Can density functional theory describe multi-reference systems?: Investigation of carbenes and organic biradicals

Kohn-Sham (KS) density functional theory (DFT) in its present approximate form cannot be applied to electron systems with strong multi-reference character. Various ways are discussed to develop DFT for multi-reference systems. The restricted open-shell singlet (ROSS) formalism is a modification of the conventional open-shell KS formalism, which makes a reliable, but still economical treatment of open-shell singlet biradicals possible. The complete-active-space DFT (CAS-DFT) method combines an explicit treatment of multi-configurational character with the DFT treatment of dynamic electron correlation effects. Due to the flexibility in the choice of the active space, this method is in principle appropriate for all kinds of multi-reference problems. Based on sample calculations for carbenes and organic biradicals, the advantages and limitations of ROSS-DFT and CAS-DFT are discussed. Some possibilities for future improvements of DFT methods for multi-reference problems are pointed out.