Extended Data Fig. 11: Vibrational characteristics of PdH from DFT calculations.

a, b, Phonon dispersion curves of hcp PdH, in which H is located at the ideal octahedral position (a) and H is displaced by 0.24 Å from the ideal position along the c axis (b). The corresponding atomic models are shown below the curves. Pd and H atoms are drawn in gray and blue, respectively. Imaginary phonon modes were found when H was positioned at the ideal octahedral site. One of those modes indicates the displacement of H along the c axis, with this rearrangement removing the imaginary modes, as shown in b. c, d, Energy landscape (ΔE) values around the octahedral position as calculated by displacing a single H atom from the center of the octahedron made by the six nearest-neighboring Pd atoms in the 48-atom supercell (2 × 2 × 3 hexagonal cell) of hcp PdH (c) and fcc PdH (d). The displacement toward the face in c is similar to the changes shown in a and b, but the instability is not captured. H atoms may adopt the ideal octahedral position at room temperature instead of collectively moving to the lower symmetry structure because of the small energy difference (∼1 meV/atom) between the two structures a and b. The energy variation in fcc PdH in d is more isotropic and lower in magnitude for the same degree of displacement than that in hcp PdH. This result agrees with the higher phonon frequencies of hcp PdH in this study compared with those of fcc PdH⁵⁴.