Bootstrap approximation for the exchange-correlation kernel of time-dependent density-functional theory

A new parameter-free approximation for the exchange-correlation kernel f_xc of time-dependent density-functional theory is proposed. This kernel is expressed as an algorithm in which the exact Dyson equation for the response, as well as an approximate expression for f_xc in terms of the dielectric function, are solved together self-consistently, leading to a simple parameter-free kernel. We apply this to the calculation of optical spectra for various small band gap (Ge, Si, GaAs, AlN, TiO₂, SiC), large band gap (C, LiF, Ar, Ne), and magnetic (NiO) insulators. The calculated spectra are in very good agreement with the experiment for this diverse set of materials, highlighting the universal applicability of the new kernel.