The transition density functional (TDF), i.e., the correlation energies for the off-diagonal matrix elements of 𝓗𝓗[𝑫𝑫(𝒓𝒓)] , can be determined rigorously among spin-complement configurations to yield the spin-adapted states. For example, the TDF correlation energy for the spin-adapted singlet state is obtained in an NOSI calculation with the constraint that the energy of the triplet state |1,0 > is identical to that of the |1,1 > state.