For practical application of the standard SF-TDDFT approach, especially for TSH simulations, it is necessary to use some kind of "state tracking" procedure that attempts to identify the best approximate multiplicity in regions of heavy spin contamination. Spin contamination tends to be relatively small near the ground-state geometry (Franck-Condon excitation point), whereas it becomes severe in bond-breaking regions of the potential surface where singlet and triplet states may be quasi-degenerate and therefore extensively mixed, in the absence of proper spin symmetry. A practical workaround is to categorize states based on their similarity to the wavefunctions computed in the previous time step, with the idea that spin multiplicities are identifiable at t = 0 so that the multiplicity of |Ψ K (t + ∆t) can be assigned based on its overlap with the states {|Ψ J (t) }. Several methods along these lines have been suggested. The use of such algorithms is not guaranteed to lead to an unambiguous identification of the states in question, but it has been used successfully in TSH simulations. 3 Augmented Spin-Flip Methods