Three Methods to Identify and Visualize Nonuniform Changes in Interatomic Interactions: Second-Difference Analysis, Anharmonicity Inversion, and Distance-Dependent NMR Absolute Shieldings

Abstract

Vibrational excitation of chemical bonds induces nonuniform distortions in the potential energy surface that reflect changes in interatomic interactions. These qualitative changes can be identified and visualized using three complementary methods. The second-difference analysis, tracking successive vibrational energy gaps, applies when all vibrational level energies and the dissociation limit are known. The anharmonicity-inversion method uses a Morse potential and requires only the vibrational energy gaps 0 → 1 and 1 → 2, along with the dissociation limit, to reveal anomalous local anharmonicity near the first excited vibrational level by comparing the Morse-predicted bond energy with the true bond energy. Finally, NMR shielding-tensor mapping permits identification of interatomic distances at which the electronic environment undergoes qualitative changes, without requiring prior knowledge of the potential. Applied to the diatomic cations C⁺–Ng and H⁺–Ng (Ng = He, Ne, and Ar), all three approaches consistently delineate specific vibrational-state or internuclear distance regions where the character of the interatomic interaction changes noticeably.