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Coordination Chemistry: Bonding Theories
Molecular Orbital Theory
Chapter 20
Coordination Chemistry: Bonding Theories
Molecular Orbital Theory
Chapter 20
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2
Review of the Previous Lecture
1. Discussed crystal field theory, an electrostatic theory that treats ligands as point charges.
Ligands create an electric field defined by the geometry in which they surround the metal. This electric field causes for a loss of degeneracy of the metal d orbitals.
2. Defined crystal field stabilization in terms of ∆.
3. Discussed the factors that contribute to the magnitude of ∆.
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1. Introduction to Molecular Orbital Theory
3
Unlike crystal field theory, molecular orbital theory accounts for covalency in M-L bonding
Electrons shared by metal ions and ligands
The identity of the ligand is important in the sharing of these electrons
Let’s examine how MOT helps us to account for and π interactions.
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2. The Spectrochemical Series
4
I- < Br - < [NCS]- < Cl- < F- < [OH]- < [ox]2- ~ H2O < [NCS]- < NH3 < en < [CN]- ~ CO
Weak field ligands Strong field ligandsLigands increasing Δoct
Small Δ High spin π donors
Large Δ Low spin π acceptors
σ donors π donors π acceptors
If splitting of the d orbitals resulted simply from the effect of point charges then anionic ligands would exert the greatest effect on the magnitude of Δ.
• OH- would be expected to induce a stronger field than H2O but does not
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3. interactions
5
z
yx
Use vectors aligned with the internuclear axes of the 6 M-L bonds as your basis set to examine interactions in coordination compounds.
Let’s use the octahedral geometry (C.N. = 6) as our point of reference:
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3. interactions
6
z
yx
Have 6 vectors to represent 6 bonds Expect the reducible representation to be composed of
6 irreducible representations
Point Group: Oh
Use group theory to identify the symmetry of the metal atomic orbitals and the ligand group orbitals that will be involved in bonding.
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7
z
yx
Oh E 8 C3 6 C2 6 C4 3 C2 (= C24) i 6 S4 8 S6 3 σh 6 σd
A1g 1 1 1 1 1 1 1 1 1 1 x2 + y2 + z2
A2g 1 1 -1 -1 1 1 -1 1 1 -1
Eg 2 -1 0 0 2 2 0 -1 2 0 (2z2 - x2 - y2 , x2 - y2)
T1g 3 0 -1 1 -1 3 1 0 -1 -1 (Rx , Ry , Rz)
T2g 3 0 1 -1 -1 3 -1 0 -1 1 (xz , yz , xy)
A1u 1 1 1 1 1 -1 -1 -1 -1 -1
A2u 1 1 -1 -1 1 -1 1 -1 -1 1
Eu 2 -1 0 0 2 -2 0 1 -2 0
T1u 3 0 -1 1 -1 -3 -1 0 1 1 (x , y , z)
T2u 3 0 1 -1 -1 -3 1 0 1 -1
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3. interactions
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z
yx
Point Group: Oh
red. rep. () = a1g + eg + t1u
6 irreducible representations as we expected
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3A. Metal atomic orbitals engaged in interactions
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z
yx
a1g : s orbital
eg : dz2 ; dx2 - y2
t1u : px ,py ,pz
For a 1st row transition metal, the orbitals would be from the3d , 4s , and 4p orbitals.
Of these, the dxy , dyz , and dxz do not engage in bondingbecause they are of the t2g symmetry Nonbonding orbitals
E
3d
4s
4p
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3B. Ligand group orbitals engaged in interactions
10
z
yx
The ligand group orbitals will have the a1g , eg , t1usymmetries and there will be a total of six.
Will be defined by atomic orbitals from the ligands thatengage in bonding
For instance,
if L = hydrogen, then s orbitals
if L = H2O, then sp3 hybrid orbitals
Let’s consider the ligand group orbitals as a set of lobesthat will overlap with the metal atomic orbital lobes.
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a1g Symmetry
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Metal Atomic Orbital Ligand Group Orbital
The a1g metal atomic orbital and LGO will generate one bonding molecular orbital and oneantibonding molecular orbital
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a1g Symmetry
12
Bonding Molecular Orbital Antibonding Molecular Orbital
Zero Nodes Six Nodal Planes
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t1u Symmetry
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Metal Atomic Orbital
Ligand Group Orbital
The t1u metal atomic orbitals and LGOs will generate three bonding molecular orbitals andthree antibonding molecular orbitals
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t1u Symmetry
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Metal Atomic Orbital
Ligand Group Orbital
Bonding Molecular Orbital
Antibonding Molecular Orbital
One Nodal Plane
Three Nodal Planes
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eg Symmetry
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Metal Atomic Orbital
Ligand Group Orbital
The eg metal atomic orbitals and LGOs will generate two bonding molecular orbitals andtwo antibonding molecular orbitals
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eg Symmetry
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Metal Atomic Orbital
Ligand Group Orbital
Bonding Molecular Orbital
Antibonding Molecular Orbital
Two Nodal Planes
Six Nodal Planes
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eg Symmetry
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Metal Atomic Orbital
Ligand Group Orbital
Bonding Molecular Orbital
Antibonding Molecular Orbital
Two nodal Cylinders
Two nodal Cylinders; six nodal planes
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eg Symmetry
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Metal Atomic Orbital
Ligand Group Orbital
Bonding Molecular Orbital
Antibonding Molecular Orbital
Two nodal Cylinders
Two nodal Cylinders; six nodal planes
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3C. Molecular Orbital Diagram for σ interaction
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The 6 metal atomic orbitals interact withthe 6 LGOs :
12 molecular orbitals• 6 bonding molecular orbitals• 6 antibonding molecular orbitals
Bonding MOs
Antibonding MOs
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3C. Molecular Orbital Diagram for σ interaction
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The 6 metal atomic orbitals interact withthe 6 LGOs :
12 molecular orbitals• 6 bonding molecular orbitals• 6 antibonding molecular orbitals
No nodes
One node
Two nodes
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3C. Molecular Orbital Diagram for σ interaction
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The 6 metal atomic orbitals interact withthe 6 LGOs :
12 molecular orbitals• 6 bonding molecular orbitals• 6 antibonding molecular orbitals
The t2g metal atomic orbitalsare nonbonding
• dxy , dyz , and dxz orbitals
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3C. Molecular Orbital Diagram for σ interaction
22
Each of the 6 ligands contributes2 electrons for a total of 12 electrons:
The 12 ligand electrons fill the bondingmolecular orbitals (a1g, t1u, eg)
The metal-ligand interactions stabilizethe 12 ligand electrons
12 e-
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3C. Molecular Orbital Diagram for σ interaction
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The 6 LGOs create an octahedral field:
∆oct is defined by the separation in the
nonbonding metal atomic orbitals t2gand
the antibonding molecular orbitals eg*
The metal d orbital electrons will fill inthese orbitals
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3C. Molecular Orbital Diagram for σ interaction
24
*
The metal-ligand interactions stabilize themetal d electrons. Recall CFSE.
3d
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3D. The 18 electron rule
25
The most stable metal-ligandinteractions in octahedral complexesare those that result in the filling ofthe metal and ligand electrons intothe bonding molecular orbitals andthe nonbonding t2g metal atomicorbitals.
Altogether, these 9 orbitals accept18 electrons
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4. π interactions
26
Consider ligand orbitals that can engage in π interactions with metals:
M L M L M L
dπ pπ dπ dπ dπ π*
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The Spectrochemical Series
27
I- < Br - < [NCS]- < Cl- < F- < [OH]- < [ox]2- ~ H2O < [NCS]- < NH3 < en < [CN]- ~ CO
σ donors π donors π acceptors
M L
dπ pπ
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4A. Let’s consider p ligand orbitals involved in and πinteractions with metals
28
Consider each of the ligand p orbitals that can engage in and π interactions with metals: 1 p orbital along the internuclear axis for interactions 2 p orbitals perpendicular to the internuclear axis for π interactions
M
L
L
LL
L
LM M
interactions π interactions
z
y
x
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4B. Use group theory to examine the π interactions withmetals
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Choose a basis set to define the symmetry of the ligand group orbitals that can engage in πinteractions The reducible representation will be defined by 12 irreducible representations
Point Group: Oh
red. rep. (π) = t2g + t2u + t1u + t1g
MM
12 irreducible representations
z
y
x
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4C. Focus on the t2g orbital symmetry
30
We will focus on the t2g orbital symmetry because this symmetry represented the nonbonding metal atomic orbitals in the molecular orbital diagram for only interactions. These orbitals can engage in π interactions.
dxy , dyz , and dxz orbitals
MM
z
y
x
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4D. Factors to consider regarding the energy of thet2g ligand group orbitals
31
The energy of the t2g ligand group orbitals will be greater or lower than the metal atomic orbitals depending on
The electronegativity difference between the ligands and the metal
Whether the LGOs are electron occupied
MM
z
y
x
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4E. Explaining the origins of the weak field ligands
32
Consider the octahedral complex [CoF6]3-:
Co3+; d6
F- is more electronegative than Co3+
The t2g LGOs will be lower in energy than the t2g metal atomic orbitals
When these orbitals interact, they will form
3 bonding molecular orbitals (t2g)and
3 antibonding molecular orbitals (t2g*)
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4E. Explaining the origins of the weak field ligands
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Consider the complex [CoF6]3-:
6 F-: Total of 36 electrons in the 18 p orbitals
• 12 electrons used for interactions
• The remaining 24 electrons can engage in π interactions, of which 6 of these belongto the t2g LGOs
M M
interactions π interactions
z
y
x
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34
Molecular Orbital Diagram including π interaction with Weak Field Ligands
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Molecular Orbital Diagram including π interaction with Weak Field Ligands
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Molecular Orbital Diagram including π interaction with Weak Field Ligands
36
[CoF6]3-
Co3+ ; d6
High spin, S = 2
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4E. Explaining the origins of the strong field ligands
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I- < Br - < [NCS]- < Cl- < F- < [OH]- < [ox]2- ~ H2O < [NCS]- < NH3 < en < [CN]- ~ CO
σ donors π donors π acceptors
L
dπ π*
M
Consider the octahedral complex [Co(CO)6]3+:
Co3+; d6
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Molecular Orbital Diagram for CO
38
LUMOt2g symmetry
The t2g LGOs are higher inenergy than the t2g metalatomic orbitals
These orbitals areunoccupied and can acceptelectrons from the metal
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39
Molecular Orbital Diagram including π interaction with Strong Field Ligands
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40
Molecular Orbital Diagram including π interaction with Strong Field Ligands
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41
Molecular Orbital Diagram including π interaction with Strong Field Ligands [Co(CO)6]3+
Co3+ ; d6
Low spin, S = 0
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4F. Revisiting the 18 electron rule
42
The most stable metal-ligand interactions inoctahedral complexes arethose that result in thefilling of the metal andligand electrons into the 9bonding molecular orbitals
Altogether, these 9 orbitalsaccept 18 electrons
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4G. π backbonding with π acceptor ligands
43
The ligand donates electrondensity to the metal through bonds
The metal donates electrondensity to the ligandthrough π bonds
dπ π*
M
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4G. π backbonding with π acceptor ligands
44
π backbonding weakens the CO bond because electron density is moved into its π*
molecular orbital:
Ths effect is more pronounced depending on the electron donation capacity ofanother ligand positioned trans to the CO ligand
dπ π*
Mtrans-L
Electron withdrawing Strengthens CO bond; Increased υCO
Electron donating Weakens CO bond; Decreased υCO
Trans influence