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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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Evidences for Pi Bonding: Metal Carbonyls
Phosphine & Phosphite Derivatives of Cr(CO)6
E id f Pi B di M t l C b l
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Evidences for Pi Bonding: Metal Carbonyls
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