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SALCS for Common Geometries (bonding)
CN = 2
SALCS for Common Geometries (bonding)
EC3v
CN = 3
A1
SALCS for Common Geometries (bonding)CN = 3
SALCS for Common Geometries (bonding)
CN = 4
SALCS for Common Geometries (bonding)
CN = 4
D4h
B1g
Eu
A1g
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 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
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
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-
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
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
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
LUMO
4d (a1g , b1g , b2g , eg)eg
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
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 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
Construction of SALCs for bonding in Td complexes
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
dx2-y2dz2 dx -ydz
dx2-y2dz2 dx -ydz
dx2-y2dz2 dx -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.