Cited by 18,777

The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.

Density-functional approximation for the correlation energy of the inhomogeneous electron gas

Perdew, John P.·1986·Physical Review B

Open this paper in CoChat — free account

Abstract

Langreth and Mehl (LM) and co-workers have developed a useful spin-density functional for the correlation energy of an electronic system. Here the LM functional is improved in two ways: (1) The natural separation between exchange and correlation is made, so that the density-gradient expansion of each is recovered in the slowly varying limit. (2) Uniform-gas and inhomogeneity effects beyond the randomphase approximation are built in. Numerical results for atoms, positive ions, and surfaces are close to the exact correlation energies, with major improvements over the original LM approximation for the ions and surfaces.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

Integrity signals

Registry

Crossref · 10.1103/physrevb.33.8822

Cites

2 of 2 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Self-Consistent Equations Including Exchange and Correlation Effects
Kohn, W., & Sham, L. J. (1965) · Physical Review · doi:10.1103/physrev.140.a1133 · Cited by 64,135
Self-interaction correction to density-functional approximations for many-electron systems
Perdew, J. P., & Zunger, A. (1981) · Physical Review B · doi:10.1103/physrevb.23.5048 · Cited by 20,887
Self-citation

Show all 2 references

Research works printed but not linked: 32

P. Hohenberg, 1964, Phys. Rev., 136, B864, 10.1103/PhysRev.136.B864 · DOI · Paper page
U. von Barth, 1972, J. Phys. C, 5, 1629, 10.1088/0022-3719/5/13/012 · DOI
A. K. Rajagopal, 1973, Phys. Rev. B, 7, 1912, 10.1103/PhysRevB.7.1912 · DOI · Paper page
S-K. Ma, 1968, Phys. Rev., 165, 18, 10.1103/PhysRev.165.18 · DOI · Paper page
H. Stoll, 1978, Theoret. Chim. Acta, 49, 143, 10.1007/PL00020511 · DOI
S. H. Vosko, 1983, J. Phys. B, 16, 3687, 10.1088/0022-3700/16/20/006 · DOI
D. C. Langreth, 1980, Phys. Rev. B, 21, 5469, 10.1103/PhysRevB.21.5469 · DOI · Paper page
D. C. Langreth, 1983, Phys. Rev. B, 28, 1809, 10.1103/PhysRevB.28.1809 · DOI · Paper page
C. D. Hu, 1985, Phys. Scr., 32, 391, 10.1088/0031-8949/32/4/024 · DOI
C. D. Hu, 1986, Phys. Rev. B, 33, 943, 10.1103/PhysRevB.33.943 · DOI
U. von Barth, 1985, Phys. Scr., 32, 353, 10.1088/0031-8949/32/4/019 · DOI
M. Norman, 1983, Phys. Rev. B, 28, 4357, 10.1103/PhysRevB.28.4357 · DOI
L. A. Cole, 1982, Phys. Rev. A, 25, 1265, 10.1103/PhysRevA.25.1265 · DOI
M. Rasolt, 1976, Phys. Rev. B, 13, 1477, 10.1103/PhysRevB.13.3290 · DOI
D. M. Ceperley, 1980, Phys. Rev. Lett., 45, 566, 10.1103/PhysRevLett.45.566 · DOI · Paper page
A. Veillard, 1968, J. Chem. Phys., 49, 2415, 10.1063/1.1670415 · DOI · Paper page
E. Clementi, 1974, At. Data Nucl. Data Tables, 14, 177, 10.1016/S0092-640X(74)80016-1 · DOI
E. Clementi, 1963, J. Chem. Phys., 38, 2248, 10.1063/1.1733957 · DOI
A. C. Pedroza, 1986, Phys. Rev. A, 33, 804, 10.1103/PhysRevA.33.804 · DOI
J. P. Perdew, 1981, Phys. Rev. A, 23, 2785, 10.1103/PhysRevA.23.2785 · DOI
E. Wikborg, 1975, Solid State Commun., 16, 335, 10.1016/0038-1098(75)90181-7 · DOI
D. C. Langreth, 1975, Solid State Commun., 17, 1425, 10.1016/0038-1098(75)90618-3 · DOI · Paper page
D. C. Langreth, 1982, Phys. Rev. B, 26, 2810, 10.1103/PhysRevB.26.2810 · DOI
E. Krotscheck, 1985, Phys. Rev. B, 32, 5693, 10.1103/PhysRevB.32.5693 · DOI
S. Baroni, 1984, J. Chem. Phys., 80, 5703, 10.1063/1.446639 · DOI
L. Wilk, 1977, Phys. Rev. A, 15, 1839, 10.1103/PhysRevA.15.1839 · DOI
M. Levy, J. Phys. Chem.
V. Sahni, 1982, Phys. Rev. B, 26, 4371, 10.1103/PhysRevB.26.4371 · DOI
V. Sahni, 1986, Phys. Rev. B, 33, 3869, 10.1103/PhysRevB.33.3869 · DOI
J. P. Perdew, 1985, Phys. Rev. Lett., 55, 1665, 10.1103/PhysRevLett.55.1665 · DOI · Paper page
J. P. Perdew, 1986, Phys. Rev. B, 33, 8800, 10.1103/PhysRevB.33.8800 · DOI · Paper page
A. D. Becke, 1986, J. Chem. Phys., 84, 4524, 10.1063/1.450025 · DOI

Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
Lee, C., Yang, W., & Parr, R. G. (1988) · Physical Review B · doi:10.1103/physrevb.37.785 · Cited by 100,874
A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
Grimme, S., Antony, J., Ehrlich, S., & Krieg, H. (2010) · The Journal of Chemical Physics · doi:10.1063/1.3382344 · Cited by 59,686
Effect of the damping function in dispersion corrected density functional theory
Grimme, S., Ehrlich, S., & Goerigk, L. (2011) · Journal of Computational Chemistry · doi:10.1002/jcc.21759 · Cited by 28,221
Chemistry with ADF
te Velde, G., Bickelhaupt, F. M., Baerends, E. J., Fonseca Guerra, C., van Gisbergen, S. J. A., Snijders, J. G., & Ziegler, T. (2001) · Journal of Computational Chemistry · doi:10.1002/jcc.1056 · Cited by 10,152
An Evaluation of Harmonic Vibrational Frequency Scale Factors
Merrick, J. P., Moran, D., & Radom, L. (2007) · The Journal of Physical Chemistry A · doi:10.1021/jp073974n · Cited by 2,735
Thirty years of density functional theory in computational chemistry: an overview and extensive assessment of 200 density functionals
Mardirossian, N., & Head-Gordon, M. (2017) · Molecular Physics · doi:10.1080/00268976.2017.1333644 · Cited by 2,307
Transport in Proton Conductors for Fuel-Cell Applications: Simulations, Elementary Reactions, and Phenomenology
Kreuer, K.-D., Paddison, S. J., Spohr, E., & Schuster, M. (2004) · Chemical Reviews · doi:10.1021/cr020715f · Cited by 2,187
Computational Thermochemistry: Scale Factor Databases and Scale Factors for Vibrational Frequencies Obtained from Electronic Model Chemistries
Alecu, I. M., Zheng, J., Zhao, Y., & Truhlar, D. G. (2010) · Journal of Chemical Theory and Computation · doi:10.1021/ct100326h · Cited by 1,667
Born-Oppenheimer molecular-dynamics simulations of finite systems: Structure and dynamics of ( H 2 O ) 2
Barnett, R. N., & Landman, U. (1993) · Physical Review B · doi:10.1103/physrevb.48.2081 · Cited by 629
Machine learning molecular dynamics for the simulation of infrared spectra
Gastegger, M., Behler, J., & Marquetand, P. (2017) · Chemical Science · doi:10.1039/c7sc02267k · Cited by 556
Surface Catalytic Coupling Reaction of p-Mercaptoaniline Linking to Silver Nanostructures Responsible for Abnormal SERS Enhancement: A DFT Study
Wu, D.-Y., Liu, X.-M., Huang, Y.-F., Ren, B., Xu, X., & Tian, Z.-Q. (2009) · The Journal of Physical Chemistry C · doi:10.1021/jp9050929 · Cited by 311
The S66x8 benchmark for noncovalent interactions revisited: explicitly correlated ab initio methods and density functional theory
Brauer, B., Kesharwani, M. K., Kozuch, S., & Martin, J. M. L. (2016) · Physical Chemistry Chemical Physics · doi:10.1039/c6cp00688d · Cited by 238
The Mechanism of Dimethyl Ether Formation from Methanol Catalyzed by Zeolitic Protons
Blaszkowski, S. R., & van Santen, R. A. (1996) · Journal of the American Chemical Society · doi:10.1021/ja954323k · Cited by 227
Fenton-like Chemistry in Water: Oxidation Catalysis by Fe(III) and H2O2
Ensing, B., Buda, F., & Baerends, E. J. (2003) · The Journal of Physical Chemistry A · doi:10.1021/jp0267149 · Cited by 216
Structure and Vibrations of Small Carbon Clusters from Coupled-Cluster Calculations
Martin, J. M. L., & Taylor, P. R. (1996) · The Journal of Physical Chemistry · doi:10.1021/jp952471r · Cited by 171
Theoretical Study of the Adsorption and Dissociation of Oxygen on Pt(111) in the Presence of Homogeneous Electric Fields
Hyman, M. P., & Medlin, J. W. (2005) · The Journal of Physical Chemistry B · doi:10.1021/jp045155y · Cited by 150
Direct estimate of conjugation and aromaticity in cyclic compounds with the EDA method
Fernández, I., & Frenking, G. (2007) · Faraday Discuss. · doi:10.1039/b606835a · Cited by 135
Demonstration and interpretation of significant asymmetry in the low-resolution and high-resolution Q y fluorescence and absorption spectra of bacteriochlorophyll a
Rätsep, M., Cai, Z.-L., Reimers, J. R., & Freiberg, A. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3518685 · Cited by 131
Adenine Tautomers: Relative Stabilities, Ionization Energies, and Mismatch with Cytosine
Fonseca Guerra, C., Bickelhaupt, F. M., Saha, S., & Wang, F. (2006) · The Journal of Physical Chemistry A · doi:10.1021/jp057275r · Cited by 127
The role of the long‐range exchange corrections in the description of electron delocalization in aromatic species
Szczepanik, D. W., Solà, M., Andrzejak, M., Pawełek, B., Dominikowska, J., Kukułka, M., Dyduch, K., Krygowski, T. M., & Szatylowicz, H. (2017) · Journal of Computational Chemistry · doi:10.1002/jcc.24805 · Cited by 107
Femtosecond X-Ray Scattering Study of Ultrafast Photoinduced Structural Dynamics in Solvated[Co(terpy)2]2+
Biasin, E., van Driel, T. B., Kjær, K. S., Dohn, A. O., Christensen, M., Harlang, T., Chabera, P., Liu, Y., Uhlig, J., Pápai, M., et al. (2016) · Physical Review Letters · doi:10.1103/physrevlett.117.013002 · Cited by 108
Quantum-Chemical Calculations of Carbon-Isotope Fractionation in CO2(g), Aqueous Carbonate Species, and Carbonate Minerals
Rustad, J. R., Nelmes, S. L., Jackson, V. E., & Dixon, D. A. (2008) · The Journal of Physical Chemistry A · doi:10.1021/jp076103m · Cited by 96
Ultrabroadband terahertz spectroscopy of a liquid crystal
Vieweg, N., Fischer, B. M., Reuter, M., Kula, P., Dabrowski, R., Celik, M. A., Frenking, G., Koch, M., & Jepsen, P. U. (2012) · Optics Express · doi:10.1364/oe.20.028249 · Cited by 83
Electrical properties of molybdenum disulfide MoS2. Experimental study and density functional calculation results
El Beqqali, O., Zorkani, I., Rogemond, F., Chermette, H., Chaabane, R. B., Gamoudi, M., & Guillaud, G. (1997) · Synthetic Metals · doi:10.1016/s0379-6779(98)80002-7 · Cited by 77
Group 4 Metal Complexes Bearing Thioetherphenolate Ligands. Coordination Chemistry and Ring-Opening Polymerization Catalysis
Della Monica, F., Luciano, E., Roviello, G., Grassi, A., Milione, S., & Capacchione, C. (2014) · Macromolecules · doi:10.1021/ma5003358 · Cited by 74
Coordination ring-opening polymerization of cyclic esters: A critical overview of DFT modeling and visualization of the reaction mechanisms
Nifant’ev, I., & Ivchenko, P. (2019) · Molecules · doi:10.3390/molecules24224117 · Cited by 72
Calculations of current densities for neutral and doubly charged persubstituted benzenes using effective core potentials
Rauhalahti, M., Taubert, S., Sundholm, D., & Liégeois, V. (2017) · Physical Chemistry Chemical Physics · doi:10.1039/c7cp00194k · Cited by 61
Mixed Ligand Cu 2+ Complexes of a Model Therapeutic with Alzheimer’s Amyloid-β Peptide and Monoamine Neurotransmitters
Kenche, V. B., Zawisza, I., Masters, C. L., Bal, W., Barnham, K. J., & Drew, S. C. (2013) · Inorganic Chemistry · doi:10.1021/ic302289r · Cited by 59
Butadiene Insertion and Constitutional Units in Ethene Copolymerizations by C2-Symmetric Metallocenes
Longo, P., Napoli, M., Pragliola, S., Costabile, C., Milano, G., & Guerra, G. (2003) · Macromolecules · doi:10.1021/ma034830j · Cited by 47
Mechanistic Investigations of the Stereoselective Rare Earth Metal-Mediated Ring-Opening Polymerization of β-Butyrolactone
Altenbuchner, P. T., Kronast, A., Kissling, S., Vagin, S. I., Herdtweck, E., Pöthig, A., Deglmann, P., Loos, R., & Rieger, B. (2015) · Chemistry – A European Journal · doi:10.1002/chem.201501156 · Cited by 46
The molecular structure of C6: A theoretical investigation
Hutter, J., & Lüthi, H. P. (1994) · The Journal of Chemical Physics · doi:10.1063/1.467661 · Cited by 43
A computational and experimental study of O-glycosylation. Catalysis by human UDP-GalNAc polypeptide:GalNAc transferase-T2
Gómez, H., Rojas, R., Patel, D., Tabak, L. A., Lluch, J. M., & Masgrau, L. (2014) · Org. Biomol. Chem. · doi:10.1039/c3ob42569j · Cited by 41
Machine learning to tame divergent density functional approximations: a new path to consensus materials design principles
Duan, C., Chen, S., Taylor, M. G., Liu, F., & Kulik, H. J. (2021) · Chemical Science · doi:10.1039/d1sc03701c · Cited by 40
Density functional theory study of model complexes for the revised nitrate reductase active site in Desulfovibrio desulfuricans NapA
Hofmann, M. (2009) · JBIC Journal of Biological Inorganic Chemistry · doi:10.1007/s00775-009-0545-1 · Cited by 35
On the generation of OH(.) radical species from H2O2 by Cu(I) amyloid beta peptide model complexes: A DFT investigation
Prosdocimi, T., De Gioia, L., Zampella, G., & Bertini, L. (2016) · JBIC Journal of Biological Inorganic Chemistry · doi:10.1007/s00775-015-1322-y · Cited by 32
An Aminoimidazole Radical Intermediate in the Anaerobic Biosynthesis of the 5,6-Dimethylbenzimidazole Ligand to Vitamin B12
Gagnon, D. M., Stich, T. A., Mehta, A. P., Abdelwahed, S. H., Begley, T. P., & Britt, R. D. (2018) · Journal of the American Chemical Society · doi:10.1021/jacs.8b05686 · Cited by 21
NSSN-Type Group 4 Metal Complexes in the Ring-Opening Polymerization of l-Lactide
Impemba, S., Roviello, G., Milione, S., & Capacchione, C. (2021) · Inorganic Chemistry · doi:10.1021/acs.inorgchem.1c01056 · Cited by 17
Dinuclear zirconium complex bearing a 1,5-bridged-calix [8]arene ligand as an effective catalyst for the synthesis of macrolactones
Lapenta, R., De Simone, N. A., Buonerba, A., Talotta, C., Gaeta, C., Neri, P., Grassi, A., & Milione, S. (2018) · Catalysis Science & Technology · doi:10.1039/c7cy02537h · Cited by 16
Gas Adsorption in Zeolites and Related Materials
(2007) · Studies in Surface Science and Catalysis · doi:10.1016/s0167-2991(07)80805-6 · Cited by 16
In-insect synthesis of oxygen-doped molecular nanocarbons
Usami, A., Kono, H., Austen, V., Phung, Q. M., Shudo, H., Kato, T., Yamada, H., Yagi, A., Amaike, K., Fujimoto, K. J., et al. (2025) · Science · doi:10.1126/science.adp9384 · Cited by 15
Electronic influence of ligand substituents in the ring-opening polymerization of l-Lactide promoted by OSSO-type zirconium complexes
Meduri, A., Mazzeo, M., Lamberti, M., Capacchione, C., & Milione, S. (2019) · Molecular Catalysis · doi:10.1016/j.mcat.2019.04.007 · Cited by 14
Accelerating materials discovery via AI-Agent integration of large language models and simulation tools
Wang, X., Zeng, Q., Xu, D.-H., Zhang, L., Jiang, G., & Yang, M. (2026) · Journal of Materials Informatics · doi:10.20517/jmi.2025.69 · Cited by 2

Authors: Perdew, J. P.
Venue: Physical Review B
Publisher: American Physical Society (APS)
Published: 1986-06-15
Volume: 33
Issue: 12
Pages: 8822-8824
ISSN: 0163-1829 (ISSN-L)
DOI: 10.1103/physrevb.33.8822
OpenAlex: W2030687437
Cited by: 18,777
References: 2
FWCI: 8.67
Type: journal article
Language: en
Open access: closed
Licence: link.aps.org/licenses/aps-default-license (vor)

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.

Density-functional approximation for the correlation energy of the inhomogeneous electron gas

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Self-check

Citations

Cites

Cited by

Metadata

Record

About these checks

Data sources