Oct. 2, 1934

Dr. Stillwell:

In your letter you suggest using radius for oxygen in between bivalent oxygen and atomic oxygen. However, I don't know what the radius of "atomic oxygen" is. I would say that it has a covalent radius (0.66 Å) giving distance to an atom to which it is bonded, and a van der Waals radius, giving distance to non-bonded atoms. No systematic study of this has been made; the v.d. Waals radius is probably about 1.5 Å, but quite variable.

It is only by using the ionic viewpoint that the radius ratio can be made useful. I used my "univalent radii" in the antimonic acid paper because these radii represent the relative sizes of ions and so should be used in simple packing considerations. The crystal radii do not represent relative sizes of ions of different charge, but contain correction factors for valence. I think you have overlooked the definition of my univalent radii -- see pp. 770 and 773 of my 1927 paper. The univalent radius for O⁼ is not the ionic radius of O^-, and the N-O distance in NO₃ ^- should not be the sum of the univalent radii, but rather this sum with a large correction factor, equal to √√10 - 2/n-1 with n=6 (Eq. 13).* This gives 2.01 x .631 = 1.27 Å. Another value is the sum of the crystal radii, 1.51 Å with about a -15% correction because of coordination number 3 (instead of 6); this gives 1.28 Å, with an uncertainty of about 0.05 Å or more because of the uncertain correction. A more reliable distance can be predicted from the covalent viewpoint. The double-bond distance is 1.22 Å (p 224), and recent studies which we have made indicate that a correction of + 0.05 Å should be made for resonance between one double & two single bonds, giving 1.27 Å. This should be reliable to within 0.01 Å.

I hope this clears up your difficulty. The only thing not discussed in detail is the use of √z₁z₂ in place of z in Eq. 13. This was used for fluorite (√2) at the bottom of the next page.

Very truly yours,

Linus Pauling

* The 10 is the product of valences 2 and 5 of O⁼ and N⁵⁺.