May 13, 1947

Prof. Kasimir Fajans

Department of Chemistry

University of Michigan

Ann Arbor, Michigan

Dear Professor Fajans:

I am glad, in answer to your letter of April 24, to add the additional comment that seems to be necessary in order to clarify the calculation on page 71 of the second edition of my book on "The Nature of the Chemical Bond." This calculation is made and described in the upper half of page 71, and it had not occurred to me that anyone could fail to follow it.

The statement is made that the O-H bond has 39% ionic character. The discussion also says, "If the bonds were independent, the structures would make the contributions indicated to the normal state of the molecule, the completely covalent structure making a contribution of 37%, each of the half-and-half structures contributions of 24%, and the completely ionic structure a contribution of 15%. Your letter and the earlier letter both refer to the way in which these numbers, 37%, 24%, and 15% are obtained.

The bond between oxygen and one of the hydrogen atoms, which we might call the first hydrogen atom, has 39% ionic character. If the bonds were independent, the ionic character of the bond to the second hydrogen atom would also be 39%, independently of the ionic or covalent state of the bonds to the first hydrogen atom. The probability that the water molecule would have ionic bonds to both the first hydrogen atom and the second-hydrogen atom would thus be 0.39 x 0.39, which is 0.1521, or to the reliability of the calculation, 15%. The probability

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of having an ionic bond to the first hydrogen atom and a covalent bond to the second hydrogen atom would be 0.39 x 0.6l, or 0.2379, that is 24%. Similarly the other half-and-half structure would make the contribution 24%. The completely covalent structure would have the probability 0.61 x O.6l, or 0.3721, that is 37%.

The discussion on page 71, in which this calculation is presented, states specifically that it refers to the condition of the bonds being independent, and the next sentence discusses the effect of an inter-action of the bonds.

I trust that this clears up the question for you. I do not believe that I shall change the presentation of the material on page 71 of the second edition of my book, because it seems to me that the calculation is clear and straightforward.

Sincerely yours,

Linus Pauling:W

cc: Dr. P.C. L. Thorne

[handwritten address]