Current-Density Functional Theory of Linear Response to Time-Dependent Electromagnetic Fields

  • G. Vignale
  • Walter Kohn


Local density approximations are known to be very useful in calculating the ground-state exchange and correlation (xc) energy of many-electron systems [1], and local approximations are gaining in importance for the description of xc effects in time-dependent situations also [2,3]. Most of the time-dependent work has dealt with a scalar time-dependent xc potential \({v_{xc}}(\vec r,\omega )\) approximated as a local functional of the time-dependent density \(n(\vec r,\omega )\) as described in the chapter “Time-dependent density functional theory” in the introductory section of this Book. Despite much progress in this scalar approach, it will be shown in this Chapter that existing approximations for v xc require modification. In particular, it will be shown that (i) there is no local density approximation for the scalar xc potential at finite frequency (ii) there is, however, a consistent local approximation for a vector xc potential \({{\vec a}_{xc}}(\vec r,\omega )\) in terms of the dynamic current density \(\vec j(\vec r,\omega )\) and its space derivatives, as well as the ground-state density and its space derivatives. This approximation is valid, at a given frequency, for sufficiently slow spatial variations of the ground-state density and of the perturbing dynamic potential. The appropriately modified vector xc potential will be derived here in some detail, thus filling out the brief description published recently [4]. New material will also be presented, providing interpretation of the findings in the simple case of one dimensional inhomogeneity.


Local Density Approximation Time Dependent Density Functional Theory Gradient Expansion Accelerate Frame Local Field Factor 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • G. Vignale
    • 1
  • Walter Kohn
    • 2
  1. 1.Department of PhysicsUniversity of MissouriColumbiaUSA
  2. 2.Department of PhysicsUniversity of CaliforniaSanta BarbaraUSA

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