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 (Δ

The formulae most frequently used to calculate magnetic moments of first row transition metal ion complexes are given below:

Where:

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 Copyr

Their visible spectra have been recorded in chloroform

1 Copyr_{2}Cl_{2} 16260 cm^{-1} (615 nm)

2 Copyr_{2}Br_{2} 15870 cm^{-1} (630 nm)

3 Copyr_{2}I_{2} 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.2 Copyr

3 Copyr

The Orgel diagram appropriate for these types of complexes is given below:

Three peaks are predicted in their electronic spectra, namely:

The energy of the third transitions is approximately ν

Hence Δ for the three complexes above can be calculated to be roughly, Δ = (ν

Copyr_{2}Cl_{2} (16260-15x750) x 5/6 = 4175 cm^{-1}

Copyr_{2}Br_{2} (15870-15x750) x 5/6 = 3850 cm^{-1}

Copyr_{2}I_{2} (14925-15x750) x 5/6 = 3063 cm^{-1}

Copyr

Copyr

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

Copyr_{2}Cl_{2} 3.87*(1+ 688/4175) = 4.49 B.M. found 4.42 BM

Copyr_{2}Br_{2} 3.87*(1+ 688/3850) = 4.57 B.M. found 4.50 BM

Copyr_{2}I_{2} 3.87*(1+ 688/3063) = 4.76 B.M. found 4.48 BM

Copyr

Copyr

In the case of the series;

CoI_{4}^{2-}, CoBr_{4}^{2-}, CoCl_{4}^{2-}, Co(NCS)_{4}^{2-}

the magnetic moments have been recorded as

4.77, 4.65, 4.59, 4.40 BM

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.