Limits for the energies of asymmetric isotopic modifications of homonuclear molecules

A method is proposed which allows rigorous upper limits to be determined for the energy levels of homonuclear molecules that are asymmetric in nuclear mass from precision energy values of their isotopic analogs. The method does not require any claculations of wave functions. The results show that the method proposed is of high accuracy and sufficient predictive strength, allowing the upper limits on the energy of asymmetric Coulomb systems to be reliably determined from the known energies of their symmetric analogs. The method may be refined if the energy of one or more Coulomb systems which are a symmetric in mass is known, using the convexity relation, or if account is taken of the dependence of the eiqenvalues on the mass-asymmetry parameter