The Journal of Physical Chemistry Letters Letter
calculations of the most stable structures as a function of
relative concentration of the two constituents identifying the
so-called convex hull of lowest energy structures. For a given
MX2 compound, we extract the structure with the lowest
energy at this 1:2 composition of the M-X phase diagram from
the database. In most cases a compound with the 1:2
composition exists as the most stable one. If that is not the
case we extract the two structures that linearly combine to give
the lowest energy of the convex energy hull at the 1:2
composition. We note that all structures are reoptimized and
energies are calculated with the approach we use here. The
fourth column, ΔHhull, shows our calculated heat of formation
with respect to the convex hull. If two structures are used to
obtain the energy of the hull, ΔHhull, then it is indicated with an
asterisk on the number. For comparison, the experimental heats
of formation for the most stable compounds are shown in the
third column when available in the OQMD database. As can be
seen, the calculated heats of formation are in good agreement
with the experimental data with a RMS deviation of only 0.09
eV. The fourth column shows the difference between columns
1 and 2, that is, how much the energy of the 2D material is
above (or below) the energy at the convex hull. The seventh
column in Table 3 shows the heat of formation of the 2H (1T)
class of structure with respect to the 1T (2H) class of structures
ΔH2H/1T (ΔH1T/2H). We find that the energy difference
between the catalytically active candidate and its analogue in
the other structure is usually not very large. As previously
mentioned HER-active materials like MoS2 and WS2 in the 1T
phase have a degree of metastability as high as 0.3 eV/atom
with respect to the 2H phase and lie above the hull by ∼0.3 eV/
atom; nevertheless, they have been synthesized and stabilized
under ambient conditions.10 Surprisingly, none of the other
HER-active materials differ from their corresponding 2D
analogue in energy by >0.3 eV/atom. Therefore, in the list of
proposed HER materials, if the material can be synthesized and
stabilized in one of the two phases, then it is highly likely that it
can be synthesized and stabilized in the other phase as well.
Some of the compounds like PdS2 and PdTe2, which have
been found to be HER-active in the current work, have also
been suggested to exist in monolayer form by Lebègue al.40 As
can be seen from Table 3a,b, PdS2 and PdTe2 lie above the hull
by ∼0.35 eV. Therefore, we choose a threshold of 0.4 eV for
ΔHhull for stability of compounds. The given criteria narrows
the list of the candidates, specifically OsS2, ReO2, OsSe2, ScO2,
and RuO2 in the 2H class of candidates and OsO2 in the 1T
class of candidates do not fulfill this criteria. The names of these
compounds are italicized in Table 3a,b. A few monolayers in
Table 3a,b have lower energy than the energy of the convex
hull. One of the reasons for this behavior might be the existence
of other more stable bulk structures than the ones considered
in the OQMD database, for example, structures obtained by
stacking the 2D layers.
Additionally, we also compare our findings of 2D materials
for HER with the recent study by Lebègue et al.40 that is based
on predicting the existence of 2D materials from experimental
bulk structures. The exiguous overlap between our results and
the ones by Lebègue al. arises from the fact that our
conclusions are based on thermodynamic arguments obtained
with ab initio calculations, whereas the work of Lebègue al.
relies more on heuristic arguments of the ability of cleaving a
bulk along a direction of weak bonding. The compounds of the
MX2 class proposed in their work are all present in our work,
thus supporting our approach. A few compounds in Table 3a,b
are written in bold. We select them based on the work by
Lebègue et al.40 by looking for “yes” in the column VI in Table
3a,b because it is highly likely that they can be synthesized and
stabilized with minimal effort.
In the current study, we suggest several 2D materials in the
2H and 1T structures as potential candidates for the hydrogen
evolution reaction. The activity of the basal plane in all of the
discovered candidates will provide a much larger number of
active sites as compared with 2D materials like 2H MoS2, where
only edges are active. Our analysis is using the calculated
adsorption free energy as a well-established descriptor for
hydrogen evolution. We furthermore investigate the stability of
the compounds in some detail by comparing heats of formation
of both competing layered phases and bulk structures. Recent
experimental stabilization of different layered phases seem to
indicate that fairly large metastability of several tenths of an eV/
atom can be overcome by appropriate synthesis routes, making
it likely that many of the suggested compounds could be
experimentally synthesized. It has recently been demonstrated
that the MoS2 and WS2 in the 1T phase can evolve hydrogen,
and these systems also appear in our screening, but other
identified systems should according to the calculations provide
higher activity. The calculations therefore invite further
investigation of some of the best candidates suggested here.
■ ASSOCIATED CONTENT
*S Supporting Information
Lattice constants and adsorption energy of hydrogen are
provided in the tables. This material is available free of charge
via the Internet at http://pubs.acs.org.
■ AUTHOR INFORMATION
The authors declare no competing financial interest.
We acknowledge CASE (Catalysis for Sustainable Energy)
initiative of the Danish Ministry of Science for funding the
project. The Center for Nanostructured Graphene is sponsored
by the Danish National Research Foundation, Project
DNRF58. We thank Jens K. Nørskov and Charlie Tsai from
SUNCAT (Stanford University) for helpful discussions.
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