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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

MagnetismCompounds possessing unpaired electrons are paramagnetic (attracted by magnetic field); thosein which the electrons are paired are diamagnetic (repelled by magnetic field).

Crystal Field Theory: Octahedral Case (See Lecture #28)Crystal Field Theory: Tetrahedral CaseThe tetrahedral crystal field splitting energy (∆T) is smaller than for octahedral complexesbecause the point charges are not directed at any orbital set.

z axis Z

L- L- Z

Y Yy axis M X

X L- L-

d 2x-axis out of the page d 2 2 zx -y

tetrahedral

z axis

ZL- L-Z

Z

M y axis YY Y

X X XL- L-

d dxy x-axis out of the page yz dxz

tetrahedral

Geometry of tetrahedral complexes result in greater orbital destabilization for dyz, dxz, dxy than for dx -y

2 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 2negative point charges and the d-orbitals that are on axis (dz

2 and dx -y2). dyz, dxz, dxy have the

2same energy with respect to each other (degenerate). dz2 and dx -y

2 have the same energy with respect to each other (degenerate).

2

29.2

(eg) E d 2 2 d 2

x -y z (t2)+ 3 + 2O d d d

5 xy xz yz

O 5 T

- 2 T - 3

T

average energy of 5 O dx

2-y

2 dz2 (e) 5

d orbitals with ligands dxy dxz dyz (t2g)

(Spherical crystal field) (Octahedral crystal field) (Tetrahedral 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 2dyz) go up in energy by 2/5, and the e orbitals (dx -y

2 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

average energy of (e)d orbitals with ligands

(Spherical crystal field) (Tetrahedral crystal field)

(c) Write dn electron configuration:

(d) How many unpaired electrons?

Crystal Field Theory: Square Planar Case

Z-axis Z

L-

L-

Mn+

L- Y-axis Y

X L- d 2 2

x -y

X-axis

Square planar lots of repulsion ligand point charges directed at orbitals Destablized compared to all other d-orbitals

Z Z-axis Z

L-

L-

Mn+

L- Y-axis Y

X

Y

X L-

dX-axis yz dxz

Square planar stabilized compared stabilized compared 2 2 2 2to dxy and dx -y to dxy and dx -y

29.3

Z

Y

X

d 2 z

much less repulsion than in octahedral crystal field. Less repulsion than

2for dx -y2 and for dxy

Z

Y

X

dxy

more repulsion than for 2dyz, dxz, and dz .

Less repulsion than for 2dx -y

2 since orbitals are 45° off axis in dxy.

29.4

d 2 2 x -y

(eg) d 2 2 d 2

x -y zE

+3/5 O dxy

O

-2/5 Oaverage energy of d-orbitals with ligands (t2g) dz

2

d d dxy xz yz

(Spherical crystal field) (Octahedral crystal field) d dyz xz

(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?

d 2 2 x -y

E dx 2 -y

2 dz 2

dxy dxy dxz dyz

dxy dxz dyz dz

2

dx 2 -y

2 dz 2

(Octahedral dxz dyz (Tetrahedral crystal field) 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.