Download T 1g A 2g

High Spin Ground States: d2, d3, d6, and d7
We have taken care of the d0, d1, d4, d5, d6, d9, and d10 configurations. Now have to do
d2, d3, d6, and d7 configurations. It turns out that all we have to do is solve d2.
d2 and d7 both are
electrons on top of
a spherical shell
yielding a splitting
pattern: 1, 2, 3
electrons
holes
1
3
d2
d7 = d5 + d2
2
d3=d5-hole2
2
d3 and d8 are both two
d-holes in a spherical
shell, yielding reversed
splitting: 3, 2, 1
3
d8=d10-hole2
1
But it is not so easy. Here is our approach:
We know the symmetry of the GS of the free d2 ion. How? We can get the terms
for d2 using the methods applied earlier to p2, etc. They are 3F, 1D, 3P, 1G, 1S.
We identify the GS as 3F. How?
We saw earlier that F in octahedral environment splits to A2g + T1g + T2g; in tetrahedral
we would get A2 + T1 + T2. Our problem is the energy ordering. Which is GS?
Thus the 3F GS for d2 splits into 3A2g + 3T1g + 3T2g. The 4F GS for d3 splits into 4A2g +
4T
4
1g + T2g. Where did the spin multiplicities come from??
But how do we decide on what becomes the GS after the splitting due to the ligands?
We use a correlation diagram. It shows the affect of increasing the ligand field
strength from zero (free ion) to very high where energy ordering is determined solely
by the occupancy of the t2g and the eg orbitals.
d2
F
r
e
e
I
o
n
t
e
r
m
s
We have two electrons in the
eg orbitals. It can be shown
that these give rise to 1A1g, 1Eg,
and 3A2g which have same
energy in strong ligand field.
Connect the terms of the same
symmetry without crossing.
Similarly, splitting occurs for these
occupancies.
Configurations
We have included
basedthe
on 3splitting
T1g originating
of d from
Splitting of free ion
electrons.
the 3P. We
Dominant
will need
initvery
immediately.
strong fields.
Same
Real complexes
terms.
symmetry as lower energy 3T1g from the 3F.
Orgel diagram for d2, d3, d7, d8 ions
This curvature will
complicate interpretation of
spectra. Same symmetry;
crossing forbidden
First look at
Energy
And now
d2 and d7 in tetrahedral
(reversed due to tetrahedral field)
T1 or T1g
7 in octahedral (2 elecs
Td12Tor
T1gT
and
d1g
1 or
on a spherical cloud)
P
and
and
T1 or T1g
T13 or T1g 8
d and d in tetrahedral (double F
reversal: d-holes and
tetrahedral)
T2 or T2g
All states shown are of the
same spin. Transitions occur
between them but weakly.
d3 and d8 in octahedral
(reversed due to d-holes).
T2 or T2g
Note the reversed ordering of the
splitting coming from F (T1/T2/A2).
The lower T1(g) now aims up and
should cross the upper T1(g) but T or T
1
1g
does not due to interaction with
the upper T1(g). Now have strong
curvature to avoid crossing.
Note the weak interaction of
A
A2gT1, the curvature.
the
2 ortwo
d2, d7 tetrahedral
A2 or A2g
0
d2, d7 octahedral
d3, d8 octahedral
d3, d8 tetrahedral
Ligand field strength (Dq)
Move to Tanabe-Sugano diagrams.
d1 – d3 and d8 – d9 which have only high spin GS are easier. Here is d2.
Correlation diagram for d2.
Convert to Tanabe-Sugano.
Tanabe-Sugano
Electronic transitions and spectra
d2 Tanabe-Sugano diagram
V(H2O)63+, a d2 complex
Configurations having only high spin GS
d2
d3
Note the two
lines curving
away from
each other.
Slight
curving.
d9
d1
d8
Note the two
lines curving
away from
each other.
Configurations having either high or low spin GS
The limit between
high spin and low spin
Determining Do from spectra
d1
Exciting
electron from t2g
to eg
d9
Exciting d-hole
from eg to t2g
Exciting d-hole
from eg to t2g
One transition allowed of energy Do
Exciting
electron from t2g
to eg
Determining Do from spectra
d3
mixing
Here the mixing is not a problem since
the “mixed” state is not involved in the
excitation.
mixing
d8
Lowest energy transition = Do
For d2 and d7 (=d5+d2) which involves mixing of the two T1g states, unavoidable problem.
Ground state and excited state
mixing which we saw earlier.
d2
But note that the
difference in
energies of two
excitations is Do.
d7
E (T1gA2g) - E (T1gT2g) = Do
Make sure you can identify the transitions!!
Can use T-S to calculate Ligand Field Splitting. Ex: d2, V(H2O)63+
Observed spectrum
u1: 17,800 cm-1
u2: 25,700 cm-1
Technique: Fit the observed energies to the diagram.
E/B
We must find a value of the splitting parameter, Do/B,
which provides two excitations with the ratio of
25,700/17,800 = 1.44
First, clearly u1 should correspond to 3T1  3T2 But note
that the u2 could correspond to either 3T1  3A2 or 3T1 
3T .
1
The ratio of u2/u1 = 1.44 is obtained at Do / B= 31
DO/B
Again, the root, basic problem
is that the two T1 s have
affected each other via mixing.
The energy gap depends to
some extent on the mixing!
Now can use excitation energies
For u1: E/B = 17,800 cm-1 /B = 29 yielding B = 610
cm-1
By using 31 = Do/B = Do/610 obtain Do = 19,000 cm-1
The d5 case
All possible transitions forbidden
Very weak signals, faint color
Jahn-Teller Effect found if there is an asymmetrically occupied e set.
octahedral d9 complex
b1g
x2-y2
z2
a1g
x2-y2
z2
b2g
xy
xy
xz
xz
yz
effect of octahedral field
yz
eg
elongation along the
x axis
Can produce two transitions.
This picture is in terms of the orbitals. Now for one derived from
the terms.
Continue with d9
Eg
2
T2g
B2g
2
D
A1g
2
Eg
B1g
Free ion term
for d9
effect of
octahedral field
GS will have d-hole
in either of the two eg
orbitals. ES puts dhole in either of the
three t2g orbitals.
effect of elongation
along z
For example, the GS
will have the d-hole in
the x2-y2 orbital which
is closer to the ligands.
Some examples of spectra
Charge transfer spectra
Metal character
LMCT
Ligand character
Ligand character
MLCT
Metal character
Much more intense bands
Coordination Chemistry
Reactions of Metal Complexes
Substitution reactions
MLn-1L' + L
MLn + L'
Labile complexes <==> Fast substitution reactions (< few min)
Inert complexes <==> Slow substitution reactions (>h)
a kinetic concept
Not to be confused with
stable and unstable (a thermodynamic concept; DGf <0)
Inert
Intermediate
d3, low spin d4-d6& d8
d8 (high spin)
Labile
d1, d2, low spin d4-d6& d7-d10
Mechanisms of ligand exchange reactions
in octahedral complexes
MLnY + X
MLnX + Y
Associative (A)
Dissociative (D)
-x
MLnX
Y
Y
MLn
MLnY
MLnX
-X
YMLnX
Interchange (I)
Y
MLnX
-X
Y- -MLn- -X
YMLn
Association or Dissociation step may be
more important and the process classified
as such.
Ia if association
is more important
Id if dissociation
is more important
YMLn
Kinetics
of dissociative reactions
Using Steady State Approximation, concentration of ML5 is always very low;
rate of creation = rate of consumption
Kinetics
of interchange reactions
Fast equilibrium
K1 = k1/k-1
k-1 >> k2
Again, apply Steady State.
For [Y] >> [ML5X]
common experimental
condition!
Kinetics of associative reactions
Principal mechanisms of ligand exchange in octahedral complexes
Dissociative
Associative
Dissociative pathway
(5-coordinated intermediate)
MOST COMMON
Associative pathway
(7-coordinated intermediate)
Experimental evidence for dissociative mechanisms
Rate is independent of the nature of L
Experimental evidence for dissociative mechanisms
Rate is dependent on the nature of L
Inert and labile complexes
Some common thermodynamic and kinetic profiles
Exothermic
(favored, large K)
Large Ea, slow reaction
Exothermic
(favored, large K)
Large Ea, slow reaction
Stable intermediate
Endothermic
(disfavored, small K)
Small Ea, fast reaction
Labile or inert?
L
L
L
M
L
L
Ea
L
L
L
L
M
L
L
M
L
L
L
X
L
X
DG
LFAE = LFSE(sq pyr) - LFSE(oct)
Why are some configurations inert and some are labile?
Inert !
Substitution reactions in square-planar complexes
the trans effect
L
X
M
T
L
+X, -Y
L
Y
M
T
(the ability of T to labilize X)
L
Synthetic applications
of the trans effect
Cl- > NH3, py
Mechanisms of ligand exchange reactions in square planar complexes
L
L
X
L
S
+S
M
L
L
M
X
L
+Y
-X
Y
L
L
L
-d[ML3X]/dt = (ks + ky [Y]) [ML3X]
M
X
L
L
M
S
L
+Y
Y
L
-X
L
L
L
L
M
Y
-S
L
M
S
Electron transfer (redox) reactions
-1e (oxidation)
M1(x+)Ln + M2(y+)L’n
M1(x +1)+Ln + M2(y-1)+L’n
+1e (reduction)
Very fast reactions (much faster than ligand exchange)
May involve ligand exchange or not
Very important in biological processes (metalloenzymes)
Outer sphere mechanism
[Fe(CN)6]3- + [IrCl6]3-
[Fe(CN)6]4- + [IrCl6]2-
[Co(NH3)5Cl]+ + [Ru(NH3)6]3+
[Co(NH3)5Cl]2+ + [Ru(NH3)6]2+
Reactions ca. 100 times faster
than ligand exchange
(coordination spheres remain the same)
A
B
"solvent cage"
r = k [A][B]
Ea
Tunneling
mechanism
A
+
B
A'
DG
+
B'
Inner sphere mechanism
[Co(NH3)5Cl)]2+ + [Cr(H2O)6]2+
[Co(NH3)5Cl)]2+:::[Cr(H2O)6]2+
[CoIII(NH3)5(m-Cl)CrII(H2O)6]4+
[CoII(NH3)5(m-Cl)CrIII(H2O)6]4+
[CoII(NH3)5(H2O)]2+
[Co(NH3)5Cl)]2+:::[Cr(H2O)6]2+
[CoIII(NH3)5(m-Cl)CrII(H2O)6]4+
[CoII(NH3)5(m-Cl)CrIII(H2O)6]4+
[CoII(NH3)5(H2O)]2+ + [CrIII(H2O)5Cl]2+
[Co(H2O)6]2+ + 5NH4+
Inner sphere mechanism
Ox-X + Red
k1
Ox-X-Red
k2
Reactions much faster
than outer sphere electron transfer
(bridging ligand often exchanged)
k3
k4
Ox(H2O)- + Red-X+
Ox-X-Red
Tunneling
through bridge
mechanism
r = k’ [Ox-X][Red] k’ = (k1k3/k2 + k3)
Ea
Ox-X
+
Red
Ox(H2O) - + Red-X +
DG