The effect of resonance on the force constants and lengths of chemical bonds

The solution of the secular equation, which gives the energy of the actual state of a molecule in terms of the energies of the resonance states and a resonance integral, has been differentiated with respect to the internuclear separation for one of the bonds in the molecule. From the first differentiation, an equation has been derived which illustrates the effect of resonance on the bond length. This has been applied to two types of resonance, viz. between covalent single and double bonds, and to ionic-covalent resonance. The second differentiation gives an equation which shows the effect of resonance on the bond force constant. Using this equation, an explanation for the decrease in vibration frequency, which occurs when certain gases are liquefied or dissolved in non-ionising solvents, has been put forward. Calculations of the magnitude of this effect for the diatomic molecules HCl, HBr, HI, and H₂ are in good agreement with the experimental facts.