calculated deviations with experiments are seperated into two parts: a systematic and uniform error related to the reference energy of O and the ones specific to diffferent oxidation statesOur results show that RPA improves both the reference energy, although the error is not completely eliminated, and simultaneously over the three oxidation states.

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Section: Resultsmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

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Formation energies of group I and II metal oxides using random phase approximation

2013

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“…For the purpose of this review, we discuss these methods only from the point of view of long-range electron correlation and refer the reader elsewhere for a more general exposition. 136,137 A starting point for the methods of this section is the random-phase approximation (RPA), in which the exchangecorrelation kernel f xc (r, r′, u) = δv xc (r, u)/δn(r′, u) in the Dyson equation (eq 18) is set to zero. Its name comes from the original derivation of the approximation, in which the fluctuations of electrons are assumed to be influenced only by in-phase Coulomb contributions, whereas out-of-phase terms are considered to be random and hence cancel out.…”

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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“…Comparison to Eqs. (19) and (11) shows that, formally, the roles of the matrices K and B is merely exchanged with respect to the dRPA-IIa energy expression. Hence, the corresponding logarithmic formula obtained after α-integration is:…”

Section: B Rpa+sosexmentioning

confidence: 99%

Dielectric Matrix Formulation of Correlation Energies in the Random Phase Approximation: Inclusion of Exchange Effects

Mussard¹,

Rocca²,

Jansen

et al. 2016

J. Chem. Theory Comput.

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Starting from the general expression for the ground state correlation energy in the adiabatic connection fluctuation dissipation theorem (ACFDT) framework, it is shown that the dielectric matrix formulation, which is usually applied to calculate the direct random phase approximation (dRPA) correlation energy, can be used for alternative RPA expressions including exchange effects. Within this famework, the ACFDT analog of the second order screened exchange (SOSEX) approximation leads to a logarithmic formula for the correlation energy similar to the direct RPA expression. Alternatively, the contribution of the exchange can be included in the kernel used to evaluate the response functions. In this case the use of an approximate kernel is crucial to simplify the formalism and to obtain a correlation energy in logarithmic form. Technical details of the implementation of these methods are discussed and it is shown that one can take advantage of density fitting or Cholesky decomposition techniques to improve the computational efficiency; a discussion on the numerical quadrature made on the frequency variable is also provided. A series of test calculations on atomic correlation energies and molecular reaction energies shows that exchange effects are instrumental to improve over direct RPA results.

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Random-phase approximation and its applications in computational chemistry and materials science

Cited by 556 publications

References 202 publications

Formation energies of group I and II metal oxides using random phase approximation

Formation energies of group I and II metal oxides using random phase approximation

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

Dielectric Matrix Formulation of Correlation Energies in the Random Phase Approximation: Inclusion of Exchange Effects

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