A Relation between Bond Force Constants, Bond Orders, Bond Lengths, and the Electronegativities of the Bonded Atoms

A relation of the form ${\mathrm{k=aN(x}}_A{x}_B{\mathrm{/d}}^2{)}^{\frac{3}{4}}\mathrm{+b}$ has been found to hold accurately for a large number of diatomic and simple polyatomic molecules in their ground states. (The average deviation of k calculated from k observed for seventy‐one cases is 1.84 percent.) Here k is the bond‐stretching force constant, d the bond length, N the bond order, and x_A and x_B are the electronegativities of the bonded atoms. If k is measured in dynes/cm×10⁻⁵ and d in Angstrom units, a and b have the values 1.67 and 0.30, respectively, for stable molecules exhibiting their normal covalencies, except those in which both bonded atoms have only one electron in the valence shell; for diatomic molecules of the alkali metals, Na₂, NaK, etc., a and b are 1.180 and −0.013, respectively; for hydrides of elements having a single electron in the valence shell, 1.180 and 0.040, respectively; and for diatomic hydrides of elements having two to four electrons in the valence shell, 1.42 and 0.08, respectively. Numerous applications of the relation are made and certain exceptions are pointed out.