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.

scholarly journals London dispersion forces without density distortion: a path to first principles inclusion in density functional theory

2020 ◽  
Vol 224 ◽  
pp. 145-165
Author(s):  
Derk Pieter Kooi ◽  
Paola Gori-Giorgi
Keyword(s):  
Ground State ◽  
First Principles ◽  
Density Functional ◽  
Dispersion Forces ◽  
Density Functionals ◽  
Functional Theory ◽  
Exchange Correlation ◽  
State Densities ◽  
London Dispersion ◽  
London Dispersion Forces

We analyse a path to construct density functionals for the dispersion interaction energy from an expression in terms of the ground state densities and exchange–correlation holes of the isolated fragments.

Exact exchange-correlation potentials in spin-density functional theory and their discontinuities at unit electron number

2009 ◽  
Vol 87 (10) ◽  
pp. 1268-1272 ◽  
Author(s):  
John P. Perdew ◽  
Espen Sagvolden
Keyword(s):  
Density Functional Theory ◽  
Spin Density ◽  
Density Functional ◽  
Electron Number ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Exchange Correlation Potential ◽  
Correlation Potential ◽  
Exact Exchange ◽  
Physical Consequences

The exact exchange-correlation potential of Kohn–Sham density functional theory is known to jump discontinuously by a spatial constant as the average electron number, N, crosses an integer in an open system of fluctuating electron number, with important physical consequences for charge transfers and band gaps. We have recently constructed an essentially exact exchange-correlation potential vxc for N electrons (0 ≤ N ≤ 2) in the presence of a –1/r external potential, i.e., for a ground ensemble of H+ ion, H atom, and H– ion densities. That construction illustrates the discontinuity at N = 1, where it equals IH – AH, the positive difference between the ionization energy and the electron affinity of the hydrogen atom. Here we construct the corresponding essentially exact spin-up and spin-down exchange-correlation potentials vxc,↑ and vxc,↓ of the Kohn–Sham spin-density functional theory, more commonly used for electronic structure calculations, for the ground ensemble with most-negative z-component of spin (or equivalently in the presence of a uniform magnetic field of infinitesimal strength). The potentials vxc, vxc,↑, and vxc,↓, which vanish as r → ∞ (except when N approaches an integer from above), are identical for 0 ≤ N ≤ 1 and for N = 2 but not for 1 < N < 2. We find that the majority or spin-down potential has a spatially constant discontinuity at N = 1 equal to IH – AH. The minority or spin-up potential has a discontinuity which is this constant in one order of limits, but is a spatially varying function in a different order of limits. This order-of-limits problem is a consequence of a special circumstance: the vanishing of the spin-up density at N = 1.

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.

scholarly journals A comparative test of different density functionals for calculations of NH3-SCR over Cu-Chabazite

2019 ◽  
Vol 21 (21) ◽  
pp. 10923-10930 ◽  
Author(s):  
Lin Chen ◽  
Ton V. W. Janssens ◽  
Henrik Grönbeck
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Density Functional Theory Calculations ◽  
Comparative Test ◽  
Density Functionals ◽  
Functional Theory ◽  
Exchange Correlation ◽  
Nh3 Scr ◽  
Different Types

A general challenge in density functional theory calculations is to simultaneously account for different types of bonds. Here, different exchange–correlation functionals are explored for O2 dissociation over Cu(NH3)2+ complexes in Cu-Chabazite.

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