Construction of Reliable Internuclear Potential Curves from Equilibrium Bond Lengths and Vibrational Frequencies

A method is presented for the construction of reliable internuclear potential curves using a previously proposed function and observed values of equilibrium bond lengths and vibrational frequencies. The function has the form $${\mathrm{V=D}}_e\text{{1−}\exp {\mathrm{[-(n\Delta r}}^2\text{/2r)]}{1+af(r)}.}$$ An explicit form is presented for the observed periodicity of the parameter a when referring to the ground states of diatomic molecules. This periodicity is shown to lead to relationships from which D_e, α_e, and x_eω_e can be calculated solely from ω_e and r_e. An empirical relationship between the values of the parameter a in the ground and the excited states is presented from which D_e, α_e, and x_eω_e can be deduced for any nonionic excited state from ω_e and r_e of that state. This latter relationship demonstrates that ω_er_e² is not constant for all states of any molecule but is dependent in a predictable manner on the other spectroscopic constants. These relationships enable potential curves to be constructed solely from a knowledge of ω_e and r_e. Calculated curves for the X¹Σ_g⁺ states of H₂ and I₂ and ground and excited states of N₂ agree extremely well with experimental curves, deviating by no more than 2% of the dissociation energy. The agreement is very good for large values of r for H₂ and I₂, which indicates that a general form exists for the interaction of bonding atoms at large distances.