Lecture-April20-Molecular Orbital...

Coordination Chemistry: Bonding Theories

Molecular Orbital Theory

Chapter 20

Coordination Chemistry: Bonding Theories

Molecular Orbital Theory

Chapter 20

2

Review of the Previous Lecture

1. Discussed magnetism in coordination chemistry and the different classification of compounds with magnetic properties

2. Evaluated the magnetic susceptibility of compounds as it depends on temperature

3. Described the property of spin crossover

4. Briefly surveyed tools to characterized the magnetic properties of compounds

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.

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

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:

3. interactions

6

z

yx

Have 6 vectors to represent 6 bonds, thereforeexpect your reducible representation to be composed of6 irreducible representations

Point Group: Oh

red () = a1g + eg + t1u

Use group theory to identify the symmetry of the metal atomic orbitals and the ligand group orbitals that will be involved in bonding.

6 irreducible representations

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

3B. Ligand group orbitals engaged in interactions

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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.

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

a1g Symmetry

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Bonding Molecular Orbital Antibonding Molecular Orbital

Zero Nodes One Spherical Node

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

t1u Symmetry

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Bonding Molecular Orbital

Antibonding Molecular Orbital

One Nodal Plane

Three Nodal Planes

eg Symmetry

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The eg metal atomic orbitals and LGOs will generate two bonding molecular orbitals andtwo antibonding molecular orbitals

eg Symmetry

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Two Nodal Planes

Two Nodal Planes, One Nodal Cylinder

eg Symmetry

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Two Nodal Cylinders

Three Nodal Cylinders

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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No nodes

One node

Two nodes


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The t2g metal atomic orbitalsare nonbonding• dxy, dyz, and dxz orbitals


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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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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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*

The metal-ligand interactions stabilize themetal d electrons. Recall CFSE.

3d

3D. The 18 electron rule

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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

4. π interactions

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Consider ligand orbitals that can engage in π interactions with metals:

M L M L M L

dπ pπ dπ dπ dπ π*

The Spectrochemical Series

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M L

dπ pπ

4A. Let’s consider p ligand orbitals involved in and πinteractions with metals

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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

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 12 vectors indicate that the reducible representation will be defined by 12 irreducible

representations

Point Group: Oh

red (π) = t2g + t2u + t1u + t1g

MM

12 irreducible representationsz

y

x

4C. Focus on the t2g orbital symmetry

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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

4D. Factors to consider regarding the energy of thet2g ligand group orbitals

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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

4E. Explaining the origins of the weak field ligands

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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*)

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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Molecular Orbital Diagram including π interaction with Weak Field Ligands


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[CoF6]3-

Co3+ ; d6

High spin, S = 2

4E. Explaining the origins of the strong field ligands

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L

dπ π*

M

Consider the octahedral complex [Co(CO)6]3+:

Co3+; d6

Molecular Orbital Diagram for CO

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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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Molecular Orbital Diagram including π interaction with Strong Field Ligands

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Molecular Orbital Diagram including π interaction with Strong Field Ligands

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Molecular Orbital Diagram including π interaction with Strong Field Ligands [Co(CO)6]3+

Co3+ ; d6

Low spin, S = 0

4F. Revisiting the 18 electron rule

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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

4G. π backbonding with π acceptor ligands

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The ligand donates electrondensity to the metal through bonds

The metal donates electrondensity to the ligandthrough π bonds

dπ π*

M

4G. π backbonding with π acceptor ligands

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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

Lecture-April20-Molecular Orbital...

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