# Computational Study Based Prediction of New Photocatalysts for water
splitting by systematic manipulation of MXene surfaces.

Swati Shaw∗ Department of Physics, Indian Institute of Technology Guwahati,
Guwahati-781039, Assam, India.  Subhradip Ghosh† Department of Physics, Indian
Institute of Technology Guwahati, Guwahati-781039, Assam, India.

###### Abstract

The compositional and structural flexibility of functionalised two-dimensional
metal carbonitrides or MXenes has been exploited through a combinatorial
search for new materials that can act as catalysts for photo-assisted water
splitting by absorbing sunlight with energy in the infra-red region. Detailed
calculations on 49 Janus MXenes where two surfaces are of asymmetric nature
are carried out by first-principles Density Functional Theory. A screening
procedure is adopted to arrive at potential candidates. Our calculations
predict four new materials whose surfaces can activate both hydrogen and
oxygen evolution reactions upon splitting water, two out of which are infra-
red active, and the rest are visible light-active. We have performed a
detailed microscopic analysis to find out the interrelations of the structural
model of surface functionalisation, the chemistry of the surfaces, the
electronic structure, and the alignment of bands with respect to the reaction
potentials that explain our results. Apart from these four compounds, we find
thirteen other compounds that are suitable for either hydrogen evolution or
oxygen reduction reactions. This study lays out a guideline for the systematic
discovery of potential new catalysts for water splitting under sunlight
irradiation.

##  1 Introduction

Photocatalysis is an advanced green technique that utilises solar energy to
produce Hydrogen. Upon absorbing enough energy from sunlight, electrons and
holes are generated and separated on the surfaces of a photocatalyst for
further consumption in water splitting reactions: the Oxygen evolution
reaction (OER) ( $H_{2}O+2h^{+}\longrightarrow\frac{1}{2}O_{2}+2H^{+}$) and
the Hydrogen evolution reaction (HER) ( $2H^{+}+2e^{-}\longrightarrow H_{2}$).
The minimum energy requirement for both reactions to happen simultaneously is
1.23 eV, with oxidation (reduction) potentials of O2(H2) are -5.67(-4.44) eV.
This means that a photocatalyst for water splitting reactions must be a
semiconductor possessing the following properties: (a) it must have a band gap
of at least 1.23 eV but less than 3 eV so that it can capture a significant
fraction of visible light which accounts for more than 40 % of the solar
energy compared to only 5 % in the ultra-violet spectrum, (b) the valence band
maxima (VBM) and the conduction band minima (CBM) must lie below the oxidation
potential of O2 and above the reduction potential of H2, respectively, (c) it
should have small exciton binding energy and low recombination rate of charge
carriers [1].

Figure 1: The Schematic Illustration of Photocatalytic Water Splitting from
surfaces of a catalyst a) in the absence of an Electric Field, b) in the
presence of an internal Electric Field Ei. $\Delta\Phi$ is the potential
difference generated between two surfaces of the material with thickness $t$.
$\Delta E_{c}$ and $\Delta E_{v}$ are the overpotentials with respect to
potentials for hydrogen evolution and oxygen evolution reactions,
respectively.

Two-dimensional (2D) materials are the sought-after ones as catalysts in
photo-induced OER and HER. The high specific area in 2D materials promotes
tremendous surface active sites to enhance photocatalytic reactions. Due to
this, the recombination rate is less, too. Moreover, the passivation of their
edges by getting functional groups attached to the surface dangling bonds
minimizes reactions with ions in the solution. The structural flexibility in
2D materials also offers tunability in their electronic structures. Recent
experiments with 2D materials and their heterostructures like Graphene and its
derivatives, Graphite Carbon Nitrides, transition metal di-chalcogenides,
black phosphorous and its derivatives demonstrate that they are quite useful
in the photocatalytic splitting of water[2, 3, 4, 5, 6, 7, 8, 9], HER in
particular.

The latest addition to this group is MXenes. MXenes, with chemical formula
Mn+1XnT${}_{n+1}(n=1,2,3,...)$ where M is a transition metal element, X either
Carbon or Nitrogen and T a surface passivating functional group, offers
tremendous structural and compositional flexibility, ideal for tuning a number
of functional properties and various applications[10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20]. MXenes, derived by exfoliating their bulk counterparts, the
MAX compounds, have functional groups T passivating the surfaces during the
synthesis process. Though the standard synthesis route enabled only -O, -F,
and -OH groups as T, recent experiments [21] demonstrated that MXene surfaces
can be functionalised with other group 16 (S, Se) and group 17 (Cl, Br, I)
elements too. As a result, the scope of investigating structure-property
relations in MXenes has widened. Experimentally, few works on MXenes as
photocatalysts for water splitting are available [22, 23]. In those works,
MXene has been used as a co-catalyst to accelerate either OER or HER on the
surfaces of other 2D materials. First-principles computational modeling and
simulations far outnumber the experiments and propose a number of M2CT2 MXenes
as catalysts that can promote simultaneous HER and OER on its surfaces [24,
25, 26, 27, 28, 29, 30]. However, in spite of various combinations of M and T,
very few compounds had the correct alignments of VBM and CBM with respect to
the oxidation and reduction potentials. All these MXenes investigated
experimentally and through first-principles simulations are active in visible
and ultra-violet parts of solar energy. This leaves out the scope to utilise
about 50 % of the solar energy for photocatalytic water splitting. This energy
comes from the Infrared part of the spectrum. However, this requires lifting
the restriction on the magnitude of the photocatalyst’s band gap. A schematic
map to achieve this, proposed by Li et al [31], is shown in Figure 1. In
Figure 1a), schematics of photocatalytic water splitting from a system
comprising two identical nanoscale surfaces under the usual model are shown.
In this case, the energy levels corresponding to both oxidation and reduction
potentials are located inside the band gap. When an electric field is applied
between these two surfaces, the energy bands bend in the direction of the
electric field, leading to a charge re-distribution with the system’s valence
band on one surface and conduction band on the other. If the electric field is
an induced one due to an intrinsic dipole moment generated because of
significant heterogeneity in the surfaces, the differences between the
oxidation potential on one surface and the reduction potential on another
surface reduce from 1.23 eV to $1.23-\Delta\Phi$ eV where $\Delta\Phi$ is the
electrostatic potential difference associated with the induced electric field
(Figure 1 b)). The idea has been successfully implemented in h-BN
functionalised by two elements having significant electronegative difference
[31], and in M2X3 (M=Al, Ga, In; X=S, Se, Te) [32]. This model has been used
to predict new photocatalysts in the Transition metal di-chalcogenide family
by constructing Janus compounds MSX (M=Mo, W; X=Se, Te)from pristine MS2 [33,
34, 35]. These compounds exhibit good solar-to-hydrogen efficiencies.
Derivation of Janus compounds from pristine M2XT2 MXenes can be done in
various different ways as heterogeneity in the surfaces is possible through
manipulation of M as well of T. In spite of the possibility, to our knowledge,
there are two works on ordered Janus MXenes exploiting their potential as
photocatalysts in water splitting reactions [36, 37]. In this work, the Janus
compounds proposed were based upon replacing one of the M surfaces of M2CO2
MXenes by another transition metal element M′. From first-principles
calculations, it was found that some of these compounds with band gaps smaller
than 1.23 eV have their CBM and VBM adjusted against the water oxidation and
reduction potentials due to the bending of bands and thus can be used as
Infra-red active photocatalysts.

Despite quite a few work on the prediction of new photocatalysts in the MXene
family, both conventional and Janus, and with mixed success, there is no
investigation that systematically explores the inter-relations of surface
compositions, structural properties, electronic structure and alignments of
bands with respect to characteristic potentials for water splitting reactions
in MXene family of compounds such that predictors for potential photocatalyst
can be formulated. Moreover, there is a void in terms of infra-red active
photocatalysts in this family. In order to address both these issues, we have
adopted a first-principles electronic structure calculations based
combinatorial approach by construction of 47 Janus MXenes and putting in place
a screening strategy for systematic exploration of possible new photocatalyst
with emphasis on the ones active in the Infra-red region. The extensive study
made predicts four new photocatalysts; among them, two are active in the
Infrared part. Apart from the prediction of new materials, this study has
demonstrated the potential stored in the Janus compounds of the MXene family
as far as catalysts for OER and HER in the presence of sunlight are concerned.

##  2 Computational Details

Density functional theory (DFT) based Plane-wave Pseudopotential method as
implemented in Vienna ab initio simulation package (VASP)[38, 39] is used for
calculations of the electronic structures.The projected-augmented wave (PAW)
[40, 41] pseudopotentials are used throughout. To obtain accurate band gaps
and electronic structures, the Heyd-Scuseria-Ernzerhof (HSE06)[42] functional
is used to treat the exchange-correlation part of the Hamiltonian. Screening
parameters of 0.2 Å-1 and mixing exchange parameters of 0.25 are used in our
calculations. The kinetic energy cut-off is set to 550 eV. To avoid artificial
interactions between periodic images, a vacuum slab of 20Å is introduced
parallel to the monolayers. For structural relaxation, the convergence
criteria of total energy and the Hellmann-Feynman forces are set as 10-6 eV
and 10-3 eV/Å, respectively. For structural optimization and densities of
states calculations, the Brillouin zones are sampled by 9$\times$9$\times$1
and 35$\times$35$\times$1 $\Gamma$-centered $k$-meshes. Due to the asymmetric
structures of our materials, a dipole correction along the normal direction of
monolayers is adopted in every calculation.

##  3 Results and Discussions

In the quest for new materials suitable for photocatalytic water splitting, we
have considered 32 M2CTT′ and 15 MM′CO2 Janus MXenes and adopted the following
screening procedure to pin down the promising materials. The procedure has the
following steps: (1) The electronic structures of all compounds are
calculated. The ones showing semiconducting behavior are considered for
further processing; (2) for each one of the materials screened, the alignments
of their band-edges, the internal electric field, and the overpotentials are
investigated; and (3) the chemical nature of the band decomposed charge
density distributions of the compounds showing appropriate band-edge
alignments in step (2) are further investigated. The compounds having VBM and
CBM contributions coming from two different surfaces, along with appropriate
band alignments and overpotentials, are considered promising catalysts for
photocatalytic water splitting. In the following section, we first discuss the
structural models of surface-passivated MXenes. Results pertaining to steps
(1)-(3) mentioned above are then presented.

Figure 2: Side and top views with possible sites of functionalisation for a)
M2X and b) MM′X MXene Surfaces. Side view of Four possible structural models
of functionalisation in Janus MXenes c) M2XTT′ d) MM′XT2 are shown.

###  3.1 Structural Models of functionalised MXenes

Pristine MXenes with chemical formula M2C have hexagonal symmetry with space
group P63/mmc (Space group 194). Upon surface passivation with identical
functional group T, symmetry of M2CT2 is reduced, making them members of
P$\bar{3}$m1 space group (Space group 164). The making of Janus MXenes MM′CT2
and M2CTT′ breaks the inversion symmetry of P$\bar{3}$m1. Consequently, the
Janus MXenes belong to P3m1 symmetry (Space group 156). There is more than one
choice for the surface functional group with regard to the site of passivation
shown in Figure 2. There are altogether four sites, two hollow sites
associated with the transition metal component (A and B in Figure 2a),b)) and
two with the C atom (C and D in Figure 2a),b)). Accordingly, there can be four
possible structural models of surface functionalised Janus MXenes: Model 1,
where the functional groups occupy sites A and B; Model 2, where they occupy
sites C and A; Model 3 where they occupy sites B and D and Model 4 where the
sites of occupancy are C and D (Figure 2c),d)). For each system considered in
this work, we have calculated the total energies of all four models. The
structural model with the lowest energy is considered the ground state
structure for a given compound.

###  3.2 Structural and Electronic properties

In this section, we systematically discuss the structural and electronic
properties of three different sets of Janus MXenes. In each case, we analyse
the results to understand the origin of these properties. In a combinatorial
study, such insights are necessary for future studies on a larger scale.

####  3.2.1  Janus M2CTT′ (M = Sc, Ti, Zr, Hf; T/T′= H, F, OH, O) MXenes

Structural information like the structural model, the lattice constants, bond
lengths, and thickness of compounds of this series are presented in Table 1.
We find that all 24 compounds investigated stabilise in Model 1 of
functionalisation. This can be understood in the following way: To fulfill the
octet rule, C and O require 4 and 2 electrons, respectively, whereas the
requirement of H, F, and (OH) is 1. All four transition metals have at least 3
valence electrons that can be used to form M-C, M-T, and M-T′ bonds. Thus, the
functional groups prefer to occupy hollow sites that are associated with the M
sites stabilising them in Model 1.

Figure 3: Atom projected densities of states of a) Sc2CTO, T = H, F, OH; b)
Sc2CTT′, T,T′ = H, F, OH, c) Ti2CTO, T = H, F, OH ; d) Ti2CTT′, T,T′ = H, F,
OH MXenes. The Fermi level in each case is set to 0 eV.

Table 1: The structural parameters and electronic ground states of M2CTT′(M = Sc, Ti, Zr, Hf; T,T′= O, OH, F, H) MXenes Systems | Electronic | Stable | Lattice-Constant | Bond-Lengths | Thickness
---|---|---|---|---|---
(M2CTT′) | ground state | Configuration | a=b | M-H | M-F | M-OH | M-O | t
|  |  | (Å) | (Å) | (Å) | (Å) | (Å) | (Å)
Sc2CHO | Metal | Model 1 | 3.27 | 2.14 | - | - | 2.03 | 4.60
Sc2CFO | Metal | Model 1 | 3.25 | - | 2.21 | - | 2.02 | 4.87
Sc2C(OH)O | Metal | Model 1 | 3.25 | - | - | 2.26 | 2.03 | 5.93
Sc2C(OH)H | Semiconductor | Model 1 | 3.30 | 2.17 | - | 2.27 | - | 5.76
Sc2C(OH)F | Semiconductor | Model 1 | 3.29 | - | 2.23 | 2.27 | - | 5.89
Sc2CHF | Semiconductor | Model 1 | 3.29 | 2.16 | 2.22 | - | - | 4.69
Ti2CHO | Metal | Model 1 | 3.02 | 2.01 | - | - | 1.98 | 4.42
Ti2CFO | Metal | Model 1 | 3.03 | - | 2.15 | - | 1.98 | 4.67
Ti2C(OH)O | Metal | Model 1 | 3.04 | - | - | 2.17 | 1.99 | 5.66
Ti2C(OH)H | Metal | Model 1 | 3.05 | 2.01 | - | 2.17 | - | 5.52
Ti2C(OH)F | Metal | Model 1 | 3.07 | - | 2.18 | 2.18 | - | 5.78
Ti2CHF | Metal | Model 1 | 3.04 | 2.00 | 2.16 | - | - | 4.52
Zr2CHO | Metal | Model 1 | 3.29 | 2.17 | - | - | 2.13 | 4.67
Zr2CFO | Metal | Model 1 | 3.29 | - | 2.31 | - | 2.13 | 4.94
Zr2C(OH)O | Metal | Model 1 | 3.30 | - | - | 2.34 | 2.14 | 5.95
Zr2C(OH)H | Metal | Model 1 | 3.31 | 2.16 | - | 2.34 | - | 5.84
Zr2C(OH)F | Metal | Model 1 | 3.32 | - | 2.34 | 2.35 | - | 6.15
Zr2CHF | Metal | Model 1 | 3.30 | 2.16 | 2.32 | - | - | 4.83
Hf2CHO | Metal | Model 1 | 3.25 | 2.14 | - | - | 2.11 | 4.64
Hf2CFO | Metal | Model 1 | 3.25 | - | 2.30 | - | 2.11 | 4.89
Hf2C(OH)O | Metal | Model 1 | 3.26 | - | - | 2.30 | 2.12 | 5.88
Hf2C(OH)H | Metal | Model 1 | 3.26 | 2.13 | - | 2.31 | - | 5.77
Hf2C(OH)F | Metal | Model 1 | 3.28 | - | 2.32 | 2.32 | - | 6.07
Hf2CHF | Metal | Model 1 | 3.26 | 2.13 | 2.30 | - | - | 4.78

The electronic ground states of the compounds in this series are compiled in
Table 1. We find that apart from three Sc-based Janus, all have metallic
ground states. To understand the reasons, we take recourse to their bonding
pictures and atom projected densities of states (Figure 3 & Figure S1,
supplementary information). Janus Sc2CHO, Sc2CFO and Sc2C(OH)O are obtained
from Sc2CO2 by replacing the O passivating the top surface (the surface of
Sc(1)) with other functional groups that have 1 electron more than O. Sc(2),
the Sc atom in the bottom surface, provides 2 electrons to the O passivating
the surface and the remaining 1 to C. Sc(1), on the other hand, after
fulfilling the requirement of H, F or (OH) passivating its surface by
providing 1 electron, supplies remaining 2 to C. As a result, there is 1
unpaired in these systems associated with Sc(1)-3$d$ C-$2p$ hybridisation.
This is responsible for the metallic ground states in these compounds and is
reflected in the features of their electronic structures near the Fermi level,
where the states are dominated by Sc(1)-$d$ and C-$p$ orbitals (Figure 3 a)).
When the Janus is formed by replacing the O passivating the surface of Sc(2)
by H, F, or (OH), no unpaired electron remains in the system. This is
responsible for the semiconducting ground states in Sc2C(OH)H, Sc2C(OH)F and
Sc2CHF. The atom projected densities of states of these compounds (Figure 3
b)) corroborate this where the states near the Fermi level are now primarily
made up of both Sc atoms and C.

The origin of metallic ground states in Ti, Zr, and Hf-based Janus considered
in this series can be understood in a similar way. All three transition metals
have 1 electron more than Sc. In the Ti series, the compounds Ti2CHO, Ti2CFO
and Ti2(OH)O have the O passivating the Ti(2) surface. The 4 electrons of
Ti(2) are provided to C and O while 1 less electron is required to be provided
by Ti(1) as its surface is passivated by H, F, or (OH). This extra electron in
the system is responsible for the metallic nature of these three compounds.
The electronic structure of these compounds (Figure 3c)) reflects this as the
states near the Fermi level are contributed mostly by Ti(1). When neither the
surfaces are passivated by O, as is the case of Ti2C(OH)H, Ti2C(OH)F and
Ti2CHF, both Ti(1) and Ti(2) have one electron each extra. The states near the
Fermi level of these compounds are thus dominated equally by the states from
Ti on both surfaces (Figure 3d)). The electronic structures of compounds in
the Zr and Hf series (Figure S1, supplementary information) can be explained
in a similar manner.

Figure 4: Atom projected densities of states for a) Sc2COS , Sc2COSe & Sc2CO2, b) Zr2COS, Zr2COSe & Zr2CO2. Fermi energy in each case is set to 0 eV. Table 2: The structural parameters and electronic ground states of M2COT′ (M=Sc,Ti, Zr, Hf and T′= S, Se) MXenes  Systems | Electronic | Stable | Lattice-Constant | Bond-Lengths | Thickness
---|---|---|---|---|---
(M2COT′) | ground state | Configuration | a=b | M-O | M-T′ | t
|  |  | (Å) | (Å) | (Å) | (Å)
Sc2COS | Semiconductor | Model 3 | 3.63 | 2.15 | 2.46 | 4.03
Sc2COSe | Semiconductor | Model 3 | 3.66 | 2.16 | 2.58 | 4.16
Ti2COS | Metal | Model 1 | 3.11 | 1.99 | 2.40 | 4.99
Ti2COSe | Metal | Model 1 | 3.12 | 2.00 | 2.56 | 5.17
Zr2COS | Semiconductor | Model 1 | 3.38 | 2.14 | 2.53 | 5.22
Zr2COSe | Metal | Model 1 | 3.38 | 2.15 | 2.69 | 5.45
Hf2COS | Semiconductor | Model 1 | 3.34 | 2.12 | 2.50 | 5.18
Hf2COSe | Metal | Model 1 | 3.34 | 2.13 | 2.66 | 5.38

####  3.2.2 The series M2COT′ (M=Sc,Ti,Zr,Hf; T′ = S, Se)

In the previous sub-section, we have found that the absence of unpaired
electrons in Janus MXenes is the reason behind the semiconducting ground state
in certain members of the series. Since the Janus MXenes considered in the
previous sub-section are created by replacement of O atoms in M2CO2 MXenes,
compounds that are all semiconductors [25, 24, 26], our next set of Janus
compounds are the ones obtained by replacing one of the O by other group 16
elements S and Se in M2CO2. S and Se are isoelectronic to O; hence, it is
expected that band filling pattern in M2COS(M2COSe) will be similar to M2CO2
and more Janus semiconductors will be produced. Unlike the compounds in the
series M2CTT′ discussed in the previous sub-section, the structural model of
surface passivation, compounds in this series stabilise in, vary (Table 2).
Sc-based compounds stabilise in Model 3, the one where T′ functional group,
instead of occupying the hollow site of the transition metal (site B, Figure
2) like O does, occupies the hollow site associated with C atom (site D,
Figure 2). Each Sc, with only 3 valence electrons, is unable to provide 4
electrons required by C and the functional groups. Therefore, even in Sc2CO2,
one of the O does not have a sufficient number of electrons to satisfy the
octet rule and prefers to occupy the hollow site of C so that it can share the
electrons of C. This is the reason why Sc2CO2 minimise total energy in Model 3
where Sc(1)(Sc(2)) surface is passivated by O occupying B(D) site.
Consequently, Sc2CO2 is a semiconductor as seen from its atom projected
densities of states (Figure 4a)). Due to different positions of passivation,
the chemical environment of the two O atoms is different. As a result, O(1)
and O(2) states occupy different parts of the occupied spectrum.
Hybridisations are also influenced by this. Near the Fermi level, strong
hybridisation is found between $p$ states of O(2), $p$ states of C, and $d$
states of both Sc atoms. Hybridisations of C-$p$ and O(2)-$p$ orbitals push
the unoccupied states at high energies, opening up a gap of $\sim$ 2 eV,
making the ground state of Sc2CO2 semiconducting. In Sc2COS(Sc2COSe), the
S(Se) replacing O(2) also prefers to occupy the hollow site of C for the same
reason O(2) occupied it in Sc2CO2. The electronic structure of these two
compounds is very similar to Sc2CO2. In both compounds, states near Fermi
level in the occupied part see strong hybridisation between Sc(2)-$d$ C-$p$
and S/Se-$p$ states. The band gap gradually decreases from Sc2CO2 to Sc2COSe
as the anti-bonding states gradually shift towards lower energy with an
increase in the size of T′ functional group. The $p$ states of T′ are more
delocalised as we go down the rows of group 16. Their hybridisations with
other atoms, therefore, fill up states at lower energies in the conduction
band and reduce the band gap.

Ti, Zr, Hf based compounds in this series stabilise in Model 1 as C and
functional groups receive the right number of electrons to satisfy the octet
rule. But, their electronic ground states (Table 2) differ considerably. The
differences in their atom-projected densities of states (Figure 4b) and Figure
S2, supplementary information) explain this. The electronic structures of
three M2CO2 compounds with M being Ti, Zr, and Hf are very similar in terms of
the identities of the orbitals hybridising strongly resulting in states near
the valence and conduction band edges. The difference is in the positions of
the bands and the edges, resulting in sizeable differences between their band
gaps. While Zr2CO2 and Hf2CO2 have band gaps $\sim$ 2 eV, band gap in Ti2CO2
is only $\sim$ 1 eV. When one O is replaced with S or Se, there is a
significant impact in the unoccupied part of the spectrum. The environment
around the two surfaces becomes different. This affects the electronic
structures of individual atoms. Notably, the densities of states of two M
atoms are now different. States of M(2), the atom having S and Se on its
surface, due to hybridisation with them, become substantially delocalised,
forming the bottom of the conduction band and reducing the band gap
considerably. Since the band gap of Ti2CO2 is smaller, such delocalisation
gives rise to states in the gap when one O is replaced with S and Se. As a
result Ti2COS and Ti2COSe are semi-metals. The reason Zr2COS, Hf2COS are
semiconductors while Zr2COSe, Hf2COSe are metals is the degree of
delocalisation of Se-hybridised states in comparison to S-hybridised states as
observed from the atom-projected densities of states.

####  3.2.3 The series MM′CO2; M,M′= Sc, Ti, Zr, Hf

Janus MXenes can also be realised by replacing one of the M surfaces of M2C
MXene with a different transition metal M′. Since all four M2CO2 MXenes where
M is Sc, Ti, Zr, and Hf, are semiconductors, in this sub-section, we look into
the structural properties and electronic ground states of MM′CO2 Janus where 6
different compounds are obtained from combinations of these four transition
metal elements. All six compounds in this series stabilise in Model 1
structure (Table 3). For the three compounds made up of Ti, Zr and Hf as the
transition metal components, both the O and the C get their necessary
electrons from the transition metal constituents. Hence, Model 1 is the
natural choice. For the three compounds where M is Sc, in spite of the
shortage of 1 electron than those required by the anions, the ground state
configuration is still Model 1. The reason can be explained the following way:
ScM′O2 compounds can be thought to be derived from Sc2CO2 by replacing Sc(2)
by Ti, Zr and Hf, all three having necessary electrons to fulfill the
requirements of M′-C and M′-O(2) bonds. As a result, unlike in Sc2CO2, the
O(2) prefers to occupy position A (Figure 2 b)). However, the electronic
ground states of Sc-based compounds are different from the other three. The
Sc-based Janus are metals, while the others are semiconductors. The difference
can be understood from the differences in their atom-projected densities of
states (Figure 5a) and Figure S3, supplementary information). The common
feature in the electronic structure of all compounds in this series is that
states near the top of the valence band are mostly made up of the $d$ states
of M′ and $p$ states of C. In the Sc-based compounds, these states are
delocalised near the Fermi level and extend into the unoccupied part of the
spectrum. This is an artefact of a single unpaired electron present in C due
to a lack of enough number of electrons in Sc. Since in the non-Sc MXenes,
there are no such unpaired electrons, the hybridised states near the top of
the valence bands are slightly deeper in energy, making these three compounds
semiconducting.

Figure 5: Atom projected densities of states of a) MM′CO2, M,M′= Ti, Zr, Hf; b) TiM′CO2, M′= Cr, Mo & W respectively. Fermi energy in each case is set to 0 eV. Table 3: The structural parameters and electronic ground states of MM′CO2 (M=Sc, Ti, Zr, Hf; M′=Ti, Zr, Hf, Cr, Mo, W) MXenes Systems | Electronic | Stable | Lattice-Constant | Bond-Lengths | Thickness
---|---|---|---|---|---
(MM′CO2) | ground state | Configuration | a=b | M-O | M′-O | t
|  |  | (Å) | (Å) | (Å) | (Å)
ScTiCO2 | Metal | Model 1 | 3.15 | 1.99 | 2.01 | 4.55
ScZrCO2 | Metal | Model 1 | 3.30 | 2.04 | 2.12 | 4.61
ScHfCO2 | Metal | Model 1 | 3.27 | 2.03 | 2.10 | 4.62
TiZrCO2 | Semiconductor | Model 1 | 3.19 | 2.02 | 2.09 | 4.52
TiHfCO2 | Semiconductor | Model 1 | 3.16 | 2.01 | 2.07 | 4.51
ZrHfCO2 | Semiconductor | Model 1 | 3.29 | 2.11 | 2.11 | 4.62
TiCrCO2 | Semiconductor | Model 3 | 2.87 | 1.94 | 1.99 | 4.61
TiMoCO2 | Semiconductor | Model 3 | 2.95 | 1.96 | 2.08 | 4.77
TiWCO2 | Semiconductor | Model 3 | 2.96 | 1.96 | 3.63 | 4.79
ZrCrCO2 | Metal | Model 3 | 3.05 | 2.07 | 3.68 | 4.72
ZrMoCO2 | Semiconductor | Model 3 | 3.10 | 2.07 | 3.77 | 4.90
ZrWCO2 | Semiconductor | Model 3 | 3.09 | 2.08 | 3.77 | 4.92
HfCrCO2 | Metal | Model 3 | 3.02 | 2.05 | 3.65 | 4.70
HfMoCO2 | Semiconductor | Model 3 | 3.08 | 2.06 | 3.74 | 4.89
HfWCO2 | Semiconductor | Model 3 | 3.07 | 2.06 | 3.75 | 4.90

####  3.2.4 The series MM′CO2, M=Ti, Zr, Hf; M′= Cr, Mo, W

The MM′CO2 series considered in this sub-section consists of a group IV
element M and a group VI element M′. Janus MXenes with such combinations are
considered because M and M′ elements considered here have significant
differences in their electronegativity, a minimum of 7%(Ti and Cr) to a
maximum of 81%(Hf and W). When M and M′ are on two different surfaces, this
difference in electronegativity can generate the internal electric field
necessary for band bending. All nine Janus MXenes in this series stabilise in
Model 3 configuration (Table 3). In these compounds, there remain two excess
electrons belonging to M′ element after fulfilling requirements of C and O on
either surface. The O atom associated with the M′ surface still prefers to
occupy C hollow sites as the large electron density of M′ repeals O and makes
site B unsuitable for it to occupy. Very large M′-O bond distances as compared
to M-O bond distances (Table 3) support this.

Figure 6:  Band Structures of 17 Janus MXenes that are potential
photocatalysts for water splitting.

Atom projected densities of states of these compounds are shown in Figure 5b)
and Figure S4, supplementary information. In all compounds, the states near
the valence band edge are dominated by M′-$d$ and O(2)-$p$ states while states
near conduction band edge are overwhelmingly contributed by hybridised
M-M${}^{\prime}d$ states. Out of the nine compounds, only two, ZrCrO2 and
HfCrO2 are semi-metals, while TiCrO2 is a semiconductor with a small band gap
of only 0.2 eV. Upon inspecting these three compounds where Cr is the M′ atom,
we find that the electronic ground state is driven by Cr states in the
unoccupied part. The semiconducting gap in TiCrO2 has been possible due to
localised Cr states in the unoccupied part; the localisation is due to strong
hybridisation with Cr. In the two semi-metal compounds, the hybridisation is
not that strong, and Cr states in the unoccupied part are more de-localised,
creating states at the Fermi level.

###  3.3 Band-Structures, Band edge alignments and Distribution of charge
densities

Our calculations reveal 17 semiconductors among the 39 Janus MXene considered
in this work. The next step for screening materials is to look at the band
structures of these 17 to find out whether a compound is a direct or indirect
band gap semiconductor and the size of its band gap. The first criterion is
important to assess a compound’s potential as a catalyst in the photo-
splitting of water. The efficiency of the photocatalytic reaction will
increase with less recombination of photo-generated electrons and holes. In
the case of a semiconductor photocatalyst with an indirect band gap, the
carriers cannot recombine as easily as in the case of a direct band gap
semiconductor photocatalyst. The size of the band gap determines the part of
the solar spectrum in which a given photocatalyst can operate. The band
structures of these semiconducting Janus are shown in Figure 6. Except
Sc2C(OH)H and Sc2C(OH)F, all other compounds have indirect band gaps. The size
of their band gaps are given in Table 4. Except 6 compounds, all others have a
band gap of less than 1.23 eV. Therefore, these 11 compounds are potential
photocatalysts that can absorb energy from the infrared part of the solar
spectrum, while the rest can be active in the visible part of the spectrum.
Our results agree very well with existing results on some of these compounds
[37, 43, 44, 45, 46, 36].

Figure 7: Schematic diagram of Photocatalytic water splitting (HER & OER) on
the aymmetric surfaces of Janus MXenes. The figure on the left (right) is for
M2CTT′(MM′CT2) MXene.

Figure 8: Re-adjusted band edges for the 17 Janus MXenes. The oxidation and
reduction potentials for OER and HER are shown by black dotted lines. CBM(VBM)
for each compound is shown by a green(blue) line.

The next step in our screening scheme is to find the electrostatic potential
difference between the surfaces due to asymmetric charge distribution, an
artefact of Janus structure, corresponding internal electric field, the
intrinsic dipole moment generated across the surfaces, and re-alignment of
band edges due to this potential difference. Once the semiconducting Janus
MXenes with appropriate band alignments are found, surface contributions to
their band decomposed charge densities are looked into. The internal electric
field $E_{i}$ and the potential difference between the surfaces $\Delta\Phi$,
induced by the intrinsic dipole moment, $P$ are given as,

$\displaystyle E_{i}$ $\displaystyle=$ $\displaystyle\frac{\Delta\Phi}{et}$
(1) $\displaystyle\Delta\Phi$ $\displaystyle=$
$\displaystyle\frac{eP}{\epsilon A}$ (2)

where $\epsilon$ is the dielectric constant, $A$ is the area of the MXene
surface, $t$ the thickness of the material and $e$ the electronic charge.
$\Delta\Phi$ is calculated as the potential difference between the bottom
surface (the surface at (00-1)) and the top surface (the surface at (001)).
Calculated values of $t$ for the semiconducting Janus MXenes are given in
Tables 1-3. Results of $E_{i},\Delta\Phi$ and $P$ are presented in Table 4.

Table 4: Band Gap (Eg), Electrostatic Potential Difference ($\Delta\Phi$) between two surfaces, Intrinsic Electric-Field (Ei), Dipole Moment (P), Over Potential ($\Delta$ Ec) between CBM and Water Reduction Potential & Over Potential ($\Delta$ Ev) between VBM and Water Oxidation Potential for the Janus semiconductors considered in this work System | Eg | $\Delta\Phi$ | Ei | P |  $\Delta$ Ec |  $\Delta$ Ev
---|---|---|---|---|---|---
| (eV) | (eV) | (V/Å) | (debye) | (eV) | (eV)
Sc2COHH | 1.00 | 3.64 | 0.63 | 0.91 | 3.70 | -0.30
Sc2COHF | 0.86 | 3.91 | 0.66 | 0.97 | 3.71 | -0.17
Sc2CHF | 1.94 | 0.21 | 0.04 | 0.05 | 1.05 | -0.13
Sc2COS | 2.57 | 1.58 | 0.39 | 0.48 | 2.78 | 0.14
Sc2COSe | 1.97 | 1.52 | 0.37 | 0.47 | 2.81 | -0.55
Zr2COS | 0.36 | 1.78 | 0.34 | 0.47 | 0.05 | 0.86
Hf2COS | 0.35 | 1.70 | 0.33 | 0.44 | 0.09 | 0.73
TiZrCO2 | 1.50 | 0.0 | 0.0 | 0.0 | 0.58 | -0.30
TiHfCO2 | 1.47 | 0.0 | 0.0 | 0.0 | 0.51 | -0.27
ZrHfCO2 | 1.72 | 0.0 | 0.0 | 0.0 | 0.24 | 0.25
TiCrCO2 | 0.20 | 1.73 | 0.38 | 0.33 | -1.66 | 2.36
TiMoCO2 | 0.64 | 1.57 | 0.33 | 0.31 | -0.69 | 1.66
TiWCO2 | 0.51 | 1.35 | 0.28 | 0.27 | -0.64 | 1.27
ZrMoCO2 | 0.56 | 1.61 | 0.33 | 0.35 | -0.55 | 1.49
ZrWCO2 | 0.86 | 1.35 | 0.27 | 0.30 | -0.12 | 1.09
HfMoCO2 | 0.69 | 1.73 | 0.35 | 0.38 | -0.37 | 1.56
HfWCO2 | 1.00 | 1.47 | 0.30 | 0.32 | -0.01 | 1.26

In cases of non-zero $P$ and $E_{i}$, we find $\Delta\Phi>0$. This means the
top surface in these compounds is always at a lower potential. The profile of
electrostatic potentials shown in Figure S5, supplementary information
corroborates this. Internal electric field $E_{i}$, therefore, acts along
negative $z$-direction. This will make the photo-generated electrons move from
(00-1)surface to (001) surface. Consequently, the Oxygen evolution reaction
(OER) and the hydrogen evolution reaction (HER) will prefer to occur on (0 0
-1) surface and (0 0 1) surface, respectively. This is schematically shown in
Figure 7. The reduction and oxidation potentials are determined by the
electrostatic potentials relative to the vacuum level. In the case of Janus
MXenes, there are two different vacuum levels corresponding to different
surfaces. Therefore, the shift in the reduction and oxidation potentials will
be different for different surfaces. The band edges should be aligned
accordingly. In Fig.8, we show the re-adjusted positions of VBM and CBM on the
two surfaces of the 17 Janus MXenes. The reduction(oxidation) overpotential
$\Delta E_{c}$($\Delta E_{v}$) associated with the water splitting are given
by

$\displaystyle\Delta
E_{c}=\left\\{E_{CBM}-(-4.44)\right\\}eV,\enskip\enskip\Delta
E_{v}=\left\\{-5.67-E_{VBM}\right\\}eV$ (3)

$E_{CBM}$ and $E_{VBM}$ are the energies of the conduction band minima and the
valence band maxima, respectively. Values of overpotentials for each compound
are given in Table 4. Positive values of $\Delta E_{c}$ and $\Delta E_{v}$
would imply alignment of CBM and VBM such that both reduction and oxidation
processes can take place. From Table 4 we find that only four compounds,
Sc2COS, Zr2COS, Hf2COS and ZrHfCO2 have both values positive. Six compounds,
Sc2C(OH)H, Sc2C(OH)F, Sc2CHF, Sc2COS, TiZrCO2,TiHfCO2, have only positive
$\Delta E_{c}$ implying that only the HER can take place. All seven MM′CO2
MXenes where M,M′ are group-IV and group-VI elements, respectively, have only
positive $\Delta E_{v}$. Consequently, only OER is possible in these
compounds.

Figure 9: The Band decomposed Partial charge densities of constituents towards
VBM and CBM of four Janus MXenes with proper band alignment are shown.

The effects of band bending due to the internal electric field and resulting
re-positioning of VBM and CBM are prominent in the Janus MXenes considered
(Figure 8). The larger the electric field, the larger is the bending. As a
consequence, large changes are observed in cases of Sc2C(OH)H and Sc2C(OH)F.
In both cases, the VBM is very close to the oxidation potential that would not
have happened without the internal electric field. More importantly, in almost
all cases, VBM and CBM, due to the band bending, lie on two different
surfaces. Only exceptions are TiCrCO2, ZrMoCO2, ZrWCO2, HfMoCO2 & HfWCO2 where
both VBM and CBM are associated with the surface containing M′ in these MM′CO2
MXenes (Figure S6, supplementary information). Though the overpotentials
associated with HER in HfWCO2 is only slightly negative, even a positive value
would not have made it suitable for water splitting as the separation of
charge carriers onto two surfaces will not be possible, enabling both HER and
OER to take place simultaneously. No band bending is found in case of TiZrCO2,
TiHfCO2 and ZrHfCO2. For these compounds, $E_{i}$ is zero as there is no
potential difference between the two surfaces (Figure S5, supplementary
information). This is due to the fact that there is a little asymmetry between
the two surfaces as the transition metal constituents are iso-electronic, have
nearly the same electronegativity, and the chemical environment around them is
nearly identical (Functional group occupies an identical position on both
surfaces and bond lengths between the transition metal and oxygen associated
with different surfaces are hardly different).

The results obtained through the systematic screening finally identify four
compounds, Sc2COS, Zr2COS, Hf2COS, and ZrHfCO2, as compounds suitable for
photocatalytic water splitting. While Sc2COS and ZrHfCO2 can utilise the
visible part of solar spectrum, Zr2COS and Hf2COS will be active in the Infra-
red region. However, the last check for their competence as photocatalysts is
done by examining their charge density isosurface distributions. Unless the
VBM and the CBM states are contributed by components of two different
surfaces, photocatalytic redox water-splitting cannot be feasible from the
thermodynamic point of view. In Figure 9, we show the charge density
distributions associated with VBM and CBM. The figures imply that
contributions to VBM and CBM are coming from different surfaces. In Sc2COS,
VBM is made up of Sc(2) $d$, C $p$ and S $p$ states while CBM is mostly due to
Sc(1) $d$ and O $p$ states. In Zr2COS, VBM is due to S states while CBM is due
to Zr(1)-C hybridised states. A similar separation of contributions is
observed in the other two compounds as well.

##  4 Conclusions

A number of first-principles-based computational models to predict
photocatalysts for water splitting in the MXene family far outnumber the
experiments. However, almost all the works have investigated systems that are
active in the visible region. Moreover, there is a lack of coherence between
those studies as those were not done in a systematic way. In this work, we
have tried to bridge that gap by adopting a combinatorial approach to generate
47 thinnest ($n=1$) MXenes with asymmetric surfaces that is Janus compounds
and apply a screening criterion to systematically arrive at the ones that can
host both OER and HER, preferably in the Infra-red part of the solar spectrum.
Our calculations predict only 4 potential candidates, out of which 2 (Zr2COS
and Hf2COS) can absorb the infra-red light while the other 2 (Sc2COS and
ZrHfCO2) will be visible-active. As a by-product of our endeavor, we found
6(7) more Janus MXenes useful for water reduction(oxidation) reactions under
Z-scheme photocatalysis. We have thoroughly investigated the role of
structural properties and the bonding nature of the constituents to find clues
that can help figure out predictors to screen materials. Our study suggests
that the location of the functional group passivating MXene surfaces is
connected with the electronic configuration of the constituents and resultant
sharing of electrons between cations and anions. This, in turn, decides the
ground state electronic property of a given Janus MXene. We also find that the
re-alignment of bands due to the internal electric field would be possible if
the two surfaces have elements or functional groups that have significantly
different electronegativity. The electronic structures of all 47 compounds
imply that a few more Janus MXenes with the semiconducting ground state can be
realised by the application of strains as they are semi-metallic in nature.
Almost all such compounds are M2CTT′, which implies that asymmetry in the
functional group is more useful in exploiting the flexibility in structure-
property relations in this family. This study provides important insights for
experimentalists looking to tap the potential of MXenes in photocatalytic
water splitting. The detailed and systematic approach adopted in our work can
also be used for a more elaborate investigation of Janus MXenes.

## Acknowledgement

The authors gratefully acknowledge the Department of Science and Technology,
India, for the computational facilities under Grant No. SR/FST/P-II/020/2009
and IIT Guwahati for the PARAM supercomputing facility where all computations
are performed. The authors would like to thank Dr. Mukul Kabir for useful
discussions.

## Author Information

Email address :
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>
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