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Molecular Orbital Theory of

Coordination Compounds

- Huheey, Keiter & Keiter, Inorganic Chemistry, 4th Edn

- F.A. Cotton, Chemical Application of Group Theory


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• Explain reasonably the electronic spectra and magnetism of TM complexes.

• The interaction b/w metal and ligand is purely electrostatic (no covalency!)

Crystal Field Theory

Evidences for covalent character:

• Nephelauxetic effect:

e-e repulsion in complexes is somewhat

less than that in a free ion

• Electron paramagnetic resonance (EPR)

spectroscopy: hyperfine splitting pattern


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Molecular Orbital TheoryIn Molecular Orbital Theory:

Orbital structure of molecules Shapes & energy order of MOs.

iiic

Construction of MOs: Decompose the system into two or more simplesubsystem whose orbitals (atomic or molecular) are known. Then allowthe orbital of the fragments to interact (LCAO).

Linear Combination of Atomic Orbitals (LCAO):

• Shape of MOs are determined by the c ’s (both magnitude & sign).

(e.g. Variation Theorem → Solve Secular equations)

• Electronic structures are obtained by placing electrons in the MOs

(starting with the lowest one).

• Interaction between two orbitals:

• Role of symmetry:

N jkic jk S i jk

H N

k

,,2,1,0)(

1


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Interactions between two orbitals

Same type Different types

ΔE

ΔE

ΔE

ΔE

Δ

1

1,

1

2,

2

2

In order to have non-zero S , orbitals must be bases for the same irreduciblerepresentation of the molecular symmetry group, i.e. they must have same

symmetry, ONLY ORBITALS OF SAME SYMMETRY INTERACT .

12

12111211

12

21

1;

)1(2 S

S H H H E

S

2S

E E

d S E E 2*

1


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MO Theory of Transition metal complexes

nd, (n+1)s, (n+1)p : minimum 9 orbitals

s, p electrons: minimum 24 orbitals

Results with N×N Secular matrix;

N = 33 (minimum)

p pmml l


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Role of Symmetry in Bonding

To construct the MOs for an AX n molecule, we need to combine the atomic orbitals on X and then match the resultant combinations with the atomic orbitals of the central atom A.With Group Theory, we can derive the linear combinations systematically.

Participating orbitals: O: 2s, 2p; H: 1s

6 × 6 Secular matrix

k

k Rn

k Ri

Rha k i )()()(

1

Reduction Formula:

y x z p B p B p s A :;:;,: 211

1. Determine the symmetries of participating orbitals:

2. Determine the characters of representation:

e.g. Water:


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Symmetry Adopted Linear Combination

k k Rk Ri

P ])([ˆ

(i) Projection Operator:

3. Determine the linear combination with appropriate symmetry:

(ii) By Inspection

Symmetry Orbitals on O Orbitals on H MO

A1 2s, 2Pz 1sa+1sb 1a1, 2a1, 3a1

B2 2Py - 1b2

B1 2Px 1sa-1sb 1b1, 2b1

S UMMA

RY


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Formation of MOs in H2O

Sym

metry

Orbitals

on O

Orbitals

on H

MO

A1 2s, 2Pz 1sa+1sb 1a1, 2a1, 3a1

B2 2Py - 1b2

B1 2Px 1sa-1sb 1b1, 2b1

2py, b2

2pz, a1

2px, b1

2s, a1


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MO Diagram for H2O

2p

2s

1sa + 1sb

1sa - 1sb


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MOTof Transition metal complexes

Metal

LI

G

A

ND

S

N jkia jk S i jk

F N

k

,,2,1,0)(

1

Variation principle:


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Octahedral ML6 Sigma Bonding

A. Finding SALC by Projection Operator Method:

)2

,22

;,,;( z d y x

d z p y p x p s

k k Rk Ri

P ])([ˆ

)654321

(4~)1

(1ˆ L L L L L L La P


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Determination of SALCs

)654321

(6

1

1 L L L L L L

g a

)65432

21

2(12

1)1( L L L L L L g e

)

6543(

4

1)2( L L L L g e

)21

(21)1(

1 L L

ut )

43(

2

1)2(1

L Lut

)65(

2

1)3(1

L Lut

a1g

eg

t1u


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A σ-bond MO Diagram of Octahedral ML6

Example:

[Co(NH3)6]3+

18e: diamagnetic

[CoF6]3-

18e: paramagnetic ??


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Tetrahedral ML4 Sigma Bonding


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Tetrahedral ML4 Sigma Bonding: MOs

[CoCl4

]2-

15e: paramagnetic


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Sq. Planar ML4 Sigma Bonding


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Sq. Planar ML4 Sigma Bonding: MOs

Typical for d8 ion:

16e: diamagnetic


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Octahedral ML6 Pi- Bonding


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Octahedral ML6 Pi- Bonding

Metal Complexes with Ligands containing π orbitals


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Octahedral ML6 Pi- Bonding: SALC’s

t2g


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Effect of Pi-bonding in MOs

Additional t2g

Example: [CoF6]3-

LGOs constructed

from 2p (F) orbitals


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Pi- Bonding & MO Theory

MO diagram for Pi-donor ligands MO diagram for Pi-acceptor ligands

Importance of π- Bonding:

• Explaining the Spectrochemical Series

• Determining patterns in ligand substitution reaction

• Reactivity & stability of organometallics

f C


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Evidences for Pi Bonding: Metal Carbonyls

Bonding Model: σ-donor (OC → M) and a π-acceptor (OC ← M)

Crystallography:

Greater π-bonding →

longer C – O bond,shorter M – C bond

Longer C – O bond than the normal C≡O in

free CO (112.8 pm) could be taken as

evidence for π bonding. However, M – C

bond length gives better indication!

Example: Re(CH3)(CO)5 Re – CO length: 200.4 pm (24 pm shorter than corresponding

σ-only bond.

E id f Pi B di M t l C b l


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Phosphine & Phosphite Derivatives of Cr(CO)6

E id f Pi B di M t l C b l


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IR Spectroscopy: (CO stretching frequency very useful)

HOMO (3σ) → LUMO (2π) causes the C – O stretching frequency to drop from2143 to 1489 cm-1.

Greater - ve charge on M → Stronger π - Bonding → Weaker C – O bond →

Lower IR frequency

Favored by system withpositive charge

accumulated on M

Favored by system with

negative charge which

enhances back

donation.

So, net charge on carbony l compounds h ave a

profo und effect on CO stretchin g frequency.

S C (CO)


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Photoelectron Spectroscopy: Cr(CO)6

νMC for Cr(CO)6 ion is 325 cm-1 (379 cm-1 for

neutral) corresponds to 14 pm increase in M – C

length on ionization

Removal of electron from t2g orbital should weaken

the M – C bond and decrease νMC


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MO Theory of Metallocenes

Chapter 15: Huhee

Chapter 7: Cotton

Sandwich Compounds: Metallocenes


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Sandwich Compounds: Metallocenes

Complexes in which a metal atom is found between two parallel carbocyclic rings:

“Sandwich compounds”. Metal-ligand bond b/w a metal & the π orbitals of C5H5.

Metallocenes & 18-electron rule: usually do not obey

SALCs of ferrocenes


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SALCs of ferrocenes

Molecular Orbitals of Cp


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Molecular Orbitals of Cp-

Molecular Orbitals of Cp


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Molecular Orbitals of Cp-

a1

e1

e2

Molecular Orbitals of cycloalkenes


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Molecular Orbitals of cycloalkenes

SALCs of [Cp Cp]2-


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SALCs of [Cp…Cp]2

Molecular Orbitals of ferrocenes


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Molecular Orbitals of ferrocenes

Molecular Orbital diagram of metallocenes


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Molecular Orbital diagram of metallocenes

Structures of Cyclopentadienyl Compounds


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Structures of Cyclopentadienyl Compounds

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