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We investigate the microscopic structure of hydrogen double-well potentials in a hydrogen-bonded ferroelectric system exposed to radioactive particles of hydrogen-ion beams. The hydrogen-bonded system is ubiquitous, forming the base of organic-inorganic materials and the double-helix structure of DNA inside biological materials. In order to determine the difference of microscopic environments, an atomic-scale level analysis of solid-state  1 H high-resolution nuclear magnetic resonance (NMR) spectra was performed. The hydrogen environments of inorganic systems represent the Morse potentials and wave function of the eigen state and eigen-state energy derived from the Schrödinger equation. The wave functions for the real space of the localized hydrogen derived from the approximated solutions in view of the atomic scale by using quantum mechanics are manifested by a difference in the charge-density distribution.

Microscopic Difference of Hydrogen Double-minimum Potential Well Detected by Hydroxyl Group in Hydrogen-bonded System