Exchange holes in inhomogeneous systems: A coordinate-space model

Becke, Axel D.; Roussel, Marc R.

doi:10.1103/physreva.39.3761

Cited by 793 publications

(541 citation statements)

References 11 publications

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“…Similar expressions can be used to calculate higher-order C n coefficients from the higher multipole moments of the exchange-hole polarization density, P x . The XDM model can also be used together with density-functional approximations for the exchange hole, 201,202 which removes the dependence on the occupied KS orbitals. 203 The triple-dipole ATM-like term can be obtained from the exchange-hole dipole model as well.…”

Section: B B Bmentioning

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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Section: B B Bmentioning

confidence: 99%

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

2017

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“…Usually, MGGA functionals include either the Laplacian of the density [20][21][22] or the kinetic energy density 6,7,[23][24][25][26][27] . Some of them, however, include both ∇ 2 n σ and τ σ 17, 28,29 . There are two reasons for the inclusion of τ σ as an alternative (or additional) inhomogeneity parameter to ∇ 2 n σ .…”

mentioning

confidence: 99%

Self-consistent meta-generalized gradient approximation within the projector-augmented-wave method

et al. 2011

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The Tao-Perdew-Staroverov-Scuseria (TPSS) meta-generalized-gradient-approximation (MGGA) and its revised version, the revTPSS, are implemented self-consistently within the framework of the projector-augmented-wave (PAW) method, using a plane wave basis set.Both TPSS and revTPSS yield accurate atomization energies for the molecules in the AE6 set, better than those of the standard Perdew-Burke-Ernzerhof (PBE) generalized-gradientapproximation. For lattice constants and bulk moduli of 20 diverse solids, revTPSS performs much better than PBE, and on average as well as PBEsol and Armiento-Mattsson (AM05), GGAs designed for solids. The latter two overestimate the atomization energies for molecules to an unacceptable degree. However, the revTPSS presents only a slight improvement over PBEsol for the prediction of cohesive energies for solids, and some deterioration with respect to PBE. We also study the magnetic properties of Fe, for which both TPSS and revTPSS predict the right ground-state solid phase, the ferromagnetic body-centered-cubic (bcc) structure, with an accurate magnetic moment.

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“…The function Q KS;g has been used in the development of some meta-GGA functionals. [38,41] Note that for the HEG, Q KS;1 becomes…”

Section: The Positive-defined Ks Kinetic Energy Densitymentioning

confidence: 99%

“…However, only a few of such functionals have been developed. [37][38][39][40][41][42][43] Due to the aforementioned numerical problems with the Laplacian, LK-meta-GGA functionals are often transformed back into K-meta-GGA functionals expressing the Laplacian in terms of s KS and rq, see for example,…”

Section: Fig Urementioning

confidence: 99%

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Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

Sala

Fabiano

Constantin

2016

Int J of Quantum Chemistry

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We present the theory of semilocal exchange-correlation (XC) energy functionals which depend on the Kohn-Sham kinetic energy density (KED), including the relevant class of meta-generalized gradient approximation (meta-GGA) functionals. Thanks to the KED ingredient, meta-GGA functionals can satisfy different exact constraints for XC energy and can be made one-electron selfcorrelation free. This leads to a better accuracy over a wider range of properties with respect to GGAs, often reaching the accuracy of hybrid functionals, but at much reduced computational cost.An extensive survey of the relevant literature on existing KED dependent XC functionals is provided, considering nonempirical, semi-empirical, and fully empirical ones. A deeper analysis and a wide benchmark are presented for functionals derived considering only exact constraints and parameters obtained from model and/or atomic systems. K E Y W O R D Sdensity functional theory, kinetic energy, meta-GGA | I N T R O D U C T I O NKohn-Sham (KS)-density functional theory (DFT) [1][2][3][4][5] is nowadays one of the most popular computational approaches in quantum chemistry, solid-state physics, and materials science. [6][7][8][9][10][11] While the ground-state description of a real system of interacting electrons requires a complicate N-electron wavefunction, in KS-DFT this is mapped onto an auxiliary system of noninteracting electrons having the same ground-state density, which can be easily described using N single-particle KS orbitals. [1,2] The correspondence between the many-electron problem and the KS system is in principle exact [1,3] and it is based on the so called exchange-correlation (XC) energy functional, which collects all the quantum electron-electron interaction terms beyond the Hartree one. [12] Within the constrained-search formalism, [13] the XC energy functional is:E xc ½q 5 min W!q hWjT 1V ee jWi2T s ½q 2J½q 5E x ½q 1U c ½q 1T c ½q ;(1) where W is an N-electron ground-state wavefunction yielding the electron density q,T is the kinetic energy (KE) operator,V ee is the electron-electron interaction operator, T s is the KE of the noninteracting system, J is the Coulomb energy, E x is the exact exchange energy, and U c and T c represent, respectively, the potential and the kinetic contributions to the DFT correlation energy E c 5U c 1T c . The important point of Equation1 is that it is an universal functional of the electron density. However, its explicit functional form is not known, and any practical realization of KS-DFT is based on an approximated XC functional. The latter determines in practice the overall accuracy of the KS-DFT calculation.The study of the exact properties of the XC energy functional as well as the development of new and improved approximations have been hot research topics in DFT for more than three decades, and a large number of XC approximations has been proposed. [12,14,15] The different XC functionals are usually classified, according to their complexity, on the so called Jacob's ladder of DFT [14,16] whic...

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Exchange holes in inhomogeneous systems: A coordinate-space model

Cited by 793 publications

References 11 publications

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

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

Self-consistent meta-generalized gradient approximation within the projector-augmented-wave method

Kinetic‐energy‐density dependent semilocal exchange‐correlation functionals

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