An extension of density functional theory to situations with significant nondynamical correlation is presented. The method is based on the spin-flip (SF) approach which is capable of describing multireference wave functions within a single reference formalism as spin-flipping, e.g., alpha-->beta, excitations from a high-spin (M-s=1) triplet reference state. An implementation of the spin-flip approach within the Tamm-Dancoff approximation to time-dependent density functional theory (TDDFT) is presented. The new method, SF-TDDFT/TDA or simply SF-DFT, describes target states (i.e., closed- and open-shell singlets, as well as low-spin triplets) by linear response from a reference high-spin triplet (M-s=1) Kohn-Sham state. Contrary to traditional TDDFT, the SF-DFT response equations are solved in a subspace of spin-flipping operators. The method is applied to bond-breaking (ethylene torsional potential), and equilibrium properties of eight diradicals. The results demonstrate significant improvement over traditional Kohn-Sham DFT, particularly for 50/50 hybrid functional. (C) 2003 American Institute of Physics.