Meta-GGA-based adiabatic time-dependent density-functional theory

The local-density approximation (LDA) to the ground-state density functional theory (DFT) is well known to allow for a generalization to the time-dependent case [1]. The assumption of the adiabaticity of the process greatly simplifies the theory. The further extension of the time-dependent DFT (TDDFT) to the generalized gradient approximation (GGA) is trivial. Here we address lifting the adiabatic TDDFT to the third rung of the ``Jacobs ladder'' [2] : We work out the kinetic energy density dependent (meta-GGA) TDDFT formalism. The new theory possesses remarkable properties not present in LDA and GGA: (i) It is non-local with respect to the particle density; (ii) In the case of bulk semiconductors, it supports the 1/q$^2$ singularity of the exchange-correlation kernel, where q is the wave-vector, the latter being important to reproduce the excitonic effect. We also present illustrative calculations of the optical absorption in semiconductors [3]. \\[4pt] [1] A. Zangwill and P. Soven, Phys. Rev. A, 21, 1561 (1980).\\[0pt] [2] J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, Phys. Rev. Lett. 91, 146401 (2003).\\[0pt] [3] V. U. Nazarov and G. Vignale, Phys. Rev. Lett. 107, 216402(2011).