The Journal of Physical Chemistry Letters Letter
to relax. (2) Remove the hydrogen from the structure obtained
from step 1 and relax the structure. (3) If the structure obtained
after step 2 is the same as the perfectly symmetric structure,
then there are no distortions present or else the structure is
distorted. (4) Cases may exist in which step 2 leads to local
minima in new structures; therefore, one has to compare the
energy obtained after step 2 and the energy of the perfectly
symmetric structure and choose the one with lower energy.
Following the steps previously outlined, the distortions
present under HER conditions can most likely be obtained.
Similar distortions in MoS2 have been explored by Kan et al.,26
but we see a wider range of distortions. Therefore, instead of
using their terminology, we categorize the distortions in a more
general way based on the space group and the size of the unit
cell.
Figure 2a,b shows the calculated standard heats of formation
of the 2D MX2 compounds in the 2H and 1T phases. In
calculating the standard heat of formation, we neglect any zeropoint
or entropic correction. As can be seen from the Figure
the region of stable compounds is very similar in the two
structures. With very few exceptions, the compound that is
stable (unstable) in one structure exhibits stability (instability)
in the other structure as well. Figure 2c shows the difference in
enthalpies of the different compounds by which we can
estimate the extent to which the two phases differ
thermodynamically. The obtained trend in the relative stability
of the 2H and 1T phases agrees well with the calculations of
Ataca et al.27 We see that for most of the compounds the
energy difference between the 2H and the 1T phase is smaller
than ∼0.4 eV/atom. Recent experiments on MoS2
10 and WS2
8
show that the distorted 1T phase despite being energetically
higher than the 2H phase by ∼0.3 eV/atom can be stabilized.
These experiments thus suggest that the metastable phase of a
2D MX2 compound with a positive heat of formation as high as
∼0.3 eV/atom relative to the stable phase can be synthesized
and stabilized under normal conditions using suitable synthetic
routes.28 Thus, the generally small energy differences shown in
Figure 2c indicate that the atomic structure of 2D MX2 can be
tuned, if required, for the application in hand. Therefore, we
explore both the 2H and 1T class of structures of MX2 to find
suitable materials for HER.
Figure 3a,b shows the energy of distorted structures with
respect to perfectly symmetric 2H and 1T structures,
respectively. The white squares denote massive reconstruction
upon relaxation, thus leading to structures neither belonging to
the 2H or 1T class of structures. We do not investigate these
systems any further. Upon analyzing the nature of reconstructions
in the more moderately distorted structures, it turns out
that the distortions occurring in the 1T structure can be
categorized in four different symmetry groups, whereas the
distortions in the 2H structure can be captured by only one
group. Starting with the structures with slightly displaced atoms
from their ideal positions in the perfect 2H and 1T structures,
that is, without symmetries in a 2 × 2 unit cell, upon relaxation,
some compounds in 1T structure gain symmetry in such a way
that all of the symmetry operations can be captured in a 2 × 1
unit cell, thus leading to reduction in the size of unit cell. This is
not the case for any of the 2H structures. Therefore, we
categorize the distorted structures based on the space groups
and the unit cell size using the tool described in ref 29. Table 1
shows the categorization of the distortions based on the space
group and the size of the reduced unit cell. The forces cannot
be brought down to exactly zero during the optimization
Figure 2. (a,b) Heatmap of standard heat of formation (in eV/atom)
of compounds in undistorted 2H and 1T structures, respectively. (c)
Difference in enthalpies between the 2H and 1T structures (in eV/
atom) of different compounds. Each compound is represented by a
square, and the constituent elements are represented by the
corresponding ordinate and abscissa of the square. The difference in
energies is in eV/atom.
Figure 3. (a,b) Energy of the distorted structures (eV/atom) with
respect to the perfectly symmetrical 2H and 1T structures,
respectively. The white squares denote massive reconstruction upon
relaxation, thus leading to structures not belonging to the 2H and 1T
class of structures.
DOI: 10.1021/acs.jpclett.5b00353
J. Phys. Chem. Lett. 2015, 6, 1577−1585
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