4 Ligand Field Theory

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Chemistry 3820 (Fall 2006)

2006 - Dr. Paul G. Hayes University of Lethbridge

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MO Diagrams for O2 and N2

Drawing MO diagrams - always same number of MOs as AOs.- more electronegative element on the right - lower in energy.

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2p 2p

2s2s

O OO2

2s

*2s

*2p

*2p

2p

2plarger E

O2

Paramagnetic

Bond order of 2 (O=O)

2 MOs like this -

perpendicular to each other

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2p 2p

2s2s

N NN2

2s

*2s

*2p

*2p

2p

2p

smaller E

N2

Diamagnetic

Bond order of 3 (N= N)

Very strong NN bond

Unlike O2, the 2p and 2p orbitals are

switched in energy (see next page)

HOMO = 2p, LUMO = *2p


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Ordering of MOs in O2 is2p, 2p, *2p, *2p but in N2 and CO, the order is 2p, 2p, *2p, *2p

Reason - O2 - larger E between s and p orbitals less orbital mixing

- larger E because across the period (B,C,N,O,F) more protons added to thenucleus, which pulls the electrons in closer to the nucleus (lower in energy). This

effect is felt more strongly by the s-orbitals than the p-orbitals, so the energy of

the s-orbitals drops more rapidly than that of the p-orbitals.

- N2 and CO - mixing between the 2p and the *2s orbitals raises the energy of the 2p

above the 2p.

Changes in the energy of the MOs of homonuclear diatomic molecules in the 2nd

period

MO Diagram for CO


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3

HOMO (slightly antibonding)

LUMO

2p

2p

2s

2s

C OCO

2s

*2s

*2p

*2p

2p

2p

- CO is isoelectronic with N2 (C has one less electron than N, O has one more) MO diagram isvery similar to that of N2.

- Diamagnetic, Bond order of 3 (C= O)

- Important: HOMO = 2p (weakly antibonding), LUMO = *2p (strongly antibonding)

- Since O is far more electronegative than C, would expect a large dipole moment with - on O.

However, CO actually has only a small dipole moment (0.1 Debye) with the

- on Carbon!Usually electronegativities are a good indication of the direction and magnitude of the dipole ona molecule, but especially in molecules where orbitals with antibonding character are occupied,things are not so straightforward.


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Pictorial Representations of Possible Bonds


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MO theory ~ Ligand Field Theory

Constructing an MO diagram for an octahedral complex

Symmetry Adapted combinations of Ligand -orbitals in an Octahedral Complex

- any combination

between t2g andligands becomes

non-bonding

- In an octahedral environment, the metal orbitals (3d, 4s, 4p for a 1st row TM) divide bysymmetry into 4 sets: s = a1g, p = t1u, axial d = eg, inter-axial d = t2g.

- The orbitals of the six ligands can be combined to give six symmetry-adapted linearcombinations which are of the correct symmetry to interact with the s, 3 x p and 2 x axial-d

orbitals, but not the inter-axial d orbitals.

- The result is that 3 orbitals (the inter-axial d-orbitals) are non-bonding, while the rest (6 metalorbitals and 6 ligand orbitals) combine to form six bonding and six anti-bonding MOs. Seenext page.

- This is a much more correct approach than crystal field theory, but is not as easy to use.


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MO energy levels for an octahedral complex

(only -bonding considered)

3d (eg + t2g)

4s (a1g)

4p (t1u)

O

a1g

eg*

t2g

t1u

eg

a1g*

t1u*

6 L

(a1g + t1u + eg)

TM

The six bonding orbitals are filled with 12 electrons from the six ligands

Orbitals shown in red (t2g and eg*) are the frontier orbitals where d-electrons reside(which is why TM MOs are often simplified to show only t2g and eg

* orbitals).


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-bonding ligands

(the above MO diagram does not take into account -bonding)

For -acceptor ligands, the bonding is SYNERGIC: -donation to the metal strengthens

-backbonding to the ligand, and -donation from the metal to the ligand strengthens the-donor component of bonding.

This is because -donation leads to increased electron density on the metal, which allows

increased -backdonation. Conversely, -backdonation reduces the amount of electron

density on the metal, which allows more -donation from the ligand to the metal.

Cr(CO)6: Octahedral complex with good -acceptor ligands

OCM

M C O

M C O

-interaction -interaction

lobe ofacceptor orbital(whole orbitalnot shown)

slightly antibondingHOMO of CO

axial d-orbitals strongly antibonding* orbitals of CO

M

L

L M L

-donor

-donor -acceptor

filled orbital empty orbital

NH3, CH3-, H-

Cl-, OH-, NR2-, OH2 CO, NO

+, CN-

M LM LM


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3d (eg + t2g)

4s (a1g)

4p (t1u)

O

a1g

eg*

t2g

t1u

eg

a1g*

t1u*

6 CO

large

(a1g + t1u + eg)

* orbitals of CO (t2g)

Cr

MO energy levels for an octahedral complex

with -acceptor ligands (e.g. [Cr(CO)6])

t2g*

-backdonation to CO from the t2g orbitals (which are non-bonding in the absence of-interactions between the metal and the ligands).

The 3 t2g orbitals and 3 high lying * orbitals of the CO ligands form 3 bonding MOs and

3 antibonding MOs.

Since the CO * orbitals are empty, the d-electrons occupy the bonding MO from thisinteraction.

The result is (1) a very large o, so the eg* orbital is likely to remain empty.

(2) the t2g orbital is strongly bonding (wants to be filled with 6 electrons)

complexes of strong -acceptor ligands are the most likely to obey the 18 electron rule


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Symmetry Adapted Linear Combinations of* orbitals in ML6 complexes

Q. Why are there only three ligand -acceptor orbitals shown in the MO diagram for CO when

there are 6 ligands, each with two empty * orbitals?

A. The 12 * orbitals of the ligands can be combined to form 12 symmetry adapted linear

combinations of atomic orbitals (3 x T1u, 3 x T2g, 3 x T1g and 3 x T2u). Only the three T2g linearcombinations are of the correct symmetry to interact with the t2g orbitals (dxy, dxz, dyz) on themetal.


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Simplified picture of how -acceptor and -donor interactions

affect the MO diagram - Only the frontier orbitals are shown

O

eg*

t2g

large

* (t2g)

[Cr(CO)6]with -backdonation

from Cr to CO

eg*

t2g*

O

small

TM complex with -donation from

Ligand to Metal

eg*

t2g

eg*

t2g*

t2g

t2g-acceptor ligands

increase O

-donor ligands

decrease O

TM complex with-bonding only

L

L

TM complex with

-bonding only

-donor ligands

-donation from the ligands to the t2g orbitals the 3 t2g metal orbitals and 3 low lying, filledligand orbitals of -symmetry form 3 bonding MOs and 3 antibonding MOs (thus t2g is

lowered and o increases).

Since the interacting ligand orbitals are full, these electrons occupy the bonding MO from thisinteraction, and the d-electrons occupy the antibonding MO.

The result is (1) a small o

(2) the t2g orbital is weakly antibonding


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MO Diagram for a Tetrahedral Complex

e.g. [Ni(PPh3)4] (Ni0, d10, 18-electron complex)

3d (eg + t2g)

4s (a1g)

4p (t1u)

a1

e

t2*

t2

a1*

t2*

Ni

(a1g + t1u + eg)

t t ~ 4/9 o

4 PPh3


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Hard and Soft Acids and Bases

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4 Ligand Field Theory