CHEM 153 - Advanced Inorganic Chemistry PROBLEM SET 3 (due ...

CHEM 153 - Advanced Inorganic Chemistry
PROBLEM SET 3 (due 28 January, 2011)
1. Consider the following oxo complexes:
a. [L 5 VO] 2+ V IV d 1
b. [L 5 CrO] 3+ Cr V d 1
c. [L 5 CrO] 2+ Cr IV d 2
d. [L 5 MnO] 3+ Mn V d 2
e. [L 5 MnO] 2+ Mn IV d 3
f. [L 5 FeO] 2+ Fe IV d 4
Part 1:
Construct a ligand-field (LF) 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 F orbitals, and the oxo 2pF + two 2pB orbitals.
Part 2:
Using your LF 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
Part 3:
a. Larry Que and coworkers reported the synthesis and isolation of a nonheme
ferryl complex (Science 2003, 299, 1037-1039). What are the Fe-O bond
properties (bond length and bond order) Are they consistent with your
predictions for 6-coordinate Fe IV How do the reported Mössbauer spectra
support these findings
b. The electronic structures and spectroscopic properties of Que’s nonheme
ferryl complex have been investigated in Ed Solomon’s laboratory (J. Am.
Chem. Soc. 2004, 126, 5378-7379). An absorption system in the 10,000
cm !1 region, called band I by Solomon, is assigned to the (xy)6(x 2 !y 2 )
transition in the ferryl spectrum. What is the electronic configuration of the
excited state formed by this transition What is the value of S (the spin
quantum number) for this excited state The energies of the transitions
associated with bands I and II are at much lower energies than the
corresponding transitions in d 1 metal-oxo complexes such as [L 5 VO] 2+ and
[L 5 CrO] 3+ . How does Solomon account for these differences

Part 4:
The first example of a trans-dioxo (D 4h ) 3d metal complex was reported in 2007
(J. Am. Chem. Soc. 2007, 129, 12416-12417). Construct an LF diagram (you
need only show the 3d levels) for the complex. What is the electronic
configuration of the ground state What is the oxo-metal bond order What are
the term symbols for the two lowest electronic excited states Did the authors
observe transitions from the ground state to these excited states in the
absorption spectrum of the complex Should they have Explain briefly.
2. The electronic absorption spectra of [Cr V (N)(CN) 5 ] 3! and [Mn V (N)(CN) 5 ] 3! are shown
below. In [Cr V (N)(CN) 5 ] 3! , the 2 B 2 [(xy)] ÷ 2 E[(xz,yz)] absorption band is at 23,300
cm !1 . In [Mn V (N)(CN) 5 ] 3! , the 1 A 1 [(xy) 2 ] ÷ 1 E[(xy)(xz,yz)] absorption band is at
19,400 cm !1 .
[Cr(N)(CN) [Cr(N)(CN)5] 5 ] 3 3!
[Mn(N)(CN) 5
] 3!
[Mn(N)(CN) 5 ] 3

Use the following orbital splitting diagram to determine the values of ) B in the Cr and
Mn complexes. Expressions for the electron-electron repulsion integrals are given
below. Assume that B = 500 cm !1 and that C/B = 4.
B
d 2 :
3 A 2 [(xz,yz) 2 ] E = 2 ) B + A ! 5B
1 A 1 [(xz,yz) 2 ] E = 2 ) B + A + 7B + 4C
1 B 1 [(xz,yz) 2 ] E = 2 ) B + A + B + 2C
1 B 2 [(xz,yz) 2 ] E = 2 ) B + A +B + 2C
1 E[(xy) 1 (xz,yz) 1 ] E = ) B + A + B + 2C
3 E[(xy) 1 (xz,yz) 1 ] E = ) B + A ! 5B
1 A 1 [(xy) 2 ] E = A + 4B + 3C
d 3 :
2 E[(xz,yz) 3 ] E = 3 ) B + 3A ! 3B + 4C
4 B 1 [(xy) 1 (xz,yz) 2 ] E = 2 ) B + 3A !15B
2 B 1 [(xy) 1 (xz,yz) 2 ] E = 2 ) B + 3A ! 6B + 3C
2 A 1 [(xy) 1 (xz,yz) 2 ] E = 2 ) B + 3A ! 6B + 3C
2 B 2 [(xy) 1 (xz,yz) 2 ] E = 2 ) B + 3A + 5C
2 A 2 [(xy) 1 (xz,yz) 2 ] E = 2 ) B + 3A ! 6B + 3C
2 E[(xy) 2 (xz,yz) 1 ] E = ) B + 3A ! 3B + 4C
3. Use the foregoing orbital splitting pattern and energy expressions in considering
high-spin/low-spin equilibria in tetragonal oxo- and nitrido-metal complexes with d 2
and d 3 configurations.
Assume that the excited-state distortion parameter 8 (as defined in the diagrams on
the following page) is about 3,400 cm !1 for both high- and low-spin states.
a) Find the ) B values at the high-spin/low-spin crossover points for d 2 and d 3
tetragonal oxo- and nitrido-metal complexes. Assume that B = 500 cm !1 and
C/B = 4.
b) Assume that you have a high-spin/low-spin equilibrium in a d 2 tetragonal oxo- or

nitrido-metal complex in which E TH = 0. What are the ) B values for high- and
low-spin forms
c) Assume that you have a high-spin/low-spin equilibrium in a d 3 tetragonal oxoand
nitrido-metal complex in which E TH = 0. What are the ) B values for high- and
low-spin forms
d) What are the relative populations of the high- and low-spin states in problems (b)
and (c)
e) Karl Wieghardt reported (Angew. Chem. Int. Ed. 2005, 44, 2908-2912) that,
unexpectedly, the ground-state total spin of the [(cyclam-acetato)Fe V (N)] + core is
S=1/2 and not S=3/2. On the basis of your answers to Problems 1, and 2(c),
discuss whether you think that this result is “unexpected”.