Exchange-Correlation Energy Functionals in the Density Functional Formalism

1984 ◽  
pp. 229-243 ◽  
Author(s):  
O. Gunnarsson ◽  
R. O. Jones
Keyword(s):  
Density Functional ◽  
Correlation Energy ◽  
Functional Formalism ◽  
Energy Functionals ◽  
Exchange Correlation

Exchange-Correlation Energy Densities and Response Potentials: Connection Between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

2019 ◽  
Author(s):  
S. Giarrusso ◽  
Paola Gori-Giorgi
Keyword(s):  
Density Functional Theory ◽  
Strong Coupling ◽  
Density Functional ◽  
Correlation Energy ◽  
Order Term ◽  
Strong Coupling Limit ◽  
Local Form ◽  
Coupling Constant ◽  
Functional Theory ◽  
Exchange Correlation

We analyze in depth two widely used definitions (from the theory of conditional probablity amplitudes and from the adiabatic connection formalism) of the exchange-correlation energy density and of the response potential of Kohn-Sham density functional theory. We introduce a local form of the coupling-constant-dependent Hohenberg-Kohn functional, showing that the difference between the two definitions is due to a corresponding local first-order term in the coupling constant, which disappears globally (when integrated over all space), but not locally. We also design an analytic representation for the response potential in the strong-coupling limit of density functional theory for a model single stretched bond.<br>

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.

Influence of nonlocality in the spin–spin interaction functional on the Pauli susceptibility of Li, Na, and K

1981 ◽  
Vol 59 (4) ◽  
pp. 500-505 ◽  
Author(s):  
A. H. MacDonald ◽  
K. L. Liu ◽  
S. H. Vosko ◽  
L. Wilk
Keyword(s):  
Spin Density ◽  
Density Functional ◽  
Alkali Metals ◽  
Spin Exchange ◽  
Local Approximation ◽  
Spin Interaction ◽  
Functional Formalism ◽  
Exchange Correlation ◽  
Experimental Values ◽  
Pauli Susceptibility

Two suggested nonlocal approximations for the spin–spin exchange-correlation interaction functional of the spin-density functional formalism have been applied to the calculation of the Pauli susceptibility, χp, of the alkali metals. The nonlocal approximations were found to imply values of the density-functional Stoner parameter, I, typically ~ 3% lower than values implied by the more usual local approximation. This qualitative trend was found to be supported by comparison of available experimental values of χp with new more accurate theoretical values for the local approximation to χp.

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