Fig. 1

Crystal structures of H-Cat and D-Cat. a Crystal structure of H-Cat viewed along the b axis. b Molecular structure of H₂Cat-EDT-TTF. c Hydrogen-bonded molecular unit H₃(Cat-EDT-TTF)₂ (supramolecule) in H-Cat. The supramolecules are formed by two [H(Cat-EDT-TTF)]^0.5+ molecules connected by the hydrogen bond. The supramolecules are stacked along the (a + c) direction, as shown in a. For clarity, a part of the stacking columns is colored red and purple in a. In the b –c plane, two face-to-face [H(Cat-EDT-TTF)]^0.5+ molecules form a strongly dimerized unit (gray ellipsoid), which generates the 2D π-electron layers connected by the O–H–O hydrogen bonds (light blue circle). d Supramolecular unit in D₃(Cat-EDT-TTF)₂. Note that δ in c, d denotes the displacement of the hydrogen and deuterium atoms from the center of the O–H–O and  O–D–O bonds, respectively. e Spin and charge structures of the 2D π-electron layer in H-Cat. The π-dimers form a slightly anisotropic triangular lattice with S = 1/2 spins (magenta arrows). Dotted and solid lines show the inter-dimer hopping integrals, t and t′, respectively. f Spin and charge structures of a 2D π-electron layer in D-Cat below the phase transition temperature T _c of 185 K. Charge disproportionation associated with deuterium localization leads to a non-magnetic ground state below T _c . The blue- and orange-colored dimers indicate the charge-rich (+0.94) and charge-poor (+0.06) sites, respectively²¹. g, h Schematics of the potential energy curves of the hydrogen atoms in H-Cat (g) and the deuterium atoms in D-Cat (h). In H-Cat, the potential energy curve is suggested to change from a double-well structure (dashed line) to a very shallow and anharmonic single-well structure (red solid line) owing to the many-body effect arising from the network of hydrogen bonds and π-electrons^22,23. In sharp contrast, the energy curve in D-Cat retains a double-well structure above T _c = 185 K (dashed line), leading to the deuterium localization at T _c (blue solid line)