The Journal of Physical Chemistry Letters Letter
evolve hydrogen, and it has been found that the optimum value
of the free energy of hydrogen adsorption (ΔGH) on the
surface of the material should be close to zero.3,8,16 The free
energy of hydrogen adsorption comes out as a descriptor based
on the Volmer−Heyrovsky route for the HER. The steps
involved in the Volmer−Heyrovsky process can be written
as33,34
+ +*→ * + − H e H (1)
2H* → H2 + 2* (2)
where * denotes the active site. At zero potential the freeenergy
difference between H+ + e− and H2 is (by definition)
zero, and the intermediate state of adsorbed hydrogen provides
an effective barrier for the process, which should be as close to
zero as possible. Therefore, to determine the reactivity of the
basal plane, we first calculate the hydrogen adsorption energy
on different sites. The adsorption energy is calculated relative to
the hydrogen molecule and the most stable clean substrate
within the given class (1T or 2H). In all of the 1T and 2H
classes of the MX2 structures, we find that the most favorable
hydrogen adsorption site on the basal plane is on top of the
chalcogen/oxygen atoms. For distorted structures, depending
on the symmetry, H will bind differently to the different
chalcogen/oxygen atoms. For further analysis we select the
adsorption site with the strongest binding. We start with onefourth
(0.25 ML) of a monolayer of coverage (one hydrogen
per four chalcogen/metal atom) and select only the
compounds binding hydrogen too strongly (ΔHH
ads ≥ −0.8)
for higher coverages. Calculations for higher H adsorption
coverages reveal massive reconstructions, and the final
structures do not belong to any of the structure in the 2H
and 1T class; therefore, we choose not to explore the cases of
higher coverage any further and focus only on one-fourth of a
monolayer of coverage in the current work. To establish the
trends in the strength of hydrogen binding, we use the heat of
adsorption (total energy differences) and incorporate zeropoint
energies and entropic effects only in the stage of
evaluating the suitability of materials for HER.
Figure 4 shows the calculated heats of hydrogen adsorption
(ΔHads
H ) on the 2H and 1T basal planes with 0.25 ML coverage
of hydrogen. Upon hydrogen adsorption, not all of the surfaces
are stable; therefore, we discard the compounds (missing data
points) in the plots that are unstable toward hydrogen
adsorption, that is, in these cases hydrogen pulls out the ‘X’
atom from the monolayer and moves far from the surface or the
structure massively reconstructs and transforms to a structure
not belonging to the 2H or 1T class. As can be seen, the heat of
adsorption varies widely by several electronvolts. An overall
trend is that the bonding strength is increased as the
electronegativity of the chalcogenide is increased. There is
clearly no simple relation between the hydrogen bonding to the
2H and 1T structures. Depending on the metal and
chalcogenide in question the bonding to the 1T class may be
stronger or weaker than the bonding to the 2H class.
To shed some light on the chemistry behind the different
adsorption energies, we shall focus on only two of the metal
groups that stand out in Figure 4. For the metals Ti, Zr, and Hf
the bonding to the 2H structure is clearly stronger than that for
the 1T, while for the metals Cr, Mo, and W we have an
opposite trend. To understand these opposite behaviors we
analyze the density of states (DOS) projected onto the ‘X’ p
orbital in MX2.16 Figure 5a−d shows the DOS of pristine
Figure 5. (a) Density of states (DOS) plot of MoS2 and TiS2 in the
2H and 1T structures. MoS2 and TiS2 belong to two different groups
as shown in Figure 4). ϵp denotes the position of the center of the p
band with respect to the Fermi level. The shaded region corresponds
to occupied states.
monolayers. The calculated position of the p-band center (ϵp)
(obtained as the first moment of the projected density of
states) with respect to the Fermi level of the pristine
monolayers explains the difference in reactivity of the two
groups. A higher-lying p level indicates possible stronger effects
of hybridization with the hydrogen s state.16 The calculated ϵp
for MoS2 in the 1T structure lies closer to the Fermi level as
compared with the 2H structure, whereas for TiS2, the ϵp for
the 2H structure lies closer to the Fermi level as compared with
the 1T structure. Table 2 shows the adsorption energy (ΔHads
H )
and center of p band for compounds selected from the groups
to which MoS2 and TiS2 belong. As can be seen from the Table,
other compounds also show the same correlation between ϵp
and ΔHads
H . These results show that the nature of the metal
atom35 along with the symmetry of the structure has a
significant effect on the reactivity.
We calculate for 0.25 ML coverage the heats of adsorption
(ΔHads
H ) including error bars (σ) with the BEEF-vdW functional
to assess the confidence interval of heats of adsorption.22 As
mentioned earlier, we add zero point and entropic corrections
of 0.32 eV in all the heats of adsorption to get the free energy of
adsorption. Here we assume that the corrections will not vary
DOI: 10.1021/acs.jpclett.5b00353
J. Phys. Chem. Lett. 2015, 6, 1577−1585
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