salcs for common geometries...

SALCS for Common Geometries (bonding)

CN = 2


EC3v

CN = 3

A1

SALCS for Common Geometries (bonding)CN = 3


CN = 4


CN = 4

D4h

B1g

Eu

A1g

SALCS for Common Geometries (bonding)CN = 5


CN = 6

Construction of MO diagrams for Transition Metal Complexes

bonding only scenario

Example: Constructing a MO forHexammine Ruthenium, [Ru(NH3)6]2+, [ ( 3)6]

NH3

NH3

2+

RuH3N NH3

point group = Oh

H3NNH3

h 48p g p h

Ru bonding AOsOh E 8C3 6C2 6C4 3C2 i 6S4 8S6 3 h 6 d /h

6 0 0 2 2 0 0 0 4 2

h = 48

A1g : 5sT1u : (5px , 5py , 5pz)Eg : (4dx2‐y2 , 4dz2 )

A1g 6 0 0 12 6 0 0 0 12 12 48 1A2g 6 0 0 -12 6 0 0 0 12 -12 0 0Eg 12 0 0 0 12 0 0 0 24 0 48 1

Pd non‐bonding AOs

T2g : (4dxy, 4dxz, 4dyz)

gT1g 18 0 0 12 -6 0 0 0 -12 -12 0 0T2g 18 0 0 -12 -6 0 0 0 -12 12 0 0A1u 6 0 0 12 6 0 0 0 -12 -12 0 0A2u 6 0 0 -12 6 0 0 0 -12 12 0 0Eu 12 0 0 0 12 0 0 0 -24 0 0 0T1u 18 0 0 12 -6 0 0 0 12 12 48 1T2u 18 0 0 -12 -6 0 0 0 12 -12 0 0

Ru2+ 6NH3

NH3

RuH3N NH3H3N

NH3

NH3

2+

33

Eg

T

A1g

T1u

dx2-y2dz2

Ru2+ 6NH3

NH3

RuH3N NH3H3N

NH3

NH3

2+

5p (t1u)

33

5s (a1g)

p ( 1u)Eg

T

4d (t2g , eg) A1g

T1u

eg

dx2-y2dz2

a

t1u

g

a1g

Eg

T

A1g

T1u

dx2-y2dz2

Ru2+ 6NH3

NH3

RuH3N NH3H3N

NH3

NH3

2+

5p (t1u)

3

t1u*

3

5s (a1g)

p ( 1u)a1g

*Eg

T

4d (t2g , eg) A1g

T1u

eg

dx2-y2dz2

a

t1u

g

a1g

a1g

t1u

Eg

T

A1g

T1u

dx2-y2dz2

Ru2+ 6NH3

NH3

RuH3N NH3H3N

NH3

NH3

2+

5p (t1u)

3

t1u*

3

5s (a1g)

p ( 1u)a1g

*Eg

T

4d (t2g , eg) t2g

eg*

A1g

T1u

eg

dx2-y2dz2

a

t1u

g

eg

a1g

a1g

t1u

Ru2+ 6NH3

NH3

RuH3N NH3H3N

NH3

NH3

2+

5p (t1u)

3

t1u*

3

5s (a1g)

p ( 1u)a1g

*Eg

T

LUMO

4d (t2g , eg) t2g

eg*

A1g

T1u

O

eg

dx2-y2dz2

HOMO

a

t1u

g

eg

a1g

a1g

t1u

Example: Constructing a MO forPlatinum Tetrachloride, [PtCl4]2‐, [ 4]

dh 16

Pt bonding AOsD4h E 2C4 C2 2C2' 2C2'' i 2S4 h 2 v 2 d /h

4 0 0 2 0 0 0 4 2 0

h = 16

A1g : 5s , 4dz2

Eu : (5px , 5py)B1g : 4dx2‐y2

A1g 4 0 0 4 0 0 0 4 4 0 16 1A2g 4 0 0 -4 0 0 0 4 -4 0 0 0B1g 4 0 0 4 0 0 0 4 4 0 16 1

Pd non‐bonding AOsA2u : 5pzB2g : 4dxy

gB2g 4 0 0 -4 0 0 0 4 -4 0 0 0Eg 8 0 0 0 0 0 0 -8 0 0 0 0A1u 4 0 0 4 0 0 0 -4 -4 0 0 0A2u 4 0 0 -4 0 0 0 -4 4 0 0 0

gEg : (4dxz, 4dyz)B1u 4 0 0 4 0 0 0 -4 -4 0 0 0

B2u 4 0 0 -4 0 0 0 -4 4 0 0 0Eu 8 0 0 0 0 0 0 8 0 0 16 1

Pt2+ 4Cl-PtCl ClCl

Cl 2-

p z

Pt2+ 4Cl-PtCl ClCl

Cl 2-

5p (a2u , eu)

5s (a1g)p z

4d (a1g , b1g , b2g , eg)

b1g

a1g

eu

a1g

Pt2+ 4Cl-PtCl ClCl

Cl 2-

5p (a2u , eu)

a1g*

5s (a1g)p z

4d (a1g , b1g , b2g , eg)

b1g

a1g

eu

g

a1g

Pt2+ 4Cl-PtCl ClCl

Cl 2-

5p (a2u , eu)

a1g*

5s (a1g)

a1g*

p z

4d (a1g , b1g , b2g , eg)

b1g

a1g

eu

g

a1g

Pt2+ 4Cl-PtCl ClCl

Cl 2-

e *

5p (a2u , eu)

eu

a1g*

5s (a1g)

a1g*

p z

4d (a1g , b1g , b2g , eg)

b1g

a1g

eu

g

a1g

eu

Pt2+ 4Cl-PtCl ClCl

Cl 2-

e *

5p (a2u , eu)

eu

a1g*

5s (a1g)

a1g*

b1g*p z

4d (a1g , b1g , b2g , eg)

b1g

a1g

eub1g

g

a1g

eu

Pt2+ 4Cl-PtCl ClCl

Cl 2-

e *

5p (a2u , eu)

eu

a1g*

5s (a1g)

a1g*

b1g*p z

4d (a1g , b1g , b2g , eg)eg

b2g

b1g

a1g

eub1g

g

a1g

eu

Pt2+ 4Cl-PtCl ClCl

Cl 2-

e *

5p (a2u , eu)

eu

a2

a1g*

5s (a1g)

a1g*

b1g*

a2up z


b2g

b1g

a1g

eub1g

g

a1g

eu

Pt2+ 4Cl-PtCl ClCl

Cl 2-

e *

5p (a2u , eu)

eu

a2

a1g*

5s (a1g)

a1g*

b1g*

a2up z

LUMO


b2g

HOMO

b1g

a1g

eub1g

g

a1g

eu

Example: Constructing a MO for Tetrakis(triphenylphosphine)Palladium, Pd(PPh3)4( p y p p ) , ( 3)4

Pd bonding AOs

A1 : 6sT2 : (6px , 6py , 6pz)

(5dxy, 5dxz, 5dyz)

Pd non‐bonding AOs

E : (5dx2‐y2 , 5dz2 )

Construction of SALCs for bonding in Td complexes

• Consider first the A1 SALC. It must have the same symmetry of the s orbital on

the central metal atom This requires that it be everywhere positive andthe central metal atom. This requires that it be everywhere positive and

unchanged by all symmetry operations

A1 1 + 2 + 3 + 4

2

4

1

3


• The T2 SALC’s must match the symmetries of the (px , py , pz ) and (dxy, dxz, dyz)orbitals, e.g. must have positive amplitude where the p orbital is positive andnegative amplitude where the p orbitals are negativenegative amplitude where the p orbitals are negative.

1 ‐ 2 + 3 ‐ 4

T2 1 ‐ 2 ‐ 3 + 42 1 2 3 4

1 + 2 ‐ 3 ‐ 4

4

2

1

3

AOs

dxy dxzdyz dz2 dx2-dy2

SALCs

T2(1 node)

T2(1 node)

MOs

dx2-y2dz2 dx -ydz

Pd0 6PPh3

PPh3

Pd PPh3Ph3P PPh3

6p (t2)

6s (a1)

5d (t2 , e)

dx2-y2dz2

a1

t2dx -ydz

dx2-y2dz2 dx -ydz

dx2-y2dz2 dx -ydz

The tetrahedral geometry is electronicallyfavored by d4 or d10 metal complexeswhere the non‐bonding orbitals are either1/2 or entirely filled, respectively.

LUMO

HOMO

dx2-y2dz2

t

dx -ydz

The tetrahedral geometry is electronicallyfavored by d4 or d10 metal complexeswhere the non‐bonding orbitals are either1/2 or entirely filled, respectively.

salcs for common geometries...

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