For ALL octahedral complexes, except high spin d^{5}, simple CFT would predict that only 1 band should appear in the electronic spectrum and that the energy of this band should correspond to the absorption of energy equivalent to Δ. In practice, ignoring spinforbidden lines, this is only observed for those ions with D free ion ground terms i.e., d^{1}, d^{9} as well as d^{4}, d^{6}.
The observation of 2 or 3 peaks in the electronic spectra of d^{2}, d^{3}, d^{7} and d^{8} high spin octahedral complexes requires further treatment involving electronelectron interactions. Using the RussellSaunders (LS) coupling scheme, these free ion configurations give rise to F free ion ground states which in octahedral and tetrahedral fields are split into terms designated by the symbols A_{2(g)}, T_{2(g)} and T_{1(g)}.
To derive the energies of these terms and the transition energies between them is beyond the needs of introductory level courses and is not covered in general textbooks[10,11]. A listing of some of them is given here as an Appendix. What is necessary is an understanding of how to use the diagrams, created to display the energy levels, in the interpretation of spectra.
In the laboratory component of the course we will measure the absorption spectra of some typical chromium(III) complexes and calculate the spectrochemical splitting factor, Δ. This corresponds to the energy found from the first transition below and as shown in Table 1 is generally between 15,000 cm^{1} (for weak field complexes) and 27,000 cm^{1} (for strong field complexes).
For the d^{3} octahedral case, 3 peaks can be predicted and these would correspond to the following transitions and energies:
where C.I. is the configuration interaction arising from the "noncrossing rule".
Complex

ν1

ν2

ν3

ν2/ ν1

ν1/ ν2

Δ/B

Ref

Cr^{3+} in emerald 
16260

23700

37740

1.46

0.686

20.4

13 
K_{2}NaCrF_{6} 
16050

23260

35460

1.45

0.690

21.4

13 
[Cr(H_{2}O)_{6}]^{3+} 
17000

24000

37500

1.41

0.708

24.5

This work 
Chrome alum 
17400

24500

37800

1.36

0.710

29.2

4 
[Cr(C_{2}O_{4})_{3}]^{3} 
17544

23866

? 
1.37

0.735

28.0

This work 
[Cr(NCS)_{6}]^{3} 
17800

23800

? 
1.34

0.748

31.1

4 
[Cr(acac)_{3}] 
17860

23800

? 
1.33

0.752

31.5

This work 
[Cr(NH_{3})_{6}]^{3+} 
21550

28500

? 
1.32

0.756

32.6

4 
[Cr(en)_{3}]^{3+} 
21600

28500

? 
1.32

0.758

33.0

4 
[Cr(CN)_{6}]^{3} 
26700

32200

? 
1.21

0.829

52.4

4 
For octahedral Ni(II) complexes the transitions would be:
where C.I. again is the configuration interaction and as before the first transition corresponds exactly to Δ.
For M(II) the size of Δ is much less than for M(III) and typical values for Ni(II) are 6500 to 13000 cm^{1} as shown in Table 2.
Complex

ν1

ν2

ν3

ν1

ν1/ ν2

Δ/B

Ref

NiBr_{2} 
6800

11800

20600

1.74

0.576

5

13 
[Ni(H_{2}O)_{6}]^{2+} 
8500

13800

25300

1.62

0.616

11.6

13 
[Ni(gly)_{3}]^{} 
10100

16600

27600

1.64

0.608

10.6

13 
[Ni(NH_{3})_{6}]^{2+} 
10750

17500

28200

1.63

0.614

11.2

13 
[Ni(en)_{3}]^{2+} 
11200

18350

29000

1.64

0.610

10.6

3 
[Ni(bipy)_{3}]^{2+} 
12650

19200

? 
1.52

0.659

17

3 
For d^{2} octahedral complexes, few examples have been published. One such is V^{3+} doped in Al_{2}O_{3} where the vanadium ion is generally regarded as octahedral, Table 3.
Complex

ν1

ν2

ν3

ν2/ ν1

ν1/ν2

Δ/B

Ref

V^{3+} in Al_{2}O_{3} 
17400

25200

34500

1.448

0.6906

30.90

13 
[VCl_{3}(MeCN)_{3}] 
14400

21400

?

1.486

0.6729

28.68

4 
K_{3}[VF_{6}] 
14800

23250

?

1.571

0.6365

24.78

4 
Interpretation of the spectrum highlights the difficulty of using the righthand side of the Orgel diagram as previously noted. For d^{2} cases where none of the transitions correspond exactly to Δ often only 2 of the 3 transitions are clearly observed and hence the calculations will have three unknowns (Δ, B and C.I.) but only 2 energies to use in the the analysis.
The first transition can be unambiguously assigned as:
^{3}T_{2g} ← ^{3}T_{1g} transition energy = 4/5 * Δ + C.I.But, depending on the size of the ligand field ( Δ) the second transition may be due to:
^{3}A_{2g} ← ^{3}T_{1g} transition energy = 9/5 * Δ + C.I.for a weak field or
^{3}T_{1g}(P) ← ^{3}T_{1g} transition energy = 3/5 * Δ + 15B' + 2 * C.I.for a strong field.
The transition energies of these terms are clearly different and it is often necessary to calculate (or estimate) values of B, Δ and C.I. for both arrangements and then evaluate the answers to see which fits better.
The difference between the ^{3}A_{2g} and the ^{3}T_{2g} (F) lines should give Δ. In this case Δ is equal to either:Solving the equations like this for the three unknowns can ONLY be done if the three transitions are observed. When only two transitions are observed, a series of equations[14] have been determined that can be used to calculate both B and Δ. This approach still requires some evaluation of the numbers to ensure a valid fit. For this reason, TanabeSugano diagrams become a better method for interpreting spectra of d^{2} octahedral complexes.
The Nephelauxetic Series is given by:
F < H_{2}O < urea < NH_{3} < en ~ C_{2}O_{4}^{2} < NCS < Cl ~ CN < Br < S^{2} ~ IThis series is consistent with fluoride complexes being the most ionic and giving a small reduction in B while covalently bonded ligands such as I give a large reduction of B.
As an example of a Cr(III) complex, using the observed peaks
found for [Cr(NH_{3})_{6}]^{3+} in Table
1 above, namely ν_{1} = 21550 cm^{1} and ν_{2} = 28500 cm^{1} the
ratio of ν_{2}/ν_{1} = 1.32.
The value of Δ is obtained directly from the first transition
so Δ/B' is equal to ν_{1}/B' and finding B' is now relatively
straightforward since from the first transition energy of 21,550
cm^{1} and the value of Δ/B' (ν1/B') of 32.6 we get:
B' = 21,550/ 32.6 or B' = 661 cm^{1}
The third peak can then be predicted to occur at 69.64 * 661 = 46030
cm^{1} or 217 nm (well in the UV region and probably
hidden by charge transfer or solvent bands).
It is important to remember that for spectra recorded in solution the width of the peaks may be as large as 12000 cm^{1} so as long as it is possible to unambiguously assign peaks, the techniques are valuable.
To overcome the problem of small diagrams found in textbooks, it was decided to generate our own TanabeSugano diagrams using spreadsheets. This was done, using the transition energies given in the Appendix, for the spinallowed transitions and using CAMMAG to generate the energies of the spinforbidden transitions.
Even so, the method of finding the correct Xintercept is somewhat tedious and timeconsuming and a different approach was devised using JAVA applets.
The JAVA applets display the transitions and when the user clicks on any region of the graph then the values of ν_{2}/ ν_{1} and ν_{3}/ν_{1} are displayed. In addition, the values of Δ/B and the Yintercepts are given as well. This simplifies the process of determining the best fit for Δ/B.
The expected ranges for the ratio of ν_{2}/ν_{1} are:
These ratios show the need for a certain degree of precision in attempting to analyse the spectra, especially for d^{7} and d^{8}. It has been suggested that instead of using ν_{2}/ ν_{1} that any two ratios can be used and graphs of these plots were produced by Lever in the 1960's[11]. Once again though the published diagrams are rather small and so the spreadsheets above contain these charts which can be printed in larger scale. The slopes of the various ratio lines vary greatly and it is useful to examine the region of interest first before deciding on which set of lines should be used for analysis. If only 2 peaks are observed then this is not an option.
For the spinallowed diagrams:Further information for use in laboratory classes is available and some example calculations are available as well.
Transitions calculated for spinallowed terms in the TanabeSugano diagrams.
Octahedral d^{3} (e.g. Chromium(III) ).
^{4}T_{2g} ← ^{4}A_{2g} , ν_{1}/B= Δ/B
^{4}T_{1g}(F) ← ^{4}A_{2g}, ν_{2}/B= ½{15 + 3( Δ/B)  √(225  18(Δ/B) + ( Δ/B)^{2} ) }
^{4}T_{1g}(P) ← ^{4}A_{2g}, ν_{3}/B= ½{15 + 3( Δ/B) + √(225  18(Δ/B) + ( Δ/B)^{2} ) }
from this, the ratio ν_{2}/ν_{1} would become:
½{15 + 3( Δ/B)  √(225  18(Δ/B) + ( Δ/B)^{2} ) } / Δ/B
and the range of Δ/B required is from ~15 to ~55
Octahedral d^{8} (e.g. Nickel(II) ).
^{3}T_{2g} ← ^{3}A_{2g}, ν1/B= Δ/B
^{3}T_{1g}(F) ← ^{3}A_{2g}, ν2/B= ½{15 + 3(Δ/B)  √(225  18(Δ/B) + ( Δ/B)^{2} ) }
^{3}T_{1g}(P) ← ^{3}A_{2g}, ν3/B= ½{15 + 3(Δ/B) + √(225  18(Δ/B) + ( Δ/B)^{2} ) }
from this the ratio ν_{2}/ν_{1} would become:
½{15 + 3( Δ/B)  √(225  18(Δ/B) + ( Δ/B)^{2} ) } / Δ/B
and the range of Δ/B required is from ~5 to ~17
Octahedral d^{2} (e.g. Vanadium(III) ).
^{3}T_{2g} ← ^{3}T_{1g} , ν1/B= ½{(Δ/B)  15 + √(225 + 18(Δ/B) + ( Δ/B)^{2} ) }
^{3}T_{1g}(P) ← ^{3}T_{1g}, ν2/B= √(225 + 18(Δ/B) + (Δ/B)^{2} )
^{3}A_{2g} ← ^{3}T_{1g}, ν3/B= ½{ 3 (Δ/B) 15 + √(225 + 18(Δ/B) + ( Δ/B)^{2} ) }
from this the ratio ν_{2}/ν_{1} would become:
√(225 + 18(Δ/B) + ( Δ/B)^{2} ) / ½{( Δ/B)  15 + √(225 + 18(Δ/B) + ( Δ/B)^{2} ) }
and the range of Δ/B required is from ~15 to ~35
Tetrahedral d^{7} (e.g. Cobalt(II) ).
^{4}T_{2} ← ^{4}A_{2}, ν1/B= Δ/B
^{4}T_{1} (F) ← ^{4}A_{2}, ν2/B= ½{15 + 3(Δ/B)  √(225  18(Δ/B) + ( Δ/B)^{2} ) }
^{4}T_{1} (P) ← ^{4}A_{2}, ν3/B= ½{15 + 3(Δ/B) + √(225  18(Δ/B) + ( Δ/B)^{2} ) }
from this the ratio ν_{2}/ν_{1} would become:
½{15 + 3(Δ/B)  √(225  18( Δ/B) + ( Δ/B)^{2} ) } / Δ/B
and the range of Δ/B required is from ~3 to ~8.
Thanks are due to Christopher Muir, for help with developing the JAVA applets.
Copyright © 19992011 by Robert John Lancashire, all rights reserved.
Created and maintained by Prof. Robert J. Lancashire