### Linus Pauling's Development of an Electronegativity Scale

The modern definition of electronegativity is due to Linus Pauling. It is:

The power of an atom in a molecule to attract electrons to itself. (p. 88)

Although electronegativity, as a concept dates back to 1809, no one had been able to quantify it until Pauling in 1932. He based his work on differences in bond energies. All page references are to "The Nature of the Chemical Bond" Third Edition (1960) by Linus Pauling.

Warning: the following discussion may get hard to follow, unless you have the underlying concepts. I'm going to try and take it real slow, step-by-step. In order to use electronegativity in your class, you don't have to understand how it came to be, so you can skip this stuff if you want. I feel safe in saying that no high school teacher is going to put this stuff on a test. What would be tested would be using the electronegativity scale, not how it came to be.

So why write this lesson? Because I want to.

Now to Pauling's ideas. He writes what is called a wave function. Here it is:

ΨAB = aΨA­B + bΨA+ + dΨA¯B+

Now, don't freak out. I'm going to explain it. Actually, the idea Pauling draws out of the above is simple. It just the mysterious (to you, the rookie) symbology gets in the way.

1. A and B are atoms of two different elements and they have different electronegativity values.
2. ΨAB stands for the actual energy of a bond. This is a value determined by experiment and is the amount needed to dissociate (or break) the bond in question. Pauling looks these values up in reference sources.
3. a, b, and d are constants. We will ignore them.
4. ΨA­B stands an energy amount that Pauling calls the "normal covalent bond" for A­B. Keep in mind that in a covalent bond, the electrons are being shared. This needs more explanation.
5. ΨA+ stands for the energy contribution arising from what Pauling calls the "additional ionic character of the bond." He shows both possible cases of ionic bonding, one where A has lost the electron and one where B has lost the electron. One of these will be predominate over the other, since the electronegativity values are different.

This additional ionic character of the bond will be the key to quantifying electronegativity.

Here is what Pauling says:

". . . the energy of an actual bond between unlike atoms is greater than (or equal to) the energy of a normal covalent bond between these atoms. This additional bond energy is due to the additional ionic character of the bond; that is, it is the additional ionic resonance energy that the bond has as compared with a bond between like atoms." (p. 80, italics his)

He proceeds to test this conclusion by calculating the "normal covalent bond" energy and comparing it with the experimentally measured bond energy. Skipping a bit of the development, he arrives at this equation:

Δ' = D(A­B) - [ D(A­A) · D(B­B) ]1/2

The symbols mean:

1. Δ' is the difference of the two values on the right side. He uses a prime because he uses Δ in a prior equation we need not discuss.
2. D(A­B) is the experimentally measured bond energy
3. [ D(A­A) · D(B­B) ]1/2 is Pauling's way to calculate the "normal covalent bond" energy. He calls it the "postulate of the geometric mean" on p. 83. It is simply multiplying the two values together and then taking the square root.
4. He had been adding the two values and dividing by two. He found the multiply/square root method gave better values.
Δ' (which is the additional ionic energy of the bond) holds the key to determining electronegativity values.

Pauling knows that Δ' is a difference (subtraction) between two different values. He postulates that this difference is due to the difference in electronegativites between the two atoms. In other words, he's looking for this relationship:

Δ' = some function of (xA - xB)

He plays with the numbers and eventually finds that dividing Δ' by 30 and then taking the square root gives him what he wants, so the correct equation is:

Δ' = 30 (xA - xB)2

The bond energy would be:

D(A­B) = [ D(A­A) · D(B­B) ]1/2 + 30 (xA - xB)2

There is one last thing to do. The equation he had represents a difference in electronegativities between two atoms. So he assigned a value of 4.0 to fluorine and from there he could calculate all the other values.

Linus Pauling was presented the 1954 Nobel Prize in Chemistry "for his research into the nature of the chemical bond and its application to the elucidation of the structure of complex substances." Here is the presentation speech at the award ceremony in December, 1954 describing his work.

After Pauling's initial announcement of his scale in 1932, others became involved in this area and developed electronegativity scales of their own. Others expanded the linear scale of pure covalent on one end and ionic on the other into a triangular plot with the three vertices being pure covalent, ionic, and metallic. The metallic bond is an important bond usually glossed over in high school. The ChemTeam hopes to someday write a tutorial on these triangular diagrams.

Research in electronegativity continues to the present day.