Molecular adaptation of an exponential potential for spectra comparison and Fisher information

This study transmuted a non-molecular exponential-type potential into a molecular potential model by satisfying the equilibrium conditions of diatomic systems. In the context of parametric Nikiforov–Uvarov method, the exact bound-state energies as well as wave functions were derived and applied to evaluate Fisher information in both position space and momentum space. The analytic energy levels were compared with experimental data (RKR values) for several molecules, the analytic results show excellent agreement for heavy systems with slowly varying potentials, while lighter molecules exhibited earlier deviations due to stronger anharmonic effects. The Fisher information patterns across different dissociation energy, reduced mass, and screening strength reveal clear reciprocal localization behaviour between the two spaces. The results confirm that the transformed potential provides a reliable molecular outline and that Fisher information serves as a sensitive tool for analyzing quantum structure under tunable interactions.