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Metal-ligand s interactions in an octahedral environment
Six ligand orbitals of s symmetry approaching the metal ion along the x,y,z axes
z
M
We can build 6 group orbitals of s symmetry as before
and work out the reducible representation
s
If you are given G, you know by now how to get the irreducible representations
G = A1g + T1u + Eg
Now we just match the orbital symmetries
s
“d0-d10 electrons”
anti bonding
“metal character”
non bonding
6 s ligands x 2e each
12 s bonding e
“ligand character”
Introducing π-bonding
2 orbitals of π-symmetry
on each ligand
We can build 12 group orbitals
of π-symmetry
Gπ = T1g + T2g + T1u + T2u
The T2g will interact with the metal d t2g orbitals. The ligand pi
orbitals do not interact with the metal eg orbitals.
We now look at things more closely.
Anti-bonding LUMO(π)
First, the CN- ligand
Some schematic diagrams showing how p bonding occurs
with a ligand having a d orbital (such as in P), or a p*
orbital, or a vacant p orbital.
ML6 s-only bonding
“d0-d10 electrons”
anti bonding
“metal character”
non bonding
6 s ligands x 2e each
The bonding orbitals, essentially the ligand lone pairs,
12 s bondingwill
e
not be worked with further.
“ligand character”
π-bonding may be introduced
as a perturbation of the t2g/eg set:
Case 1 (CN-, CO, C2H4)
empty π-orbitals on the ligands
ML π-bonding (π-back bonding)
t2g (π*)
These are the SALC
formed from the p
orbitals of the ligands
that can interac with
the d on the metal.
t2g
eg
eg
Do
D’o
Do has increased
t2g
Stabilization
t2g (π)
ML6
s-only
ML6
s+π
(empty π-orbitals on ligands)
π-bonding may be introduced
as a perturbation of the t2g/eg set.
Case 2 (Cl-, F-)
filled π-orbitals on the ligands
LM π-bonding
eg
Do has decreased
eg
D’o
t2g (π*)
Do
Destabilization
t2g
t2g
Stabilization
t2g (π)
ML6
s-only
ML6
s+π
(filled π-orbitals)
Putting it all on one
diagram.
Strong field / low spin
Weak field / high spin
Spectrochemical Series
Purely s ligands:
D: en > NH3 (order of proton basicity)
p donating which decreases splitting and causes high spin:
D: H2O > F > RCO2 > OH > Cl > Br > I (also proton basicity)
p accepting ligands increase splitting and may be low spin
D: CO, CN-, > phenanthroline > NO2- > NCS-
Merging to get spectrochemical series
CO, CN- > phen > en > NH3 > NCS- > H2O > F- > RCO2- > OH- > Cl- > Br- > I-
Strong field,
p acceptors
large D
low spin
s only
Weak field,
p donors
small D
high spin
Turning to Square Planar Complexes
z
y
x
Most convenient to use a local coordinate
system on each ligand with
y pointing in towards the metal. py to be used
for s bonding.
z being perpendicular to the molecular plane. pz
to be used for p bonding perpendicular to the
plane, p^.
x lying in the molecular plane. px to be used
for p bonding in the molecular plane, p|.
ML4 square planar complexes
ligand group orbitals and matching metal orbitals
s bonding
p bonding (in)
p bonding
(perp)
ML4 square planar complexes
MO diagram
eg
s-only bonding
Sample bonding
Angular Overlap Method
An attempt to systematize the interactions for all geometries.
1
1
4
M
7
8
3
11
M
M
2
9
5
6
2
12
10
6
The various complexes may be fashioned out of the ligands
above
Linear: 1,6
Tetrahedral: 7,8,9,10
Trigonal: 2,11,12 Square planar: 2,3,4,5
T-shape: 1,3,5
Trigonal bipyramid: 1,2,6,11,12
Square pyramid: 1,2,3,4,5
Octahedral: 1,2,3,4,5,6
Cont’d
All s interactions with the ligands are stabilizing to the
ligands and destabilizing to the d orbitals. The interaction of a
ligand with a d orbital depends on their orientation with
respect to each other, estimated by their overlap which can be
calculated.
The total destabilization of a d orbital comes from all the
interactions with the set of ligands.
For any particular complex geometry we can obtain the
overlaps of a particular d orbital with all the various ligands
and thus the destabilization.
ligand
dz2
dx2-y2
dxy
dxz
dyz
1
1 es
0
0
0
0
2
¼
¾
0
0
0
3
¼
¾
0
0
0
4
¼
¾
0
0
0
5
¼
¾
0
0
0
6
1
0
0
0
0
7
0
0
1/3
1/3
1/3
8
0
0
1/3
1/3
1/3
9
0
0
1/3
1/3
1/3
10
0
0
1/3
1/3
1/3
11
¼
3/16
9/16
0
0
12
1/4
3/16
9/16
0
0
Thus, for example a dx2-y2 orbital is destabilized by (3/4 +6/16) es
= 18/16 es in a trigonal bipyramid complex due to s interaction.
The dxy, equivalent by symmetry, is destabilized by the same
amount. The dz2 is destabililzed by 11/4 es.