Example: Constructing a ‐only MO diagramfor Iron Pentacarbonyl, Fe(CO)5y , ( )5

D3h

Example: Constructing a MO forIron Pentacarbonyl, Fe(CO)5y , ( )5

Example: Constructing a MO forIron Pentacarbonyl, Fe(CO)5y , ( )5

Fe bonding AOsFe bonding AOs

A1‘  :  4s , 3dz2

E‘    :  (4px , 4py ) (3dx2‐y2, 3dxy)

A2‘’ :  (4pz)

Fe non‐bonding AOs

E‘’   :  (3dxz, 3dyz)

a2''

e'

a1' a1'

Fe0 5CO

CO

FeOCCOCO

CO

4p (a2'', e')

a2''

4s (a1')

4p (a2 , e )

e'

3d (a1' , e', e'')a1'*

a1' a1'

a2''

e'

a1' 2a1'a1 , 2a1

a1'

Fe0 5CO

CO

FeOCCOCO

CO

4p (a2'', e')

a2''

4s (a1')

p ( 2 , )2a1'*

e'

3d (a1' , e', e'')a1'*

a1' a1'

a2''

e'

a1', 2a1'a1 , 2a1

a1'2a1'

Fe0 5CO

CO

FeOCCOCO

CO

4p (a2'', e')

a2''

4s (a1')

p ( 2 , )2a1'*

e'*

e'

3d (a1' , e', e'')a1'*

ea1' a1'

a2''

e'

a1', 2a1'e' a1 , 2a1

a1'

e

2a1'

Fe0 5CO

CO

FeOCCOCO

CO

4p (a2'', e')

a2''*

a2''

4s (a1')

p ( 2 , )2a1'*

e'*

e'

3d (a1' , e', e'')a1'*

ea1' a1'

a2''

e'

a1', 2a1'

a2''

e' a1 , 2a1

a1'

e

2a1'

Fe0 5CO

CO

FeOCCOCO

CO

4p (a2'', e')

a2''*

e'* a2''

4s (a1')

p ( 2 , )2a1'*

e'*

e'

3d (a1' , e', e'')e''

a1'*

ea1' a1'

a2''

e'

a1', 2a1'

a2''

e' a1 , 2a1

a1'

e

2a1'

Fe0 5CO

CO

FeOCCOCO

CO

4p (a2'', e')

a2''*

e'* a2''

4s (a1')

4p (a2 , e )2a1'*

e'*

e'

3d (a1' , e', e'')e''

a1'*

ea1' a1'

a2''

e'

a1' 2a1'

a2''

e' a1 , 2a1

a1'

e

2a1'

Fe0 5CO

CO

FeOCCOCO

CO

4p (a2'', e')

a2''*

e'* a2''

LUMO

4s (a1')

p ( 2 , )2a1'*

e'*

e'

HOMO

LUMO

3d (a1' , e', e'')e''

a1'*

ea1' a1'

HOMO

a2''

e'

a1', 2a1'

a2''

e' a1 , 2a1

a1'

e

2a1'

Fe0 5CO

CO

FeOCCOCO

CO

4p (a2'', e')

a2''*

e'* a2''

4s (a1')

p ( 2 , )2a1'*

e'*

e'

3d (a1' , e', e'')e''

a1'*

ea1' a1'

a2''

e'

a1', 2a1'

a2''

e' a1 , 2a1

a1'

e

2a1'

a2''

e'

a1' a1'

Construction of MO diagrams for Transition Metal Complexes

bonding complexes

Example: Constructing a MO forChromium Hexacarbonyl, Cr(CO)6y , ( )6

Example: Constructing a MO forChromium Hexacarbonyl, Cr(CO)6y , ( )6

Oh E 8C3 6C2 6C4 3C2 i 6S4 8S6 3 h 6 d /h

h = 48

h 3 2 4 2 4 6 h d

12 0 0 0 -4 0 0 0 0 0

A1 12 0 0 0 -12 0 0 0 0 0 0 0A1g 12 0 0 0 -12 0 0 0 0 0 0 0A2g 12 0 0 0 -12 0 0 0 0 0 0 0Eg 24 0 0 0 -24 0 0 0 0 0 0 0T1g 36 0 0 0 12 0 0 0 0 0 48 1T2g 36 0 0 0 12 0 0 0 0 0 48 1A1u 12 0 0 0 -12 0 0 0 0 0 0 0A2u 12 0 0 0 -12 0 0 0 0 0 0 0Eu 24 0 0 0 -24 0 0 0 0 0 0 0uT1u 36 0 0 0 12 0 0 0 12 0 48 1T2u 36 0 0 0 12 0 0 0 12 0 48 1

d

Example: Constructing a MO forChromium Hexacarbonyl, Cr(CO)6y , ( )6

• Cr ‐bonding AOs

T2g : (3dxy, 3dxz, 3dyz)

T1u : (4px , 4py , 4pz)

• T2g previously considered non‐bonding in ‐bondingschemescheme

• T1u combines with T1u SALC in in ‐bonding scheme

• T1g , T2u ‐SALCs are non‐bonding

• T AOs overlap more effectively with T SALC thus the bonding interaction is• T1u AOs overlap more effectively with T1u ‐SALC thus the ‐bonding interaction isconsidered negligible or at most only weakly‐bonding.

dx2-y2dz2

T2g3 x

dx2-y2dz2

T2g3 x

dx2-y2dz2

T2g3 x

dx2-y2dz2

T2g3 x

LUMO

O

dx2-y2dz2 HOMO

Dewar‐Chatt‐Duncanson model

v(CO)  cm‐1

[Ti(CO)6]2‐ 1748

[V(CO)6]‐ 1859 

( )Cr(CO)6 2000

[Mn(CO)6 ]+ 2100

[Fe(CO)6 ]2+ 2204[Fe(CO)6 ] 2204

Summary of ‐bonding in Oh complexes

donor ligands result in L→M bonding, a smaller o favoring high spinconfigurations and a decreased stability.

acceptor ligands result in M→L bonding, a larger ofavoring low spin configurations with an increasedstability.

Example: Constructing MOs for Titanium Tetraisopropoxide, Ti(OiPr)4p p , ( )4

O

TiO O

O

OiPr

TiiPrO OiP

OiPrO

point group = Td

OiPr

z

x

y

Example: Constructing MOs for Titanium Tetraisopropoxide, Ti(OiPr)4p p , ( )4

OiPr

h = 24

TiiPrO OiPr

OiPr

Td E 8C3 3C2 6S4 6 d /h

8 -1 0 0 0

point group = Td

z

A1 8 -8 0 0 0 0 0A2 8 -8 0 0 0 0 0E 16 8 0 0 0 24 1

x

E 16 8 0 0 0 24 1T1 24 0 0 0 0 24 1T2 24 0 0 0 0 24 1

y

Example: Constructing MOs for Titanium Tetraisopropoxide, Ti(OiPr)4p p , ( )4

Th OiP SALC i d f fill d d bit l th O t• The OiPr SALCs are comprised of filled px and py orbitals on the O atoms.

• Ti bonding AOs

E : (3dz2, 3dx2‐y2) E :  (3dz , 3dx y )

T2 : (4px , 4py , 4pz)

(3dxy, 3dxz, 3dyz)

• The T1 SALC is non‐bonding.

• Significant overlap occurs between the E SALC and the e AOs on Ti (3dz2, 3dx2‐y2)

• As the 4p AOs on Ti (t2) are primarily involved in ‐bonding we will assume that they have negligible ‐interaction here.

[It is very likely that there is extensive d‐pmixing involved in this system.]

Ti+4 4 OiPr

OiPr

TiiPrO OiPr

OiPr

4p (t2)

t2*

a1*

4s (a1) t2*

3d (t2 , e)

e, t1 , t2e

a1

t2

t

dx2-y2dz2

a1

t2

Ti+4 4 OiPr

OiPr

TiiPrO OiPr

OiPr

4p (t2)

t2*

a1*

4s (a1) t2*

3d (t2 , e)

e, t1 , t2e

a1

t2

t

dx2-y2dz2

a1

t2

Ti+4 4 OiPr

OiPr

TiiPrO OiPr

OiPr

4p (t2)

t2*

a1*

4s (a1)

e*

t2*

3d (t2 , e)

e, t1 , t2

a1

t2

t

e

dx2-y2dz2

a1

t2

Ti+4 4 OiPr

OiPr

TiiPrO OiPr

OiPr

4p (t2)

*

t2*

a1*

4s (a1)

e*

t2

3d (t2 , e)

e, t1 , t2

a1

t2

t

e

t2

dx2-y2dz2

a1

t2

Ti+4 4 OiPr

OiPr

TiiPrO OiPr

OiPr

4p (t2)

*

t2*

a1*

4s (a1)

e*

t2

3d (t2 , e)

e, t1 , t2t1

a1

t2

t

e

t2

dx2-y2dz2

a1

t2

Ti+4 4 OiPr

OiPr

TiiPrO OiPr

OiPr

4p (t2)

*

t2*

a1*

4s (a1)

e*

t2

3d (t2 , e)

e, t1 , t2t1

a1

t2

t

e

t2

a1

t2

dx2-y2dz2