Download Magnetic properties of complexes

NPTEL – Chemistry and Biochemistry – Coordination Chemistry (Chemistry of transition
elements)
Magnetic properties of complexes
K.Sridharan
Dean
School of Chemical & Biotechnology
SASTRA University
Thanjavur – 613 401
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TableofContents
1 Types of magnetism ..................................................................................................................... 3 1.1 Diamagnetism ........................................................................................................................ 3 1.2 Paramagnetism ...................................................................................................................... 3 1.3 Ferromagnetism .................................................................................................................... 3 1.4 Antiferromagnetism .............................................................................................................. 3 1.5 Variation of magnetic susceptibility with temperature ........................................................ 4 1.6 Curie temperature (TC) .......................................................................................................... 4 1.7 Neel temperature (TN) ........................................................................................................... 4 1.8 Components of paramagnetism ............................................................................................ 4 1.9 Theoretical paramagnetic moment ....................................................................................... 5 2 Quenching of magnetic moments ................................................................................................ 5 3 Magnetic moment & structure ..................................................................................................... 7 3.1 Lanthanides ........................................................................................................................... 8 3.2 Spin‐cross over region and effect of temperature ................................................................ 9 4 References .................................................................................................................................. 10 Page 2 of 10
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NPTE
EL – Chemistrry and Bioche
emistry – Coo
ordination Che
emistry (Chem
mistry of transsition
eleme
ents)
1 Ty
ypes of magnettism
1.1 Diamagn
D
netism
This
s arises du
ue to paired
d electrons. When all the electro
ons in a molecule are
e
pairred, it is ca
alled a dia
amagnetic compound.
c
This compound will be slightlyy
repe
elled by the
e external magnetic
m
fie
eld.
1.2 Paramag
P
gnetism
This
s is due to
o unpaired
d electrons in a compound. The compoun
nd will be
mod
derately atttracted by the external magnetic field. The
e dipoles w
will not be
aligned uniform
mly but at ra
andom in th
he absence
e of externa
al field.
1.3 Ferromag
F
gnetism
In this
t
compo
ound the magnetic
m
dip
poles are a
arranged in
n a paralle
el manner
eve
en in the absence
a
off magnetic field. Hen
nce, these compound
ds will be
mag
gnetic even
n in the abs
sence of ex
xternal mag
gnetic field. These co
ompounds
are strongly atttracted by external
e
ma
agnetic field
d.
1.4 Antiferro
A
omagnetis
sm
In this
t
case, the magne
etic dipoles
s are arra nged antip
parallel. Th
hese
com
mpounds arre weakly atttracted by external fie
eld.
Paramagn
netic
netic
Ferromagn
Antiferromagnetic
10
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1.5 Variation of magnetic susceptibility with temperature
The variation of different types of magnetic susceptibility with temperature is
shown in Figure 1.5.1.
Ferromagnetic
Paramagnetic
TN
TC
Antiferromagnetic
Diamagnetic
Fig 1.5.1 Magnetic susceptibility and temperature
1.6 Curie temperature (TC)
At this temperature, ferromagnetism changes to paramagnetism.
1.7 Neel temperature (TN)
Antiferromagnetism changes to paramagnetism at this temperature.
1.8 Components of paramagnetism
When unpaired electrons are present in a molecule, they have spin and orbital
motions. Paramagnetism results due to these spin and orbital angular motion.
The spin and orbital motion can couple in three ways, viz., spin-spin, orbitalorbital, and spin-orbital.
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1.9 Theoretical paramagnetic moment
This is the magnetic moment incorporating all the three types of coupling, viz.,
spin-spin, orbital- orbital, and spin-orbital. This is given by Equation 1.1
  g J ( J  1),
1.1
where μ is the magnetic moment, J is the total angular momentum quantum
number and g is the Landé splitting factor for the electron.
Lande splitting factor, g, is defiened by Equation 1.2.
g  1
J ( J  1)  S ( S  1)  L( L  1)
2 J ( J  1)
1.2
where
J  L  S , L  S  1,....., L  S
1.3
L is the orbital-angular momentum and S is the spin-angular momentum.
When the spin-orbit coupling is negligible or absent in a complex but there is
significant spin and orbital contribution, the above equation transforms as
Equation 1.4.:
  [4S ( S  1)  L( L  1)]
1.4
2 Quenching of magnetic moments
The observed magnetic moments in complexes are somewhat less than the
expected values Equation 1.4 in the absence of spin-orbit coupling or when it is
negligible:
The reason for this decrease in the value is that the actual orbital contribution is
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always less than the expected (ideal) value. The orbital angular momentum is
high in the free metal ion and it is reduced when ligands are attached to it. When
the orbital contribution to the magnetic moment is zero, we say that the orbital
contribution to the magnetic moment is quenched.
When the ground state of a complex is either A or E, the orbital contribution will
be quenched. In other words, there is no orbital angular momentum for these
states.
Reason
‘A’ state is non-degenerate because it has only one level. Hence, rotation
cannot change one orbital into another equivalent orbital.
‘E’ state is doubly degenerate, which means that there are two energy levels
with the same energy. The orbitals giving rise to this are dx2-y2 and dz2. One
orbital cannot be changed into another by rotation because their shapes are
different.
Hence, A and E terms do not have orbital angular momentum. In other words,
orbital angular momentum is quenched in these cases.
Thus, complexes having A or E ground states will have no orbital angular
momentum contribution to the magnetic moment and hence, they will have
lower values than expected.
T state
This is a triply degenerate state caused by the t2g orbitals, dxy, dyz, and dzx.
They have similar shape and hence, one orbital can be transformed into another
by simple rotation. Thus, if an electron is present in a dxy orbital, it can occupy
the dyz or dzx by simple rotation about the proper axis and the electron can
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rotate in an orbit producing magnetic moment. Hence, the orbital angular
momentum will not be quenched and the orbital angular momentum contribution
will add to the total magnetic moment of the complex
Configurations
d1
d2
d3
d4
d5
d6
d7
d8
d9
Ground-state term
2
T2g
3
T1g
4
A2g
5
Eg (high-spin)
3
T1g (low-spin)
6
A1g (high-spin)
2
T2g (low-spin)
5
T2g (high-spin)
1
A1g (low-spin)
4
T1g (high-spin)
2
Eg (low-spin)
3
A2g
2
Eg
Orbital contribution
Yes
Yes
No
No
Yes
No
Yes
Yes
No
Yes
No
No
No
3 Magnetic moment & structure
In the case of lanthanide complexes, all types of coupling should be considered,
viz., spin-spin, spin-orbital, and orbital-orbital. Incorporating all these, we have
equation 1.1, which gives the theoretical magnetic moment for a complex:
When the spin-orbit coupling and the orbital angular momentum are zero, the
magnetic moment is given by the equation 3.1.
  2 S ( S  1)
3.1
The equation 3.1 is known as the spin-only formula to get the magnetic
moment. S = n/2, where ‘n’ is the number of unpaired electrons. Substituting
this value of S in the equation 3.1 we get Equation 3.2.
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  2 (n / 2)(n/ 2  1)
3.2
  n(n  2)
3.3
This is known as the spin-only formula.
As far as the first row transition metals (3d series) are considered, spin-only
formula works well showing that the orbital angular momentum does not
contribute significantly to the magnetic moment.
Example 1: Iron(III) complex
It is a d5 system. The high-spin complex, whose electronic configuration is
t2g3eg2, has five unpaired electrons. Using the above equation, we can calculate
the magnetic moment using Equation 3.3.
  5(5  2)  5.92 B.M .
3.4
However, the experimental value was found to be in the range 5.70-6.00 B.M.
In the low-spin complex the electronic configuration g is t2g5eg0. There will be
one unpaired electron. That is, n=1. Hence, the calculated value of μ =
[n(n+2)]1/2 = 31/2 = 1.73 BM. The experimental value is in the range 2.0-2.5 BM.
3.1 Lanthanides
Here, all the three kinds of couplings are significant and hence the spin-only
formula will not give the correct value for magnetic moment. The reason is that
the d-orbitals are deeply buried and hence are not perturbed by the ligands.
Therefore, all the three components of coupling contribute appreciably to the
magnetic moment.
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3.2 Spin-cross over region and effect of temperature
Magnetic measurements will tell us whether the complex is a high-spin or lowspin complex as explained earlier. Many transition metal ions are able to form
high-spin and low-spin complexes depending up on the strength of the ligand
field. When the ligand is of intermediate field strength, both high-spin and lowspin complexes can coexist in equilibrium.
Example:
Fe2+ can form both high-spin, Fe(H2O)62+, and low-spin, Fe(CN)62-, complexes.
The high-spin complex has electronic configuration, t2g4eg2 and has 4 unpaired
electrons. Hence, S=4/2 =2 and is paramagnetic. The electronic configuration of
low-spin complex is t2g6eg0. S = 0 and is paramagnetic as there are no unpaired
electrons.
In octahedral complexes, the d6 system will be having
5
T2g as the ground
state in weak-field cases and 1A1g as the ground state in strong-field cases.
This is shown below:
5
E
Cross-over point
1
∆
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T2g
A1g
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Near the cross-over point, the difference in energy between the two spin states
is very small and hence, they exist in equilibrium near this point. The actual
population of the states depends on the temperature.
For the complexes of iron(II) mentioned above, the high-spin complex is
predominant at high temperature and the low-spin complex is predominant at
low temperature.
4 References
1. “Inorganic Chemistry: Principles of Structure and Reactivity”, James
E.Huheey, Ellen A.Keiter, Richard L.Keiter, Okhil K.Medhi, Pearson
Education, Delhi, 2006
2. “Inorganic Chemistry”, Shriver and Atkins, 3/e, Oxford University Press,
2002,
3. “Concise Inorganic Chemistry”, 5/e, Blackwell Science, 2005,
4. “Concepts and Models of Inorganic Chemistry”, 3/e, John Wiley & Sons
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