Exact exchange-correlation kernels for optical spectra

Time-dependent density-functional theory (TDDFT) is in principle a powerful technique for simulating the time-evolution of systems of interacting electrons. Whilst TDDFT has had notable successes, the usual adiabatic functionals within the linear response regime can fail badly when applied to problems such as optical absorption spectra. By reverse-engineering numerically exact calculations of the ground and excited many-body states, and response functions, of prototype one-dimensional systems, we obtain the exact exchange-correlation kernel f_xc(x,x',ω) for each system. We explore the properties of these exact xc kernels, and suggest how common approximations may be improved.