Magnetic Moments

Magnetic moments are often used in conjunction with electronic spectra to gain information about the oxidation state and stereochemistry of the central metal ion in coordination complexes.
(Determination of the magnetic moment using the Gouy method has been simplified by the use of an on-line template or spreadsheet.)

For first row transition metal ions in the free ion state, ie isolated ions in a vacuum, all 5 of the 3d orbitals are degenerate.
In octahedral complexes, a simple crystal field theory approach suggests that for these ions the d orbitals are no longer degenerate but are split such that 2 orbitals, the dx2-y2 and the dz2 are at higher energy than the dxy, dxz, dyz.

For ions with between 4 and 7 d electrons, this gives rise to 2 possible arrangements called either high spin-low spin or weak field-strong field respectively. See an interactive JAVA script for examples.

In tetrahedral complexes the orbitals are again split, such that 2 orbitals (the dx2-y2 and the dz2) are now at lower energy than the remaining 3.
Tetrahedral complexes are ALL high spin since the difference between the 2 subsets of orbitals is much smaller than is found in octahedral complexes (Δtet= 4/9 Δoct).
The formulae most frequently used to calculate magnetic moments of first row transition metal ion complexes are given below:
formulae for magnetic moments
The first formula is known as the spin only formula, the second takes into account possible contributions from orbital angular momentum and the third is used to make small adjustments when the ground term for the metal ion is either A or E.
S is the spin quantum number = 1/2 for each unpaired electron
L is the orbital angular momentum
α is a constant = 2 for E and 4 for A ground terms
λ is the spin orbit coupling constant
Δ is the crystal field splitting parameter found from the spectrum of the complex.

To illustrate:
predict the variation of the magnetic moments for the series of tetrahedral complexes Copyr2Cl2, Copyr2Br2 and Copyr2I2.
Their visible spectra have been recorded in chloroform
vis spectra of CoPyr2X2 complexes
and from the centre of their main absorption bands in the visible region, ν (in wavenumbers cm-1) can be seen to be roughly:
1 Copyr2Cl2 16260 cm-1 (615 nm)
2 Copyr2Br2 15870 cm-1 (630 nm)
3 Copyr2I2 14925 cm-1 (670 nm)
These peaks represent the third electronic transition expected for these complexes, the other bands occurring in the infrared region, so although we may be able to place the halides into order of the spectrochemical series, we need to consult an Orgel diagram before trying to calculate Δ.
The Orgel diagram appropriate for these types of complexes is given below:
Orgel diagram for F state
oct d3,d8 tet d2,d7    ←-----------------------------------→    oct d2,d7 tet d3,d8
and for d7 tetrahedral the ground term is 4A2.

Three peaks are predicted in their electronic spectra, namely:

4T2    ← 4A2     ν1
4T1(F) ← 4A2     ν2
4T1(P) ← 4A2     ν3 ** the band observed in the visible region

The energy of the third transitions is approximately ν3 = 6/5 Δ + 15B (where B is the Racah parameter and ignoring configuration interactions). For Co(II) tetrahedral complexes B has generally been found to be about 750 cm-1.
Hence Δ for the three complexes above can be calculated to be roughly, Δ = (ν3 - 15x750) x 5/6, or:

Copyr2Cl2 (16260-15x750) x 5/6 = 4175 cm-1
Copyr2Br2 (15870-15x750) x 5/6 = 3850 cm-1
Copyr2I2 (14925-15x750) x 5/6 = 3063 cm-1

For three unpaired electrons the spin only magnetic moment is predicted to be 3.87 BM.
Using a value for the free ion spin orbit coupling constant (λ) of -172 cm-1 then a better approximation of the magnetic moment can be obtained by using the third formula above. This would give a value of:

Copyr2Cl2     3.87*(1+ 688/4175) = 4.49 B.M. found 4.42 BM
Copyr2Br2     3.87*(1+ 688/3850) = 4.57 B.M. found 4.50 BM
Copyr2I2       3.87*(1+ 688/3063) = 4.76 B.M. found 4.48 BM

In the case of the series;

CoI42-, CoBr42-, CoCl42-, Co(NCS)42-
the magnetic moments have been recorded as
4.77,      4.65,      4.59,      4.40 BM

showing even more clearly the inverse effect of the spectrochemical series on the magnetic moment.

return to the CHEM2101 (C21J) course outline

Copyright © 1995-2010 by Robert John Lancashire, all rights reserved.

Created and maintained by Prof. Robert J. Lancashire,
The Department of Chemistry, University of the West Indies,
Mona Campus, Kingston 7, Jamaica.
Created Dec 1995. Links checked and/or last modified 12th October 2010.