The formalism of time-dependent density functional theory and density functional response functions is reviewed from the perspective of partitioning techniques and projections, the hallmark of the school of quantum chemistry represented by P.O. Lowdin. Extension to open-shell density functional theory is described, reviewing some of its common problems. Sample calculations on hyper-Raleigh scattering in the diamagnetic and paramagnetic complexes of copper bound to (glycyl)glycine dipeptide are presented.