February 5, 1968

TO: Hunter Hill

FROM: Linus Pauling

SUBJECT: Theory of Metals

I was interested to have you tell me the other day that you yourself had the idea that my theory of metals, described in my 1938 Physical Review paper and later papers, did not account for electrical conductivity and other characteristic properties of metals. I had thought everyone, including physicists, knew that the theory did account for these properties, as well as for other properties that I was especially interested in discussing because of the unsatisfactory nature of the discussion by earlier theories of the electronic structure of metals. I am writing to point out that in my papers, beginning in 1938, I have mentioned the explanation of metallic conductivity and other characteristic properties of metals, although my references to these matters may have been so succinct as to have been overlooked by some readers.

For example, on page 900 of my 1938 paper, describing the lithium crystal as involving covalent bonds resonating among the available positions, I state that "this qualitative description of the interactions in the metal is compatible with quantum mechanical treatments which have been given the problem", with a reference to Slater, Physical Review 35, 509 (1935). In the paper there is a diagram showing that the band A is only partially filled. I think that I assumed that readers who knew the earlier work on the electronic theory of metals would realize that this feature in common of my theory and the ordinary electronic theory (Pauli, Sommerfeld, and so on) would lead to essentially the same explanation of electrical conductivity.

In my paper in Nature, 161, 1019 (I94P) I pointed out that the metallic orbital is the feature of the electronic structure of metals that permits the unsynchronized resonance of electron pairs from one interatomic position to another, leading to the characteristic metallic properties: "The electronic conductivity and other characteristic properties of metals may be described in terms of the transfer of the positive and negative charges from atom to atom accompanying the resonance of the valence bonds." In my paper in Physica, 15, 23 (1949) there is the following statement: "The process of electrical conductivity can be described on this picture as the preferential motion of the positive charges and negative charges from atom to atom through the crystal, under the influence of the field, in the way corresponding to a flow of electrical current, and the other characteristic metallic properties can similarly be described in terms of the resonance of the valence bonds.

Also, a little later on, there is the sentence "It seems likely that in many cases the treatment that has been carried out of the properties of metals on the basis of the molecular-orbital theory can be translated with little change into the resonating-valence-bond language. Thus a rough approximation to the wave function for a metal can be made by considering the independent resonance of electron pairs (bonds) among all of the interatomic positions in the crystal..."

There is then some discussion of the theoretical treatment described in ay paper in the Proceedings of the Royal Society, A196, 343 (1948). In this paper a way of formulating a wave function in terms of pairs of electrons is described. A wave function is discussed in which there are individual terms representing the motion of a pair of electrons, involving a momentum vector for the pair of electrons in the Bloch function.

There is also a discussion of Brillouin zones for these resonating electron pairs, and the statement that when one of these Brillouin zones is filled low electrical conductivity and brittleness may be expected, as discussed by Pauling and Ewing, Rev. Mod. Phys. 20, 112 (1948).

Essentially the same statements are made in my paper in Journal de Chimie Physique, 46, 276 (1948). In the discussion (page 284) Mott raised some questions, and Mulliken said that he thought that my ideas were compatible with the Bloch theory and the molecular orbital treatment of metals. Born, Néel, and Coulson discussed various aspects of the theory. Coulson said that the essential point of my theory was that pairs of electrons moved from place to place in the crystal to give electrical conductivity, whereas in the earlier treatments individual electrons were considered to move. Nobody felt that my treatment did not account for electrical conductivity.

In ray paper in the Journal of the Chemical Society, 1948, 1461, the paragraph on the resonance of bonds among various positions ends with the sentence "The electrical conductivity of metals may be described as resulting from the motions of these negative and positive charges through the crystal."

I think that the papers mentioned above (1948, 1949) were the first to discuss the motion of pairs of electrons In a metal. I don't remember when the discussion by Cooper was published. Bardeen once told me that their ideas about superconductivity were somewhat similar to ray earlier ideas.

My paper on ring currents in aromatic compounds that I mentioned to you is in the Journal of Chemical Physics, 4, 673 (1936).

Linus Pauling

LP: jj

cc: Professor Matthias