scholarly journals Exchange-correlation magnetic fields in spin-density-functional theory

2019 ◽  
Vol 100 (12) ◽  
Author(s):  
Edward A. Pluhar ◽  
Carsten A. Ullrich
Keyword(s):  
Density Functional Theory ◽  
Magnetic Fields ◽  
Spin Density ◽  
Density Functional ◽  
Functional Theory ◽  
Exchange Correlation

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.

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>

scholarly journals Application of time-dependent current-density-functional theory to nonlocal exchange-correlation effects in polymers

2003 ◽  
Vol 118 (3) ◽  
pp. 1044-1053 ◽  
Author(s):  
M. van Faassen ◽  
P. L. de Boeij ◽  
R. van Leeuwen ◽  
J. A. Berger ◽  
J. G. Snijders
Keyword(s):  
Density Functional Theory ◽  
Current Density ◽  
Density Functional ◽  
Time Dependent ◽  
Correlation Effects ◽  
Functional Theory ◽  
Exchange Correlation
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