4 ligand field theory (1)

Hayes – University of Lethbridge MO theory ~ Ligand Field Theory Constructing an MO diagram for an octahedral complex Symmetry Adapted combinations of Ligand σ-orbitals in an Octahedral

© 2006 - Dr Paul G Hayes – University of Lethbridge

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 -

2s 2s

σ 2s

σ *2s

σ *2p

π *2p

π 2p

σ2p

larger ∆ E

Bond order of 2 (O=O)

2 MOs like this -perpendicular to each other

-

2s 2s

σ 2s

σ *2s

σ *2p

π *2p

π 2p

σ 2p

smaller ∆ E

Bond order of 3 (N= N) Very strong NN bond

Unlike O2, the σ2p and π2p orbitals are switched in energy (see next page) HOMO = σ2p, LUMO = π*2p

Ordering of MOs in O2 is σ2p, π2p, π*2p, σ*2p but in N2 and CO, the order is π2p, σ2p, π*2p, σ*2p

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

- larger ∆E because across the period (B,C,N,O,F) more protons added to the nucleus, 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 σ2p and the σ*2s orbitals raises the energy of the σ2p

above the π2p

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

MO Diagram for CO

© 2006 - Dr Paul G Hayes – University of Lethbridge

HOMO (slightly antibonding)

LUMO 2p

2p

2s 2s

σ 2s

σ *2s

σ *2p

π *2p

π 2p

σ 2p

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

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

- Important: HOMO = σ2p (weakly antibonding), LUMO = π*2p (strongly antibonding)

- Since O is far more electronegative than C, would expect a large dipole moment with δ- on O However, CO actually has only a small dipole moment (0.1 Debye) with the δ- on Carbon! Usually electronegativities are a good indication of the direction and magnitude of the dipole on

a molecule, but especially in molecules where orbitals with antibonding character are occupied, things are not so straightforward

Pictorial Representations of Possible Bonds

© 2006 - Dr Paul G Hayes – University of Lethbridge

MO theory ~ Ligand Field Theory Constructing an MO diagram for an octahedral complex

Symmetry Adapted combinations of Ligand σ-orbitals in an Octahedral Complex

- any combination between t2g and ligands becomes non-bonding

- In an octahedral environment, the metal orbitals (3d, 4s, 4p for a 1st row TM) divide by symmetry 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 linear combinations 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 metal orbitals and 6 ligand orbitals) combine to form six bonding and six anti-bonding MOs See next page

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

MO energy levels for an octahedral complex

(only σ-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)

© 2006 - Dr Paul G Hayes – University of Lethbridge

π-bonding ligands

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

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

π-backbonding to the ligand, and π-donation from the metal to the ligand strengthens the

σ-donor component of bonding

• This is because σ-donation leads to increased electron density on the metal, which allows increased π-backdonation Conversely, π-backdonation reduces the amount of electron density on the metal, which allows more σ-donation from the ligand to the metal

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

O C M

lobe of

acceptor orbital

(whole orbital

not shown)

slightly antibonding HOMO of CO

axial d-orbitals strongly antibonding

π * orbitals of CO

M

L

σ -donor

filled orbital empty orbital

NH3, CH3-, H

-Cl-, OH-, NR 2-, OH 2 CO, NO+, CN

3d (eg + t2g)

4s (a1g)

4p (t1u)

∆ O

a1g

eg*

t2g

t1u

eg

a1g*

t1u*

6 CO

large

(a1g + t1u + eg)

π * orbitals of CO (t2g)

Cr

MO energy levels for an octahedral complex

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

t2g*

• π-backdonation to CO from the t2g orbitals (which are non-bonding in the absence of

π-interactions between the metal and the ligands)

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

3 antibonding MOs

• Since the CO π* orbitals are empty, the d-electrons occupy the bonding MO from this interaction

• 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)

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

© 2006 - Dr Paul G Hayes – University of Lethbridge

Symmetry Adapted Linear Combinations of π* orbitals in ML6 complexes

Q Why are there only three ligand π-acceptor orbitals shown in the MO diagram for CO when there are 6 ligands, each with two empty π* orbitals ?

A The 12 π* 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 linear combinations are of the correct symmetry to interact with the t2g orbitals (dxy, dxz, dyz) on the metal

Simplified picture of how π-acceptor and π-donor interactions affect the MO diagram - Only the frontier orbitals are shown

∆ O

eg*

t2g large

π * (t2g)

[Cr(CO) 6 ] with π -backdonation from Cr to CO

eg*

t2g*

∆ O

small

TM complex with π -donation from Ligand to Metal

eg*

t2g

eg*

t2g*

t2g

t 2g π -acceptor ligands

increase ∆O

π -donor ligands decrease ∆O

TM complex with

σ -bonding only

L

L

TM complex with

σ -bonding only

π-donor ligands

• π-donation from the ligands to the t2g orbitals à the 3 t2g metal orbitals and 3 low lying, filled ligand orbitals of π-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 this interaction, and the d-electrons occupy the antibonding MO

• The result is (1) a small ∆o

(2) the t2g orbital is weakly antibonding

© 2006 - Dr Paul G Hayes – University of Lethbridge

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)

4 PPh3

Hard and Soft Acids and Bases