Online citations, reference lists, and bibliographies.
← Back to Search

Accurate And Simple Analytic Representation Of The Electron-gas Correlation Energy.

Perdew, Wang
Published 1992 · Physics, Medicine

Cite This
Download PDF
Analyze on Scholarcy
Share
We propose a simple analytic representation of the correlation energy ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$ for a uniform electron gas, as a function of density parameter ${\mathit{r}}_{\mathit{s}}$ and relative spin polarization \ensuremath{\zeta}. Within the random-phase approximation (RPA), this representation allows for the ${\mathit{r}}_{\mathit{s}}^{\mathrm{\ensuremath{-}}3/4}$ behavior as ${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}\ensuremath{\infty}. Close agreement with numerical RPA values for ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$,0), ${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$,1), and the spin stiffness ${\mathrm{\ensuremath{\alpha}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$)=${\mathrm{\ensuremath{\partial}}}^{2}$${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{c}}$(${\mathit{r}}_{\mathit{s}}$, \ensuremath{\zeta}=0)/\ensuremath{\delta}${\mathrm{\ensuremath{\zeta}}}^{2}$, and recovery of the correct ${\mathit{r}}_{\mathit{s}}$ln${\mathit{r}}_{\mathit{s}}$ term for ${\mathit{r}}_{\mathit{s}}$\ensuremath{\rightarrow}0, indicate the appropriateness of the chosen analytic form. Beyond RPA, different parameters for the same analytic form are found by fitting to the Green's-function Monte Carlo data of Ceperley and Alder [Phys. Rev. Lett. 45, 566 (1980)], taking into account data uncertainties that have been ignored in earlier fits by Vosko, Wilk, and Nusair (VWN) [Can. J. Phys. 58, 1200 (1980)] or by Perdew and Zunger (PZ) [Phys. Rev. B 23, 5048 (1981)]. While we confirm the practical accuracy of the VWN and PZ representations, we eliminate some minor problems with these forms. We study the \ensuremath{\zeta}-dependent coefficients in the high- and low-density expansions, and the ${\mathit{r}}_{\mathit{s}}$-dependent spin susceptibility. We also present a conjecture for the exact low-density limit. The correlation potential ${\mathrm{\ensuremath{\mu}}}_{\mathit{c}}^{\mathrm{\ensuremath{\sigma}}}$(${\mathit{r}}_{\mathit{s}}$,\ensuremath{\zeta}) is evaluated for use in self-consistent density-functional calculations.



This paper is referenced by
10.3390/molecules21081020
X-ray Single Crystal Structure, DFT Calculations and Biological Activity of 2-(3-Methyl-5-(pyridin-2’-yl)-1H-pyrazol-1-yl) Ethanol
S. Radi (2016)
10.1109/JPROC.2012.2197810
Quantum Transport Modeling From First Principles
J. Maassen (2013)
10.1088/0953-8984/24/30/305001
Surface defects on ZnO nanowires: implications for design of sensors.
M. Spencer (2012)
10.3390/computation5030039
Time-Dependent Density-Functional Theory and Excitons in Bulk and Two-Dimensional Semiconductors
V. Turkowski (2017)
10.1039/A705290A
Study of pyridine and its derivatives adsorbed on a TiO2(110)–(1×1)surface by means of STM, TDS, XPS and MD calculation in relation to surface acid[ndash ]base interaction
S. Suzuki (1998)
10.1038/s41598-017-18018-1
Prediction of Mechanical Twinning in Magnesium Silicate Post-Perovskite
P. Carrez (2017)
10.1002/QUA.560520858
A study of small systems containing H and O atoms using nonlocal functionals: comparisons with ab initio and experiment
J. M. Seminario (1994)
10.1021/la2012028
Potential energy surfaces for oxygen adsorption, dissociation, and diffusion at the Pt(321) surface.
J. M. Bray (2011)
10.1016/J.MATCHEMPHYS.2017.12.085
Spin state transition in Bi1−xLaxCoO3 perovskite alloys: DFT+U study
N. Benayad (2018)
Computational investigation of the reaction mechanism of aristolochene synthase
N. J. Young (2009)
10.1039/c5nr08708b
Identification of the current path for a conductive molecular wire on a tripodal platform.
M. A. Karimi (2016)
10.1007/BF01114982
Extension of the local-spin-density exchange-correlation approximation to multiplet states
A. D. Becke (1995)
10.1016/S1380-7323(96)80100-2
Systematic Model Chemistries Based on Density Functional Theory: Comparison with traditional Models and with Experiment
M. Frisch (1996)
10.1063/1.472829
Treatment of the outlying charge in continuum solvation models
A. Klamt (1996)
10.1002/CBER.19971300817
Raman and Infrared Spectra and Quantum Chemical Calculations for Trichlorophosphoranylidenesulfamoyl Chloride, CISO2N=PCI3
R. M. S. áglvarez (1997)
Mathematical contributions to the calculations of electronic structures
D. Gontier (2015)
10.1002/jcc.20775
Electric field convergence versus atomic basis sets in all‐siliceous zeolites
A. Larin (2008)
10.1073/pnas.1423145112
Semilocal density functional obeying a strongly tightened bound for exchange
J. Sun (2015)
10.1126/science.aaf3762
Characterization of berkelium(III) dipicolinate and borate compounds in solution and the solid state
M. Silver (2016)
10.1073/pnas.1802741115
Facet-specific interaction between methanol and TiO2 probed by sum-frequency vibrational spectroscopy
Deheng Yang (2018)
10.1039/C3CE41158C
NMR-crystallographic study of two-dimensionally self-assembled cyclohexane-based low-molecular-mass organic compounds
M. Schmidt (2013)
Universidade de São Paulo Instituto de Química de São Carlos
L. A. Terrabuio (2013)
10.1002/(SICI)1097-461X(1998)69:4<513::AID-QUA8>3.0.CO;2-Y
Polynomial and Pad Representations for the Kinetic ComponentTc[?] of the Correlation Energy Density Functional
Shubin Liu (1998)
10.1007/BF03161893
Influence of hydrogen bonds on the electronicg-tensor and13C-hyperfine tensors of13C-labeled ubiquinones — EPR and ENDOR study
O. Nimz (1998)
10.1021/acsomega.0c03160
Modulating the Electronic, Optical, and Transport Properties of CdTe and ZnTe Nanostructures with Organic Molecules: A Theoretical Investigation
Feifei Xia (2020)
10.1063/1.475791
Towards an accurate gold carbonyl binding energy in AuCO+: Basis set convergence and a comparison between density functional and conventional methods
Thomas K. Dargel (1998)
10.1016/S0039-6028(98)00363-X
The surface energy of metals
L. Vitos (1998)
10.1016/S0009-2614(98)00549-1
A DYNAMICAL DENSITY FUNCTIONAL STUDY OF CO MIGRATION IN THE REPPE CARBONYLATION
F. Angelis (1998)
10.1063/1.475939
Pressure-induced change of the stereochemical activity of a lone electron pair
B. Winkler (1998)
10.1088/0953-8984/10/32/007
d-to-s bonding in GaN
P. Dudesek (1998)
10.1016/S0040-4039(99)00542-0
Reinvestigation of σ-allyl cations: High level Ab initio quantum mechanical predictions
K. Baldridge (1999)
10.1016/S0009-2614(99)00567-9
Local mode overtone intensities of SiH4 and GeH4 from a bond dipole model with an ab initio calculated dipole moment surface
H. Lin (1999)
See more
Semantic Scholar Logo Some data provided by SemanticScholar