Abstract
The scalar f(xc) and tensor f(xc) exchange-correlation (xc) kernels are key ingredients of the time-dependent density functional theory and the time-dependent current density functional theory, respectively. We derive a comparatively simple relation between these two kernels under the assumption that the dynamic xc can be considered "weak." A calculation of the frequency-dependent dielectric function of silicon using this relation in conjunction with Vignale-Kohn f(xc) demonstrates a potential of our method to account for the dynamic many-body effects within the rigorous scheme of time-dependent density functional theory. Our formula provides a bridge between the scalar f(xc), which directly enters many applications, and the tensor f(xc) which, due to its locality in space, is much easier to approximate.
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