Analytic potential with adjusted parameters for diatomic molecules

A method has been developed for computing the eigenvalues of a given potential in the radial equation for diatomic molecules. This method is simple, accurate, and can be applied not only to energy eigenvalues but also to the eigenvalues of any parameter that may be included in the potential. An analytic expression for the potential can be found in terms of simple functions (as the Gaussian function) by the following method: As many parameters as are needed are included in the potential. Then, the values of these parameters are adjusted so that the computed eigenvalues agree with the experimental values. Some parameters are also adjusted in order that the computed rotational constants agree with the experimental values. The rotational constants are computed very accurately by computing rotational eigenvalues, and without using numerical integration of eigenfunctions. The present method was applied to the ground state $X{}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ of ${\mathrm{N}}_2^{+}$. The computed dissociation energy agrees with one of the two possible dissociation energies of ${\mathrm{N}}_2^{+}$ and thus determines the correct value.