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Coordination Chemistry
Bonding in transition-metal complexes
Crystal field theory: an electrostatic model
-
+
-
-
The metal ion will be positive and therefore attract the negatively charged ligands
But there are electrons in the metal orbitals, which will experience repulsions
with the negatively charged ligands
Ligand/d orbital interactions
Orbitals point at ligands
(maximum repulsion)
Orbitals point
between ligands
(less pronounced repulsion)
The two effects of the crystal field
Splitting of d orbitals in an octahedral field
eg
3/5 Do
Do
2/5 Do
t2g
Do is the crystal field splitting
E(t2g) = -0.4Do x 3 = -1.2Do
E(eg) = +0.6Do x 2 = +1.2Do
The magnitude of the splitting
(ligand effect)
Strong
field
Weak
field
The spectrochemical series
CO, CN- > phen > NO2- > en > NH3 > NCS- > H2O > F- > RCO2- > OH- > Cl- > Br- > I-
The magnitude of the splitting
(metal ion effect)
Strong
field
Weak
field
D increases with increasing formal charge on the metal ion
D increases on going down the periodic table
The splitting constant
must depend on both the
ligand and the metal.
Do ≈ M ∑ nlLl x 103
Predicts value of D (cm-1)
nl is # of ligands Ll
Placing electrons in d orbitals
Strong field
Weak field
Strong field
Weak field
d1
d2
d3
d4
When the 4th electron is assigned it will either go into the higher
energy eg orbital at an energy cost of D0 or be paired at an energy
cost of P, the pairing energy.
d4
Strong field =
Low spin
(2 unpaired)
Weak field =
High spin
(4 unpaired)
P < Do
P > Do
Notes: the pairing energy, P, is made up of two parts. 1) Coulombic
repulsion energy caused by having two electrons in same orbital
Pairing Energy, P
The pairing energy, P, is made up of two parts.
1) Coulombic repulsion energy caused by having two electrons in
same orbital. Destabilizing energy contribution of Pc for each
doubly occupied orbital.
2) Exchange stabilizing energy for each pair of electrons having the
same spin and same energy. Stabilizing contribution of Pe for
each pair having same spin and same energy
P = sum of all Pc and Pe interactions
Placing electrons in d orbitals
d5
1 u.e.
5 u.e.
d6
0 u.e.
4 u.e.
d8
2 u.e.
2 u.e.
d7
1 u.e.
3 u.e.
d9
1 u.e.
1 u.e.
d10
0 u.e.
0 u.e.
Positive
favors high
spin. Neg
favors low
spin.
Enthalpy of Hydration of hexahydrate
Splitting of d orbitals in a tetrahedral field
t2
Dt
e
Dt = 4/9Do
Always weak field (high spin)
Magnetic properties of metal complexes
Diamagnetic complexes
very small repulsive
interaction with external
magnetic field
no unpaired electrons
Paramagnetic complexes
attractive interaction with
external magnetic field
some unpaired electrons
s  n(n  2)
Measured magnetic moments include contributions from both
spin and orbital spin. In the first transition series complexes the
orbital contribution is small and usually ignored.
Coordination Chemistry:
Molecular orbitals for metal complexes
The symmetry of metal orbitals in an octahedral environment
A1g
T1u
The symmetry of metal orbitals in an octahedral environment
T2g
Eg
The symmetry of metal orbitals in an octahedral environment
s
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
Anti-bonding LUMO(π)
The CN- ligand
Some schematic diagrams showing how p bonding occurs
with a ligand having a d orbital (P), a p* orbital, and 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*)
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)
Adding in water, hydroxide and carboxylate
D: H2O > F > RCO2 > OH > Cl > Br > I
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
ML4 square planar complexes
MO diagram
s-only bonding
- bonding
A crystal-field aproach: from octahedral to tetrahedral
L
L
L
M
L
L
M
L
L
L
L
L
Less repulsions along the axes
where ligands are missing
A crystal-field aproach: from octahedral to tetrahedral
A correction to preserve
center of gravity
The Jahn-Teller effect
Jahn-Teller theorem:
“there cannot be unequal occupation of orbitals with identical energy”
Molecules will distort to eliminate the degeneracy
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.