The Electronic Spectra of Transition Metals

The electronic excitations in transition metal complexes are most often found in the visible

and ultraviolet regions (10,000-50,000 cm-1) of the spectrum and are due to 4 different

types of transition;

Ligand spectra

π→π* and n→π*, typically high in energy

Counter-ion spectra

e.g. nitrates, phosphates

Charge-transfer spectra

metal to ligand charge transfer (MLCT), ligand to metal charge transfer (LMCT),

metal to metal charge transfer (MMCT) and inter-valence charge transfer (IVCT)

Ligand-field spectra

Perhaps the most important, subject to previously encountered selection rules;

Δs=0, Δl=±1. d→d transitions are already breaking the latter and so extinction

coefficients are likely in the range ε=10-100 M-1 cm-1, if they break the spin selection

rule this can become as low as ε=<1 M-1 cm-1

Ligand-field Spectra

In order to fully comprehend the UV spectrum of a complex it is necessary to first consider

the arrangement of electrons within the d-orbitals of the metal and the various states (using

Russell-Saunders state symbols) arising from the dn configuration.

In Oh Symmetry First Excited Term In Td Symmetry

d1 2D 2T2g+2Eg 2E+2T2

d2 3F 3T1g+3T2g+

3A2g 3P→3T1g 3A2+3T2+3T1

d3 4F 4T1g+4T2g+

4A2g 4P→4T1g 4A2

+4T2+4T1

d4 5D 5T2g+5Eg 5T2+5E

d5 6S 6A1g 6A1 d6 5D 5T2g+

5Eg 5T2+5E d7 4F 4T1g+

4T2g+4A2g 4P→4T1g 4A2

+4T2+4T1

d8 3F 3T1g+3T2g+

3A2g 3P→3T1g 3A2+3T2+3T1

d9 2D 2T2g+2Eg 2E+2T2

In general it can be seen that;

i. octahedral dn splits inversely to octahedral d10-n (this is called hole formalism)

ii. dn splits in the same way as dn+5

iii. octahedral dn splits in the same way as tetrahedral d10-n

iv. d5 is unique

For d2, d3, d7 and d8 the A2g symbol will always represent the most symmetric state and the T2g state

will always be an intermediate between the T1g and A2g states.

Calculating the Number of Microstates and Their Identities

The number of permutations possible for n electrons in r orbitals is given by;

( )

It is possible to form a table of S against ML in which all possible microstates are represented, from

here it is possible to ‘extract’ the term symbols associated with that electronic configuration .

Jorgensen’s Rule of Average Environment

The position of the peak in a complex, MX3L3 can be approximated as being midway between that

for MX6 and ML6, although there will be a shift away from octahedral geometry that must be

accounted for.

Relative energies in d2, d3, d7 and d8 (both Oh and Td fields)

The d2 configuration gives a 3F ground state with 3P, 1G, 1D and 1S excited terms. Spin allowed

transitions will arise between the states originating from the triplet terms. In an octahedral field, 3F

splits to give T1g, T2g and A2g states while the 3P splits to give a T1g state.

The Orgel diagram1 (Figure 1) shows how the order of transitions can be dependent on the strength

of the octahedral field.

Figure 1 - The Orgel diagram for the transitions of d2 and d

7 in an octahedral field

According to the aforementioned rules, the above diagram is also a description of the transitions

possible in octahedral d7. It is also a description of tetrahedral d3 and d8.

Hole formalism can also be applied to give Figure 2. It is important to note that two states of the

same symmetry label must never cross in energy (the non-crossing rule). The left-hand side of the

diagram applies to d2/d7 in a tetrahedral field and d3/d8 in an octahedral field, the opposite of the

right hand side as described in Figure 1.

1 An Orgel diagram shows the relative energies of different states as a product of a given field

P

F

A2g

T1g(P)

T2g

T1g(F)

Oh field strength

#

Tanabe-Sugano Diagrams

Similar to Orgel diagrams, a Tanabe-Sugano diagram provides information on the energies required

to transfer between terms in a complex, however, they are applicable to both high and low-spin

configurations. The ground state is held at 0 with all other states then relative to this state. The d2

Tanabe-Sugano diagram (Figure 3) below helps to explain the dependence of some transitions on

the ligand field strength and the independence of others, for any two states with parallel energy

curves the transition will occur at a characteristic energy. The gradient of the line is also a level of

how susceptible the transition is to peak-broadening, the broadening is due to molecular vibrations

that vary the field strength and so any transition independent of field strength will give a sharp peak

in the spectrum.

Figure 3 - The Tanabe-Sugano diagram for a d2

configuration

P

F

A2g

T1g(P)

T2g

T1g(F) A2g

T1g(P)

T2g

T1g(F)

Figure 2 - The Orgel diagram for d2, d

3, d

7 and d

8 (for both tetrahedral and octahedral

fields)

Racah Parameters

In the free ion the Racah parameters (A,B and C) are a measure of electron repulsion. The free ion

value of B is a measure of electron repulsion within the d orbitals, this value decreases upon

complexation. The implication of this is that inter-electron repulsion has been reduced and therefore

the d orbital electron clouds have expanded to some extent, this is the nephelauxetic effect. This

reduction in B is caused, in the most part, by the covalency in the complex – this increases the

average separation between d-electrons. This relationship between the covalency in the M-L bond

and the reduction in the value of the B parameter gives rise to the nephelauxetic series.

A new term, β, can be defined in terms of the B values for the complex and the free ion (Equation 1)

and the values of β for common ligands can then be used to arrange the ligands in order of

increasing covalency (i.e. decreasing β) (Equation 2).

Equation 1- Calculation of β

( )

Equation 2 - The nephelauxetic series

Fluoride gives a β value close to 1 (i.e. it forms complexes with very little covalency), iodide can give

values as low as 0.3.

A similar series can be formed for metal ions, using a constant ligand it can be shown that the more

polarising the metal ion, the more covalent the bond will be, hence β will decrease according to

Equation 3.

Equation 3 - The nephelauxetic series for metal ions

The Energy Level Diagram for d2/d7(Oh)

The energy values of the 4 states found in d2 now depend on three factors;

a. the crystal field splitting parameter, Δ

b. the separation between the 3F and the 3P (note that this varies with Δ)

c. the magnitude of the interaction between the 3T1g(F) and the 3T1g(P)

The energy levels, in terms of Δ and B, are given by;

( )

[

( )

⁄ ]

( )

[

( )

⁄ ]

It is possible to then calculate the energy of a transition by simple subtraction of the necessary

energy terms. Furthermore it is possible to form a plot of ν1/ν2 (the energies, in wavenumbers, of

two transitions) against Δ/B and as a result from the energies of two transitions, calculate back to

the Racah B parameter and the crystal splitting energy of a given complex.

It is worth noting that although the difference in energy between the first and third transition is

equal to Δ and this would provide a much simpler mathematical route to the calculation of Δ (and

subsequently B), the third transition is buried among π→π* transitions and is difficult to observe.

The Energy Level Diagram for d3/d8(Oh)

In terms of Δ and B, the energy levels of the states attainable in a d3 configuration are given by;

( )

[

( )

]

( )

[

( )

]

d2 and d8 in Td fields

In tetrahedral complexes the splitting is smaller (ΔTd≈4/9 ΔOh) and so the transitions are of a lower

energy. For d2 this means that the lowest energy transition is often in the IR region and so only two

of the three peaks will be observed in a UV/Vis spectrum. With d8 this is less likely although still

possible.

d3 and d7 in Td fields

High spin d3 and d7 gives rise to two quartet states and several doublet states in a tetrahedral field.

High spin d5

High spin d5 has only one term, 6A1g. There are several very weak transitions possible to various

quartet states, there are also doublet states present however a transition from the sextet to a

doublet is doubly spin forbidden.

d6 low spin

For d6 low spin the ground state is now a singlet, the 1A1g. The possible transitions are;

1A1g→3T1g (spin forbidden and therefore weak, low energy)

1A1g→1T1g

(E=Δ - C)

1A1g→1T2g (E=Δ + 16B - C)

1 weak and 2 strong transitions are a tell-tale sign of d6 low spin.

Magnetic Susceptibility

Magnetic moment and spin-only magnetic moment, μ and μs.o, can be calculated by Equation 4 and

Equation 5. The latter only truly applies to first row transition metals

Equation 4 - The equation for magnetic moment

√ ( ) ( )

Equation 5 - The equation for spin-only magnetic moment

√ ( ) √ ( )

The values given by the second equation are often readily predictable, μ≈n+0.8, caution must be

maintained but as an approximation this is suitable in most cases.

The second and third row transition metals have degenerate sets of orbitals with the same shape,

these provide an orbital contribution. These orbitals must be asymmetrically filled, as a result

phenomenon like Jahn-Teller distortions quench this contribution.

In practical terms, for Oh compounds, this will only arise from asymmetrically filled t2g orbitals since

the eg orbitals are degenerate but have different shapes. This is summarised below, it is clear that

only triplet ground states give rise to first order orbital contributions. These contribution

d configuration Oh (Low Spin) Oh (High Spin) Td (High Spin)

d1 T2g YesT1g YesA2g No

E No

d2 A2 No

d3 T1 Yes

d4 T1g Yes Eg No T2 Yes

d5 T2g Yes A1g No A1 No

d6 A1g No T2g Yes E No

d7 Eg No T1g Yes A2 No

d8 A2g No T1 Yes

d9 Eg No T2 Yes

Second order orbital contributions due to mixing of A and E terms with excited triplet states can also

be possible, in this case the effective magnetic moment can be calculated (Equation 6).

Equation 6 - Calculation of the effective magnetic moment

( (

))

For d1 to d4, λ is positive (i.e. μeff<μs.o), the opposite is true of d5 to d9.

Despite having unpaired electrons, d6 low spin can also display paramagnetism due to mixing of the 1A1g with the 1T1g and 1T2g terms.