# Lecture 19: Magnetic properties and the Nephelauxetic effect by IKbImvd8

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```									Lecture 19: Magnetic properties
and the Nephelauxetic effect

connection
balance      to balance
left: the Gouy
balance for
Gouy determining
Tube the magnetic
susceptibility
sample        thermometer
of materials

north              south

electromagnet
Magnetic properties

Magnetic susceptibility (μ) and the spin-only formula.
Materials that are diamagnetic are repelled by a magnetic
field, whereas paramagnetic substances are attracted into
a magnetic field, i.e. show magnetic susceptibility. The
spinning of unpaired electrons in paramagnetic
complexes of d-block metal ions creates a magnetic field,
and these spinning electrons are in effect small magnets.
The magnetic susceptibility, μ, due to the spinning of the
electrons is given by the spin-only formula:

μ(spin-only) =        n(n + 2)

Where n = number of unpaired electrons.
Magnetic properties
The spin-only formula applies reasonably well to metal ions from the
first row of transition metals: (units = μB,, Bohr-magnetons)

Metal ion dn configuration       μeff(spin only) μeff (observed)
Ca2+, Sc3+        d0                  0                0
Ti3+              d1                  1.73             1.7-1.8
V3+               d2                  2.83             2.8-3.1
V2+, Cr3+         d3                  3.87             3.7-3.9
Cr2+, Mn3+        d4                  4.90             4.8-4.9
Mn2+, Fe3+        d5                  5.92             5.7-6.0
Fe2+, Co3+        d6                  4.90             5.0-5.6
Co2+              d7                  3.87             4.3-5.2
Ni2+              d8                  2.83             2.9-3.9
Cu2+              d9                  1.73             1.9-2.1
Zn2+, Ga3+        d10                 0                0
Example:

What is the magnetic susceptibility of [CoF6]3-,
assuming that the spin-only formula will apply:

[CoF6]3- is high spin Co(III). (you should know this).
High-spin Co(III) is d6 with four unpaired electrons,
so n = 4.                                                  energy

eg
We have μeff      =        n(n + 2)

=       4.90 μB
t2g
high spin d6 Co(III)
Spin and Orbital contributions to
Magnetic susceptibility
For the first-row d-block metal ions the main contribution to
magnetic susceptibility is from electron spin. However,
there is also an orbital contribution from the motion of
unpaired electrons from one d-orbital to another. This
motion constitutes an electric current, and so creates a
magnetic field (see next slide). The extent to which the
orbital contribution adds to the overall magnetic moment is
controlled by the spin-orbit coupling constant, λ. The
overall value of μeff is related to μ(spin-only) by:

μeff   =     μ(spin-only)(1 - αλ/Δoct)
Diagrammatic representation of spin and
orbital contributions to μeff

spinning                       d-orbitals
electrons

spin contribution – electrons are      orbital contribution - electrons
spinning creating an electric          move from one orbital to
current and hence a magnetic           another creating a current and
field                                  hence a magnetic field
Spin and Orbital contributions to
Magnetic susceptibility

μeff   =    μ(spin-only)(1 - αλ/Δoct)

In the above equation, λ is the spin-orbit coupling
constant, and α is a constant that depends on the ground
term: For an A ground state, α = 4. and for an E ground
state, α = 2. Δoct is the CF splitting. Some values of λ are:

Ti3+ V3+   Cr3+ Mn3+ Fe2+ Co2+ Ni2+ Cu2+
λ,cm-1   155 105     90 88     -102 -177 -315 -830
Spin and Orbital contributions to
Magnetic susceptibility

Example: Given that the value of the spin-orbit coupling
constant λ, is -316 cm-1 for Ni2+, and Δoct is 8500 cm-1,
calculate μeff for [Ni(H2O)6]2+. (Note: for an A ground
state α = 4, and for an E ground state α = 2).

High-spin Ni2+ = d8 = A ground state, so α = 4.
n = 2, so μ(spin only) = (2(2+2))0.5 = 2.83 μB

μeff   =   μ(spin only)(1 - (-316 cm-1 x (4/8500 cm-1)))
=   2.83 μB x 1.149

=   3.25 μB
Spin and Orbital contributions to
Magnetic susceptibility

The value of λ is negligible for very light atoms, but
increases with increasing atomic weight, so that for
heavier d-block elements, and for f-block elements, the
orbital contribution is considerable. For 2nd and 3rd row d-
block elements, λ is an order of magnitude larger than for
the first-row analogues. Most 2nd and 3rd row d-block
elements are low-spin and therefore are diamagnetic or
have only one or two unpaired electrons, but even so, the
value of μeff is much lower than expected from the spin-
only formula. (Note: the only high-spin complex from the
2nd and 3rd row d-block elements is [PdF6]4- and PdF2).
Ferromagnetism:
In a normal paramagnetic material, the atoms containing the unpaired
electrons are magnetically dilute, and so the unpaired electrons in one atom
are not aligned with those in other atoms. However, in ferromagnetic
materials, such as metallic iron, or iron oxides such as magnetite (Fe3O4),
where the paramagnetic iron atoms are very close together, they can create
an internal magnetic field strong enough that all the centers remain aligned:

unpaired electrons                        unpaired electrons aligned in their
oriented randomly    unpaired electrons   own common magnetic field
a) paramagnetic,
magnetically
dilute in e.g.
[Fe(H2O)6]Cl2.
Fe     separated by
diamagnetic atoms
atoms                                                     b) ferromagnetic,
as in metallic
Fe or some
a)                        b)                              Fe oxides.
Antiferromagnetism:

electron spins in opposite        Here the spins on the
directions in alternate metal atoms   unpaired electrons
become aligned in
opposite directions so
that the μeff approaches
zero, in contrast to
ferromagnetism, where
μeff becomes very large.
An example of anti-
ferromagnetism is found
in MnO.
antiferromagnetism
The Nephelauxetic Effect:
The spectrochemical series indicates how Δ varies for
any metal ion as the ligand sets are changed along the
series I- < Br- < Cl- < F- < H2O < NH3 < CN-. In the same
way, the manner in which the spin-pairing energy P
varies is called the nephelauxetic series. For any one
metal ion P varies as:
Note: F-
has largest   F- > H2O > NH3 > Cl- > CN- > Br- > I-
P values

The term nephelauxetic means ‘cloud expanding’. The
idea is that the more covalent the M-L bonding, the more
the unpaired electrons of the metal are spread out over
the ligand, and the lower is the energy required to spin-
pair these electrons.
The Nephelauxetic Effect:
The nephelauxetic series indicates that the spin-pairing
energy is greatest for fluoro complexes, and least for iodo
complexes. The result of this is that fluoro complexes are
the ones most likely to be high-spin. For Cl-, Br-, and I-
complexes, the small values of Δ are offset by the very
small values of P, so that for all second and third row d-
block ions, the chloro, bromo, and iodo complexes are low-
spin. Thus, Pd in PdF2 is high-spin, surrounded by six
bridging fluorides, but Pd in PdCl2 is low-spin, with a
polymeric structure:                  bridging chloride

Cl        Cl        Cl        Cl        Cl    low-spin d8
square-planar
Pd        Pd        Pd        Pd         palladium(II)

Cl        Cl        Cl        Cl        Cl
The Nephelauxetic Effect:
Δ gets larger down groups, as in the [M(NH3)6]3+
complexes: Co(III), 22,900 cm-1; Rh(III), 27000 cm-1;
Ir(III), 32,000 cm-1. This means that virtually all
complexes of second and third row d-block metal
ions are low-spin, except, as mentioned earlier,
fluoro complexes of Pd(II), such as [PdF6]4- and
PdF2. Because of the large values of Δ for Co(III), all
its complexes are also low-spin, except for fluoro
complexes such as [CoF6]3-. Fluoride has the
combination of a very large value of P, coupled with
a moderate value of Δ, that means that for any one
metal ion, the fluoro complexes are the most likely to
be high-spin. In contrast, for the cyano complexes,
the high value of Δ and modest value of P mean that
its complexes are always low-spin.
Distribution of high- and low-spin
complexes of the d-block metal ions:
Co(III) is big exception – all low-spin except for [CoF6]3-

1st row tend to be high-spin except for CN- complexes

2nd and 3rd row are all low-spin except for PdF2 and [PdF6]4-
Empirical prediction of P values:
Because of the regularity with which metal ions follow
the nephelauxetic series, it is possible to use the
equation below to predict P values:

P      =     Po(1 - h.k)

where P is the spin-pairing energy of the complex, Po is
the spin-pairing energy of the gas-phase ion, and h and
k are parameters belonging to the ligands and metal ions
respectively, as seen in the following Table:
Empirical prediction of P values:

Metal Ion   k       Ligands     h

Co(III)     0.35    6 Br-       2.3
Rh(III)     0.28    6 Cl-       2.0
Co(II)      0.24    6 CN-       2.0
Fe(III)     0.24    3 en        1.5
Cr(III)     0.21    6 NH3       1.4
Ni(II)      0.12    6 H2O       1.0
Mn(II)      0.07    6 F-        0.8
Example:
The h and k values of Jǿrgensen for two
9-ane-N3 ligands and Co(II) are 1.5 and      H               H
N       N
0.24 respectively, and the value of Po in
the gas-phase for Co2+ is 18,300 cm-1,               N
with Δ for [Co(9-ane-N3)2]2+ being 13,300            H
cm-1. Would the latter complex be                9-ane-N3
high-spin or low-spin?

To calculate P for [Co(9-ane-N3)2]2+:
P = Po(1 - (1.5 x .24)) = 18,300 x 0.64 = 11,712 cm-1
P = 11,712 cm-1 is less than Δ = 13,300 cm-1, so the
complex would be low-spin.
Example:
The value of P in the gas-phase for Co2+ is 18,300 cm-1,
while Δ for [Co(9-ane-S3)2]2+ is 13,200 cm-1. Would the
latter complex be high-spin or low-spin? Calculate the
magnetic moment for [Co(9-ane-S3)2]2+ using the spin-
only formula. Would there be anything unusual about
the structure of this complex in relation to the Co-S
bond lengths?                                           energy

eg
P = 18,300(1 – 0.24 x 1.5) = 11,712 cm-1.
Δ at 13,200 cm-1 for [Co(9-ane-S3)2]2+ is
t2g
larger than P, so complex is low-spin.
CFSE = 13,200(6 x 0.4 – 1 x 0.6) = 23,760 cm-1.
Low-spin d7 would be Jahn-Teller distorted, so would
be unusual with four short and two long Co-S bonds
(see next slide). μeff = (1(1+2))0.5 = 1.73 μB
Structure of Jahn-Teller distorted
[Co(9-ane-S3)2]2+ (see previous problem)

longer axial Co-S
bonds of 2.43 Å S

S                               S       S
Co            S

S                 S

S
S
shorter in-plane
Co-S bonds of 2.25 Å

9-ane-S3
Structure of [Co(9-ane-S3)2]2+
(CCD: LAFDOM)

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