v.santhanam - kar

V.SANTHANAMDEPARTMENT OF CHEMISTRY

SCSVMV

LIMITATIONS OF VBT

The valence bond approach could not explain the following

Electronic spectra

Magnetic moments of most complexes.

So a more radical approach was put forward which had only room for electrostatic forces

CRYSTAL-FIELD THEORY

Model explaining bonding for transition metal complexes

Originally developed to explain properties for crystalline material

Electrostatic interaction between lone-pair electrons result in coordination.

CFT assumptions

Separate metal and ligand high energy

Coordinated Metal - ligand stabilized

Destabilization due to ligand -d electron repulsion

Splitting due to octahedral field.

Crystal Field Theory

The electron pairs on the ligands are viewed as point negative charges

They interact with the d orbitals on the central metal.

The nature of the ligand and the tendency toward covalent bonding is ignored.

d Orbitals

Approach of ligands – Oh field

Crystal Field Theory

The repulsion between ligand lone pairs and the d orbitals on the metal results in a splitting of the energy of the d orbitals.

Crystal field theory

d-orbitals align along the octahedral axis d-orbitals align along the octahedral axis will be affected the most.will be affected the most.

More directly the ligand attacks the metal More directly the ligand attacks the metal orbital, the higher the energy of the d-orbital, the higher the energy of the d-orbital.orbital.

In an octahedral field the degeneracy of the In an octahedral field the degeneracy of the five d-orbitals is liftedfive d-orbitals is lifted

i

Ligand approach octahedral field – eg set

Ligand approach octahedral field – t2g set

Splitting of the d-Orbitals

The dThe dz2z2 and d and dx2-y2 x2-y2 orbitals lie on the same orbitals lie on the same axes as negative charges.axes as negative charges.

Therefore, there is a large, unfavorable Therefore, there is a large, unfavorable interaction between ligand (-) orbitals.interaction between ligand (-) orbitals.

These orbitals form the degenerate These orbitals form the degenerate high energy pair of energy levels.high energy pair of energy levels.

d Orbital Splitting

In some texts and articles, the gap in the d orbitals is assigned a value of 10Dq.

The upper (eg) set goes up by 6Dq, and the lower set (t2g) goes down by 4Dq.

The actual size of the gap varies with the metal and the ligands.

The dThe dxyxy , d , dyxyx and d and dxzxz orbitals bisect the orbitals bisect the negative charges.negative charges.

Therefore, there is a smaller repulsion Therefore, there is a smaller repulsion between ligand & metal for these orbitals.between ligand & metal for these orbitals.

These orbitals form the degenerate low These orbitals form the degenerate low energy set of energy levels.energy set of energy levels.

d-orbitals not pointing directly at axis are least affected (stabilized) by electrostatic interaction

d-orbitals pointing directly at axis are affected most by electrostatic interaction

d Orbital Splitting

________

Spherical

field

__ __dz2 dx2-y2

__ __ __dxy dxz dyz

∆o + 0.6∆o

- 0.4∆o

Octahedral field

eg

t2g

Free ion

Splitting pattern – Oh field

The energy gap is The energy gap is referred to as referred to as ∆ο (10 Dq)

Also known as Also known as crystal field splitting crystal field splitting energyenergy

Factors affecting the magnitude of splitting

Many experiments have shown that the magnitude of splitting is depending upon both metal and ligands.

JORGENSON’S RELATION

∆ο = ∆ο = f . gf . g

f – metal parameterg – ligand parameter

Metal factors

Charge on the metal ion

Number of d- electrons

Principle quantum number of the metal d electron

Number of d electrons - I

Different charges same metal (No. of d electrons)

[Fe(H2O)6]2+ - 3 d 6 - 10,400 cm-1

[Fe(H2O)6]3+ - 3d5 - 13,700 cm-1

[Co(H2O)6]2+ - 3 d7 - 9,300 cm-1

[Co(H2O)6]3+ - 3d6 - 18,200 cm-1

Number of d electrons - II

Same charge different metal ions

[Co(H2O)6]2+ - 3 d7 - 9,300 cm-1

[Ni(H2O)6]2+ - 3 d8 - 8,500 cm-1

Charge on the metal ion

Same charge different metal

[V(H2O)6]2+ - 3d3 - 12,400 cm-1

[Cr(H2O)6]2+ - 3d3 - 17,400 cm-1

summary

For complexes having same geometry and same ligands the crystal field splitting

Increases with the increase in charge on the ion (Same number of d - electrons)

Decreases with increasing number of d - electrons (Same charge on the ion)

Principle quantum number

With increasing n value the splitting increases[Co(NH3)6]3+ - 3d6 - 23,000 cm-1

[Rh(NH3)6]3+ - 4d6 - 34,000 cm-1

[Ir(NH3)6]3+ - 5d6 - 41,000 cm-1

Effect of ligand field strength

Weak field Free ion strong field

Crystal field stabilisation energy

Already it is seen that t2g levels are lowered while eg levels are raised in energy.

The d – electron and ligand repulsion only increases the energy.

But the energy content of the system must be a constant.

So to maintain the centre of gravity the t2g levels are getting lowered to an equivalent amount.

+ 0.6 ∆o

- 0.4 ∆o

eg

t2g

Total energy change = 2 x (+ 0.6∆o) + 3 (- 0.4 ∆o) = 0

Crystal field stabilisation energy

Depending upon the field created by the ligands the electrons are occupying the various orbitals available.

When t2g levels are getting filled the system is getting lowered in energy

Energy content increases if eg levels are filled If both of them are filled then the difference

between increases and decrease in energy is calculated which is called crystal field stabilisation energy

CFSE

Gain in energy = + 0.6 ∆o x p Loss in energy = - 0.4 ∆o x q

Net change in energy = [+ 0.6 x p + - 0.4 x q] ∆o∆o = 10Dq

CFSE = [ -4Dq x q + 6Dq x p]

Splitting and Pairing energy Pairing energy is the energy required for

accommodating second electron as a spin pair to the first one in an orbital, against the electrostatic repulsion.

When the ligands are stronger, the splitting of d orbitals is high.

If splitting energy is more than the pairing energy then according to Hund’s rule the incoming electrons start to pair in the t2g level itself

.

Fourth e- has choice: Higher orbital if ∆ is small; High spin Lower orbital if ∆ is large: Low spin.

Weak field ligands - Small ∆ - High spin complex Strong field Ligands -Large ∆ - Low spin complex

d1 –d3 systems

Weak field Free ion strong field

∆ο∆ο

CFSE d1 - - 4Dqd2 - - 8Dq

d3 - - 12Dq

Weak field d4 Free ion strong field

CFSE - -6Dq CFSE - - 16Dq + P

Weak field d5 -Free ion strong field

CFSE - - 20Dq + 2PCFSE - 0 Dq

Weak field d6 -Free ion strong field

CFSE - - 24Dq + 3PCFSE - -4Dq +P

Weak field d7 Free ion strong field

CFSE - - 18Dq + 3PCFSE - -8Dq +2P

Weak field d8 Free ion strong field

CFSE - - 12Dq + 3PCFSE - -12Dq +3P

Weak field d9 Free ion strong field

CFSE - -6Dq +4P

Weak field d10 Free ion strong field

CFSE - 0Dq +5P

Crystal Field Stabilization Energy

The first row transition metals in water are all weak field, high spin cases.

dn CFSE dn CFSE1 -4Dq 6 -4Dq + P

2 -8Dq 7 -8Dq + 2P

3 -12Dq 8 -12Dq + 3P

4 -6Dq 9 -6Dq + 4P

5 0 10 0 + 5P

High Spin vs. Low Spin

3d metals are generally high spin complexes except with very strong ligands. CN- forms low spin complexes, especially with M3+ ions.

4d & 5d metals generally have a larger value of ∆o than for 3d metals. As a result, complexes are typically low spin.

Colour of the complex

The colors exhibited by most transition metal complexes arises from the splitting of the d orbitals.

As electrons transition from the lower t2g set to the eg set, light in the visible range is absorbed.

Colour of the complexes

The splitting due to the nature of the ligand can be observed and measured using a spectrophotometer

Smaller values of ∆o result in colors in the green range. Larger gaps shift the color to yellow.

Spectrochemical / Fajan –Tsuchida series

Depending on the ligands present in a complex the splitting value varies.

By taking a particular metal, in a fixed geometric field, the ligands are arranged in the increasing order of the splitting caused by them

Spectrochemical / Fajan –Tsuchida series

I- < Br- <S2- <Cl- < NO3- < N3

- < F-< OH- <

C2O42- < H2O < NCS- < CH3CN < pyridine <

NH3 < en < bipy < phen < NO2- < PPh3 < CN- < CO

Field Strength increases

Field Strength increases

Field Strength increases

Color Absorption of Co3+ Complexes The Colors of Some Complexes of the CoThe Colors of Some Complexes of the Co 3+ 3+ IonIon

The complex with fluoride ion, [CoFThe complex with fluoride ion, [CoF66]]3+3+ , is high spin and has one absorption band. , is high spin and has one absorption band. The other complexes are low spin and have two absorption bands. In all but one The other complexes are low spin and have two absorption bands. In all but one case, one of these absorptionsis in the visible region of the spectrum. The case, one of these absorptionsis in the visible region of the spectrum. The wavelengths refer to the center of that absorption band.wavelengths refer to the center of that absorption band.

Complex IonComplex Ion Wavelength of Wavelength of Color of Light Color of Light Color of ComplexColor of Complex light absorbed light absorbed Absorbed Absorbed

[CoF[CoF66] ] 3+3+ 700 (nm)700 (nm) RedRed GreenGreen

[Co(C[Co(C22OO44))33] ] 3+3+ 600, 420600, 420 Yellow, violetYellow, violet Dark greenDark green

[Co(H[Co(H22O)O)66] ] 3+3+ 600, 400600, 400 Yellow, violetYellow, violet Blue-greenBlue-green

[Co(NH[Co(NH33))66] ] 3+3+ 475, 340475, 340 Blue, violetBlue, violet Yellow-orangeYellow-orange

[Co(en)[Co(en)33] ] 3+3+ 470, 340470, 340 Blue, ultraviolet Blue, ultraviolet Yellow-orangeYellow-orange

[Co(CN)[Co(CN)66] ] 3+3+ 310310 Ultraviolet Ultraviolet Pale YellowPale Yellow

The Spectrochemical Series

The complexes of cobalt (III) show the shift in color due to the ligand.

(a) CN– (b) NO2– (c) phen (d) en (e) NH3

(f) gly (g) H2O (h) ox2– (i) CO3 2–

Experimental Evidence for CFSE

The hydration energies of the first row transition metals should increase across the period as the size of the metal ion gets smaller.

M2+ + 6 H2O(l) M(H2O)62+

The heats of hydration show two “humps” consistent with the expected LFSE for the metal ions. The values for d5 and d10 are the same as expected with a LFSE equal to 0.

Experimental Evidence for CFSE

Experimental Evidence of CFSEddoo dd11 dd22 dd33 dd44 dd55 dd66 dd77 dd88 dd99 dd1010

LFSELFSE

In terms In terms of of ΔΔoo

00 .4.4 .8.8 1.21.2 .6.6 00 .4.4 .8.8 1.21.2 .6.6 00

Structure of spinels

Spinels are mixed oxides having general formula AB2O4

A is a divalent metal ion i.e. - A2+

B is a trivalent metal ion i.e. - B3+

The metals A and B may be same or different In spinels the oxide ions are arranged in cubic

close packed lattice

Structure of spinels

In such situation each oxide ion will have 12 neighboring oxide ion at equidistant

The lattice contains two types of coordination sites

Octahedral holes- surrounded by six oxide ions – one hole per one oxide ion

Tetrahedral holes –surrounded by four oxide ions – two holes per one oxide ion

Structure of spinels

Number of tetrahedral holes is twice the number of octahedral holes.

There are three types of spinels

Normal Inverse Partially inverse

Normal spinel

All the divalent cations occupy one of the eight available tetrahedral holes

Trivalent cations occupy the octahedral holes Represented as A2+[B3+

2]O4

Examples: FeCr2O4, Mn3O4, FeCr2S4, ZnAl2S4 and ZnCr2Se4

Structure of spinels

Structure of spinel - MgAl2O4

Inverse spinels

All divalent ions and half of the trivalent ions occupy octahedral holes and other half of the trivalent cations in the tetrahedral holes.

Represented as B3+[A2+B2+]O4

Examples: CuFe2O4, MgFe2O4, Fe3O4, TiMn2O4, TiFe2O4, TiZn2O4 and SnZn2O4

Partial inverse spinels

Examples of partially inverse spinel structures include MgFe2O4, MnFe2O4 and NiAl2O4

Reason for inversion

Let us consider the mixed oxides Mn3O4 (Normal spinel) and Fe3O4 (inverse spinel)

Oxide ions are creating a weak field The table shows values of CFSE for the ions in

different sites

Site Mn3+ (d4) Mn2+ (d5) Fe3+ (d5) Fe2+ (d6)Octahedral 6Dq 0 0 4Dq

Tetrahedral 1.78Dq 0 0 2.67Dq

The values clearly shows that both trivalent ions are having higher CFSE values at octahedral holes.

So preferably they tend to occupy the octahedral sites

This makes all the Mn3+ ions to occupy the octahedral sites and Mn2+ ions in tetrahedral sites

Thus Mn3O4 is a normal spinel

In the case of Fe3O4 , Fe3+ ions are expected to be in the tetrahedral holes .

Fe3+ ion in an octahedral hole is having higher CFSE.

So half of them are occupying octahedral sites making the structure inverse

Stabilisation of oxidation state

By using the CFSE values the stability of certain oxidation state of a metal can be explained.

In aqueous solutions Co2+ is stable and Co3+ is not formed easily

This is a direct consequence of higher CFSE for [Co(H2O)6]2+ (d7) [-8Dq]than [Co(H2O)6]3+ (d8) [-4Dq]

Similarly [Co(NH3)6]3+ (d6) [-24Dq] has higher CFSE than [Co(NH3)6]2+ (d7) [-18Dq] so it is more stable.

Stereochemistry of complexes

Based on CFSE values we can say that why Cu2+ is forming only square planar complexes rather than octahedral

SP symmetry complex has higher CFSECu2+ in SP CFSE = 1.22 ∆oCu2+ in Oh CFSE = 0.18 ∆o