1. Lecture 28 Electronic Spectra of Coordination Compounds MLx (x = 4,6) 1) Terms of a free d2 metal atom
The total number of microstates for an isolated metal of d2 configuration is (10!)/(8!2!) = 45. The whole set of terms includes:
3F (S=1, L=3) (2·1+1)·(2·3+1)=21 microstates,
3P (S=1, L=1) (2·1+1)·(2·1+1)=9 microstates,
1G (S=0, L=4) (2·0+1)·(2·4+1)=9 microstates,
1D (S=0, L=2) (2·0+1)·(2·2+1)=5 microstates and
1S (S=0, L=0) (2·0+1)·(2·0+1)=1 microstate
TOTAL: microstates
The calculated term energy sequence is 3F (lowest), 1D, 3P, 1G, 1S (highest).
The wavefunctions for S, P, D, F etc. terms are of the same symmetry as for s, p, d, f etc orbitals. Therefore the terms will be split by a ligand field in the same way as the corresponding orbitals are (check the appropriate character table!).

2. 2) Term splitting for octahedral d2 metal complexes
When placed in a ligand field, the five terms of d2 atom will be split. The splitting is a function of the ligand field symmetry and strength.
Each term is split so that the energy loss of the destabilized terms is compensated by the energy gain of the stabilized terms.
At the infinitely strong ligand field electron – electron interactions are negligible. The resulting energy levels will be eg and t2g. Three configurations will be possible: (eg)2, (eg)1(t2g)1 and (t2g)2. Oh
A1g
x2+y2+z2 Eg
(2z2-x2-y2, x2-y2)
T2g
(xz, yz, xy)
A2u
xyz
T1u
(x,y,z)
x3, y3, z3
T2u
x(z2-y2),…

3. 3) The number of bands: octahedral d2 and d8 complexes
Often correlation diagrams for dn, d10-n Oh and Td complexes are combined. The “bottom” part of the diagram for octahedral and tetrahedral d2 and d8 complexes looks like:
To find the number of the spin-allowed absorption bands it will be enough to find all terms which have the same multiplicity as the ground state term.
Note that the multiplicity of the ground state terms for d2 and d8 configurations is the same at any field strength. It is true for certain configurations only (octahedral d1, d2, d3, d8, d9)
For d2 and d8 metal complexes there are three more terms of the same multiplicity as the ground state term (triplet). Therefore, we expect three bands in the electronic absorption spectra of these complexes.

4. 4) High spin complexes of d1-4, d6-9 configurations: Orgel diagrams
The information about the number and the relative energy of available terms of the same multiplicity as the multiplicity of the ground state for the case of high spin complexes is given by Orgel diagrams.
It is enough to have two diagrams for the cases of d1 and d2 metal configurations to find spin-allowed transitions for any high spin octahedral or tetrahedral d1-4, d6-9 complexes: dn behaves as d5+n and opposite to d10-n and d5-n.
With the help of Orgel diagrams: 1) the observed absorption bands can be assigned to certain transitions; 2) one can predict blue or red shifts for each of the absorption bands as the ligand field changes.

5. 5) Qualitative analysis of electron absorption spectra: Oh d8 complexes
According to the Orgel diagram for octahedral d8 metal complexes, such complexes exhibit 3 absorption bands due to d-d transitions.

6. 6) Qualitative analysis of electron absorption spectra: Oh d4 and d6 complexes
For an octahedral high-spin d4 metal complex, Cr(OH2)62+, a single absorption band is observed at cm-1 (5Eg  5T2g) as expected (see Orgel diagram below).

7. 7) Qualitative analysis of electron absorption spectra: Oh d3 and d7 complexes
For an octahedral d3 metal complex, CrF63-, three absorption bands are observed: (4A2g  4T2g), (4A2g  4T1g(F)), and (4A2g  4T1g(P)) cm-1 as expected (see Orgel diagram below, left half).
For an octahedral d7 high-spin complex, Co(OH2)62+, three observed absorption bands are 8100 (4T1g(F)  4T2g), (4T1g(F)  4A2g), and (4T1g(F)  4T1g(P)) cm-1 as expected (see Orgel diagram below, right half).