25 September 1952

Prof. Charles Coulson

64 Old Road

Headington, Oxford

England

Dear Coulson:

I am glad to write to you about your book on valence, and my review of it in NATURE.

I myself am sorry that I didn't like it more. I was troubled to submit the review, after I had written it; but after thinking over the letter for some time, I decided that the review as written expressed my opinion honestly, and that I should submit it - in any case I had agreed to write the review, before seeing the book.

You note that I did not say in my review either that the book has too much mathematics, or that it has too little. I may have suggested that it has one or the other.

As to my criticism of hybridization, I think that it is justified.

First, let me mention the case of HCl, page 209. In your letter you say that you did not say in the book that the two hybrids were equivalent. Actually, on page 209 you say "However, if we first hybridize the chlorine 3s and 3p to form the two hybrids I and II shown in Figure 17, …," and Figure 17 shows two equivalent hybrids. In your letter you say that the drawing was not as you had meant; but in fact the drawing is in the book, and it and the text of the book are the justification for the statement in my review.

I have made quantitative calculations about hybridization in HCl, with the result mentioned in my review. You say in your letter that you doubt if the inequality in the sp hybrids of the bond and the lone pair is as great as I state.

In your letter you refer me to Moffit's paper for discussion of carbon monoxide; this paper is referred to by you also on page 212 of your book, where you discuss carbon monoxide. First, I might point out that you say that the hybrids of 2s and 2p_x for carbon will probably not differ much from the digonal forms s ± p_x; Moffitt in his paper, however, states that the unshared pair occupies an orbital with

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three quarters s character, with the sigma bond orbital having only one quarter s character. I think that Moffitt's statement is much closer to the truth than your statement, and I would not have criticized his statement so strongly.

Nevertheless, I do not think that Moffit's paper provides a justification for either his statement or your statement. On referring to his paper I find that, on page 528, he says "We shall suppose that in the neighborhood of r_ex is changing fairly rapidly and has a value sin-1 l/2 √3 at r = r_e. This corresponds to a bond orbital for the carbon atop with one quarter s character. However, Moffitt has not evaluated this quantity; he has just "supposed" it. He has not obtained it by the process of minimizing the energy as a function of the hybridization parameter; or, if he has, he has not communicated this part of his considerations in the published paper. I may mention that on page 525 he makes a statement about an expectation that I do not subscribe to, namely, that the s orbital would be, at short distances, more strongly sigma-bonding than the p orbital.

I may say that I would criticize the discussion on page 212 on the grounds that you have not considered hybridization for oxygen. Moffitt says that the high promotional energy for oxygen permits him to ignore hybridization for this atom, but I do not think that this is justified. I expect a small amount for oxygen as well as for carbon.

I hope that you will let me know about any errors that you find in this letter. I am deeply interested in these questions - the structure of carbon monoxide, the structure of hydrogen chloride, and so on; and if I an wrong in my ideas - and calculations - about the structures of these molecules I shall be glad to be set right.

It may be that when I speak of hybridization I am using a different meaning for the term than other people as you say in your letter. This leads me to another comment about your book. Unless I have been guilty of a serious oversight of other people's work, I discovered (or invented) hybridization, and was the first to publish the major part of the material contained in your Chapter 8, which has the title Hybridization (I may say that I did not make use of this word in my early papers). The first mention of the combination of the s orbital and 3p orbitals to form four orbitals directed toward the corners of a regular tetrahedron was given in my 1928 paper. A detailed discussion of hybridization, with discussion of the overlap integrals and of the strength of bond orbitals, of tetrahedral hybrid orbitals, trigonal and digonal hybrids, and so on, was given, in my 1931 paper. I think that my 1931 paper might well have been referred

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to at several places in the first sixteen pages of this chapter, rather than first on the seventeenth page, and then only with reference to spd hybridization. Of course, I agree with you (page 219) that there is arbitrariness in hybridization, just as there is in resonance theory; but despite that I think that the introduction of hybrid bond orbitals, and the rather extended discussion of them given in my 1931 paper, constituted a significant contribution to chemical theory, and I have felt especially well pleased about this 1931 paper for twenty-one years now. I may say that I have greater confidence in some of my own simple calculations than in some of the very complicated calculations, involving a larger number of arbitrary decisions, that have been published.

While on this subject I may say that I feel that the resonance discussion of carbon monoxide referred to on page 212 is better than Moffitt's discussion. Also, the last sentence of the next to the last paragraph on this page, about the election-donor properties of carbon monoxide, is written in such a way us to suggest that these properties are understood on the molecular orbital basic but not on the valence—bond basis. In fact, I do not think that there is any significance to the argument, which involves the assumption that a better bond can be formed if the orbital used for the bond is already present in one of the participating molecules, rather than if a change in hybridization occurs on the formation of a new bond, and I do not think that this argument is justified.

Let me mention a few other points.

Page 39. Goudsmit is misspelled in the legend of the figure, but is given correctly in the index.

Page 78. The footnote says "Pauling, Chem. Rev. 1928, but the significance of the symmetry or anti-symmetry was first stressed by Lennard-Jones, 1929." This statement seems to me to indicate that the significance of the symmetry or anti-symmetry was not stressed in my 1928 paper, whereas on rereading it I think that it was.

Page 133. Here you say "Pauling, on purely empirical grounds, first suggested that… ." The whole discussion of electronegativities in my 1932 paper was based on theoretical arguments - quantum mechanical arguments. I do not think that your sentence gives the reader the correct impression about my introduction of the electronegativity scale, the concept of stabilization of bonds through partial ionic character, and so on. A related matter is the use of the expression "purely numerical calculations" in line 7 of page 127. The calculations were quantum mechanical calculations, for a simplified system.

Again, on page 133, you say that it was left to Mulliken to find a better measure of electronegativity. I am not at all sure that Mulli-

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ken's measure is a better measure. In particular, Mulliken has good values of the quantities that enter into his measure only for the univalent atoms, so that his electronegativity expression is restricted in its application.

Page 135. At the bottom of the page you say that Mulliken's estimates of electronegativity are fundamentally more precise than are Pauling's, since they are based entirely on observable quantities. My values are, of course, based on heats of reaction, and only on heats of reaction, and these are observable quantities. It seems to me that your statement is wrong, in that it suggests that my values are not entirely on observable quantities.

Page 191. I doubt that it is justified to say that trigonal orbitals, described above on this page as being entirely equivalent, are needed to describe the carbon atom in the ethylene molecule.

Similarly I myself doubt that the hybridizations given in the table on page 200 are justified.

Page 208. I have been intending for some time to tell you that I think that it is unwise to define a bond dipole moment in such a way as to include the contribution of the electrons in hybrid orbitals about the two separate atoms. It is, of course, true that a carbon atom in the state sp³ has zero electric dipole moment. It is a matter of arbitrariness whether the dipole moment is to be considered as composed of four equal moment vectors directed toward tetrahedral corners or not. If the hybridization regains unchanged on, for example, the stretching of a bond, or the bending of bond, the inclusion of the atomic dipole in the bond dipole might lead to an incorrect prediction about the value of the derivative of the dipole moment. Of course, someone who understood the situation completely would not be led into error, but I am sure that many people have misunderstood your statement that the dipole moment of the C-H bond in methane has a direction such as to make the hydrogen atom negative, and leave the carbon positively charged. I may say that in any case, no matter what definition is used, I do not believe that your statement that the polarity of C-H is probably reversed on going from methane to aromatic, ethylenic, and acetylenic carbon is correct.

I must say that I recognize that some of my comments reflect my opinion about questions to which a final answer has not yet been given.

I hope that you will write to me again about the matter of degree of extent of hybridization in molecules like HCl and carbon monoxide. My feeling about this matter is that the extent of hybridization cannot be nearly so great as suggested in your book - that is, in molecules

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in which the atoms have unshared electron pairs. If the promotion energy is of the order of magnitude of 10 electron volts, then a resonance energy (off-diagonal energy term) of one or two electron volts corresponds to 1 percent or 4 percent hybridization. In exceptional cases the off-diagonal energy term might be as large as three electron volts, giving 8 percent hybridization, but this situation has not arisen in the calculations that I have made.

I trust that you are getting settled nicely in Oxford. I had hoped to see you this summer, but my inquiries about you were not successful in leading me to you.

With beat regards, I am

Sincerely yours,

Linus Pauling:W