Microstates

   In discussing the spectra of octahedral d² complexes, we have emphasized the physical principles underlying the number of bands in the electronic spectrum. We now present a more formal treatment involving the construction of a table of microstates  . Table 1.1 shows all possible combinations of two unpaired d electrons; for parallel spins, the terms must be triplets (S = 1) and in addition to the ³F ground state, the only excited state is the ³P. It can be shown from group theory that in an octahedral field, D, F and G, but not S and P, terms split.

Term             Components in an octahedral field

S                             A_1g

P                             T1g

D                            Eg +T2g

F                            A2g + T2g +  T1g

G                           A1g +‏ Eg +‏ T2g ‏+ T1g

     Similar splittings occur in a tetrahedral field, but the g labels given above are no longer applicable. For a d² ion in an octahedral field, the possible triplet terms are therefore ³A_2g, ³T_2g and ³T_1g derived from the triplet ³F ground term, and the ³T₁ derived from the triplet ³P excited term.