Exercises:
1) Vanadocene (V(Cp)2, Cp = cyclopentadienyl) has eff = 3.78 B. What is the oxidation state
of this complex?
A eff of 3.78 B indicates a d3 electronic configuration. This points to a vanadium oxidation
state of +2.
2) The effective magnetic moment of an octahedral Co(II) complex was found to be eff = 4.0
B. What ist the electron configuration of this complex?
Co(II) has a d7 configuration, and can thus have a low or high-spin configuration. The
expectation values for the two configurations (with S = 3/2 or S = ½), calculated with the spinonly formula,
eff  2 S ( S  1)  B
are 3.87 (h.s.) and 1.73 (l.s.). The experimental value of eff = 4.0 B is closer to the former
value. Hence, this Co(II) complex is a high-spin complex, t2g5eg2.
3) The room-temperature magnetic moment µeff for [Cr(en)3]Br2 is 4.75 µB. Is this complex
low-spin or high-spin (en = ethylenediamin = NH2CH2CH2NH2)?
In this complex chromium is divalent (Cr(II)). Cr2+ has a d4 configuration, and thus can have a
low or high-spin configuration. The expectation values for the two configurations (with S = 2
or S = 1), calculated with the spin-only formula,
eff  2 S ( S  1)  B
are 4.90 (h.s.) and 2.83 (l.s.). The experimental value of eff = 4.75 B is closer to the former
value. Hence, this Cr(II) complex is a high-spin complex, t2g3eg1.
4) For octahedral complexes, there are only certain dn configurations, which can adopt highspin and low-spin configurations. Which dn configurations are these? Are high-spin/low-spin
phenomena also possible for tetrahedral complexes?
For octahedral complexes, high-spin / low-spin phenomena are possible for d4, d5, d6, and d7
configurations. For tetrahedral complexes, high-spin / low-spin phenomena are feasible only
for d3, d4, d5, and d6 configurations. However, since t = 4/9 o, most tetrahedrally
coordinated complexes are high-spin.
5) The cobalt complex [Co(1-nor)4] (1-nor = 1-norbornene) is a tetrahedral complex with lowspin configuration (S = ½, d5). What are possible reasons for this unexpected behaviour?
1-norbornene is a sterically demanding ligand, the Co has a high oxidation state (i.e. +IV), the
1-norbornene ligand is a strong ligand (see spectrochemical series); all these features increase
t.
6) The magnetic moments of [Mn(H2O)6]2+, [Fe(H2O)6]3+, [MnCl4]2− und [FeCl4]− is
invariably 5.92 µB. What does that tell you about the geometrical and electronic structure of
the complexes? Why ist the spin-only formula in these cases so useful?
[Mn(H2O)6]2+: d5, t2g3eg2, high-spin, octahedral
[Fe(H2O)6]3+: d5, t2g3eg2, high-spin, octahedral
[MnCl4]2–: d5, e2t3, high-spin, tetrahedral
[FeCl4]–: d5, e2t3, high-spin, tetrahedral.
The complexes have an A ground term. (L = 0).
7) Determine the Russel-Saunders term symbol 2S+1LJ for the groundterm of the following
ions:
a) Ti3+, b) Ni2+, c) Cr3+, d) Ce3+, e) Ho3+, f) Er3+, g) La3+, h) Lu3+
solution:
Step 1) n, determine the number of unpaired electrons
=> S = n/2
Step 2) determine L:
Sum of ml-values for the spin-arrangment with lowest energy (Hund’s Rules),
Assign L according to the following table
L 0
1
2
3
4
5
6
S
P
D
F
G
H
I
Step 3) determine J:
J = (L–S) for less than half-filled shells
J = (L+S) for more than half-filled shells
Ti3+, d1,
n = 1, S = ½, Ms = 2∙1/2 + 1 = 2
ml
2 1 0 -1 -2
L = 2, => 2D
J = L – S = 2 – 1/2 = 3/2 => 2D3/2
Ni2+, d8,
n = 2, S = 1, Ms = 2∙1 + 1 = 3
ml
2 1 0 -1 -2
L = (2 × 2) + (2 × 1) +(2 × 0) – 1 – 2 = 3, => F
J = L + S = 3 + 1 = 4 => 3F4
Cr3+, d3,
n = 3, S = 3/2, Ms = 2∙3/2 + 1 = 4
ml
2 1 0 -1 -2
L = (1 × 2) + (1 × 1) + (1 × 0) = 3, => F
J = L – S = 3 – 3/2 = 3/2 => 4F3/2
Ce3+, f1
n = 1, S = 1/2, Ms = 2∙1/2 + 1 = 2
ml
3 2 1 0 -1 -2 -3
L = (1 × 3) = 3, => 2F
J = L – S = 3 – 1/2 = 5/2 => 2F5/2
Ho3+, f10
n = 4, S = 2, Ms = 2∙2 + 1 = 5
ml
3 2 1 0 -1 -2 -3
L = (2 × 3) + (2 × 2) + (2 × 1) +(1 × 0) – (1 × 1) – (1 × 2) – (1 × 3) = 6, => I
J = L + S = 6 + 2 = 8 => 5I8
Er3+, f11, n = 3, S = 3/2, MS = 4, L = 6, J = 15/2 => 4I15/2
La3+: f0, n=0, S=0, MS=1, L = 0, J = 0, => 1S0
Lu3+: f14, n=0, S=0, MS=1, L = 0, J = 0, => 1S0
8) For which of the following ions do you expect an orbital contribution to the magnetic
moment?:
a) V3+, b) Cr3+, c) Ti4+, d) Fe3+ (low-spin), e) Fe3+ (high-spin)
One expects an orbital contribution for ions with T ground terms: These are V3+ (3T1g) and
Fe3+, low-spin (2T2g), see the Table below.
9) Calculate the value of the effective magnetic moment for the following ions:
a) Ti3+, Ce3+, Yb3+, Ho3+, Eu3+.
Hint:
for Lanthanid ions (Ce3+-Eu3+):

 g J J ( J  1)
B
S ( S  1)  L( L  1)  J ( J  1)
gJ  1 
2 J ( J  1)
where S, L and J can be taken from the ground term symbols
Ce3+: 2F5/2, S = 1/2, L = 3, J = 5/2, gJ = 0.857, = 2.535B
Yb3+: 2F7/2, S = ½, L = 3, J = 7/2, gJ = 1.143,  = 4.536B
Ho3+: 5I8, S = 2, L = 6, J = 8, gJ = 1.25,  = 10.607B
Eu3+:  = 0 B
10) Calculate the effective magnetic moment for Dy2(SO4)3∙8H2O.
See 9.
,
11) Sketch qualitatively the temperature dependence of eff versus T for Curie-Paramagnets.
Sketch the temperature dependence of eff versus T for ions with a) A (or E) ground terms, b)
T ground terms?
12) The temperature dependence of the iron complex [Fe(NCS)2(phen)2] is shown in the
figure. Explain the curve.
The complex is high-spin at temperatures above 180 K and low-spin below 180K.
Tab.1 Calculated and experimental values for meff (in B) for octahedral complexes.
Number
Groundterm Electron
Ligand
eff(calc.) eff(exp.) Orbital
of d
of free ion
configuration fieldmomentum
electrons
groundterm
expected?
2
2
1 (Ti3+)
D
t2g1
T2g

 Yes
3
3
2 (V3+)
F
t2g2
T1g

 Yes
3+
4
3
4
3 (Cr )
F
t2g
A2g

 No
3+
5
3 1
5
4 (Mn )
D
t2g eg
Eg

 No
3
t2g4eg0
T1g

 Yes
3+
6
3 2
6
5 (Fe )
S
t2g eg
A1g

 No
5 0
2
t2g eg
T2g

 Yes
2+
5
4 2
5
6 (Fe )
D
t2g eg
T2g

 Yes
6 0
1
t2g eg
A1g
No


4
4
7 (Co2+)
F
t2g5eg2
T1g

 Yes
6 1
2
t2g eg
Eg

 No
2+
3
6 2
3
8 (Ni )
F
t2g eg
A2g

 No
2+
2
6 3
2
9 (Cu )
D
t2g eg
Eg

 No