The Journal of Physical Chemistry Letters Letter
Figure 1. (a) Top view of a 1T monolayer (P3̅2/m1 space group). (b) Monolayer with distortions belonging to the 1T class and P1 spacegroup with
unit cell size 2 × 2. (c) Monolayer with distortions belonging to the 1T class and P1̅ spacegroup with unit cell size 2 × 2. (d) Monolayer with
distortions belonging to the 1T class and P1 spacegroup with unit cell size 2 × 1. (e) Monolayer with distortions belonging to the 1T class and P3m1
spacegroup with unit cell size 2 × 2. (f) Top-view of a 2H monolayer (P6̅m2 space group). (g) Monolayer with distortions belonging to the 2H class
and P1 spacegroup with unicell size 2 × 2. Unit cells have been drawn (black solid lines) to show the size of the unit cell, and a few selected bonds
(black broken lines) between metal atoms have been shown to highlight the difference between different structures.
difference of the 2H and 1T phases for hydrogen adsorption,
we show that the relative position of the p level of ‘X’ with
respect to the Fermi level plays a decisive role for hydrogen
adsorption. On the basis of the descriptor employed to screen
the materials for HER, we point to many new possible 2D HER
materials beyond the few that are already known.
In the present work, we use GPAW,17 an electronic structure
code based on the projector-augmented wave (PAW)18
formalism. The PBE19 functional is used for the calculation
of lattice constants, and the calculated lattice constants have
been used throughout the work. Structures showing distortions
have been reoptimized, and the recalculated lattice constants
are used. We calculate the heat of formation using the fitted
elemental reference phase energies (FERE) scheme employed
over the PBE calculated energies, as proposed by Stevanovic et
al.20 A grid spacing of 0.18 Å is used to expand the wave
functions in real space, and a Fermi−Dirac smearing of 0.05 eV
is employed to accelerate the convergence. The Brillouin zone
for the smallest unit cell (1 × 1) is sampled using a
Monkhorst−Pack21 scheme with a k-point mesh of 18 × 18
× 1, and for 2 × 2 unit cells, we use a 9 × 9 × 1 k-point grid. All
optimizations are carried out using a Quasi-Newton algorithm,
and the forces are converged down to 0.05 eV/Å for all
relaxations. Spin-polarized calculations are performed for the
calculation of lattice constants as well as for the adsorption
energies. Adsorption energies are calculated using the BEEFvdW
functional.22 Uncertainties in adsorption energies are
explicitly calculated using the ensemble of functionals proposed
in ref 22. The calculated uncertainties are used to estimate the
probability that a given material will have the free-energy
descriptor for HER lying within a given range. The calculated
probabilities help to rank the different materials based on their
suitability23 for HER. We add several corrections to the
calculated total energy differences to estimate the adsorption
free energy. The zero point energy corrections to the energies
of all systems are to a first order approximation taken to be the
same as the ones calculated for the 1T-MoS2 monolayer
structure. We get the zero-point correction of the adsorbed
hydrogen as 0.39 eV at the standard state. We ignore the
entropic corrections for the adsorbed state while calculating the
total correction as in ref 15. The zero-point energy of the H2
molecule has been taken from the ref 24 and is found to be 0.54
eV. The entropic correction of 0.40 eV from the gas-phase H2 is
taken from ref 25. By taking the difference of the corrections in
the gas phase and the adsorbed state, ΔZPE comes out as 0.12
eV and −TΔS comes out as 0.20 eV; therefore, ΔZPE − TΔS
comes out to be 0.32 eV.
The current work focuses on the 2H and 1T structures and
their distorted derivatives of 2D metal dichalcogenides and
oxides some of which have been realized in recent experiments.
10−12 The structural difference between the 1T and 2H
phases originates from the difference in coordination environment
around the metal atom. The 2H phase of MX2 has a
trigonal prismatic structure with ‘M’ at the center of the prism
and ‘X’ at the vertices, where the 1T phase has an octahedral
coordinated structure with ‘M’ at the center of the octahedron
and ‘X’ at the vertices. Figure 1a,f shows the top view of the 2H
and 1T structure, respectively. Figure 1b−e,g represents
distorted derivatives of the 2H and 1T structures, which will
be discussed later. The significant difference in atomic structure
of the two phases might lead to differences in their
thermodynamic and electronic properties. The difference in
thermodynamic properties will directly influence the relative
stability of the two phases, whereas different electronic
properties will have an effect on the chemical reactivity. To
detect the distortions, if any, in the 2H and 1T structures, we
follow the steps: (1) Adsorb the hydrogen in the 2 × 2 unit cell
to break the symmetry of the structure and allow the structure
DOI: 10.1021/acs.jpclett.5b00353
J. Phys. Chem. Lett. 2015, 6, 1577−1585
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