Lecture 19: Magnetic properties

and the Nephelauxetic effect

sample

south

thermometer

GouyTube

electromagnet

balance

north

connectionto balance

left: the Gouy balance for determining the magneticsusceptibilityof materials

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.

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 0Ti3+ d1 1.73 1.7-1.8V3+ d2 2.83 2.8-3.1V2+, Cr3+ d3 3.87 3.7-3.9Cr2+, Mn3+ d4 4.90 4.8-4.9Mn2+, Fe3+ d5 5.92 5.7-6.0Fe2+, Co3+ d6 4.90 5.0-5.6Co2+ d7 3.87 4.3-5.2Ni2+ d8 2.83 2.9-3.9Cu2+ d9 1.73 1.9-2.1Zn2+, Ga3+ d10 0 0

Magnetic properties

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.

We have μeff = n(n + 2)

= 4.90 μB

eg

t2g

energy

high spin d6 Co(III)

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)

Spin and Orbital contributions to Magnetic susceptibility

Diagrammatic representation of spin and orbital contributions to μeff

spin contribution – electrons are orbital contribution - electronsspinning creating an electric move from one orbital tocurrent and hence a magnetic another creating a current and field hence a magnetic field

d-orbitalsspinningelectrons

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).

Spin and Orbital contributions to Magnetic susceptibility

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:

Ferromagnetism:

a) b)

a) paramagnetic, magnetically dilute in e.g.

[Fe(H2O)6]Cl2.

b) ferromagnetic,as in metallicFe or someFe oxides.

Fe atoms

unpaired electrons

separated bydiamagnetic atoms

unpaired electrons aligned in their own common magnetic field

unpaired electronsoriented randomly

Antiferromagnetism:

Here the spins on theunpaired electronsbecome aligned in opposite directions sothat the μeff approacheszero, in contrast toferromagnetism, whereμeff becomes very large.An example of anti-ferromagnetism is foundin MnO.

antiferromagnetism

electron spins in oppositedirections in alternate metal atoms

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:

F- > H2O > NH3 > Cl- > CN- > Br- > 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.

The Nephelauxetic Effect:

Note: F-

has largestP values

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:

The Nephelauxetic Effect:

Pd

Cl

Pd

Cl

Pd

Cl Cl Cl

Cl

Pd

Cl

Cl

Cl

Cl

bridging chloride

low-spin d8

square-planarpalladium(II)

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.

The Nephelauxetic Effect:

Distribution of high- and low-spin complexes of the d-block metal ions:

2nd and 3rd row are all low-spin except for PdF2 and [PdF6]4-

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

Co(III) is big exception – all low-spin except for [CoF6]3-

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:

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

Empirical prediction of P values:

The h and k values of Jǿrgensen 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 Δ for [Co(9-ane-N3)2]2+ being 13,300

cm-1. Would the latter complex be

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:

N N

N

H

HH

9-ane-N3

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?

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 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

eg

t2g

energy

Structure of Jahn-Teller distorted [Co(9-ane-S3)2]2+ (see previous problem)

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

longer axial Co-S bonds of 2.43 Å

Co

shorter in-planeCo-S bonds of 2.25 Å

S S

S

9-ane-S3

S

S

S

S

S

S