Development of the Bond-Charge Model for Vibrating Diatomic Molecules

The bond‐charge model of a vibrating diatomic molecule previously described by Borkman, Simons, and Parr [J. Chem. Phys. 49, 1055 (1968); 50, 58 (1969)] is embedded in an exact theory of molecular vibrations near equilibrium, and shown to be a natural first approximation to the exact description. The model, based upon the Fues potential, $${\mathrm{W=W}}_0{\mathrm{+W}}_1{\mathrm{/R+W}}_2{\mathrm{/R}}^2,$$ is made exact by letting the quantities W₁ and W₂ depend on ${\mathrm{R:\; W}}_1{\mathrm{=W}}_1{\mathrm{(R),\hspace{0.17em}W}}_2{\mathrm{=W}}_2\mathrm{(R)}$ , with the electronic potential energy and kinetic energy, respectively, still having the forms ${\text{2W}}_0{\mathrm{+W}}_1\mathrm{/R}$ and −W₀+W₂/R². It is shown that, with no loss of accuracy, one may take $W_1^{\prime }{\mathrm{(R}}_e{\mathrm{)=W}}_2^{\prime }{\mathrm{(R}}_e\text{)=0}$ , which establishes the previous parameterization of W₁ and W₂ in terms of a bond charge q. A potential function of the form $${\mathrm{W=W}}_0+\frac{W_1}{R}+\frac{W_2}{R^2}+\frac{W_3{\mathrm{(R-R}}_e{)}^3}{R^2}\mathrm{+···}$$ is generated from a ``multipole expansion'' of the electronic potential energy, and a model is given which includes interactions between atomic dipoles at the nuclei and bond charges. The atomic dipoles are related to the number of valence electrons of an atom, accounting for the periodic‐table column dependence of force constant relations recently pointed out by Calder and Ruedenberg. The model is shown to possess the properties $${\mathrm{(\partial W/\partial q)}}_{{\mathrm{R-R}}_e}\text{=0\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{and}{\mathrm{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}(dq/dR)}}_{{\mathrm{R-R}}_e}\text{=0,}$$ in accord with recent studies on the nature of charge densities and bond orders.