3. Ligand Field Theory-II

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Electronic spectra of transition metal complexes

Characteristics of electronic spectra

a) Wavelength Energy of electronic transition

b) Shape. Gaussian Band Shape - coupling of electronic and vibrational states

c) Intensity. Molar absorptivity, (M1cm1) due to probability of electronic transitions.

d) Number of bands Transitions between States of given dn configuration.

Electronic transitions are controlled by quantum mechanical selection rules which determine the probability (intensity) of the transition.

Transition εmax (M1cm1)

Spin and Symmetry forbidden "d-d" bands 0.02 - 1

Spin allowed and Symmetry forbidden "d-d" bands (Oh) 1 - 10 (Td) 10 – 103

Spin and Symmetry allowed LMCT and MLCT bands 103 - 5 x 104

Band intensity in electronic spectra ()

Spin Selection Rule: There must be no change in the spin multiplicity (2S + 1) during the transition.

i.e. the spin of the electron must not change during the transition.

Symmetry (Laporte) Selection Rule: There must be a change in parity (g ↔ u) during the transition

Since s and d orbitals are g (gerade) and p orbitals are u(ungerade), only s ↔ p and p ↔ d transitions are allowed and d → d transition are formally forbidden. [i.e. only transitions for which Δl = ± 1 are allowed]. d → d bands are allowed to the extent that the starting or terminal level of the transition is not a pure d-orbital. (i.e. it is a molecular orbital of the complex with both metal and ligand character).

States for dn configurationsRussel-Saunders Coupling

• Angular momentum of individual electrons couple to give total angular momentum for dn configuration ML = ∑ml

• Spin momentum of individual electron spins couple together to give total spin, S = ∑s

• Inter-electronic repulsions between the electrons in the d orbitals give rise to ground state and excited states for dn configurations.

• States are labeled with Tern Symbols

• Electonic transitions between ground and excited states are summarized in Orgel and Tanabe-Sugano diagrams .

• Term Symbols (labels for states) contain information about L and S for state Hund’s Rules. i) Ground state has maximum spin, S ii) For states of same spin, ground state has maximum L.

Triple degeneracy of a d2 ion’s 3T2g

ground state due to three possible sites for hole in t2g level

Singly degenerate 3T2g ground state. Only one possible arrangement for three electrons in t2g level

Singly degenerate 3T2g ground state. Only one possible arrangement for six t2g electrons.

Triple degenerate ground state for d7 Three possible sites for hole in t2g level

Ground State Excited States

Number of d-d bands in electronic spectrumExcitation from ground state to excited stated of dn configuration

Labeling of d-d bands in electronic spectrum.

• Consider states of dn configuration

• Determine free ion ground state Term Symbol (labels for states)

• Assign splitting of states in ligand field

• Spectroscopic labeling of bands.

• Orgel diagrams (high-spin)• Tanabe-Sugano diagrams (high-spin and low-spin)

Individual electron l = 2, ml = 2, 1, 0, -1, -2Maximum ml = l

l = 0, 1, 2, 3, Orbital: s, p, d , f _______________________________

dn configuration, L = 0, 1, 2, 3, 4 Term Symbol S, P, D, F, G

ML = Σ ml, maximum ML = L

Spin Multiplicity = 2 S +1

Free ion ground state Term Symbols for dn configurations

Term Symbols (labels for states) contain information about L and S for ground state

Hund’s Rules. i) Ground state has maximum spin, S

ii) For states of same spin, ground state has maximum L

2 1 0 -1 -2ml =l = 2,SL 2S + 1

2 1/2 2

3 3/2 4

0 5/2 6

L = ML(max) ML = ml S = s

Termsymbol

2 1 0 -1 -2ml =l = 2,SL 2S + 1

3 3/2 4

2 1/2 2

L = ML(max) ML = ml S = s

Termsymbol

Term Symbol2D3F

4F5D6S

Free Ion Ground Statedn Splitting of States in Oh ligand field

2D 2T2g + 2Eg

3F4F5D6S

3T1g + 3T2g + 3A2g

4T1g + 4T2g + 4A2g5T2g + 5Eg

Splitting of the weak field dn ground state terms in an octahedral ligand field

Correlation of spectroscopic terms for dn configuration in Oh complexes

AtomicTerm

Numberof states

Terms in OhSymmetry

S 1 A1gP 3 T1gD 5 T2g + EgF 7 T1g + T2g + A2g

Ground state determined by inspection of degeneracy of terms for given dn

od1 od2 d3 od4

4T1g(P)

3T1g(P)

2T2g2Eg 3T1g

3T1g(P)

Orgel Diagrams

Ti3+ V2+ Cr3+ Mn3+

The d-d bands of the d2 ion [V(H2O)6]3+

(a) [Ni(H20)6]2+ (b) [Ni(NH3)6]2+

E(3F) = A - 8B

E(1D) = A - 3B + 2C

E(3P) = A+7B

Racah Inter-electronic Repulsion Parameters (B, C)

3F 3P3F 1D

= 5B + 2C

The Tanabe-Sugano diagram for the d2 ion

Evidence for covalent bonding in metal-ligand interactionsThe Nephelauxetic Effect (“cloud expansion”)

Reduction in electron-electron repulsion upon complex formation

Racah Parameter, B: electron-elctronic repulsion parameter

Bo is the inter- electronic repulsion in the gaseous Mn+ ion.B is the inter- electronic repulsion in the complexed MLx

n+ ion.

The smaller values for B in the complex compared to free gaseous ion is taken as evidence of smaller inter-electronic repulsion in the complex due to a larger “molecular orbital” on account of overlap

of ligand and metal orbital, i.e. evidence of covalency (cloud expansion”).

Nephelauxetic Ratio, β = B Bo

Nephelauxetic Effect

Nephelauxetic Ligand Series

I < Br < CN < Cl < NCS < C2O42- < en < NH3 < H2O < F

Small β Large β Covalent Ionic

Nephelauxetic Metal Series

Pt4+ < Co3+ < Rh3+~Ir3+ < Fe3+ < Cr3+ < Ni2+ < V4+< Pt2+~ Mn2+ Small β Large β Large overlap Small overlap

Covalent Ionic

Empirical Racah parameters, h, kβ = 1– [h(ligand) x k(metal)]

Cr(NH3)63+ β = 1 –hk

β = 1 –(1.4)(0.21) = 0.706

Cr(CN)63- β = 1 –hk

β = 1 –(2.0)(0.21) = 0.580

Bo - B = hligands x kmetal ion

Typical Δo and λmax values for octahedral (ML6) d-block metal complexes__________________________________________________________________Complex Δo cm-1 ~ λmax (nm) Complex Δo cm-1 λmax (nm)___________________________________________________________________________________[Ti(H2O)6]3+ 20,300 493 [Fe(H2O)6]2+ 9,400 1064[V(H2O)6]3+ 20,300 493 [Fe(H2O)6]3+ 13,700 730[V(H2O)6]2+ 12,400 806 [Fe(CN)6]3- 35,000 286[CrF6]3- 15,000 667 [Fe(CN)6]4- 33,800 296[Co(H2O)6]3+, l.s. 20,700 483 [Fe(C2O4)3]3- 14,100 709[Cr(H2O)6]2+ 14,100 709 [Co(CN)6]3- l.s. 34,800 287[Cr(H2O)6]3+ 17,400 575 [Co(NH3)6]3+ l.s. 22,900 437[Cr(NH3)6]3+ 21,600 463 [Ni(H2O)6]2+ 8,500 1176[Cr(en)3]3+ 21,900 457 [Ni(NH3)6]2+ 10,800 926[Cr(CN)6]3- 26,600 376 [Ni(en)3]2+ 11,500 870___________________________________________________________________________________

1. Assign the metal oxidation state in the following compounds.

a. K2[PtCl6]b. Na2[Fe(CO)4]c. [Mn(CH3)(CO)5]

2. Account for the following:

The manganous ion, [Mn(H2O)6]2+, reacts with CN- to form [Mn(CN)6]4- which has

= 1.95 B.M., but with I- to give [MnI4]2- which has = 5.93 B. M.

[Co(NH3)6]Cl3 is diamagnetic, whereas Na3[CoF6] is paramagnetic ( = 5.02 B.M).

[PtBr2Cl2]2 is diamagnetic and exists in two isomeric forms, whereas [NiBr2Cl2]2

has a magnetic moment, = 3.95 B.M., and does not exhibit isomerism.

Copper(II) complexes are typically blue with one visible absorption band in their

electronic spectra whereas copper(I) complexes are generally colorless. Assign a spectroscopic label to the Cu2+ transition.

3. Ligand Field Theory-II

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