The Journal of Physical Chemistry Letters Letter
process; therefore, to overcome inaccuracies in the forces, we
employ a cutoff of 0.05 Å on the rotations/translations to
identify the symmetry operations. For six structures where the
difference in energy of the distorted structure and the perfectly
symmetrical structure is <0.01 eV per atom, we categorize them
into the symmetrical structure for the previously mentioned
reason. We find that for all of the distorted structures in the 2H
class, the type of distortion is similar to the one shown in
Figure 1g. Therefore, we categorize them in the same class as
those that have the unit cell size of 2 × 2 and the space group
P1. Figure 1b−e shows the four different types of distortions
observed in the 1T structure. There are subtle differences in all
of these four groups. Panel b does not have any symmetry and
thus belongs to the P1 group, panel c shows the distortions
similar to panel b but has an inversion symmetry and thus
belongs to P1̅as also observed by Tongay et al. for ReS2.30 The
distortions in panel d are such that the structure forms stripes
with periodicity of one unit cell, resulting in a unit cell size of 2
× 1. Panel e has the least distortion and inherits most of the
symmetry operations from the symmetric 1T structure and
belongs to the P3m1 space group.
Additionally, as previously mentioned, discarding distorted
phases that differ in energy from the perfectly symmetric
structures by <0.01 eV per atom might result in missing some
of the charge density wave (CDW) phases, for example, in
TiS2.31,32 In the case of TiS2 we found that for a 12 atom unit
cell (2 × 2 unit cell) the distorted and the perfectly symmetric
structure differ by only ∼0.04 eV (∼0.004 eV per atom). It
turns out that due to similar energy differences the CDW
phases of other compounds, for example, TaS2, are all discarded
due to the previously mentioned reason. Discarding the CDW
phases does not affect our results for the HER, which is
dependent only on the energy differences, which are very small
in the previously mentioned cases.
In previous works the strength of hydrogen binding on a
catalyst surface has been used as a descriptor for the ability to
2
OTable 1. Categorization of Different Compounds Based on
the Deviation of Their Structures from Perfect 2H or 1T
Structures and the Size of the Unit Cella
class MX2 group unit cell class MX2 group unit cell
2H CoS2 P1 2× 2 2H CoSe2 P1 2× 2
2H IrS2 P1 2× 2 2H OsS2 P1 2× 2
2H OsSe2 P1 2× 2 2H PdS2 P1 2× 2
2H PdSe2 P1 2× 2 2H PdTe2 P1 2× 2
2H ReO2 P1 2× 2 2H ReS2 P1 2× 2
2H ReSe2 P1 2× 2 2H RhS2 P1 2× 2
2H RhSe2 P1 2× 2 2H RhTe2 P1 2× 2
2H RuO2 P1 2× 2 2H RuS2 P1 2× 2
2H RuSe2 P1 2× 2 2H ScS2 P1 2× 2
2H ScSe2 P1 2× 2
1T CoS2 P1 2× 2 1T CrS2 P1 2× 2
1T CrSe2 P1 2× 2 1T FeS2 P1 2× 2
1T IrS2 P1 2× 2 1T IrSe2 P1 2× 2
1T ReO2 P1 2× 2 1T ReTe2 P1 2× 2
1T RhS2 P1 2× 2 1T RuS2 P1 2× 2
1T RuTe2 P1 2× 2 1T MoO2 P1 2× 1
1T MoS2 P1 2× 1 1T MoSe2 P1 2× 1
1T MoTe2 P1 2× 1 1T OsS2 P1 2× 1
1T OsSe2 P1 2× 1 1T OsTe2 P1 2× 1
1T WS2 P1 2× 1 1T WSe2 P1 2× 1
1T WTe2 P1 2× 1 1T ReS2 P1̅ 2 × 2
1T ReSe2 P1̅ 2 × 2 1T RuSe2 P1̅ 2 × 2
1T TaO2 P1̅ 2 × 2 1T CoSe2 P3m1 2× 2
1T IrTe2 P3m1 2× 2 1T NbO2 P3m1 2× 2
1T OsO2 P3m1 2× 2 1T RhSe2 P3m1 2× 2
1T RuO2 P3m1 2×2 1T WP3m1 2× 2
aThe class represents the type of undistorted structure to which the
compound belongs, the group represents the space group of the
distorted structure as per Herman−Maugin notation, and the unit cell
represents the size of the reduced unit cell with respect to the 1 × 1
unit cell of the perfect 2H or 1T structures.
Figure 4. Adsorption energies of the individual groups of compounds. The grouping of the compounds is based on the position of the metal atom of
MX2 in the periodic table. The missing data points in the plots show the instability of those compounds toward hydrogen adsorption; that is, in these
cases hydrogen pulls out the ‘X’ atom from the monolayer and moves far from the surface. All energies shown in the ordinates are in electronvolts.
DOI: 10.1021/acs.jpclett.5b00353
J. Phys. Chem. Lett. 2015, 6, 1577−1585
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