MnPSe3 Monolayer: A Promising 2D Visible‐Light Photohydrolytic Catalyst with High Carrier Mobility

The 2D material single‐layer MnPSe3 would be a promising photocatalyst for water splitting, as indicated by the proper positions of band edges, strong absorption in visible‐light spectrum, broad applicability (pH = 0 – 7), and high carrier mobility.

Since the experimental realization of graphene, [ 1 ] 2D materials have been receiving signifi cant attention due to their unique physical and chemical properties which mainly arise from their topological effects and high surface-bulk ratios. Graphene has predominated as the most widely studied 2D material. Intractably, lack of a band gap limits its practical applications to high speed switching devices, photocatalysts, etc. [ 2 ] Nevertheless, the successful preparation of graphene has prompted researchers to investigate more 2D materials such as hexagonal BN, [ 3 ] transition metal dichalcogenides (TMDs), [ 4 ] silicene, [ 5 ] germanane, [ 5b , 6 ] phosphorene, [ 7 ] and MXene. [ 8 ] These 2D materials attract intensive interest due to their novel electronic, mechanical or photocatalytic behaviors, [ 9 ] making up the shortages of graphene and expanding the applications of 2D materials to fi eld-effect transistors (FETs) [ 10 ] and photocatalysts. [ 11 ] Recently, a new kind of 2D materials (exemplifi ed by MnPSe 3 ) was proposed by Li et al. [ 12 ] Then, a series of MPS 3 (M = Fe, Mn, Ni, Cd, Zn) and MPSe 3 (M = Fe, Mn) were explored by Du et al. [ 13 ] Particularly, bulk crystals and few-layer samples of MPX 3 (X = S, Se) were obtained and characterized in experiments. The previous reports indicated that the band gaps of these MPX 3 bulks range from 1.3 to 3.5 eV, [ 13 ] suggesting the light absorption at a wide wavelength for photocatalysts.
Hydrogen generation by photocatalytic water splitting would present a promising method for solar energy conversion and play a very important role in solving serious environmental problems. [ 14 ] However, inability to utilize visible light, low quantum yield, and fast backward reaction limit the practical application of photocatalytic water splitting. [ 15 ] 2D materials with an appropriate band gap (i.e., ≈2-3 eV) would exhibit more effi cient use of visible light in the photocatalytic process. Moreover, 2D nature means short distance for the generated electrons and holes to migrate, reducing the possibility of ρ is the density, and g is the gravitational acceleration. Assuming the length of the monolayer l to be 100 µm, the ratio of the vertical deformation and the length h / l is shown in Table  S1 of the Supporting Information, which indicates that MPS 3 (M = Fe, Mn, Ni, Cd, Zn) and MPSe 3 (M = Fe, Mn) monolayers have suffi cient rigidity to form freestanding 2D monolayers without substrates.
Then the possibility of mechanical exfoliation from the bulk was checked by calculating the cleavage energy. The relative energy of the bulk increases with the separation distance and converges to the ideal cleavage energy gradually. The optimized lattice constants for the bulk structures are shown in Table S2 of the Supporting Information, which are consistent with the experimental data indicating the credibility of the calculations. As shown in Figure 1 b, the cleavage energy (0.29-0.54 J m −2 ) is comparable to the experimentally estimated value of graphite (≈0.37 J m −2 ), [ 19 ] meaning that it is not very diffi cult to exfoliate monolayers from the bulk in experiments. The theoretical cleavage strength σ could be obtained by computing the maximum derivative of E cl as shown in Figure 1 b. The cleavage strength of MPS 3 (M = Fe, Mn, Ni, Cd, Zn) and MPSe 3 (M = Fe, Mn) (1.2-2.1 GPa) is even lower than that of graphite (≈2.1 GPa), [ 20 ] which further indicates that the exfoliation of bulk is feasible in experiments.
We next investigated the electronic properties of the monolayers. As shown in Table S3 of the Supporting Information, MnPS 3 and MnPSe 3 monolayers are direct-band-gap semiconductors with the band gap of 3.14 and 2.32 eV, respectively, consistent with the previous report. [ 12 ] The valence band maximum (VBM) and the conduction band minimum (CBM) are both located at the K point. Other monolayers are indirect-band-gap semiconductors. More details are provided in the Supporting Information.
To further understand the compositions of VBM and CBM for MPS 3 and MPSe 3 monolayers, the partial density of states (PDOS) are computed. As shown in Figure 1 d and Figure S3 of the Supporting Information, the CBM and VBM of all the monolayers mainly originate from the p states of S/Se and the d states of metal atoms, respectively.
The band structures and PDOS indicate that the band gaps of MPS 3 (M = Fe, Mn, Ni, Cd, Zn) and MPSe 3 (M = Fe, Mn) monolayers range from 1.90 to 3.44 eV, which exceed the free energy of water splitting of 1.23 eV. In addition to the magnitude of the band gap, the band edges must straddle the redox potentials of water. To check this, the work functions of these monolayers were calculated and are shown in Table S4 of the Supporting Information.
For the water splitting reaction, the redox potential depends on the pH value. [ 16b , 21 ]  . Considering that sulfi des and selenides might be unstable in an acidic environment, the redox potential for water splitting reaction at neutral environment (pH = 7) was also calculated. The schematic diagram is shown in Figure 3 for the positions of band edges of MPS 3 (M = Fe, Mn, Ni, Cd, Zn) and MPSe 3 (M = Fe, Mn) monolayers for photocatalytic water splitting. Except FePSe 3 , whose CBM is lower than the reduction potential of H + /H 2 at pH = 7, the band edges of the rest compounds straddle the redox potentials of water at pH = 0 and 7. The results indicate that these materials are candidates for water-splitting photocatalysts without an external bias voltage. More fascinatingly, besides the advantages Another very important condition for photocatalytic water splitting is that the materials should capture a signifi cant fraction of visible spectrum because it counts for more than 40% of the solar spectrum.
To investigate the performance under light, the optical absorption coeffi cient was calculated and is shown in Figure 4 . The corresponding imaginary parts ε 2 of the dielectric function is shown in Figure S4 of the Supporting Information. The absorption coeffi cient is defi ned as the decay of light intensity spreading in a unit length of medium. FePSe 3 , MnPSe 3 , FePS 3 , and NiPS 3 monolayers exhibit obvious optical absorption in visible spectrum and among them, the absorption of FePSe 3 and MnPSe 3 is stronger. However, FePSe 3 might have no photocatalytic activity for water splitting at neutral environment. For MnPSe 3 , there are two absorption peaks in visible spectrum, indicating the strong optical absorption. Besides, the direct gap would make MnPSe 3 more advantageous over other materials. The results indicate that MnPSe 3 monolayer would exhibit better performance for photocatalytic water splitting. To investigate the effects of the layer number on the electronic properties and optical absorption of MnPSe 3 , MnPSe 3 bilayer was considered. More details are shown in Figures S5-S7 of the Supporting Information. The results indicate that MnPSe 3 bilayer could also exhibit catalytic activity for photocatalytic water splitting under visible light.
To further evaluate the performance of MnPSe 3 monolayer as photocatalysts, the carrier effective mass and carrier mobility were investigated for quantitative evaluation on the ability to transfer electron/hole along the specifi c direction.
The effective masses of electrons ( m e *) and holes ( m h *) are calculated by fi tting parabolic functions to CBM and VBM, respectively. As shown in Table 1 , m e * and m h * along the direction of a (Figure 1 a)    general smaller than those of some common photocatalysts. [ 22 ] The smaller effective mass indicates that the transfer of carriers to the reactive sites would be easier in the photocatalytic process.
To compute the DP constant E 1 , the VBM and CBM position of MnPSe 3 monolayer with respect to the vacuum level as a function of the uniaxial strain ε along a direction is shown in Figure S8 of the Supporting Information. On the basis of the obtained | m *|, C 2D , and | E 1 |, the calculated carrier mobility of the 2D MnPSe 3 monolayer at room temperature ( T = 300 K) is shown in Table 1 . The electron mobility is 625.9 cm 2 V −1 S −1 while the hole mobility is 34.7 cm 2 V −1 S −1 . The carrier mobility of MnPSe 3 monolayer could be comparable to or even higher than that of many other 2D semiconductors, such as MoS 2 monolayer (≈200 cm 2 V −1 S −1 ), [ 23 ] hydrogenated graphene (≈105 cm 2 V −1 S −1 ), fl uorinated graphene (≈45 cm 2 V −1 S −1 ), BN (≈487 cm 2 V −1 S −1 ), and BC 2 N (≈180 cm 2 V −1 S −1 ). [ 24 ] Moreover, the huge difference between the carrier mobility of electrons and holes indicates that the effective separation of electron-hole pairs and the small probability of recombination for photogenerated carriers. In addition, 2D materials are very promising candidates as photocatalysts, with high specifi c surface area available for photocatalytic reactions, short distance for the generated electrons and holes to migrate, and further reduced probability in the recombination of photogenerated carriers. [ 15b ] Overall, MnPSe 3 monolayer has many features, strong absorption in visible-light spectrum, photocatalytic water splitting into H 2 and O 2 simultaneously, broad applicability (pH = 0-7), high carrier mobility, and feasible synthesis in experiments. Thus, MnPSe 3 monolayer is a promising candidate as photocatalysts for water splitting.
In conclusion, the structure and stability of 2D metal phosphorus trichalcogenides monolayers were explored by fi rst-principles computations, which indicate that these 2D monolayers could be obtained in experiments by exfoliating the corresponding bulk. The calculated band gaps and band edge positions from accurate HSE06 functional predict that MPS 3 (M = Fe, Mn, Ni, Cd, Zn) and MPSe 3 (M = Fe, Mn) monolayers are promising candidates as photocatalysts for water splitting. Particularly, MnPSe 3 monolayer is a direct-band-gap semiconductor which exhibits obvious absorption in visible-light spectrum. Moreover, our calculations of effective mass and carrier mobility for MnPSe 3 monolayer illustrate the transfer of carriers to the reactive sites would be easier and the probability of recombination would be lower for photogenerated carriers in the photocatalytic process. These results refl ect that 2D MnPSe 3 monolayer could be a promising photocatalyst for water splitting.

Experimental Section
Our fi rst-principles computations based on density functional theory (DFT) were performed with a plan-wave basis set as implemented in the Vienna ab initio simulation package (VASP). [ 25 ] The projector augmented wave (PAW) was used to describe the ion-electron interaction. [ 26 ] The generalized gradient approximation (GGA) expressed by the functional of Perdew, Burke, and Ernzerhof (PBE). [ 27 ] A 500 eV cutoff was used for the plane-wave basis set. The DFT-D3 method with Becke-Jonson damping was adopted to accurately account for the van der Waals force for weak interactions. [ 28 ] A Monkhorst-Pack k-point mesh of 7 × 7 × 1 was used for 2D sheet, 7 × 7 × 2 for selenide bulk and 6 × 3 × 5 for sulfi de bulk. To study 2D systems under periodic boundary conditions (PBC), a vacuum space with at least 15 Å was inserted between the MPX 3 sheets and the periodically repeated images. Moreover, considering that GGA functional systematically underestimates the band gaps, [ 29 ] we computed the band structures with the HSE06 hybrid functional. [ 30 ] The computation of the phonon dispersion spectrums was calculated through CASTEP code with fi nite displacement method as implemented in Materials Studio. [ 31 ] To investigate the optical absorption, the imaginary part of dielectric function ε 2 was calculated. The expression for ε 2 was given as where the indices c and v refer to the conduction and valence band states, respectively, which were determined by the HSE06 functional here, and → u ck is the cell periodic part of the orbital at the k-point → k . The absorption coeffi cient α(ω) was calculated by [ 32 ] α ω ω ε ω ε ω ε ω ( ) where ε 1 is the real part of dielectric function, which could be obtained from ε 2 by Kramer-Kronig relationship. For inorganic semiconductors, the electron coherence length is close to the acoustic phonon wavelength, which is much longer than the bonds. As a result, phonon scattering dominates the intrinsic mobility which can be described by the deformation potential theory. [ 33 ] For 2D materials, the carrier mobility is given by   Table 1. Effective mass | m *| ( m e , the mass of free electrons), in-plane stiffness C 2D (N m −1 ), DP constant | E 1 | (eV), and carrier mobility μ (cm 2 V −1 S −1 ) for electrons and holes along the direction of a (Figure 1 a) ( 3) where T is the temperature, 300 K was adopted in this study, e is the electron charge, and h is the reduced Planck constant. m* is the effect mass defi ned as m* = h -2 (∂ 2 E ( k )/∂ k 2 ) −1 , where k is the wave vector, and E ( k ) is the energy corresponding to the wave vector k . E 1 is the DP constant denoting the shift of band edges induced by uniaxial strain, E 1 = ∂ E edge /∂ ε . C 2D is the in-plane stiffness as shown in Table S1 of the Supporting Information.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.