Derivation of an Internuclear Potential Function from a Quantum-Mechanical Model

A simple quantum‐mechanical model of bond formation is presented which allows the derivation of an internuclear potential function of the form $${\mathrm{V=-D}}_e\exp {\mathrm{(-n\Delta R}}^2\text{/2R),}$$ where n=k_eR_e/D_e. The method makes use of a delta‐function model whereby bond formation is described by the shifting of atomic delta functions into molecular delta functions. The predicted results for H₂⁺ are nearly exact for all bond properties while the results for H₂ are more accurate than those for all but the most elaborate methods used previously. The model has also been used to calculate values of R_e, D_e, ω_e, and ω_ex_e for a large number of stable excited states of H₂ with good results. Advantages of the method are that the same form for the internuclear potential function is obtained for multi‐electronic bonds as for one and two electron bonds, and that multi‐electronic bond systems can be handled by one‐dimensional methods. Theoretical values for the parameter, n, for multi‐electronic bonds are calculated which agree well with values obtained from experimental data. A disadvantage of the method is that the problem of bond formation has been oversimplified by using arbitrary assumptions.