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Communications: On the relation between the scalar and tensor exchange-correlation kernels of the time-dependent density-functional theory
3.V. U. Nazarov and G. Vignale, Bull. Am. Phys. Soc. 53(2), P13–00009 (2008).
10.E. K. U. Gross, J. F. Dobson, and M. Petersilka, Density Functional Theory II, Topics in Current Chemistry, Vol. 181 (Springer-Verlag, Berlin, 1996), pp. 81–172.
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The scalar and tensor exchange-correlation (xc) kernels are key ingredients of the time-dependent density functional theory and the time-dependent current density functionaltheory, 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 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 , which directly enters many applications, and the tensor which, due to its locality in space, is much easier to approximate.
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