Difference Density in the C-F Bond

Transcript of an interview with

Prof. Jack D. Dunitz (ETH Zurich)

in the courtyard of the Swedish Royal Academy of Sciences

Friday, September 13, 2002

For video click either (160 x 120, 5.6 Meg) or (240 x 180, 10.3 Meg)
For figures click here. (or see Helv. Chim. Acta, 66, 123 (1983)

J. M. McBride:

Well, Jack, every year in class we talk about what bonds are and “How do you know?”  The ultimate evidence is electron-density difference maps.

One of the best examples is the tetrafluorodicyanobenzene, which we talk about. But when we come to the end of the day, somebody always asks, “Where is the bond between carbon and fluorine?”

So, what do we say?


Well, I would say that the conventional wisdom about the chemical bond, which one finds in many textbooks of chemistry, is based on the hydrogen molecule.  The hydrogen molecule has only got two electrons, so you don’t have to worry about the Pauli Exclusion Principle.  You can’t have more than two electrons in the same part of space.[1]

When you are dealing with atoms which contain more than two electrons, and particularly more than a half-filled  shell, and you want to make chemical bonds between such elements, you have a real problem here.

Now, about difference maps.

A difference map is a difference between the actual electron density and some standard electron density - some nominal electron density - and there is no agreement about what one should pick.

Our standpoint was that the model which is most neutral with regard to the symmetry of the situation starts off with a spherically-averaged atom.

Now the spherically-averaged fluorine atom in its four tetrahedral orbitals has got seven electrons in four orbitals, and therefore the spherically-averaged orbital pointing towards the carbon atom contains seven-fourths of an electron, if my calculation is right.

If the carbon atom, neutral, spherically averaged, is going to contribute one electron, then that simple superposition is going to end you up there with more than two electrons in the same region of space, and as we all know that’s not allowed. So the actual molecule, the actual bond, has to have not more that the sum of two electron densities, but less.

And that’s my interpretation of the C-F bond density.

Some authorities, such as Klaus Rudenberg, want to...

Klaus Rudenberg wrote a hundred-page article in the '60s about the hydrogen molecule and its standing as a basis for the chemical bond, and Klaus would like to take as the standard atom, not the spherically averaged atom, but the oriented ground-state atom.  And since fluorine has a ground state of doublet P, there is one direction, call it the direction along the bond, which you can organize so that it has only one electron in that direction and then one plus one - that comes out OK, if you do it that way.

The same thing, by the way, occurred when you look at O-O bonds, because you get more than two in the middle, or even N-N.

Yep. So does that do it?


That answers my question.  Thank you, Jack.

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[1] Note the reference to quantum mechanics, which we will be discussing shortly.

copyright 2002 J. M. McBride