Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding...

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Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20

Transcript of Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding...

Page 1: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

Coordination Chemistry: Bonding Theories

Molecular Orbital Theory

Chapter 20

Coordination Chemistry: Bonding Theories

Molecular Orbital Theory

Chapter 20

Page 2: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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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 ∆.

Page 3: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

1. Introduction to Molecular Orbital Theory

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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

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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

Page 5: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

3. interactions

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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:

Page 6: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

3. interactions

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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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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

Page 8: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

3. interactions

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z

yx

Point Group: Oh

red. rep. () = a1g + eg + t1u

6 irreducible representations as we expected

Page 9: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Page 10: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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.

Page 11: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Page 12: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

a1g Symmetry

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Bonding Molecular Orbital Antibonding Molecular Orbital

Zero Nodes Six Nodal Planes

Page 13: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Page 14: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Page 16: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Page 19: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

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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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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

Page 24: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

3C. Molecular Orbital Diagram for σ interaction

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*

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

3d

Page 25: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Page 26: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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*

Page 27: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

The Spectrochemical Series

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I- < Br - < [NCS]- < Cl- < F- < [OH]- < [ox]2- ~ H2O < [NCS]- < NH3 < en < [CN]- ~ CO

σ donors π donors π acceptors

M L

dπ pπ

Page 28: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Page 29: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Page 30: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Page 31: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Page 32: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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*)

Page 33: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Page 34: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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Molecular Orbital Diagram including π interaction with Weak Field Ligands

Page 35: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

Molecular Orbital Diagram including π interaction with Weak Field Ligands

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Page 36: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

Molecular Orbital Diagram including π interaction with Weak Field Ligands

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[CoF6]3-

Co3+ ; d6

High spin, S = 2

Page 37: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Page 38: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Page 39: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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Molecular Orbital Diagram including π interaction with Strong Field Ligands

Page 40: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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Molecular Orbital Diagram including π interaction with Strong Field Ligands

Page 41: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Co3+ ; d6

Low spin, S = 0

Page 42: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Page 43: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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

Page 44: Coordination Chemistry: Bonding Theories Molecular Orbital ......Coordination Chemistry: Bonding Theories Molecular Orbital Theory Chapter 20 2 Review of the Previous Lecture 1. Discussed

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