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Physical Review Letters

Spin-Density Functionals from Current-Density Functional Theory and Vice Versa:A Road towards New Approximations

Klaus Capelle, Eberhard K. U. Gross

Published Mar 10, 1997• 157 citations
Publisher

Abstract

It is shown that the exchange-correlation functional of spin-density functional theory is identical, on a certain set of densities, with the exchange-correlation functional of current-density functional theory. This rigorous connection is used to construct new approximations of the exchange-correlation functionals. These include a conceptually new generalized-gradient spin-density functional and a nonlocal current-density functional.

DOI
10.1103/physrevlett.78.1872

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It is shown that the exchange-correlation functional of spin-density functional theory is identical, on a certain set of densities, with the exchange-correlation functional of current-density functional theory. This rigorous connection is used to construct new approximations of the exchange-correlation functionals. These include a conceptually new generalized-gradient spin-density functional and a nonlocal current-density functional.
It has been known for some time that the exchange-correlation potential in time-dependent density functional theory is an intrinsically nonlocal functional of the density as soon as one goes beyond the adiabatic approximation. In this paper we show that a much more severe nonlocality problem, with a completely different physical origin, plagues the exchange-correlation potentials in time-dependent spin density functional theory. We show how the use of the spin current density as the basic variable solves this problem, and we provide an explicit local expression for the exchange-correlation fields as functionals of the spin currents.
It has been known for some time that the exchange-correlation potential in time-dependent density-functional theory is an intrinsically nonlocal functional of the density as soon as one goes beyond the adiabatic approximation. In this paper we show that a much more severe nonlocality problem, with a completely different physical origin, plagues the exchange-correlation potentials in time-dependent spin-density functional theory. We show how the use of the spin current density as a basic variable solves this problem, and we provide an explicit local expression for the exchange-correlation fields as functionals of the spin currents.
Based on exact limits and quantum Monte Carlo simulations, we obtain, at any density and spin polarization, an accurate estimate for the energy of a modified homogeneous electron gas where electrons repel each other only with a long-range Coulombic tail. This allows us to construct an analytic local-spin-density exchange-correlation functional appropriate to new, multideterminantal versions of the density functional theory, where quantum chemistry and approximate exchange-correlation functionals are combined to optimally describe both long- and short-range electron correlations.
We propose a novel density-functional approach to antiferromagnetism and spin-density waves. Nonlocal antiferromagnetic correlations and possible noncollinear spin configurations are incorporated via a staggered density, which enters the formalism on the same footing as the particle density. We establish the pertinent generalization of the Hohenberg-Kohn theorem, derive the associated Kohn-Sham equations, outline the construction of approximations for the corresponding exchange and correlation functional, discuss the relation of the present method to other density-functional approaches, and report a first application to a simple model system.
Approximations for the ground-state exchange-correlation potential of density-functional theory have reached a high level of sophistication. By contrast, time- or frequency-dependent exchange-correlation potentials are still being treated in a local approximation. Here we propose a novel approximation scheme, which effectively brings the power of the generalized gradient approximation (GGA) and meta-GGA to time-dependent density-functional theory. The theory should allow a more accurate treatment of strongly inhomogeneous electronic systems (e.g. molecular junctions) while remaining essentially exact for slowly varying densities and slowly varying external potentials.
We use the exact strong-interaction limit of the Hohenberg-Kohn energy density functional to approximate the exchange-correlation energy of the restricted Kohn-Sham scheme. Our approximation corresponds to a highly nonlocal density functional whose functional derivative can be easily constructed, thus transforming exactly, in a physically transparent way, an important part of the electron-electron interaction into an effective local one-body potential. We test our approach on quasi-one-dimensional systems, showing that it captures essential features of strong correlation that restricted Kohn-Sham calculations using the currently available approximations cannot describe.