Quantum Delocalization of Molecular Hydrogen in Alkali-Graphite Intercalates

The adsorption of molecular hydrogen (${\mathrm{H}}_2$) in the graphite intercalation compound ${\mathrm{KC}}_{24}$ is studied both experimentally and theoretically. High-resolution inelastic neutron data show spectral features consistent with a strong pinning of ${\mathrm{H}}_2$ along a single axis. First-principles calculations provide novel insight into the nature of ${\mathrm{H}}_2$ binding in intercalates but fail to account for the symmetry of the ${\mathrm{H}}_2$ orientational potential deduced from experiment. The above discrepancy disappears once the ${\mathrm{H}}_2$ center of mass is allowed to delocalize in the quantum-mechanical sense across three vicinal adsorption sites, naturally leading to the well-known saturation coverage of $\sim 2{\mathrm{H}}_2$ per metal atom in this material. Our results demonstrate that ${\mathrm{H}}_2$ storage in metal-doped carbon substrates can be severely affected by hitherto unexplored quantum-mechanical effects.

Figure 1

(a) Evolution of the (003) peak with $x$ as measured on IRIS. The inset shows integrated intensities (symbols) and accompanying fits (lines) using the model described in the text; (b) shows the INS data from IRIS and TOSCA (inset).

Figure 2

${\mathrm{K}}^{+}-{\mathrm{H}}_2$ potential energy curves. The cartoon defines radial ($R$) and angular ($\Theta$, $\varphi$) variables. The inset shows the angular potential at $R_{\mathrm{eq}}$; symbols correspond to PW-DFT calculations whereas the solid line corresponds to the long-range expansion described in the text (quadrupole and polarizability values taken from Ref. 31).

Figure 3

PW-DFT results: (a) View along the $c$ axis (white lines define the unit cell). The trigonal subunit cell and its center are shown in red. White circles denote three adjacent ${\mathrm{H}}_2$ sites. The blue dashed line shows the direction of the radial energy cut in Fig. 4; (b) side view of the minimum-energy configuration; (c) electron-density-difference map obtained by subtracting the ${\mathrm{KC}}_{14}$ and ${\mathrm{H}}_2$ densities from that of ${\mathrm{KC}}_{14}{\mathrm{H}}_2$. Red (blue) denotes electron density gain (loss).

Figure 4

Radial and angular (inset) scans for the ${\mathrm{H}}_2$-GIC complex. $R$, $\theta$, and $\varphi$ retain the same meaning as in Fig. 2. Dashed lines in the inset correspond to fits using Eq. (1).