This means that ∆ αβ (Eq. ( )) becomes nearly zero, and the density matrix of the α and β states contribute almost equally in the energy weighting scheme. In particular, when two states are averaged, the energy-weighted density matrix for XDW is roughly equivalent to that of XMS, and therefore it is rather natural that the relative energy for both methods is similar. Consequently, the difference between MECI entries of XMS and XDW in Table is primarily due to the difference in the S 0 energy at the D 6h structure. As discussed below, that will not be the case if more states are averaged.