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Yuniar Ponco Prananto

Tanabe-Sugano DiagramJahn-Teller Effect

In order to accurately interpret the electronic spectra of transition metal complexes, a series of diagrams have been created.

These diagrams are used to assign transitions (initial energy state and final energy state) to peaks observed in the spectra, and to calculate the value of ∆o.

Tanabe-Sugano diagrams have the lowest energy state (the ground state) plotted along the horizontal axis. The energy of excited states can then be readily compared to the ground state.

� Tanabe-Sugano diagrams are used in coordination chemistry to predict absorptions in the UV and visible electromagnetic spectrum of coordination compounds.

� The results from a Tanabe-Sugano diagram analysis of a metal complex can also be compared to experimental spectroscopic data. They are qualitatively useful and can be used to approximate the value of 10Dq, the ligand field splitting energy. Tanabe-Sugano diagrams can be used for both high spin and low spin complexes.

� Tanabe-Sugano diagrams can also be used to predict the size of the ligand field necessary to cause high-spin to low-spin transitions.

� In a Tanabe-Sugano diagram, the ground state is used as a constant reference. The energy of the ground state is taken to be zero for all field strengths, and the energies of all other terms and their components are plotted with respect to the ground term.

� The x-axis of a Tanabe-Sugano diagram is expressed in terms of the ligand field splitting parameter, Dq, or Δ, divided by the Racah parameter B. The y-axis is in terms of energy, E, also scaled by B.

� Three Racah parameters exist, A, B, and C, which describe various aspects of interelectronic repulsion. A is an average total interelectron repulsion. A is constant among d-electron configuration, and it is not necessary for calculating relative energies, hence its absence from Tanabe and Sugano's studies of complex ions. B and C correspond with individual d-electron repulsions. C is necessary only in certain cases. B is the most important of Racah's parameters in this case.

� One line corresponds to each electronic state. The bending of certain lines is due to configuration interactions of the excited states.

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� Although electronic transitions are only "allowed" if the spin multiplicity remains the same (i.e. electrons do not change from spin up to spin down or vice versa when moving from one energy level to another), energy levels for "spin-forbidden" electronic states are included in the diagrams.

� Each state is given its symmetry label (e.g. A1g, T2g, etc.), but "g" and "u" subscripts are usually left off because it is understood that all the states are gerade. Labels for each state are usually written on the right side of the table, though for more complicated diagrams (e.g. d6) labels may be written in other locations for clarity.

� Term symbols (e.g. 3P, 1S, etc.) for a specific dn free ion are listed, in order of increasing energy, on the y-axis of the diagram. The relative order of energies is determined using Hund's rules.

Hund’s RulesIn atomic physics, Hund's rules refer to a set of rules formulated by German physicist Friedrich Hund around 1927, which are used to determine the term symbol that corresponds to the ground state of a multi-electron atom. In chemistry, rule one is especially important and is often referred to as simply Hund's rules.

The three rules are:

� For a given electron configuration, the term with maximum multiplicity has the lowest energy. Since multiplicity is 2S+1 equal to , this is also the term with maximum S. S is the spin angular momentum.

� For a given multiplicity, the term with the largest value of L has the lowest energy, where L is the orbital angular momentum.

� For a given term, in an atom with outermost sub-shell half-filled or less, the level with the lowest value of J lies lowest in energy. If the outermost shell is more than half-filled, the level with highest value of J is lowest in energy. J is the total angular momentum, J = L + S.

� These rules specify in a simple way how the usual energy interactions dictate the ground state term. The rules assume that the repulsion between the outer electrons is very much greater than the spin-orbit interaction which is in turn stronger than any other remaining interactions. This is referred to as the LS coupling regime.

� Full shells and sub-shells do not contribute to the quantum numbers for total S, the total spin angular momentum and for L, the total orbital angular momentum. It can be shown that for full orbitals and sub-orbitals both the residual electrostatic term (repulsion between electrons) and the spin-orbit interaction can only shift all the energy levels together. Thus when determining the ordering of energy levels in general only the outer valence electrons need to be considered.

Term Degeneracy States in an octahedral field

S 1 A1g

P 3 T1g

D 5 Eg + T2g

F 7 A2g + T1g + T2g

G 9 A1g + Eg + T1g + T2g

H 11 Eg + T1g + T1g + T2g

I 13 A1g + A2g + Eg + T1g + T2g + T2g

Splitting of Term Symbols from Spherical to Octahedral Symmetry

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� Certain Tanabe-Sugano diagrams (d4, d5, d6, and d7) also have a vertical line drawn at a specific Dq/B value, which corresponds with a discontinuity in the slopes of the excited states' energy levels. This pucker in the lines occurs when the spin pairing energy, P, is equal to the ligand field splitting energy, Dq.

� Complexes to the left of this line (lower Dq/B values) are high-spin, while complexes to the right (higher Dq/B values) are low-spin.

� There is no low-spin or high-spin designation for d2, d3, or d8.

d2 --electron configurations-- d3

d4 --electron configurations-- d5 d6 --electron configurations-- d7

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d8 electron configurations

Unnecessary diagrams: d1, d9 and d10

� d1

There is no electron repulsion in a d1 complex, and the single electron resides in the t2g orbital ground state. A d1 octahedral metal complex, such as [Ti(H2O)6]3+, shows a single absorption band in a UV-vis experiment. The term symbol for d1 is 2D, which splits into the 2T2g and 2Eg states. The t2g

orbital set holds the single electron and has a 2T2g state energy of -4Dq. When that electron is promoted to an eg orbital, it is excited to the 2Eg

state energy, +6Dq. This is in accordance with the single absorption band in a UV-vis experiment. Thus, this simple transition from 2T2 to 2Eg does not require a Tanabe-Sugano diagram.

• d9

Similar to d1 metal complexes, d9 octahedral metal complexes have 2D spectral term. The transition is from the (t2g)

6(eg)3 configuration (2Eg state) to the

(t2g)5(eg)

4 configuration (2T2g state). This could also be described as a positive "hole" that moves from the eg to the t2g orbital set. The sign of Dq is opposite that for d1, with a 2Eg ground state and a 2T2g excited state. Like the d1 case, d9

octahedral complexes do not require the Tanabe-Sugano diagram to predict their absorption spectra.

• d10

There are no d-d electron transitions in d10 metal complexes because the d orbitals are completely filled. Thus, UV-vis absorption bands are not observed and a Tanabe-Sugano diagram does not exist.

Applications as a qualitative tool

In a centrosymmetric ligand field, such as in octahedral complexes of transition metals, the arrangement of electrons in the d-orbital is not only limited by electron repulsion energy, but it is also related to the splitting of the orbitals due to the ligand field. This leads to many more electron configuration states than is the case for the free ion. The relative energy of the repulsion energy and splitting energy defines the high-spin and low-spin states.

Considering both weak and strong ligand fields, a Tanabe-Sugano diagram shows the energy splitting of the spectral terms with the increase of the ligand field strength. It is possible for us to understand how the energy of the different configuration states is distributed at certain ligand strengths. The restriction of the spin selection rule makes it is even easier to predict the possible transitions and their relative intensity.

Although they are qualitative, Tanabe-Sugano diagrams are very useful tools for analyzing UV-vis spectra: they are used to assign bands and calculate Dq values for ligand field splitting.

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Note:

� Tanabe-Sugano diagrams are utilized in determining electron placements for high spin and low spin metal complexes. However, they are limited in that they have only qualitative significance. Even so, Tanabe-Sugano diagrams are useful in interpreting UV-vis spectra and determining the value of 10Dq.

� Tetrahedral Tanabe-Sugano diagrams are not commonly found in textbooks because ΔT for tetrahedral complexes is approximately 4/9 of ΔO for an octahedral complex. The consequence of the magnitude of ΔT results in the tetrahedral complexes being high spin.

� Orgel diagrams are best used for the treatment of tetrahedral complexes.

Interpretation of Spectra – d3 and d8

The Tanabe-Sugano diagram can be used to assign transitions to each absorption.

Interpretation of Spectra – d3 and d8

The first peak is due to the 4A2g(F)� 4T2g(F) transition and has an energy equal to ∆o.

ν1

ν1

Interpretation of Spectra – d3 and d8

The second peak is due to the 4A2g(F)� 4T1g(F) transition.

ν2

ν1ν2

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Interpretation of Spectra – d3 and d8

The third peak is due to the 4A2g(F)� 4T1g(P) transition.

ν3

ν1ν2

ν3

Interpretation of Spectra – d5

(high spin)

There are no spin allowed transitions for d5 high spin configurations. Extinction coefficients are very low, though the selection rule is relaxed by spin-orbit coupling.

Mn2+ compounds are white to pale pink in color.

References1. Racah, Giulio (1942). "Theory of complex spectra II". Physical Review 62: 438–462. 2. Tanabe, Yukito; Sugano, Satoru (1954). "On the absorption spectra of complex ions I". Journal

of the Physical Society of Japan 9 (5): 753–766. 3. Tanabe, Yukito; Sugano, Satoru (1954). "On the absorption spectra of complex ions II". Journal

of the Physical Society of Japan 9 (5): 766–779.4. Tanabe, Yukito; Sugano, Satoru (1956). "On the absorption spectra of complex ions III". Journal

of the Physical Society of Japan 11 (8): 864–877. 5. Atkins, Peter; Overton, Tina; Rourke, Jonathan; Weller, Mark; Armstrong, Fraser; Salvador, Paul;

Hagerman, Michael; Spiro, Thomas et al (2006). Shriver & Atkins Inorganic Chemistry (4th ed.). New York: W.H. Freeman and Company. pp. 478–483.

6. Douglas, Bodie; McDaniel, Darl; Alexander, John (1994). Concepts and Models of Inorganic

Chemistry (3rd ed.). New York: John Wiley & Sons. pp. 442–458. 7. Cotton, F. Albert; Wilkinson, Geoffrey; Gaus, Paul L. (1995). Basic Inorganic Chemistry (3rd d.).

New York: John Wiley & Sons. pp. 530–537.8. Bertolucci, Daniel C. (1978). Symmetry and Spectroscopy: An Introduction to Vibrational and

Electronic Spectroscopy. New York: Dover Publications, Inc.. pp. 403–409, 539. 9. Lancashire, Robert John (4–10 June 1999), "Interpretation of the spectra of first-row transition

metal complexes", CONFCHEM, ACS Division of Chemical Education10. Lancashire, Robert John (25 September 2006). "Tanabe-Sugano diagrams via spreadsheets".

Retrieved 29 November 2009.11. Jørgensen, Chr Klixbüll (1954). "Studies of absorption spectra IV: Some new transition group

bands of low intensity". Acta Chem. Scand. 8 (9): 1502–1512. 12. Jørgensen, Chr Klixbüll (1954). "Studies of absorption spectra III: Absoprtion Bands as Gaussian

Error Curves". Acta Chem. Scand. 8 (9): 1495–1501.

Jahn-Teller Distortion

Long axialCu-O bonds= 2.45 Å

four short in-planeCu-O bonds= 2.00 Å

[Cu(H2O)6]2+

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The Jahn-Teller (J-T) theorem states that in molecules/ ions that have a degenerate ground-state, the molecule/ion will distort to remove the degeneracy. This is a fancy way of saying that when orbitals in the same level are occupied by different numbers of electrons, this will lead to distortion of the molecule. For us, what is

important is that if the two orbitals of the eg level have different numbers of electrons, this will lead to J-T distortion. Cu(II) with its d9 configuration is degenerate and has J-T distortion:

The Jahn-Teller Theorem

egeg

eg

t2gt2g

d8

t2g

High-spin Ni(II) – only one way of filling the eg level – not degenerate, no J-T distortion

energy

Cu(II) – two ways of filling eg level – it isdegenerate, and has J-T distortion

d9

Ni(II)

Structural effects of Jahn-Teller distortion

two long axialCu-O bonds= 2.45 Å

[Cu(H2O)6]2+

J-T distortion lengthens axial Cu-O’s

[Ni(H2O)6]2+

no J-T distortion

four short in-planeCu-O bonds= 2.00 Å

All six Ni-O bondsequal at 2.05 Å

The CF view of the splitting of the d-orbitals is that those aligned with the two more distant donor atoms along the z-coordinate experience less repulsion and so drop in energy (dxz, dyz, and dz2), while those closer to the in-plane donor atoms (dxy, dx2-y2) rise in energy.

An MO view

of the splitting is that

the dx2-y2 in

particular overlaps

more strongly with the ligand donor orbitals, and so is raised in energy. Note that all d-orbitals with a ‘z’ in the subscript drop in energy.

Splitting of the d-subshell by Jahn-Teller distortion

eg

t2g

energy

dxz

dx2-y2

dyz

dxy

dz2

Cu(II) in regular octa-hedral environment

Cu(II) after J-T distortion

Structural effects of Jahn-Teller distortion on [Cu(en)2(H2O)2]2+

long axial Cu-O bonds of 2.60 Å

water

Cu

N

N

N

N

CCD:AZAREY

ethylenediamine

Shortin-planeCu-Nbonds of2.03 Å

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Structural effects of Jahn-Teller distortion on [Cu(en)3]2+

Cu

long axial Cu-N bonds of 2.70 Å

N

N

N

N

N

N

Short in-planeCu-N bonds of2.07 Å

CCD:TEDZEI

0

2

4

6

8

10

12

0 1 2 3 4 5 6 7 8 9 10 11

logK

1(en

).

d-electrons configuration

log K1(en) as a function of no of d-electrons

double-humpedcurve

Ca2+Mn2+

Zn2+

rising baselinedue to ioniccontraction

= CFSE

Extra stabilization due to J-Tdistortion

Thermodynamic effects of Jahn-Teller distortion:

Cu(II)

Experimental Evidence of LFSE

do d1 d2 d3 d4 d5 d6 d7 d8 d9 d10

LFSE 0 .4Δo .8 1.2 .6 0 .4 .8 1.2 .6 0

d-electron configurations that lead to Jahn-Teller distortion:

energy

egeg eg

eg

t2g t2g t2gt2g

d4 high-spin d7 low-spin d8 low-spin d9

Cr(II) Co(II) Co(I), Ni(II), Pd(II) Cu(II)Mn(III) Ni(III) Rh(I),Pt(II), Au(III) Ag(II)

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The strength of the Jahn-Teller effect is tabulated below: (w=weak, s=strong)

Σ e- 1 2 3 4 5 6 7 8 9 10

High

spin* * * s - w w * * *

Low

spinw w - w w - s - s -

*There is only 1 possible ground state configuration.- No Jahn-Teller distortion is expected.

Yuniar Ponco Prananto

Charge Transfer Spectra

Many transition metal complexes exhibit strong charge-transfer absorptions in the UV or visible range. These are much more intense than d�d transitions, with extinction coefficients ≥ 50,000 L/mol-cm (as compared to 20 L/mol-cm for d�d transitions).

In charge transfer absorptions, electrons from molecular orbitals that reside primarily on the ligands are promoted to molecular orbitals that lie primarily on the metal. This is known as a charge transfer to metal (CTTM) or ligand

to metal charge transfer (LMCT). The metal is reduced as a result of the transfer.

Examples of these intense absorptions can be seen in the permanganate ion, MnO4

-. They result from electron transfer between the metal and the ligands.

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LMCT typically occurs in complexes with the metal in a fairly high oxidation state. It is the cause of the intense color of complexes in which the metal, at least formally, has no d electrons (CrO4

2-, MnO41-).

LMCT occurs in the permangate ion, MnO41-. Electrons from the filled

p orbitals on the oxygens are promoted to empty orbitals on the manganese. The result is the intense purple color of the complex.

MLCT typically occurs in complexes with π acceptor ligands. The empty π* orbitals on the ligands accept electrons from the metal upon absorption of light. The result is oxidation of the metal.

Examples of MLCT include iron(III) with acceptor ligands such as CN- or SCN-. The complex absorbs light and oxidizes the iron(III) to iron(IV) state.

The metal may be in a low oxidation state (0) with carbon monoxide as the ligand. Many of these complexes are brightly colored, and some appear to exhibit both types of electron transfer.

Latihan Soal

1. Jelaskan apa yang dimaksud dengan: (a) prinsip keelektronetralan Pauling; (b) CFSE; (c) deret spektrokimia; (d) kompleks medan kuat dan medan lemah; (e) Efek Jahn-Teller!

2. Jelaskan kelebihan dan kelemahan teori berikut dalam menjelaskan sifat – sifat senyawa kompleks (a) Teori ikatan valensi; (b) Teori medan kristal; (c) dan Teori orbital molekul!

3. Jelaskan 4 faktor yang mempengaruhi nilai 10Dq (Δo)!

4. Gambarkan dua orbital molekul dari kompleks [NiCl4]2-

(Ar Ni = 28) ketika bersifat diamagnetik maupun paramagnetik!

5. Jelaskan mengapa konfirgurasi elektron d1, d9, dan d10

tidak memiliki / memerlukan diagram Tanabe-Sugano!

6. Mengapa pada kompleks Co(II) medan kuat cenderung terjadi distorsi Jahn-Teller, sedangkan pada kompleks Co(II) medan lemah tidak?