where E BS is the energy of a broken-symmetry approximation to the low-spin state. However, the calculated J with the above formula does not eliminate the spin contamination errors. Therefore, with the assumption that the spin-contamination in the high spin state is negligible i.e., < S 2 > HS ∼ = < S 2 > exact HS , the spin-projected energy of LS state, (E LS AP ), without spin contamination error is obtained as follows ,66