Magnetic Moments
Lecture 4. CHEM1902 Coordination
Chemistry
Magnetic moments are often used in conjunction with electronic
spectra to gain information about the oxidation number and
stereochemistry of the central metal ion in coordination
complexes.
A common laboratory procedure for the determination of the
magnetic moment for a complex is the Gouy method which involves weighing
a sample of the complex in the presence and absence of a magnetic
field and observing the difference in weight. A template is
provided for the calculations involved.
For first row transition metal ions in the free ion state, i.e.
isolated ions in a vacuum, all 5 of the 3d orbitals are
degenerate.
A simple crystal field theory approach to the bonding in these
ions assumes that when they form octahedral complexes, the energy of the d
orbitals are no longer degenerate but are split such that two
orbitals, the dx2-y2 and the dz2
(eg subset) are at higher energy than the
dxy, dxz, dyz orbitals (the
t2g subset).
For octahedral ions with between 4 and 7 d electrons, this gives rise to 2
possible arrangements called either high spin/weak field or
low spin/strong field respectively. The energy gap is dependent on
the position of the coordinated ligands in the SPECTROCHEMICAL
SERIES.
See an interactive JAVA
applet for examples.
Note: For CHEM1902, we assume that all Co(III), d6 complexes
are octahedral and LOW spin, i.e. t2g6.
In tetrahedral complexes, the energy levels of the orbitals are
again split, such that the energy of two orbitals, the dx2-y2 and
the dz2 (e subset) are now at lower energy (more
favoured) than the remaining three dxy,
dxz, dyz (the t2 subset) which are
destabilised.
Tetrahedral complexes are ALL high spin since the difference
between the 2 subsets of energies of the orbitals is much smaller than
is found in octahedral complexes.
The usual relationship quoted between them is:
Δtet ≈ 4/9 Δoct.
Square planar complexes are less commmon than tetrahedral and
for CHEM1902 we will assume that the only ions forming
square planar complexes are d8 e.g. Ni(II), Pd(II), Pt(II), etc.
d8 can therefore be either square planar or tetrahedral.
As with octahedral complexes, the energy gap between the dxy and
dx2-y2 is Δoct
and these d8 systems are all considered strong field / low spin
complexes hence they are all diamagnetic, μ=0 Bohr Magneton (B.M.).
The formula used to calculate the spin-only magnetic moment can
be written in two forms; the first based on the number of
unpaired electrons, n, and the second based on the
total electron spin
quantum number, S. Since for each unpaired electron, n=1 and
S=1/2 then the two formulae are clearly related and the answer obtained
must be identical.
μso= √n(n+2) B.M.
μso= √4S(S+1) B.M. - a variation of this will be introduced in the
second year Inorganic course: μS+L = √{4S(S+1) + L(L+1)} B.M.
Comparison of calculated spin-only magnetic
moments with experimentally observed data for some octahedral
complexes
| Ion |
Config |
μso / B.M. |
μobs / B.M. |
| Ti(III) |
d1 (t2g1) |
√3 = 1.73 |
1.6-1.7 |
| V(III) |
d2 (t2g2) |
√8 = 2.83 |
2.7-2.9 |
| Cr(III) |
d3 (t2g3) |
√15 = 3.88 |
3.7-3.9 |
| Cr(II) |
d4 high spin (t2g3 eg1) |
√24 = 4.90 |
4.7-4.9 |
| Cr(II) |
d4 low spin (t2g4) |
√8 = 2.83 |
3.2-3.3 |
| Mn(II)/ Fe(III) |
d5 high spin (t2g3 eg2) |
√35 = 5.92 |
5.6-6.1 |
| Mn(II)/ Fe(III) |
d5 low spin (t2g5) |
√3 = 1.73 |
1.8-2.1 |
| Fe(II) |
d6 high spin (t2g4 eg2) |
√24 = 4.90 |
5.1-5.7 |
| Co(III) |
d6 low spin (t2g6) |
0 |
0 |
| Co(II) |
d7 high spin (t2g5 eg2) |
√15 = 3.88 |
4.3-5.2 |
| Co(II) |
d7 low spin (t2g6 eg1) |
√3 = 1.73 |
1.8 |
| Ni(II) |
d8 (t2g6 eg2) |
√8 = 2.83 |
2.9-3.3 |
| Cu(II) |
d9 (t2g6 eg3) |
√3 = 1.73 |
1.7-2.2 |
Comparison of calculated spin-only magnetic
moments with experimental data for some tetahedral
complexes
| Ion |
Config |
μso / B.M. |
μobs / B.M. |
| Cr(V) |
d1 (e1) |
√3 = 1.73 |
1.7-1.8 |
| Cr(IV) / Mn(V) |
d2 (e2) |
√8 = 2.83 |
2.6 - 2.8 |
| Fe(V) |
d3 (e2 t21) |
√15 = 3.88 |
3.6-3.7 |
| - |
d4 (e2 t22) |
√24 = 4.90 |
- |
| Mn(II) |
d5 (e2 t23) |
√35 = 5.92 |
5.9-6.2 |
| Fe(II) |
d6 (e3 t23) |
√24 = 4.90 |
5.3-5.5 |
| Co(II) |
d7 (e4 t23) |
√15 = 3.88 |
4.2-4.8 |
| Ni(II) |
d8 (e4 t24) |
√8 = 2.83 |
3.7-4.0 |
| Cu(II) |
d9 (e4 t25) |
√3 = 1.73 |
- |
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The Department of Chemistry, University of the West Indies,
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