Topic

# Hybrid functional

About: Hybrid functional is a(n) research topic. Over the lifetime, 4063 publication(s) have been published within this topic receiving 734293 citation(s).

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Journal Article
Abstract: Generalized gradient approximations (GGA’s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. [S0031-9007(96)01479-2] PACS numbers: 71.15.Mb, 71.45.Gm Kohn-Sham density functional theory [1,2] is widely used for self-consistent-field electronic structure calculations of the ground-state properties of atoms, molecules, and solids. In this theory, only the exchange-correlation energy EXC › EX 1 EC as a functional of the electron spin densities n"srd and n#srd must be approximated. The most popular functionals have a form appropriate for slowly varying densities: the local spin density (LSD) approximation Z d 3 rn e unif

117,932 Citations

Journal ArticleDOI: 10.1063/1.464913
Abstract: Despite the remarkable thermochemical accuracy of Kohn–Sham density‐functional theories with gradient corrections for exchange‐correlation [see, for example, A. D. Becke, J. Chem. Phys. 96, 2155 (1992)], we believe that further improvements are unlikely unless exact‐exchange information is considered. Arguments to support this view are presented, and a semiempirical exchange‐correlation functional containing local‐spin‐density, gradient, and exact‐exchange terms is tested on 56 atomization energies, 42 ionization potentials, 8 proton affinities, and 10 total atomic energies of first‐ and second‐row systems. This functional performs significantly better than previous functionals with gradient corrections only, and fits experimental atomization energies with an impressively small average absolute deviation of 2.4 kcal/mol.

Topics: Hybrid functional (61%), , Kohn–Sham equations (54%) ...read more

80,847 Citations

Journal Article
Chengteh Lee1, Weitao Yang1, Robert G. Parr1Institutions (1)
15 Jan 1988-Physical Review B
Abstract: A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock density matrix, is restated as a formula involving the density and local kinetic-energy density. On insertion of gradient expansions for the local kinetic-energy density, density-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calculations on a number of atoms, positive ions, and molecules, of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.

Topics: , , Electronic density (56%) ...read more

77,776 Citations

Journal Article
Axel D. Becke1Institutions (1)
15 Sep 1988-Physical Review A
Abstract: Current gradient-corrected density-functional approximations for the exchange energies of atomic and molecular systems fail to reproduce the correct 1/r asymptotic behavior of the exchange-energy density. Here we report a gradient-corrected exchange-energy functional with the proper asymptotic limit. Our functional, containing only one parameter, fits the exact Hartree-Fock exchange energies of a wide variety of atomic systems with remarkable accuracy, surpassing the performance of previous functionals containing two parameters or more.

Topics: Hybrid functional (62%), ,  ...read more

42,343 Citations

Open accessJournal Article
Walter Kohn1, L. J. Sham1Institutions (1)
15 Nov 1965-Physical Review
Abstract: From a theory of Hohenberg and Kohn, approximation methods for treating an inhomogeneous system of interacting electrons are developed. These methods are exact for systems of slowly varying or high density. For the ground state, they lead to self-consistent equations analogous to the Hartree and Hartree-Fock equations, respectively. In these equations the exchange and correlation portions of the chemical potential of a uniform electron gas appear as additional effective potentials. (The exchange portion of our effective potential differs from that due to Slater by a factor of $\frac{2}{3}$.) Electronic systems at finite temperatures and in magnetic fields are also treated by similar methods. An appendix deals with a further correction for systems with short-wavelength density oscillations.

Topics: Jellium (56%), Hartree–Fock method (55%), Thomas–Fermi model (55%) ...read more

42,177 Citations

##### Performance
###### Metrics
No. of papers in the topic in previous years
YearPapers
20225
2021165
2020211
2019191
2018216
2017246

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Topic's top 5 most impactful authors

Gustavo E. Scuseria

75 papers, 29.9K citations

Alfredo Pasquarello

41 papers, 1.3K citations

Martin Kaupp

41 papers, 1.8K citations

John P. Perdew

39 papers, 125.8K citations

Donald G. Truhlar

38 papers, 28.5K citations

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