The Golden ratio, ionic and atomic radii and bond lengths

Abstract

This work arose from the author's finding that the ratio of the radius of hydrogen, estimated recently (C.H. Suresh, N. Koga, J. Phys. Chem. A, 105, 5940 (2001)) by density functional methods, to the ground state Bohr radius is the Golden ratio, which operates in a variety of natural phenomena. It is found that the Golden ratio indeed plays a quantitative role in atomic physics. The interesting results are (1) that it arises in atomic dimensions due to the electrostatic forces between negative and positive charges; (2) that the energy of atomic hydrogen is actually equivalent to the energy of the simplest atomic condenser with the Golden mean capacity; (3) that the origin of two terms in the Rydberg equation for absorption and emission is in fact in the ground state term; (4) that all atoms can be assigned definite values of cationic and anionic radii based on the Golden ratio and covalent radii; (5) that these radii are additive and explain quantitatively bond lengths like those of alkali halides, of hydrides of many elements and of many other bonds, whether covalent or ionic or both; and (6) that the work functions of alkali metals can be evaluated using the bond lengths.

Acknowledgement

The author is grateful for the grant from Project of the Ministry of Industry and Trade of the Czech Republic, Nr. 1H-PK/42.