Naming of electronic states:

In names of electronic states, e.g. 4A2g, the labels A, E,

and T, stand for non-degenerate, doubly degenerate, and

triply degenerate, while the numeric superscript stands

for the multiplicity of the state, which is the number of

unpaired electrons plus one. Note that the electronic

states can be ground states (states of lowest energy) or

excited states:

4A2g

t2g

eg

Multiplicity =

3 unpaired electrons + 1

= 4

Non-degenerate

ground state =

‘A’

g = gerade

energy

eg eg eg

t2g t2g 6A2g

3T2g 1A2g

Non-degenerate triply degenerate non-degenerate

Multiplicity

= 5 + 1

energy

t2g

Naming of electronic states (contd.):

NOTE: In determining degeneracy, one can re-arrange the electrons, but

the number of unpaired electrons must stay the same, and the number

of electrons in each of the eg and t2g levels must stay the same.

Multiplicity

= 2 + 1

Multiplicity

= 0 + 1

eg eg eg

t2g t2g

5Eg 5T2g

2Eg

eg eg eg

t2g t2g

3A2g 1Eg

3T2g

Naming of electronic states (contd.):

t2g

t2g

ground state excited state excited state

ground state excited state ground state

energy

Electronic transitions:

eg eg

eg eg

t2g t2g

t2g t2g

3A2g →3T2g

3A2g →1Eg

3A2g 3T2g

3A2g 1Eg

ground state excited state

visible infrared UV

green 3A2g →3T2g

3A2g →1Eg

[Ni(H2O)6]2+

The electronic spectrum of [Ni(H2O)6]2+:

λ,

The complex looks green, because it absorbs only weakly at 500 nm,

the wavelength of green light.

On the previous slide we saw the two bands due to the 3A2g →

3T2g and 3A2g →1Eg transitions. The band at λ =

1180 nm which is the 3A2g →3T2g transition shown below,

corresponds to Δ for the complex. This is usually

expressed as Δ in cm-1 = (1/λ(nm)) x 107 = 8500 cm-1.

The electronic spectrum of [Ni(H2O)6]2+:

eg eg

t2g t2g

3A2g →3T2g 3A2g 3T2g Δ

= Δ

= 8500

cm-1

Note the weak band at 620 nm that corresponds to the 3A2g →

1Eg transition. The electron that is excited moves

within the eg level, so that the energy does not involve Δ,

but depends on the value of P, the spin-pairing energy.

The point of interest is why this band is so weak, as

discussed on the next slide.

The electronic spectrum of [Ni(H2O)6]2+:

eg eg

t2g t2g

3A2g →1Eg 3A2g 1Eg Δ

= 16100

cm-1

The electronic spectrum of [Ni(H2O)6]2+:

The two peaks at higher energy resemble the 3A2g→3T2g transition, but

involve differences in magnetic quantum numbers of the d-orbitals,

and are labeled as 3A2g→3T1g(F) and 3A2g→

3T1g(P) to reflect this:

3A2g →3T2g

3A2g →3T1g(F)

3A2g →3T1g(P)

3A2g →1Eg

λ,

[Ni(H2O)6]2+

The Selection rules for electronic transitions

There are three levels of intensity of the bands that we observe in the spectra of complexes of metal ions. These are governed by two selection rules, the Laporte selection rule, and the spin selection rule. The Laporte selection rule reflects the fact that for light to interact with a molecule and be absorbed, there should be a change in dipole moment. When a transition is ‘forbidden’, it means that the transition does not lead to a change in dipole moment.

The Laporte Selection rule: This states that transitions where there is no change in parity are forbidden:

g→g u→u g→u u→g forbidden allowed

All transitions within the d-shell, such as 3A2g→3T2g are

Laporte forbidden, because they are g→g. Thus, the

intensity of the d-d transitions that give d-block metal

ions their colors are not very intense. Charge transfer

bands frequently involve p→d or d→p transitions, and so

are Laporte-allowed and therefore very intense.

The Spin Selection rule: This states that transitions that

involve a change in multiplicity (or number of unpaired

electrons) are forbidden. This accounts for why

transitions within the d-shell such as 3A2g→1Eg that

involve a change of multiplicity are much weaker than

those such as 3A2g→3T2g that do not.

The Selection rules for electronic transitions

The Selection rules for electronic transitions

3A2g →3T2g

Charge-transfer band – Laporte and spin allowed – very intense

[Ni(H2O)6]2+ a

b c

3A2g →1Eg Laporte and spin forbidden – very weak

a, b, and c, Laporte

forbidden, spin

allowed, inter-

mediate intensity

The three types of bands present in e.g. [Ni(H2O)6]2+ are:

1) Laporte-allowed plus spin allowed charge transfer

bands of very high intensity

2) Laporte-forbidden plus spin-allowed d→d transitions

(e.g. 3A2g→3T2g) of moderate intensity

3) Laporte forbidden plus spin-forbidden d→d transitions

(3A2g→1Eg) of very low intensity.

The Intensity of bands in complexes of d-block ions: