Crystal Field Theory

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CCrryyssttaal l FFiieelld d TThheeoorryy

The relationship The relationship between colors between colors and complex and complex metal ionsmetal ions

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Transition Metal Transition Metal GemsGems

Transition Metal Transition Metal GemsGems

Gemstone owe their color from trace transition-metal ions

Corundum mineral, Al2O3: Colorless

Cr Al : Ruby

Mn Mn Al: Al: Amethyst

Fe Fe Al: Al: Topaz

Ti &Co Ti &Co Al: Al: SapphireSapphire

Beryl mineral, BeBeryl mineral, Be3 3 AlAl 2 2SiSi66OO1818: Colorless: Colorless

Cr Cr Al : Al : EmeraldEmerald

Fe Al : Aquamarine

Gemstone owe their color from trace transition-metal ions

Corundum mineral, Al2O3: Colorless

Cr Al : Ruby

Mn Mn Al: Al: Amethyst

Fe Fe Al: Al: Topaz

Ti &Co Ti &Co Al: Al: SapphireSapphire

Beryl mineral, BeBeryl mineral, Be3 3 AlAl 2 2SiSi66OO1818: Colorless: Colorless

Cr Cr Al : Al : EmeraldEmerald

Fe Al : Aquamarine

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Crystal-Field TheoryCrystal-Field Theory

Model explaining bonding for transition metal complexesModel explaining bonding for transition metal complexes• Originally developed to explain properties for crystalline material

• Basic idea:

Electrostatic interaction between lone-pair electrons result in coordination.

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EnergeticsEnergetics

CFT - Electrostatic between metal ion and donor atomCFT - Electrostatic between metal ion and donor atom

i) Separate metal and ligand high energy

ii) Coordinated Metal - ligand stabilized

iii) Destabilization due to ligand -d electron repulsion

iv) Splitting due to octahedral field.

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Ligand-Metal InteractionLigand-Metal InteractionCrystal Field Theory - Describes bonding in Metal Complexes

Basic Assumption in CFT:Electrostatic interaction between ligand and metal

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

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

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

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d-Orbitals and Ligand d-Orbitals and Ligand InteractionInteraction(Octahedral Field)(Octahedral Field)

Ligands approach metal

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

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Splitting of the d-OrbitalsSplitting of the d-OrbitalsOctahedral field Splitting Pattern:

The energy gap is The energy gap is referred to as referred to as (10 Dq) (10 Dq) , the , the crystal field crystal field splitting energy.splitting energy.

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

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

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

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

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

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

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Magnitude of CF Splitting (Magnitude of CF Splitting ( or 10Dq) or 10Dq)Color of the Complex depends on magnitude of Color of the Complex depends on magnitude of

1. Metal: Larger metal 1. Metal: Larger metal larger larger Higher Oxidation State Higher Oxidation State larger larger 2. Ligand: Spectrochemical series2. Ligand: Spectrochemical series

ClCl-- < F < F-- < H < H22O O < NH< NH33 < en < NO < en < NO22-- < (N-bonded) < CN < (N-bonded) < CN--

Weak field Ligand: Weak field Ligand: Low electrostatic interaction: small CF splitting.Low electrostatic interaction: small CF splitting.

High field LigandHigh field Ligand: High electrostatic interaction: large CF splitting.: High electrostatic interaction: large CF splitting.

Spectrochemical series: Increasing Spectrochemical series: Increasing

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Electron Configuration in Octahedral Electron Configuration in Octahedral FieldField

Electron configuration of metal ion:Electron configuration of metal ion:

s-electrons are lost first. s-electrons are lost first.

TiTi3+3+ is a d is a d11, V, V3+3+ is d is d22 , and Cr , and Cr3+3+ is d is d33

Hund's rule:Hund's rule:

First three electrons are in separate First three electrons are in separate d orbitals with their spins parallel.d orbitals with their spins parallel.

Fourth e- has choice:Fourth e- has choice:

Higher orbital if Higher orbital if is small; High spin is small; High spin

Lower orbital if Lower orbital if is large: Low spin. is large: Low spin.

Weak field ligandsWeak field ligands

Small Small , High spin complex , High spin complex

Strong field LigandsStrong field Ligands

Large Large , Low spin complex , Low spin complex

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High Spin Vs. Low Spin (dHigh Spin Vs. Low Spin (d11 to d to d1010))Electron Configuration for Octahedral complexes of metal ion having dElectron Configuration for Octahedral complexes of metal ion having d11 to to dd1010 configuration [M(H configuration [M(H22O)O)66]]+n+n. . Only the dOnly the d44 through d through d77 cases have both high-spin and low spin configuration cases have both high-spin and low spin configuration..

Electron configurations for octahedral complexes of metal ions having from d1 to d10 configurations. Only the d4 through d7 cases have both high-spin and low-spin configurations.

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Color Absorption of CoColor Absorption of Co3+3+ Complexes Complexes

The Colors of Some Complexes of the CoThe Colors of Some Complexes of the Co3+ 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

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Colors & How We Colors & How We Perceive itPerceive it

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Artist color wheelArtist color wheelshowing the colors whichshowing the colors whichare complementary to oneare complementary to oneanother and the wavelengthanother and the wavelengthrange of each color.range of each color.

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Black Black & & WhiteWhite

If a sample absorbs all If a sample absorbs all wavelength of visible light, wavelength of visible light, none reaches our eyes from none reaches our eyes from that sample. Consequently, it that sample. Consequently, it appears black.appears black.

When a sample absorbs light, what we see is the sum When a sample absorbs light, what we see is the sum of the remaining colors that strikes our eyes.of the remaining colors that strikes our eyes.

If the sample absorbs noIf the sample absorbs novisible light, it is white visible light, it is white or colorless.or colorless.

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AbsorptionAbsorption and and ReflectionReflection

If the sample If the sample absorbsabsorbsall but all but orangeorange, , thethesample appears sample appears orange.orange.

Further, we also perceive orange Further, we also perceive orange color when visible light of all colors color when visible light of all colors except except blue blue strikes our eyes. In a strikes our eyes. In a complementary fashion, if the complementary fashion, if the sample absorbed only orange, it sample absorbed only orange, it would appear blue; blue and orange would appear blue; blue and orange are said to be complementary are said to be complementary colors.colors.

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Light absorption Properties of Metal Light absorption Properties of Metal ComplexesComplexes

Recording the absorption SpectrumRecording the absorption Spectrum

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Complex Influence on Complex Influence on ColorColor

Compounds of Transition metal complexes solution.Compounds of Transition metal complexes solution.

[Fe(H2O)6]3+

[Co(H2O)6]2+

[Ni(H2O)6]2+

[Cu(H2O)6]2+

[Zn(H2O)6]2+

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Color Absorption of CoColor Absorption of Co3+3+ ComplexesComplexes

The Colors of Some Complexes of the Co3+ IonComplex Ion Wavelength of

Light Absorbed(nm)

Color of Light Absorbed

Color ofComplex

[CoF6]3+ 700 Red Green

[Co(C2O4)3]3+ 600, 420, Yellow, violet Dark green

[Co(H2O)6]3+ 600, 400, Yellow, violet Blue-green

[Co(NH3)6]3+ 475, 340 Blue,

ultraviolet

Yellow-orange

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

[Co(CN)6]3+ 310 Ultraviolet Pale yellow

The complex with fluoride ion, [CoFThe complex with fluoride ion, [CoF66]]3+3+ , is high spin and has one absorption , is high spin and has one absorption

band. The other complexes are low spin and have two absorption bands. In band. 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 all but one case, one of these absorptionsis in the visible region of the spectrum. The wavelengths refer to the center of that absorption band.spectrum. The wavelengths refer to the center of that absorption band.

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Octahedral, Tetrahedral & Square Octahedral, Tetrahedral & Square PlanarPlanar

CF Splitting pattern for CF Splitting pattern for various molecular geometryvarious molecular geometry

M

dz2dx2-y2

dxzdxydyz

M

dx2-y2 dz2

dxzdxy dyz

M

dxz

dz2

dx2-y2

dxy

dyz

OctahedralOctahedralTetrahedralTetrahedral Square planarSquare planar

Pairing energy Vs. Weak field < Pe

Strong field > Pe

Pairing energy Vs. Weak field < Pe

Strong field > Pe

Small High SpinSmall High Spin Mostly d8

(Majority Low spin)

Strong field ligands

i.e., Pd2+, Pt2+, Ir+, Au3+

Mostly d8

(Majority Low spin)

Strong field ligands

i.e., Pd2+, Pt2+, Ir+, Au3+

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SummarySummary

Crystal Field Theory provides a basis for explaining many Crystal Field Theory provides a basis for explaining many features of transition-metal complexes. Examples include features of transition-metal complexes. Examples include why transition metal complexes are highly colored, and why transition metal complexes are highly colored, and why some are paramagnetic while others are diamagnetic. why some are paramagnetic while others are diamagnetic. The spectrochemical series for ligands explains nicely the The spectrochemical series for ligands explains nicely the origin of color and magnetism for these compounds. origin of color and magnetism for these compounds. There is evidence to suggest that the metal-ligand bond There is evidence to suggest that the metal-ligand bond has covalent character which explains why these has covalent character which explains why these complexes are very stable. Molecular Orbital Theory can complexes are very stable. Molecular Orbital Theory can also be used to describe the bonding scheme in these also be used to describe the bonding scheme in these complexes. A more in depth analysis is required however.complexes. A more in depth analysis is required however.