The spin-flip approach within time-dependent density functional theory: Theory and applications to diradicals

Y. Shao, M. Head-Gordon, and A. I. Krylov
J. Chem. Phys. 118, 4807 – 4818 (2003)

An extension of density functional theory to situations with significant non-dynamical correlation is presented. The method is based on the spin-flip (SF) approach which is capable of describing multi-reference wave functions within a single reference formalism as spin-flipping, e. g., α→β, excitations from a high-spin (M_s = 1) triplet reference state. An implementation of the spin-flip approach within time-dependent density functional theory (TDDFT) is presented. The new method, SF-TDDFT 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.

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