13 Tanabe Sugano Diagrams

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13 Tanabe Sugano Diagrams - MIT

1 5 04, Principles of Inorganic Chemistry II Prof Daniel G Nocera Lecture 4 May 11: Tanabe Sugano Diagrams A Tanabe-Sugano (TS) diagram plots the energy dependence of the various ligand

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1

5.04, Principles of Inorganic Chemistry II

Prof. Daniel G. Nocera

Lecture 4 May 11: Tanabe Sugano Diagrams

A Tanabe-Sugano (TS) diagram plots the energy dependence of the various ligand field states (or terms) with field strength. The strength of the ligand field is defined o . The energy of the state is given by E. Both the state term energy and field strength are normalized to B, where B is a measure of the two-electron energy. The lowest energy term is set = 0, and all other states are defined energetically relative to the ground state. For d n counts that can be high or low spin (d 4 -d 7 ), there will be a discontinuity in the TS diagram at the ligand field strength at which there is crossover from high spin to low spin. Let"s consider electronic spectra of aquo complexes of first row TMs: d 1 , Ti 3+ max = 20,300 cm -1 , ε ~ 4 M -1 cm -1 only one transition; the shoulder in the spectrum is due to Ti(H 2 O) 5 (OH) 2+ 2 =BE 10 Dq = 20,300 cm -1 , Dq = 2,030 cm -1 d 9 , Cu 2+ max = 12,000 cm -1 , ε ~ 11 M -1 cm -1

As with d

1 ion, for the d 9 ion, expect only one band, but clearly there is a shoulder. This due to a

Jahn-Teller distortion

(vide infra) 3 =BE 10 Dq = 12,000 cm -1 , Dq = 1,200 cm -1

The shoulder on the Cu

2+ absorption band arises from a Jahn-Teller distortion. Jahn-Teller effect - a molecule with an orbitally degenerate ground state will distort to remove the degeneracy and consequently lower its overall energy. In the case of Cu(H 2 O) 62+
, the molecule can axially elongate or compress to remove the degeneracy of the ground state (O h

ĺ D

4h ). The JT effect does not say if elongation or compression will occur, only that here will be a distortion. Analyzing Cu(H 2 O) 62+
for an axial elongation (note, there will be an equatorial compression since energy cannot be created or destroyed in the distortion), 4 Generally, the JT effect is most pronounced when M-L σ* orbitals are involved. This is why the JT distortion is observed in Cu 2+ but not in Ti 3+ , where the JT distortion arises from orbitals which are non-bonding. d 2 , V 3+ max = 17,200 cm -1 , ε ~ 6 M -1 cm -1 max = 25,600 cm -1 , ε ~ 8 M -1 cm -1

From the d

2 configuration, get terms of 3 F, 1 D, 3 P, 1 G and 1

S. Note that spin allowed

transitions (ΔS = 0) will prevail (i.e., be the most intense). Thus we will assume that the two transitions observed in the above absorption spectrum arise from the 3 F and 3

P states since the

F is the ground state.

2 P 3 F 3 T 1g 3 A 2g 3 T 2g 3 T 1g 10 Dq 8 Dq this corresponds to a 2e transition, therefore transitions to this state should be exceptionally weak (due to low absorption cross-section... i.e. isospatial and isotemporal absorption of the two photons needed for the two- electron promotion is very unlikely) 5 Accordingly, the most reasonable assignments therefore are, 3 T 1g (F) ĺ 3 T 1g (P) 25,600 cm -1 transition 3 T 1g (F) ĺ 3 T 2g (P) 17,200 cm -1 transition Note, in a TS diagram, the energy of the transition is not plotted - the transition energy is normalized to B. Thus the transition cannot be fit directly on the TS diagram. However, by taking a ratio of the two transitions, B can be eliminated: 49.1

200,17600,25

FT FT EFT PT E

BFT FT EBFT PT E

g13g23g13g13 g13g23g13g13 From the TS diagram, this ratio of 1.49 is best fit at Dq/B = 2.8 (see next page). At this value of Dq/B, the E/B values for the two states are: 11g23 cm 664 = Bor

Bcm 200,17 9.25

BFT E 11g13 cm 661 = Bor

Bcm 600,25 7.38

BPT E B avg = 663 cm -1

With B in hand, Dq may now be evaluated,

8.2BDq=

Dq = 2.8(B) = 2.8(663 cm

-1 ) = 1,860 cm -1 o = 18,600 cm -1 6 d 2

TS diagram

70
60
50
40
30
20 10 0123
3 F 1 D 3 P 1 G 1 S 1 A 1g1 E g3 A 2g 1 T 1g 1 T 2g 3 T 1g 3 T 2g 1 E g 1 T 2g 3 T 1g 1 A 1g E/B Dq/B 7 From the fit Dq and B values, may now determine energies of all other transitions (including the spin for bidden ones) of V(H 2 O) 63+
. The 2e transition should fall at...

54BFT FAE

g13g23 =← at Dq/B = 2.8 E( 3 A 2g (F)← 3 T 1g (F)) = 54(B) = 54(662 cm -1 ) = 35800 cm -1

Note: the B value for V

3+ complexed by H 2

O is smaller than the free ion value

of 860 cm -1 . Remember B is a measure of the interelectronic repulsion... in the complex, the metal d orbitals mix with the ligand orbitals. Owing to the covalency, the spatial dimension of the orbitals in which the d-electrons reside increases... since operator for interelectronic repulsion goes as 1 r ij ... as r ij increases, interelectronic repulsion decreases and hence B decreases.quotesdbs_dbs8.pdfusesText_14

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