SALCS for Common Geometries (bonding)
CN = 2
SALCS for Common Geometries (bonding)
CN = 3
C 3v
E
A1
SALCS for Common Geometries (bonding)
CN = 3
SALCS for Common Geometries (bonding)
CN = 4
SALCS for Common Geometries (bonding)
CN = 4
D 4h
B1g
Eu
A 1g
SALCS for Common Geometries (bonding)
CN = 5
SALCS for Common Geometries (bonding)
CN = 6
Construction of MO diagrams for Transition Metal Complexes
 bonding only scenario
Example: Constructing a MO for
Hexammine Ruthenium, [Ru(NH
, [ ( 3)6]2+
2+
NH3
H3N
H3N
NH3
NH3
Ru
NH3
point g
p
group
p = Oh
Oh
E
6
A 1g
A 2g
Eg
T 1g
T 2g
A 1u
A 2u
Eu
T 1u
T 2u
6
6
12
18
18
6
6
12
18
18
8C 3 6C 2 6C 4 3C 2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
12
-12
0
12
-12
12
-12
0
12
-12
2
h = 48
i 6S 4 8S 6 3
0
6 0
6 0
12 0
-6 0
-6 0
6 0
6 0
12 0
-6
0
-6
0
0
0
0
0
0
0
0
0
0
0
0
0
h
4
6
/h
d
Ru bonding AOs
2
0
12 12
0
12 -12
0
24 0
0 -12 -12
0 -12 12
0 -12 -12
0 -12 12
0 -24 0
0
12 12
0
12 -12
48
0
48
0
0
0
0
0
48
0
1
0
1
0
0
0
0
0
1
0
A1g : 5s
T1u : (5px , 5py , 5pz)
Eg : (4dx2‐y2 , 4dz2 )
Pd non‐bonding AOs
T2g : (4dxy, 4dxz, 4dyz)
Ru2+
H3N
H3N
2+
NH3
NH3
Ru NH3
NH3
6NH3
Eg
T 1u
A 1g
dz2
dx2-y2
Ru2+
H3N
H3N
2+
NH3
NH3
Ru NH3
NH3
6NH3
p ((t1u)
5p
Eg
5s (a1g)
T 1u
4d (t2g , eg)
dz2
A 1g
dx2-y2
eg
t1u
a1g
Ru2+
H3N
H3N
2+
NH3
NH3
Ru NH3
NH3
6NH3
p ((t1u)
5p
Eg
5s (a1g)
T 1u
4d (t2g , eg)
dz2
A 1g
dx2-y2
eg
t1u
a1g
Eg
T 1u
A 1g
dz2
dx2-y2
Ru2+
H3N
H3N
2+
NH3
NH3
Ru NH3
6NH3
NH3
t1u*
p ((t1u)
5p
a1g*
Eg
5s (a1g)
T 1u
4d (t2g , eg)
dz2
A 1g
dx2-y2
eg
t1u
t1u
a1g
a1g
Eg
T 1u
A 1g
dz2
dx2-y2
Eg
T 1u
A 1g
dz2
dx2-y2
Ru2+
H3N
H3N
2+
NH3
NH3
Ru NH3
NH3
6NH3
t1u*
p ((t1u)
5p
a1g*
Eg
5s (a1g)
T 1u
eg*
4d (t2g , eg)
dz2
A 1g
t2g
dx2-y2
eg
eg
t1u
a1g
t1u
a1g
Ru2+
H3N
H3N
2+
NH3
NH3
Ru NH3
NH3
6NH3
t1u*
p ((t1u)
5p
a1g*
Eg
5s (a1g)
LUMO
T 1u
eg*
O
4d (t2g , eg)
A 1g
t2g
HOMO
dz2
dx2-y2
eg
eg
t1u
a1g
t1u
a1g
Example: Constructing a MO for
2‐
Platinum Tetrachloride, [PtCl
,[
]
4
d
h = 16
D 4h
A 1g
A 2g
B1gg
B2g
Eg
A 1u
A 2u
B1u
B2u
Eu
E 2C 4
C 2 2C 2' 2C 2'' i 2S 4
4
0
4
4
4
4
8
4
4
4
4
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
-4
4
-4
0
4
-4
4
-4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
h
4
4
4
4
4
-8
-4
-4
-4
-4
8
2
2
4
-4
4
-4
0
-4
4
-4
4
0
v
2
/h
d
Pt bonding AOs
0
0
0
0
0
0
0
0
0
0
0
16
0
16
0
0
0
0
0
0
16
1
0
1
0
0
0
0
0
0
1
A1g : 5s , 4dz2
Eu : (5px , 5py)
B1g : 4dx2‐y2
Pd non‐bonding AOs
A2u : 5pz
B2gg : 4dxy
Eg : (4dxz, 4dyz)
Pt2+
pz
Cl
Cl
Cl
Pt Cl
24Cl-
Pt2+
Cl
Cl
Cl
Pt Cl
24Cl-
5p (a2u , eu)
pz
5s (a1g)
4d (a1g , b1g , b2g , eg)
b1g
eu
a1g
Pt2+
Cl
Cl
Cl
Pt Cl
24Cl-
a1g*
5p (a2u , eu)
pz
5s (a1g)
4d (a1g , b1g , b2g , eg)
b1g
eu
a1gg
a1g
Pt2+
Cl
Cl
Cl
Pt Cl
24Cl-
a1g*
5p (a2u , eu)
pz
5s (a1g)
a1g*
4d (a1g , b1g , b2g , eg)
b1g
eu
a1gg
a1g
Pt2+
Cl
Cl
Cl
Pt Cl
24Cl-
a1g*
5p (a2u , eu)
pz
5s (a1g)
a1g*
4d (a1g , b1g , b2g , eg)
b1g
eu
a1gg
a1g
Pt2+
Cl
Cl
Cl
Pt Cl
24Cl-
eu*
a1g*
5p (a2u , eu)
pz
5s (a1g)
a1g*
4d (a1g , b1g , b2g , eg)
b1g
eu
eu
a1g
a1gg
Pt2+
Cl
Cl
Cl
Pt Cl
24Cl-
eu*
a1g*
5p (a2u , eu)
pz
5s (a1g)
b1g*
a1g*
4d (a1g , b1g , b2g , eg)
b1g
b1g
eu
a1g
eu
a1gg
Pt2+
Cl
Cl
Cl
Pt Cl
24Cl-
eu*
a1g*
5p (a2u , eu)
pz
5s (a1g)
b1g*
a1g*
4d (a1g , b1g , b2g , eg)
b2g
eg
b1g
b1g
eu
a1g
eu
a1gg
Pt2+
Cl
Cl
Cl
Pt Cl
24Cl-
eu*
a1g*
5p (a2u , eu)
pz
5s (a1g)
a2u
2
b1g*
a1g*
4d (a1g , b1g , b2g , eg)
b2g
eg
b1g
b1g
eu
a1g
eu
a1gg
Pt2+
Cl
Cl
Cl
Pt Cl
24Cl-
eu*
a1g*
5p (a2u , eu)
pz
5s (a1g)
a2u
2
b1g*
a1g*
4d (a1g , b1g , b2g , eg)
b2g
eg
b1g
b1g
eu
a1g
eu
a1gg
Pt2+
Cl
Cl
Cl
Pt Cl
24Cl-
eu*
a1g*
5p (a2u , eu)
LUMO
pz
a2u
2
b1g*
5s (a1g)

a1g*
HOMO
4d (a1g , b1g , b2g , eg)
b2g
eg
b1g
b1g
eu
a1g
eu
a1gg
Example: Constructing a MO for Tetrakis(triphenylphosphine)Palladium, Pd(PPh
( p
yp p
)
, (
3)4
Pd bonding AOs
A1 : 6s
T2 : (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.
atom This requires that it be everywhere positive and
unchanged by all symmetry operations
A1  1 + 2 + 3 + 4
4
2
3
1
Construction of SALCs for  bonding in Td complexes
•
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 and
negative amplitude where the p orbitals are negative.
negative
1 ‐ 2 + 3 ‐ 4
1 ‐ 2 ‐ 3 + 4
T2
1 + 2 ‐ 3 ‐ 4
4
2
1
3
Construction of SALCs for  bonding in Td complexes
AOs
dxy
SALCs
T2
(1 node)
MOs
T2
(1 node)
dyz
dxz
dz2
dx2-dy2
dz2
dx2-y2
PPh3
Pd
Pd0
Ph3P
PPh3
PPh3
6PPh3
6p (t2)
6s (a1)
5d (t2 , e)
dz2
dx2-y2
t2
a1
dz2
dx2-y2
dz2
dx2-y2
dz2
dx2-y2
dz2
dx2-y2
dz2
dx2-y2
dz2
dx2-y2
dz2
dx2-y2
The tetrahedral geometry is electronically
favored by d4 or d10 metal complexes
where the non‐bonding orbitals are either
1/2 or entirely filled, respectively.
LUMO
HOMO
t
dz2
dx2-y2
The tetrahedral geometry is electronically
favored by d4 or d10 metal complexes
where the non‐bonding orbitals are either
1/2 or entirely filled, respectively.