Lecture 19: Magnetic properties and the Nephelauxetic effect

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Lecture 19 Magnetic properties and the
Nephelauxetic effect
connection to balance
balance
left the Gouy balance for determining the
magnetic susceptibility of materials
Gouy Tube
sample
thermometer
south
north
electromagnet
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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.
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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

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Example

• What is the magnetic susceptibility of CoF63-,
  assuming that the spin-only formula will apply
• CoF63- is high spin Co(III). (you should know
  this). High-spin Co(III) is d6 with four unpaired
  electrons, so n 4.
• We have µeff n(n 2)
• 4.90 µB

energy
eg
t2g
high spin d6 Co(III)
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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, ?. The overall
  value of µeff is related to µ(spin-only) by
• µeff µ(spin-only)(1 - a?/?oct)

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Diagrammatic representation of spin and orbital
contributions to µeff
d-orbitals
spinning 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
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Spin and Orbital contributions to Magnetic
susceptibility

• µeff µ(spin-only)(1 - a?/?oct)
• In the above equation, ? is the spin-orbit
  coupling constant, and a is a constant that
  depends on the ground term For an A ground
  state, a 4. and for an E ground state, a 2.
  ?oct is the CF splitting. Some values of ? are
• Ti3 V3 Cr3 Mn3 Fe2
  Co2 Ni2 Cu2
• ?,cm-1 155 105 90 88 -102
  -177 -315 -830

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Spin and Orbital contributions to Magnetic
susceptibility

• Example Given that the value of the spin-orbit
  coupling constant ?, is -316 cm-1 for Ni2, and
  ?oct is 8500 cm-1, calculate µeff for
  Ni(H2O)62. (Note for an A ground state a 4,
  and for an E ground state a 2).
• High-spin Ni2 d8 A ground state, so a 4.
• n 2, so µ(spin only) (2(22))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

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Spin and Orbital contributions to Magnetic
susceptibility

• The value of ? 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, ? 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 PdF64- and
  PdF2).

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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 aligned in their own common
magnetic field
unpaired electrons oriented randomly
unpaired electrons

• paramagnetic,
• magnetically
• dilute in e.g.
• Fe(H2O)6Cl2.
• b) ferromagnetic,
• as in metallic
• Fe or some
• Fe oxides.

separated by diamagnetic atoms
Fe atoms
a) b)
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Antiferromagnetism
Here the spins on the 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.
electron spins in opposite directions in
alternate metal atoms
antiferromagnetism
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The Nephelauxetic Effect

• The spectrochemical series indicates how ?
  varies for any metal ion as the ligand sets are
  changed along the series I- lt Br- lt Cl- lt F- lt
  H2O lt NH3 lt 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
• F- gt H2O gt NH3 gt Cl- gt CN- gt Br- gt I-
• 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.

Note F- has largest P values
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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 ? 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
low-spin d8 square-planar palladium(II)
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The Nephelauxetic Effect

• ? gets larger down groups, as in the M(NH3)63
  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 PdF64- and PdF2. Because of the large
  values of ? for Co(III), all its complexes are
  also low-spin, except for fluoro complexes such
  as CoF63-. Fluoride has the combination of a
  very large value of P, coupled with a moderate
  value of ?, 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 ? and modest value
  of P mean that its complexes are always low-spin.

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Distribution of high- and low-spin complexes of
the d-block metal ions
Co(III) is big exception all low-spin except
for CoF63-
1st row tend to be high-spin except for CN-
complexes
2nd and 3rd row are all low-spin except for PdF2
and PdF64-
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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

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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

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Example

• The h and k values of J?rgensen for two
• 9-ane-N3 ligands and Co(II) are 1.5 and
• 0.24 respectively, and the value of Po in
• the gas-phase for Co2 is 18,300 cm-1,
• with ? for Co(9-ane-N3)22 being 13,300
• cm-1. Would the latter complex be
• high-spin or low-spin?
• To calculate P for Co(9-ane-N3)22
• P Po(1 - (1.5 x .24)) 18,300 x 0.64
  11,712 cm-1
• P 11,712 cm-1 is less than ? 13,300 cm-1, so
  the
• complex would be low-spin.

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Example

• The value of P in the gas-phase for Co2 is
  18,300 cm-1, while ? for Co(9-ane-S3)22 is
  13,200 cm-1. Would the latter complex be
  high-spin or low-spin? Calculate the magnetic
  moment for Co(9-ane-S3)22 using the spin-only
  formula. Would there be anything unusual about
  the structure of this complex in relation to the
  Co-S bond lengths?
• P 18,300(1 0.24 x 1.5) 11,712 cm-1.
• ? at 13,200 cm-1 for Co(9-ane-S3)22 is
• 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(12))0.5
  1.73 µB

energy
eg
t2g
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Structure of Jahn-Teller distorted
Co(9-ane-S3)22 (see previous problem)
longer axial Co-S bonds of 2.43 Å
S
S
Co
S
S
S
S
shorter in-plane Co-S bonds of 2.25 Å
Structure of Co(9-ane-S3)22 (CCD LAFDOM)