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5.111 Principles of Chemical Science
Fall 2008
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29.1
5.111 Lecture Summary #29
Transition Metals
Topic: Crystal Field Theory Continued, and Magnetism
Chapter 16 p 631-637
Magnetism
Compounds possessing unpaired electrons are paramagnetic (attracted by magnetic field); those
in which the electrons are paired are diamagnetic (repelled by magnetic field).
Crystal Field Theory: Octahedral Case (See Lecture #28)
Crystal Field Theory: Tetrahedral Case
The tetrahedral crystal field splitting energy (∆T) is smaller than for octahedral complexes
because the point charges are not directed at any orbital set.
z axis
L
Z
Z
L
Y
y axis
M
X
X
L
L-
Y
x-axis out of the page
dz2
dx2-y2
tetrahedral
z axis
L
Z
L
M
Z
Z
y axis
L
Lx-axis out of the page
Y
Y
X
X
dyz
Y
X
dxz
dxy
tetrahedral
Geometry of tetrahedral complexes result in greater orbital destabilization for dyz, dxz, dxy than for
dx2-y2 and dz2 (opposite of octahedral). There is more repulsion between the ligand negative point
charges and the d-orbitals that are 45° off axis (dyz, dxz, dxy) than there is between the ligand
negative point charges and the d-orbitals that are on axis (dz2 and dx2-y2). dyz, dxz, dxy have the
same energy with respect to each other (degenerate). dz2 and dx2-y2 have the same energy with
respect to each other (degenerate).
29.2
E
(eg)
dz2
dx2-y2
O
+3
5
O
dxy
(Spherical crystal field)
O
5
dxy
dxz dyz
dyz
+ 2
5
T
-2
average energy of
d orbitals with ligands
dxz
(t2)
dx2-y2
dz2 (e)
- 3
5
(t2g)
(Tetrahedral crystal field)
(Octahedral crystal field)
∆T is the tetrahedral crystal field splitting energy
Again, ∆T is smaller than ∆o because the point charges are not directed at any orbital set in a
tetrahedral crystal field. Because ∆T is small, many tetrahedral complexes are high spin. You
can assume that they are all high spin.
Because the overall energy in the tetrahedral crystal field is maintained, t2 orbitals (dxy, dxz, and
dyz) go up in energy by 2/5, and the e orbitals (dx2-y2 and dz2) go down in energy by 3/5.
Tetrahedral Example for Cr3+
(a) figure out d electron count
(b) draw tetrahedral crystal field splitting diagram, label orbitals, and fill in electrons
E
(t2)
T
(e)
average energy of
d orbitals with ligands
(Spherical crystal field)
(Tetrahedral crystal field)
(c) Write dn electron configuration:
(d) How many unpaired electrons?
T
T
29.3
Crystal Field Theory: Square Planar Case
Z-axis
Z
Z
L
L-
Mn+
L-
Y-axis
Y
X
X
L
Y
dz2
dx2-y2
X-axis
Square planar
lots of repulsion
ligand point charges
directed at orbitals
Destablized compared
to all other d-orbitals
Z
Z-axis
much less repulsion than
in octahedral crystal field.
Less repulsion than
for dx2-y2 and for dxy
Z
Z
L
L-
Mn+ L-
LX-axis
Square planar
Y-axis
X
X
dyz
Y
Y
Y
X
dxz
dxy
stabilized compared stabilized compared more repulsion than for
to dxy and dx2-y2
to dxy and dx2-y2
dyz, dxz, and dz2.
Less repulsion than for
dx2-y2 since orbitals are
45° off axis in dxy.
29.4
dx2-y2
dx2-y2
E
(eg)
dz2
+3/5
O
dxy
O
average energy of d-orbitals
with ligands
(Spherical crystal field)
dxy
dxz
-2/5
(t2g)
dyz
O
dz2
(Octahedral crystal field)
dyz
dxz
(Square planar crystal field)
The overall energy of the square planar crystal field is maintained as well, but the relative
energies of each of the d-orbitals are more complicated and you are not expected to know them.
Putting it all together: If a Ni2+ (d8) center in an enzyme is found to be diamagnetic, does it have
square planar, tetrahedral, or octahedral geometry?
dx2-y2
E
dx2-y2
dz2
dxy
dxy
dxz dyz
(Octahedral
crystal field)
dz
2
dxz dyz
dxy
dx2-y2
dxz dyz
dz2
(Tetrahedral crystal field)
(Square planar
crystal field)
Answer:
An example of a square planar Ni site in Nature is found in enzyme called acetyl-CoA synthase.