tanabe sugano diagrams

Zehra DurmuşFatih UniversityDecember, 2010

Tanabe-Sugano Diagrams

• Until Yukito Tanabe and Satoru Sugano published their paper On the absorption spectra of complex ions, little was known about the excited electronic states of complex metal ions.

• The plots of the energies calculated for the electronic states of each electron configuration are now known as Tanabe-Sugano diagrams.

Orgel diagramsd1, d6/d4, d9

Orgel diagrams

Tanabe-Sugano diagrams illustrate the

relative energies of states in a quantitativefashion– They are drawn for a fixed ratio of B/C(~4)– The ground state always lies on the x axis– They can be used along with spectra toestimate both Δ and B for a given complex. Tanabe-Sugano diagrams include

the effect of mixing states with the same symmetry

– Electronic states with the samesymmetry cannot cross they always mix– This introduces the curvature seen for many of the lines on the plot

Tanabe-Sugano diagrams

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Tanabe-Sugano diagrams for Oh d2 & d3

Free-ion configuration: d2

• For 17,000 cm-1: 3T2g ← 3T1g

25,000 cm-1: 3T1g(P) ← 3T1g(F)

• Ratio of 25,000/17,000 = 1.5. This ratio can be founding the Tanabe-Sugano diagram as indicated. ΔO/B = 25

• The horizontal intercept for the first transition gives E/B = 23

therefore, B = 17,000 cm-1/23 = 740 cm-1

• ΔO/B = 25, hence, ΔO = 25 · 740 cm-1 = 18,500 cm-1.

V(OH2)63

+

Using a TS diagram

Interpretation of TS diagram for Oh d2

http://wwwchem.uwimona.edu.jm:1104/courses/Tanabe-Sugano/TSintro.html

25,600/17,200 = 1.49B = 665 cm-1, D = 18,600

Interpretation of TS diagram for Oh d3

[Cr(NH3)6]3+

ν1=21,550 cm-1 ν2=28,500 cm-1

28,500/21,550 = 1.32 D/B=30E1/B=32 E2/B=42 B = 660 cm-1

=D 19800 cm-1

Tanabe-Sugano diagrams include the effect of mixing states with the same symmetry– If two terms of the same symmetry approach upon increasing fieldstrength, they do not cross, but bend away from each other.– This introduces the curvature seen for many of the lines on the plot

Non-crossing Rule

Tanabe-Sugano diagrams for Oh d4

d5 & d6

Tanabe-Sugano diagrams for Oh d7 & d8

Abrupt change in slope of 4T1

at about Δ/B ~ 22 occurs whenthe ground state changes from4T1 to 2E and everything isplotted relative to the energyof the ground state– High-spin to low-spintransition occurs as theligand field strength isincreased and Δ becomesgreater than the spin pairingenergy.

High-spin low-spin transitions andTanabe Sugano diagrams

3P

3F

D E

D E = 15 B

B is Racah parameter constant and it is measure of electron-electron repulsion

microstates with same multiplicty

Cloud Expanding Effect

- M - L bonds show partial covalent character

- Metal orbitals size increase

- electron-electron repulsion decreases

β = B(Complex)/B(free ion)

The nephelauxetic effect of the ligands, increasing thus:

F− < H2O < NH3 < en < [NCS - N]− < Cl− < [CN]− < Br− < N3− < I−

This series is consistent with fluoride complexes being the most ionic and bromide complexes the most covalent.

The nephelauxetic effect of the central metal ion. Mn(II) < Ni(II) Co(II) < Mo(II) > Re (IV) < Fe(III) < Ir(III) < Co(III) < Mn(IV)

Cloud Expanding

Electron-electron repulsion at complexes lower than free ions.

The Nephelauxetic Effect

[M(H2O)6]n+

(24*700)

(35*700)

Absorption spectrum of ruby: Cr3+ imourities in Al2O3.Assignments according to energy levels in the down.

octahedral TiCl64-

two absorption bands at u1 = 7600 cm-1 and u2 = 14,500 cm-1

Using Tanabe-Sugano diagrams assign these spectroscopic transitions. u1 3T2g <- 3T1g

u2 3T1g <- 3T1g

Estimate values for Δ and B' for TiCl64-

Ti2+ d2

u1/u2 ~ 1.91. This corresponds to Δ/B ~ 16.7For u2= E/B ~ 28.0 Δ/B =~ 16.7.This gives B = 518 cm-1 and Δ = 8648 cm-1

B for gas phase free Ti2+ is 718 cm-1. Explain why the free ion value is different from the one you have just determined?

B for the complex is lower than for the free ion as in the complex the electrons are partially delocalized onto the ligands and this reduces the amount of electron electron repulsion.

Cr(OH2)62

+

Two bands are observed: 14,200 cm-1 >36000 cm-1

• High-spin (the aqua ligand is a weak-field ligand). • For d4 ion, (T2g)3 (eg)1 configuration.• 5Eg is the ground state. The only quintet excited

state 5T2g, • The second band >36000 cm-1 must be a charge-

transfer (CT) band.• The 5T2g ← 5Eg excitation is the lowest (and the only)

spin-allowed excitation.• The energy corresponds directly to ΔO. ΔO = 14,200 cm-1 The value of B cannot be determined.

Fe(OH2)62+

Free-ion configuration: d6 weak field, high spin: (t2g)4 (eg)2.• the ground state is 5T2g. • Only one quintet excited state: 5Eg. • The excited state is also susceptible to

Jahn-Teller distortion, as a consequence, there is a splitting of the band. The higher transition corresponds to ΔO.

• ΔO = 11,000 cm-1. The value of B cannot be determined.

Free-ion configuration: d5 (high spin)6A1g is the ground state. There are no sextet excited states, so all transitions are spin-forbidden.1. 18,000 cm-1: 4T1g ← 6A1g2. 23,000 cm-1: 4T2g ← 6A1g3. 24,500 cm-1: 2T2g ← 6A1g4. 24,700 cm-1: 4A1g,4Eg ← 6A1g5. 28,300 cm-1: 2A2g,2T1g ← 6A1g6. 30,000 cm-1: 4Eg ← 6A1gRatio of 2:1 1.28:1 3:1 1.36:1 4:1 1.37:1 5:1 1.57:1 6:1 1.67:1These ratios fit at the vertical intercept of ΔO/B = 11.For the lowest transition: E/B =24, B = 18,000 cm-

1/24 = 750 cm-1.Since ΔO/B = 11, ΔO = 9000 cm-1. (textbook has ΔO = 8500 cm-1)

[Mn(H2O)6]2+ (1 M ) solution spectrum

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