A Simple Modification of Morse's Rule

Abstract

MORSE¹ introduced an empirical rule to the effect that ω_e, r_e≈10^-21 cm² …(1),where ω_e,r_e respectively, are the equilibrium nuclear vibration frequency (in cm.^-1) and the equilibrium nuclear separation (in cm.) of a diatomic molecule, as deduced from spectra. In a recent paper², dealing with the classification of non-hydride diatomic molecules into groups and periods, I have emphasised the importance of the group number n, equal to the number of shared electrons, or total number of valency electrons of the two separate atoms. The way in which the errors from the strict requirements of Morse's rule distribute themselves in certain periods suggests that the insertion of some function of the group number into the Morse expression might lead to better agreement with observation. For non-hydride diatomic molecules of the period containing two completed K rings associated with each nucleus, I have derived the following empirical modification of Morse's relationship: