The Journal of Physical Chemistry Letters Letter
H 1T ϵp ΔHads
much for different compounds, hence we choose the same
correction as we have calculated for 1T-MoS2 monolayer
structure. Since the optimum value of free energy (ΔGopt) for
HER is ∼0.0 eV, we consider the range of free energy from
−0.5 to 0.5 eV to take into account the effect of coverage,
strain, and so on.8,36 Having an allowable range of free energy,
mean adsorption energies along with uncertainties allows us to
calculate the probability (P(|ΔG| ≤ 0.5)) of a material having
free energy for HER in the given interval. Assuming a Gaussian
distribution of uncertainties around the mean value, E̅, of the
adsorption, probabilities can be calculated as
∫
+̅ ⎛
1
2
0.5 2
E
|Δ | ≤ = −
πσ − −̅
σ
⎝ ⎜
⎞
⎠ ⎟
P G
E
( 0.5) exp
E
2
d
E
2 0.5
2
(3)
The calculated probabilities will help in narrowing down the
material space for potential experimental investigation by
discarding the materials with very small probabilities. In Figure
6, we show the compounds in the 2H and 1T class of structures
ranked according to the calculated probability measure. The
Figure includes compounds with a probability as low as 0.15.
This leads to 21 compounds in the 2H class of structures and
26 compounds in the 1T class of structures. For each
compound, the calculated free energy is shown together with
the error bar from the BEEF−vdW ensemble. We see that
MoS2 and WS2 appear on the list of candidates for the 1T
structure (although not with the highest probability) in support
of the recent experiments indicating possible hydrogen
evolution for these systems.8,10 The only compounds that
appear on both the 2H and 1T lists are NbS2, RhS2, RuS2, IrS2,
CoS2, ScSe2, RuO2, and TaTe2, illustrating the fact that the
chemical activity is very sensitive to the crystal structure.
Having identified possible 2D materials with promising
binding properties for hydrogen, it is appropriate to investigate
the stability of these materials further. There are two
possibilities that may hamper the growth and stability of the
2H or 1T phases of the 2D materials found to be active for
HER: (1) much higher stability of the competing bulk
structures or the standard states, thus leading to the
dissociation of the 2D phase into these compounds, and (2)
relative stability of the 2H and 1T phases also matters. For
example, if the 2H phase of a material is HER-active but is
much higher in energy than the 1T structure, it is unlikely that
the material can be synthesized and stabilized in the 2H
structure. Therefore, the HER-active 2D materials must not lie
above a certain degree of metastability with respect to the
competing bulk structures or the standard states, and also it
should not be energetically too high with respect to the other
2D phase of the material. In the present work, we do not
explore the stability of compounds in water because a recent
study has shown that with stabilizing agents compounds can be
stabilized in water, making this criterion less important.37 The
presence of water might also have an effect on the adsorption
energies, but in the current work having a fairly wide window of
the free energy of adsorption for the candidate materials, we
expect to have allowed for the effect of water.
Calculated data to address the previously described issues are
collected in Table 3a,b. The second column of the Table shows
the calculated standard heats of formation, ΔH, for the
monolayers (as shown for all the compounds in Figure 2) in
the 2H and 1T classes of structure, respectively. The third
column ΔHhull is calculated using structural information from
the OQMD database.38 The OQMD database contains
standard DFT energy calculations for a large selection of
known compounds from the ICSD database39 plus a number of
standard structures. In the case of binary systems, this results in
Table 2. Heat of Adsorption of Hydrogen, ΔHads
H , and the
Center of the p Band, ϵp, for Compounds Belonging to
Different Groups in the 2H and 1T Structuresa
2H ϵp ΔHads
H
MoS2 −2.00 1.68 ± 0.07 MoS2 −1.23 0.10 ± 0.13
MoSe2 −1.74 1.82 ± 0.13 MoSe2 −1.46 0.64 ± 0.11
WS2 −2.32 1.95 ± 0.08 WS2 −1.37 0.23 ± 0.14
WSe2 −2.03 2.03 ± 0.14 WSe2 −1.29 0.78 ± 0.15
TiS2 −1.02 −0.05 ± 0.13 TiS2 −1.45 0.40 ± 0.09
TiSe2 −0.89 0.44 ± 0.12 TiSe2 −1.38 0.90 ± 0.10
ZrS2 −0.96 0.11 ± 0.10 ZrS2 −1.42 0.94 ± 0.07
ZrSe2 −0.80 0.51 ± 0.10 ZrSe2 −1.34 1.19 ± 0.09
aGrouping of the compounds is performed based on the group of the
periodic table to which the metal atom in MX2 belongs.
H ) in the range of (−0.5, 0.5) eV along with uncertainties for 0.25
Figure 6. (a) 2H compounds having a free energy of hydrogen adsorption (ΔGads
ML coverage and probabilities (P(|ΔG| ≤ 0.5)) as calculated from eq 3. Red error bars indicate that the structure is unstable with respect to the
standard states.
DOI: 10.1021/acs.jpclett.5b00353
J. Phys. Chem. Lett. 2015, 6, 1577−1585
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