The shell model for the exchange-correlation hole in the strong-correlation limit

2016 ◽  
Vol 145 (12) ◽  
pp. 124104 ◽  
Author(s):  
Hilke Bahmann ◽  
Yongxi Zhou ◽  
Matthias Ernzerhof
Keyword(s):  
Shell Model ◽  
Strong Correlation ◽  
Exchange Correlation ◽  
Correlation Hole

scholarly journals The Many-Body Exchange-Correlation Hole at Metal Surfaces

2009 ◽  
Vol 5 (4) ◽  
pp. 895-901 ◽  
Author(s):  
Lucian A. Constantin ◽  
J. M. Pitarke
Keyword(s):  
Metal Surfaces ◽  
Many Body ◽  
Exchange Correlation ◽  
Correlation Hole ◽  
The Many

scholarly journals Exchange–correlation functionals from the strong interaction limit of DFT: applications to model chemical systems

2014 ◽  
Vol 16 (28) ◽  
pp. 14551-14558 ◽  
Author(s):  
Francesc Malet ◽  
André Mirtschink ◽  
Klaas J. H. Giesbertz ◽  
Lucas O. Wagner ◽  
Paola Gori-Giorgi
Keyword(s):  
Strong Interaction ◽  
Strong Correlation ◽  
Chemical Systems ◽  
Exchange Correlation ◽  
Exchange Correlation Potential ◽  
Correlation Potential ◽  
1D Model

The strong-interaction limit of DFT provides an exchange–correlation potential that is able to describe strong correlation in 1D model chemical systems.

EXCHANGE-CORRELATION FUNCTIONALS FROM THE IDENTICAL-PARTICLE ORNSTEIN-ZERNIKE EQUATION: BASIC FORMULATION AND NUMERICAL ALGORITHMS

2010 ◽  
Vol 24 (25n26) ◽  
pp. 5115-5127 ◽  
Author(s):  
ROGELIO CUEVAS-SAAVEDRA ◽  
PAUL W. AYERS
Keyword(s):  
Correlation Function ◽  
Correlation Energy ◽  
Identical Particle ◽  
Numerical Algorithms ◽  
Direct Correlation Function ◽  
Correlation Integral ◽  
Exchange Correlation ◽  
Theory Of Liquids ◽  
Correlation Hole ◽  
Particle Nature

We adapt the classical Ornstein-Zernike equation for the direct correlation function of classical theory of liquids in order to obtain a model for the exchange-correlation hole based on the electronic direct correlation function. Because we explicitly account for the identical-particle nature of electrons, our result recovers the normalization of the exchange-correlation hole. In addition, the modified direct correlation function is shorted-ranged compared to the classical formula. Functionals based on hole models require six-dimensional integration of a singular integrand to evaluate the exchange-correlation energy, and we present several strategies for efficiently evaluating the exchange-correlation integral in a numerically stable way.

DENSITY FUNCTIONALS AND SMALL INTERPARTICLE SEPARATIONS IN ELECTRONIC SYSTEMS

1995 ◽  
Vol 09 (14) ◽  
pp. 829-838 ◽  
Author(s):  
KIERON BURKE ◽  
JOHN P. PERDEW
Keyword(s):  
Spin Density ◽  
Density Functional ◽  
Electronic System ◽  
Electronic Systems ◽  
Hole Density ◽  
Density Functionals ◽  
Sum Rule ◽  
Exchange Correlation ◽  
Strongly Interacting ◽  
Correlation Hole

We review some recent results concerning the probability that two electrons will be found close together in any interacting electronic system, and why this probability is usually well approximated by local (LSD) and semilocal spin density functional theories. The success of these approximations for the energy in "normal" systems is explained by the usual sum rule arguments on the system- and spherically-averaged exchange-correlation hole density <n xc (u)>, coupled with the nearly correct, but not exact, behavior of these approximations as the interelectronic separation u → 0. We argue that the accuracy of the LSD on-top hole density in "normal" systems is due to its accuracy in the noninteracting, weakly-interacting, and strongly-interacting limits.

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