Erratum: Tight bound and convexity constraint on the exchange-correlation-energy functionalsin the low-density limit, and other formal tests of generalized-gradient approximations [Phys. Rev. B48, 11638 (1993)]

1997 ◽  
Vol 55 (19) ◽  
pp. 13321-13321 ◽  
Author(s):  
Anonymous
Keyword(s):  
Correlation Energy ◽  
Low Density ◽  
Generalized Gradient ◽  
Tight Bound ◽  
Density Limit ◽  
Exchange Correlation ◽  
Convexity Constraint ◽  
Low Density Limit

GROUND-STATE ENERGY OF THE ELECTRON GAS WITH THE MODIFIED COULOMB POTENTIAL 1/rp

2011 ◽  
Vol 25 (15) ◽  
pp. 2019-2030
Author(s):  
LIANGJIE FU ◽  
YUAN CHEN
Keyword(s):  
Ground State Energy ◽  
Coulomb Potential ◽  
Ground State ◽  
State Energy ◽  
Correlation Energy ◽  
Electron Gas ◽  
High Density ◽  
Low Density ◽  
Density Limit ◽  
Low Density Limit

In this paper, due to the effect of positively-charged screening holes, Coulomb potential energy 1/r is modified to be 1/rp, which is assumed to deviate slightly from the former. Using many-body perturbation theory, we obtain a simple analytic representation of the ground-state energy and correlation energy for a uniform electron gas. Our results agree with those obtained by the numerical and semi-analytic methods at low-density limit. Higher ground-state energies at high-density limit are calculated from our model. High order r expansion terms are found at high-density region. A curve of transition density versus p is drawn via the Misawa spin-scaling relation, which is in consistent with Perdew's study at low-density limit.

Low-density limit of the Nagel-Schreckenberg model

2000 ◽  
Vol 63 (1) ◽  
Author(s):  
Ding-wei Huang ◽  
Chung-wei Tsai
Keyword(s):  
Low Density ◽  
Density Limit ◽  
Low Density Limit

EXPLORING THE ADIABATIC CONNECTION BETWEEN WEAK- AND STRONG-INTERACTION LIMITS IN DENSITY FUNCTIONAL THEORY

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1672-1683 ◽  
Author(s):  
JOHN P. PERDEW ◽  
STEFAN KURTH ◽  
MICHAEL SEIDL
Keyword(s):  
Perturbation Theory ◽  
Density Functional ◽  
Correlation Energy ◽  
Interaction Strength ◽  
Kcal Mole ◽  
Generalized Gradient ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Density Functional Perturbation Theory ◽  
Simple Interaction

If the electron-electron repulsion in an atom or molecule were very weak, it could be treated by orbital-based perturbation theory. If this repulsion were very strong, it could be treated in a model of strict correlation. A simple interaction strength interpolation between these two limits, at fixed electron density, can describe the reality that lies between the extremes. By working entirely within a sophisticated density functional approximation, the meta-generalized gradient approximation, we find that the interpolation error is only about 0.1% for the exchange-correlation energy and about 4 kcal/mole = 0.17 eV for the atomization energy. We also find that real systems probably lie close to the radius of convergence of density functional perturbation theory.

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