Problem Set 3

Chemistry 153 – Advanced Inorganic Chemistry
Problem Set 3 (due 27 January, 2012)
1. Consider the following oxo complexes:
[L 5 VO] 2+ V IV d 1
[L 5 CrO] 3+ Cr V d 1
[L 5 CrO] 2+ Cr IV d 2
[L 5 MnO] 3+ Mn V d 2
[L 5 MnO] 2+ Mn IV d 3
[L 5 FeO] 2+ Fe IV d 4
a. Construct an MO diagram for C 4v [L 5 MO] n+ (L is an uncharged ligand, for example, H 2 O or NH 3 )
using the following orbitals: five metal 3d orbitals, one set of five ligand σ orbitals, and the oxo
2pσ + two 2pπ orbitals.
b. Using your MO diagram, for each of the above examples, fill in the d electrons and predict the
ground‐state electronic configuration. With this prediction, calculate the metal‐oxo bond order.
Based on your results, do you think that a complex of the form [L 5 CoO] n+ could exist Why or
why not
2. The atomic d‐orbitals in tetrahedral (T d ) symmetry transform as the irreducible representations t 2
and e. When the z‐axis is chosen to coincide with the S 4 axis of this point group, the standard real d‐
orbital functions form basis sets for t 2 and e representations as:
d
2
z
~
e:
2
d
x
(2z
2
x y
2 2
( x y
1 2
2
2
3
2
y
~
2
)
d
)
; t 2 : d
d
xz
yz
xy
~
~
~
3xz
3yz
3xy
This set of functions is well‐adapted to molecules of tetragonal symmetry, but is less convenient for
molecules of trigonal symmetry. An alternative approach to the description of molecules of trigonal
symmetry could begin with the T d point group but with the z‐axis coincident with the threefold
rotation axis. This coordinate transformation can be accomplished with a 45 rotation about the z‐
axis followed by a 54.7 rotation about the new x‐axis. Defining the original coordinate system as
x,y,z, and the new coordinate system as X,Y,Z, leads to the following transformations:
X
Y
Z
1
2
1
6
1
3
1
2
1
6
1
3
0 x
2
y
3
1
z
3
1
x
2
1
y
2
z
0
1
6
1
6
2
3
1
3 X
1
Y
3
1
Z
3
a. Assume that you have a tetrahedral ML 4 molecule in which M is located at the origin of both
coordinate systems. If the L‐atoms are found at the positions [½, ½, ½], [½,½, ½], [½,½,½],

and [½, ½, ½] in the coordinate system with fourfold quantization, what are their positions in
the coordinate system with threefold quantization
b. Use the real d‐orbital functions to find basis sets for the t 2 and e representations of the T d point
group in the coordinate system with trigonal quantization.
3. In 1993, Wilkinson and Hursthouse reported
(Polyhedron, 1993, 12, 2009‐2012) the preparation
and X‐ray crystal structure of Ir(O)(mes)3 (mes =
mesityl, 2,4,6‐trimethylphenyl). The structure of the
complex is shown to the right.
a. Construct an MO diagram for C 3v Ir(O)(mes) 3
using the following orbitals: five metal 5d orbitals, one set of three ligand σ orbitals, and the oxo
2pσ + two 2pπ orbitals.
b. Extend your diagram to illustrate the correlation between the trigonally quantized ML 4 orbitals
and the MOs of Ir(O)(mes) 3 .
c. Is there a unique set of d‐orbitals in C 3v symmetry that forms a basis for the e irreducible
representation If so, what is that set of d‐orbitals If not, what is the implication for the
molecular orbitals of e symmetry in Ir(O)(mes) 3
d. Using your MO diagram, fill in the d electrons and predict the ground‐state electronic
configuration. With this prediction, is the metal‐oxo bond order shown above correct Why or
why not Do you think that a complex of the form [Ir(O)(mes) 3 ] 2− could exist Why or why not
e. Does Ir(O)(mes) 3 represent a breach of the oxo wall Why or why not