Hydrogen intercalation in ${\mathrm{MoS}}_2$

We investigate the structure and energetics of interstitial hydrogen and hydrogen molecules in layered $2H\text{−}{\mathrm{MoS}}_2$, an issue of interest both for hydrogen storage applications and for the use of ${\mathrm{MoS}}_2$ as an (opto)electronic material. Using first-principles density functional theory we find that hydrogen interstitials are deep donors. ${\mathrm{H}}_2$ molecules are electrically inactive and energetically more stable than hydrogen interstitials. Their equilibrium position is the hollow site of the ${\mathrm{MoS}}_2$ layers. The migration barrier of a hydrogen molecule is calculated to be smaller than 0.6 eV. We have also explored the insertion energies of hydrogen molecules as a function of hydrogen concentration in ${\mathrm{MoS}}_2$. For low concentrations, additional inserted ${\mathrm{H}}_2$ molecules prefer to be located in hollow sites (on top of the center of a hexagon) in the vicinity of an occupied site. Once two molecules have been inserted, the energy cost for inserting additional ${\mathrm{H}}_2$ molecules becomes much lower. Once all hollow sites are filled, the energy cost increases, but only by a modest amount. We find that up to $13{\mathrm{H}}_2$ molecules can be accommodated within the same interlayer spacing of an areal $3\times 3$ supercell.

Figure 1

Atomic configurations of (a) ${\mathrm{H}}_i^0$ (or ${\mathrm{H}}_i^{-})$, (b) ${\mathrm{H}}_i^{+}$, (c) perpendicular-, and (d) parallel-aligned ${\mathrm{H}}_2$ molecules in ${\mathrm{MoS}}_2$ structures. Both side views and top views are provided.

Figure 2

Formation energy as function of Fermi level for interstitial H and interstitial ${\mathrm{H}}_2$ molecules in ${\mathrm{MoS}}_2$. The zero of Fermi energy corresponds to the VBM, and the H chemical potential is set to half the energy of an ${\mathrm{H}}_2$ molecule at $T=0$.

Figure 3

(a) Migration pathway and (b) potential energy for a parallel ${\mathrm{H}}_2$ molecule migrating between two neighboring stable sites. Image 1 in (a) is the initial stable structure. Image 4 in (a) shows the structure corresponding to the saddle point.

Figure 4

(a) Inequivalent insertion sites for a second ${\mathrm{H}}_2$ molecule in a $3\times 3\times 1$ supercell when one molecule is already present at site $A$. (b) Dependence of the insertion energy for a second ${\mathrm{H}}_2$ molecule on the insertion location, when one ${\mathrm{H}}_2$ molecule is already present at site $A$. The dashed lines are guides to the eye.

Figure 5

(a) Lattice constant $c$ in the out-of-plane direction and (b) insertion energy of the $n\text{th}{\mathrm{H}}_2$ molecule as a function of $n$ in a $3\times 3\times 1{\mathrm{MoS}}_2$ supercell. The dashed lines indicate the separation between $n=13$ and $n=14$, which is discussed in the main text. ${\mu }_{\mathrm{H}}$ is set to half the energy of an ${\mathrm{H}}_2$ molecule.

Figure 6

Equilibrium structures of ${\mathrm{MoS}}_2$ in $3\times 3\times 1$ supercell with (a) two, (b) six, (c) eight, and (d) eleven ${\mathrm{H}}_2$ molecules. Both side (top panel) and top (bottom panel) views are shown.