11 July 1955

Professor H. C. Longuet-Higgins

The Chemical Laboratory

University of Cambridge

Cambridge, England

Dear Longuet-Higgins:

I have read with interest your paper by Roberts, in the last issue of the Proceedings of the Royal Society, on the electronic structure of an icosahedron of boron atoms. I am in general pleased with your results, but there is one point that I should like to discuss with you. Some years ago I began work along similar lines, and the work is in fact being continued now by Dr. Hoerni, who will remain here for another year.

You have reached the conclusion that the tetragonal structure for boron reported by Hoard and his co-workers cannot be of the closed-shell type. I think that there is a flaw in your argument. First, I am not sure that each of the two tetrahedral boron atoms in the unit must bear an extra electron, and form four single bonds with its neighbors. Let us, however, assume that this is so, and that 16 electrons of the total of 150 in the unit are tied up in this way. There remain 134 electrons. Let us assume that 26 electrons per icosahedron are then involved in filling the closed shells. There then remain 30 electrons per unit, which are to be assigned to the bonds connecting boron icosahedra. There are 20 bonds of this sort per unit, which would require 40 electrons if the bonds were single bonds. I suggest, however, that the bonds are not single bonds, but are three-quarters bonds, requiring only one and one half electrons per bond - that is, I suggest that a treatment of the entire crystal, with the icosahedra conjugated together, would show that this number of electrons corresponds to a closed shell.

I might point out that your assumption that the outward-pointing orbitals of the icosahedron are all involved in forming single bonds, rather than fractional bonds, does not correspond to the assumption made for the inward-pointing orbitals - namely, that only those with a positive value of the energy parameter (corresponding to stabilization) are to be occupied. In your Table 5 four of the outward-pointing orbitals, rather than 12, are given positive values of the energy parameter. By including the five orbitals with symmetry V, which have a small negative value of this parameter, a total of 9 would be obtained, corresponding to an average of three-quarters occupancy. This is not exactly right, of course, because it includes the two boron atoms bonded to tetrahedral borons, as well as the other ten. But, of course, the icosahedron of boron atoms does not have true icosahedral symmetry in this tetragonal structure, in which two of the twelve boron atoms are bonded to tetrahedral boron atoms, and the other ten are not. I do not think that the argument that you have given is justification for throwing doubt on the structure described by Hoard and his co-workers.

There is another point that I may make. If your assumption were correct, the boron-boron distance between icosahedra should be significantly less than that within an icosahedron. I do not think that the x-ray evidence supports this. It is true that the structure determinations for B₄C and tetragonal boron are not precise ones. However, the problem is the same in CaB₆, which is the substance which we have also been treating theoretically. In CaB₆ each boron atom forms four bonds within an octahedron, and a fifth bond pointing out from the octahedron. You would probably treat this problem in an analogous way to that in which you have treated the problem of ocosahedral structures, whereas we have been considering the problem of the entire crystal, involving conjugated octahedra. Your assumption would in this case mean that the bonds pointing out from an octahedron are single bonds, involving two electrons per bond, and leaving only 1.2 electrons per bond within the octahedron. Twenty years ago Weinbaum and I made a very careful study of CaB₆, and we were able to show that the boron-boron distances between octahedra are identical, to within 0.01 Å, with those within an octahedron. It is evident that these bonds are of essentially the same type, involving about 1.33 electrons per bond.

Sincerely yours,

[Linus Pauling]

Linus Pauling:W

To: Professor Pauling From: H. Segall Date: 7-11-55 E

SUBJECT: The Average of Amino Acid Residues Contained in the Unit Cell of Collagen.

A survey of the recent literature was made to collect consistent on the unit cell dimensions, density and average residue weight for collagen. The most complete work on dry and wet untreated kangaroo tail tendon was reported by Rougvie and Bear (J. Amer. Leather Chemists Assn., 48, 735 (1953)). A less comprehensive investigation was made by Dr. R. A. Pasternak of this Institute and was contained in a report to Professor Pauling on March 11, 1954.

According to the report of Dr. Schroeder of Nov. 6, 1952 the existing chemical analyses of the amino acid content of mammalian collagen are sufficiently consistent not to warrant any further determinations at present. An average residue weight of 92.6 was taken from the work of Bowes and Kenton (Biochem. J., 43, 358 (1948))

(1) Rougvie and Bear reported the equatorial spacing of exhaustively dried kangaroo tail tendon as 10.6 A. The sample was dried for one week over P₂O₅ at room temperature. Although this value is slightly higher than other reported values it is consistent with their measurements of the equatorial spacing as a function of the water content of collagen from dry to water saturated specimens. The usual meridional distance of 2.86 Å was also reported. The volume of the hexagonal unit cell is accordingly V = 2.86 x 10.6²/cos 30 = 371.1 A³.

The density of dry unpurified collagen was determined by flotation in bromheptane and carbon tetrachloride by Rougvie and Bear. Their reported value of 1.34 is close to other reported values of dry collagen and gelatin. The weight for a mole of units is then

M = V x d x N = 371.1 x 10-24 x 1.34 x 6.023 x 1023 = 299.5 gms

By taking 92.6 as the average residue weight the average number of amino acid residues in the unit cell, n, is found to be

[Data Equation]

The uncertainties in this value of n are the average residue weight (1 or 2%) and the density. The presence of non-collagenous material in the unpurified sample may affect the observed density.

(2) The experimental values as determined by Dr. Pasternak for hydrated collagen containing 16.3% water are as follows:

meridional spacing = 2.88 Å

equatorial spacing = 11.54 Å

density = 1.32

By taking an average residue weight of 93.3 and adding 18.6 for the water associated with it he obtained an apparent molecular weight of 111.9. The calculated value of n was 3.15.

Rougvie and Bear have shown that from 0 to about 20 g water/100 g collagen the sorbed water was effective in increasing the volume of the unit cell according to its normal density of 1.00. Greater hydration increases the volume at a considerable smaller rate. Thus it can be said that Dr. Pasternak’s value of n is fortuitously close to Bear’s value since his water of hydration falls within the 0 to 20 range.

(3) The value of 3.23 as the average number of amino acid residues in the unit cell of collagen calculated from the data of Rougvie and Bear is probably accurate to 3 or 4 per cent. The reasonably exhaustive work of Rougvie is sufficient for the present.

Herbert Segall