Wednesday, March 12, 2014

Notes on Linus Pauling and Magnetic Susceptibility (I)

Linus Pauling is such a big name that whatever text I read, I see his name. He is one of the most important chemists and I truly believe that he deserved at least 3 Nobel Prizes in Chemistry. So, instead of writing a single post about him, I decided to write small pieces as often as I can. After all, there is no way I can tell everything I want to tell about him in one single post. 

I was just reading an inorganic chemistry text and I came across his name at least 10 times in the first 27 pages. Consequently, I decided that it is a good idea to write the most interesting part about him so far.

In early 20th century,  chemists were trying to assign oxidation states to some transition metals and trying to find out the electronic structure of them. They were able to measure the spin. magnetic moments and permanent dipoles of the metal complexes but it was not an easy task to find the correct electronic structure. For example, in 1941, Dwyer and Nyholm prepared several Rhodium complexes and they thought that it was Rh(II). But, they could not understand why the complexes were diamagnetic. Note that Rh(II) has a d7 electron configuration therefore should me paramagnetic and Rh(III) has d6. The answer came in 1960 when it was discovered that the complexes had hydrides and the oxidation state of Rh was three.

Linus Pauling predicted that diamagnetic Ni(II) complexes should be 4 coordinate and at that time this was not observed yet. Later, he also successfully predicted several other geometries for Au(III), Ag(II) and Co(II) complexes. 

He had some unsuccessful predictions too and the most well known of these is his ideas about Vitamin C. Anyway, although his Valence Bond theory is a very successful theory to explain bonding, but for transition metals it was not good enough. I will give the example in the book now.

The magnetic moment of [FeF6]3- is 5.9 Bohr magneton and the moment for  [Fe(CN)6]3- is 1.9 . These suggest that there are 5 and 1 unpaired electrons respectively. In order to explain this, he tried to use Valence Bond Theory and also suggested that the bonding in the first complex was ionic whereas it was covalent for the second complex. 

Better explanations came with Molecular Orbital, Crystal Field and Ligand Field theories. Simply, we now say that F- is a weak field ligand and CN- is a strong field ligand. Therefore, for Fe(III) (d5) in octahedral field the electrons occupy the orbitals like these and give rise to the observed moments:

While at it, I should mention that we can simply calculate the spin only moment by


where n is the number of unpaired electrons. But, because there is also the orbital motion of electrons, another moment is also added to the spin only moments. From my undergrad experience in the tests or practice problems, I saw moments like 2 point something for one unpaired electron etc. So, the experimental values are sometimes very close, sometimes a little bit larger.

So, in theory spin only moments can be summarized in this table:

Number of unpaired electrons
Spin only moment (Bohr magneton)
1 1.73
2 2.83
3 3.87
4 4.91
5 5.92

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