Metal-ligand s interactions in an octahedral environment

1
Metal-ligand s interactions in an octahedral
environment
Six ligand orbitals of s symmetry approaching the
metal ion along the x,y,z axes
We can build 6 group orbitals of s symmetry as
before and work out the reducible representation
2
s
If you are given G, you know by now how to get
the irreducible representations G A1g T1u
Eg
3
Now we just match the orbital symmetries
s
4
d0-d10 electrons
6 s ligands x 2e each
5
Introducing p-bonding
2 orbitals of p-symmetry on each ligand
We can build 12 group orbitals of p-symmetry
6
Gp 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.
7
Anti-bonding LUMO(p)
First, the CN- ligand
8
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.
9
ML6 s-only bonding
d0-d10 electrons
The bonding orbitals, essentially the ligand lone
pairs, will not be worked with further.
6 s ligands x 2e each
10
p-bonding may be introduced as a perturbation of
the t2g/eg set Case 1 (CN-, CO, C2H4) empty
p-orbitals on the ligands M?L p-bonding (p-back
bonding)
These are the SALC formed from the p orbitals of
the ligands that can interac with the d on the
metal.
t2g (p)
t2g
eg
eg
t2g
t2g (p)
ML6 s-only
ML6 s p
(empty p-orbitals on ligands)
11
p-bonding may be introduced as a perturbation of
the t2g/eg set. Case 2 (Cl-, F-) filled
p-orbitals on the ligands L?M p-bonding
eg
eg
t2g (p)
t2g
t2g
t2g (p)
ML6 s-only
ML6 s p
(filled p-orbitals)
12
Putting it all on one diagram.
13
Spectrochemical Series
Purely s ligands D en gt NH3 (order of proton
basicity)

• donating which decreases splitting and causes
  high spin
• D H2O gt F gt RCO2 gt OH gt Cl gt Br gt I (also proton
  basicity)

p accepting ligands increase splitting and may be
low spin
D CO, CN-, gt phenanthroline gt NO2- gt NCS-
14
Merging to get spectrochemical series
CO, CN- gt phen gt en gt NH3 gt NCS- gt H2O gt F- gt
RCO2- gt OH- gt Cl- gt Br- gt I-
Weak field, p donors small D high spin
Strong field, p acceptors large D low
spin
s only
15
Turning to Square Planar Complexes
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.
16
ML4 square planar complexes ligand group orbitals
and matching metal orbitals
s bonding
p bonding (in)
p bonding (perp)
17
ML4 square planar complexes MO diagram
eg
s-only bonding
18
A crystal-field aproach from octahedral to
tetrahedral
Less repulsions along the axes where ligands are
missing
19
A crystal-field aproach from octahedral to
tetrahedral
20
The Jahn-Teller effect
Jahn-Teller theorem there cannot be unequal
occupation of orbitals with identical energy
Molecules will distort to eliminate the degeneracy
21
(No Transcript)
22
Angular Overlap Method
An attempt to systematize the interactions for
all geometries.
The various complexes may be fashioned out of the
ligands above
Linear 1,6 Trigonal 2,11,12 T-shape 1,3,5
Square pyramid 1,2,3,4,5 Octahedral 1,2,3,4,5,6
Tetrahedral 7,8,9,10 Square planar
2,3,4,5 Trigonal bipyramid 1,2,6,11,12
23
Contd
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.
24
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.