First principles study of optoelectronic and photocatalytic performance of novel transition metal dipnictide XP2 (X = Ti, Zr, Hf) monolayers

Low cost and highly efficient two dimensional materials as photocatalysts are gaining much attention to utilize solar energy for water splitting and produce hydrogen fuel as an alternative to deal with the energy crisis and reduce environmental hazards. First principles calculations are performed to investigate the electronic, optical and photocatalytic properties of novel two dimensional transition metal dipnictide XP2 (X = Ti, Zr, Hf) monolayers. The studied single layer XP2 is found to be dynamically and thermally stable. TiP2, ZrP2 and HfP2 systems exhibit semiconducting nature with moderate indirect band gap values of 1.72 eV, 1.43 eV and 2.02 eV, respectively. The solar light absorption is found to be in energy range of 1.65–3.3 eV. All three XP2 systems (at pH = 7) and the HfP2 monolayer (at pH = 0) that straddle the redox potentials, are promising candidates for the water splitting reaction. These findings enrich the two dimensional family and provide a platform to design novel devices for emerging optoelectronic and photovoltaic applications.


Introduction
The reduction in fossil fuels and challenges to energy sources have forced the scientic society to search for environment friendly and efficient green energy fuels for sustainable development of a clean society. 1 Hydrogen is considered as an ideal energy carrier source due to its abundance on earth, low pollution emission 2 and highest energy per mass ratio. To produce hydrogen from water, photocatalytic water splitting is the most favorable method. For a few decades, researchers have been devoted to producing some novel metal-based inexpensive environment friendly photocatalytic materials. 3 Twodimensional materials like hexagonal boron nitride (h-BN) and transition metal dichalcogenides (TMDCs) have invoked considerable interest aer the successful development of graphene in 2004. 4 Single layer transition metal dichalcogenides have tremendous applications like optoelectronics, spintronics, valleytronics, photovoltaic devices, gas sensing, and catalysis due to their suitable band gap, good mechanical properties and absorption coefficients. [5][6][7][8] The developed nano-and mesostructures, phosphides and phosphates have shown good exibility and electrical conductivity 9 in comparison with oxides and polymers, and are ideal for storing electrochemical energy based on faradaic redox reactions. 10 Ranking 10 th in the abundance in the earth crust, phosphorus is considered very effective for hydrogen evolution 11 and reports have shown that P played main role in photo catalysts. 12 Due to low band gap, good stability and electrical conductivity, transition metal phosphides (TMPs) are considered as good semiconductor materials. 13 Many compounds of phosphorus including phosphides and metal phosphates have been studied for super capacitors, 14 lithium ion batteries 15 and catalysts. 16 Phosphorus make variety of phosphides when react with various elements in periodic table. 17 For making transition metal phosphides, large atomic radius (0.109) of phosphorus makes it favorable in designing various crystal structures. 9 Doping of some noble metals Pt, Pd, Au make photocatalytic material very efficient for photocatalytic hydrogen production 18,19 but their applications are limited due to high cost. 20 Therefore, search for more effective and cheap catalysts are very essential and highly demanding. 21 Generally, two conditions must be fullled for photocatalytic material: (1) its conduction band edge should be more negative than H 2 energy level, (2) the valence band edge must be lower than the energy level of oxygen. 22 Despite of efficient performance of hydrogen evolution reaction (HER) for using catalyst in water splitting, controlling the basic structural composition is still a challenge. 23,24 C. Y. Son and coworkers have synthetically developed FeP and FeP 2 nanowires and demonstrated high electro-catalytic performance for P-rich FeP 2 nanowires in acidic and basic solution. FeP 2 revealed remarkable performance for water splitting. Transition metal phosphides have been discovered recently to decompose methyl orange efficiently and to produce hydrogen by photocatalytic activity. 25 These ndings have opened new windows for searching of novel photocatalysts and screening of new materials. 26,27 Recent reports show MoP 2 is used to produce hydrogen as semi-metallic photocatalyst. MoP 2 nanosheets possess excellent electronic properties with high active site density exposure. 28 Many early transition metal dipnictides (TMDPs) have been explored in orthorhombic and OsGe 2 or MoP 2 type-phase. [28][29][30][31][32][33][34][35][36] However, TMDPs with hexagonal graphene-like structure remains unexplored.
In this paper, we theoretically studied structural, electronic, optical, and photocatalytic properties of novel 2D transition metal dipnictides XP 2 (X ¼ Ti, Zr, Hf). Our results show that XP 2 (X ¼ Ti, Zr, Hf) with stable graphene-like hexagonal geometry are semiconductors with moderate band gaps which show good optical activity in visible and near ultraviolet region. Furthermore, the band edge positions straddle the water redox potential, predicting XP 2 monolayers as suitable candidates for photocatalytic water splitting.

Computational details
The projector augmented plane wave (PAW) 37,38 scheme was employed using density functional theory (DFT) implemented in Vienna ab initio simulation package (VASP). 39,40 The electronic band structure is calculated using Perdew-Burke-Ernzerhof (PBE) 41 functional. The semi-empirical van der Waals (vdW) corrections are considered as proposed by Grimme. 42,43 We relaxed XP 2 monolayers and converged energy to 10 À5 eV and residual forces to 10 À4 eVÅ À1 . A G-centered Monkhorst-Pack k-meshes of 6 Â 6 Â 1 were used for structural relaxation of monolayers and for optimized structures upgraded to 12 Â 12 Â 1 with 500 eV was used as plane-wave cutoff energy. A vacuum layer of 25Å in direction of out-of-plane was used to preclude interaction between layers. The converged PBE wave functions were used as starting point of Heyd-Scuseria-Ernzerhof (HSE06). 44 VASP associated phonopy code was used for phonon spectra calculation. Harmonic interatomic force constant is used as input via Phonopy code that is attained by density functional perturbation theory (DFPT). 45,46 A 5 Â 5 Â 1 supercell with energy cut-off (500 eV) was used for phonon spectrum.

Results and discussion
The transition metal dipnictides XP 2 (X ¼ Ti, Zr, and Hf) like transition metal dichalcogenides 47,48 exhibit the same hexagonal structure having trigonal prismatic 2H phase with  Table 1 The calculated lattice constant (a inÅ), bond length (P-X inÅ), bond angle (q P-X-P in degree) between X and P atoms, and band gap (E g in eV) using PBE-and HSE06 functionals, of XP 2 monolayers Monolayer a (Å) P-X (Å) (q P-X-P ) E g-PBE (eV) E g-HSE06 (eV) transition metal (X-atom) sandwiched between two phosphorus atoms as shown in Fig. 1(a). The optimized lattice parameters, bond lengths (d X-P ), bond angle (q P-X-P ) and calculated band gap using PBE and HSE06 schemes are listed in Table 1. The phonon band spectrum of XP 2 (X ¼ Ti, Zr, Hf), displayed in Fig. 1(b-d), consists of three lowest frequency acoustic modes with no imaginary frequency at the G-point. This conrms that all studied monolayers are dynamically stable. Further, the thermal stability of all XP 2 monolayers has been ascertained by performing ab initio molecular dynamics (AIMD) calculations at room temperature. The snap shots of the nal geometry of XP 2 monolayers with energy uctuation versus time (5000 ps) have been shown in Fig. 1(e-g). All single layer XP 2 have no considerable energy uctuations and possess no broken bonds in the nal structures at 300 K, indicating the experimental fabrication of understudy systems. Aer conrmation of structural stability and manufacturing possibility of monolayers XP 2 , electronic band structure and density of states (DOS) are calculated (as displayed in Fig. 2(a- Fig. 2 (a-c) The calculated electronic band structure represented by blue solid lines (PBE-functional) and red solid lines (HSE06 functional), and (d-f) partial density of states (PDOS) of TiP 2 , ZrP 2 and HfP 2 , respectively.  c)) to gain deep insight into their electronic properties. According to our calculations, XP 2 (X ¼ Ti, Zr, Hf) monolayers reveal semiconducting behavior with indirect band gap of 0.70 eV, 0.67 eV and 1.23 eV respectively with PBE functional. In addition, the hybrid functional (HSE06) 44 is used to make correction to the self-interaction (SIF) error which underestimates band gap. The calculated band structure of XP 2 monolayers exhibits the same band character with larger band gap values 1.72 eV (TiP 2 ), 1.43 eV (ZrP 2 ) and 2.02 eV (HfP 2 ). Red and blue colors represent HSE06 and PBE band structure as shown in Fig. 2(a-c). For TiP 2 and ZrP 2 systems, the conduction band minimum (CBM) lies at the M-point and valence band maximum (VBM) lies at the G-point of the Brillouin zone, representing an indirect band nature. In case of HfP 2 , CBM lies between M and G point while VBM lies at G-point of the Brillouin zone indicating an indirect semiconducting behavior. Similar trend is observed for other two dimensional materials. 25,28,49,50,52,54 The analysis of individual states contributing near the Fermi level (E F ) is obtained by plotting the partial density of states (PDOS) of understudy systems. The X-d (orange), P-s (pink), P-p (cyan) orbitals and Fermi level (E F ) represented by blue dashed line are shown in Fig. 2(d-f). The PDOS of X-s and X-p states found deeper in energy region are avoided here. It is obvious from Fig. 2(d-f) that both VBM and CBM are predominantly attributed by P-s orbital of all XP 2 systems.
The optical behavior of XP 2 systems is crucial for exploring the absorption and conversion of sunlight into electric current for various applications. Complex dielectric function specically describes optical properties by formula 3(u) ¼ 3 1 (u) + i3 2 (u). 49 In the present work, the optical absorption spectra in terms of imaginary part 3 2 (u) is calculated between 0-7.0 eV energy range, as shown in Fig. 3. From 3 2 (u) spectra of all XP 2 systems, a considerable visible light absorption is found between 1.65-3.3 eV energy range, suggesting these monolayers as promising candidates for solar energy absorber and photovoltaic applications.
Generally, the band gap of a material must be larger than 1.23 eV to perform the photocatalytic activity for water splitting. Using HSE06 functional, the calculated band gap values of XP 2 monolayers exceed free energy value (1.23 eV), implying that XP 2 monolayers satises the water splitting reaction. The valence band edge (E VB ) and conduction band edge (E CB ) positions are obtained by using HSE06 functional, schematically represented in Fig. 4. The standard redox potentials for photocatalytic water splitting mechanism are calculated by: E O2/H2O ¼ À5.67 eV + pH Â 0.059 eV and E H + /H2 ¼ À4.44 eV + pH Â 0.059 eV. 49-53 Therefore, we considered redox potential levels for water as shown in Fig. 4. For HfP 2 monolayer, the band edge potentials (both E VB and E CB ) straddle the standard redox potentials at pH ¼ 0. However, the valence band edge of TiP 2 and ZrP 2 monolayers found above the standard oxidation potential thus, fails to perform oxidation evolution reaction at pH ¼ 0. More interestingly, all XP 2 monolayers with both E VB and E CB located below and above the standard redox potentials at pH ¼ 7, indicates the ability to dissociate water into H + /H 2 and O 2 /H 2 O under the irradiation of sun light. Similar behavior has also been reported in other literature. 27,[49][50][51][52][53][54] These ndings predict XP 2 monolayers as efficient candidates for photocatalysis and photovoltaic applications.

Conclusion
In summary, the rst principles calculations are performed to investigate the structural, electronic, optical properties and photocatalytic activity of transition metal dipnictides XP 2 (X ¼ Ti, Zr, Hf) monolayers. All single layer systems are dynamically and thermally stable. Two-dimensional TiP 2 , ZrP 2 and HfP 2 are indirect semiconductors (with band gap values 1.72 eV, 1.43 eV and 2.02 eV, respectively) with both VBM and CBM mainly attributed by P-s state. A considerable absorption of solar light is found between 1.65-3.3 eV. More interestingly, all XP 2 systems (at pH ¼ 7) and HfP 2 monolayer (at pH ¼ 0) are capable to perform redox reactions of water splitting. These results pave the path for designing future optoelectronic and photovoltaic devices.

Conflicts of interest
There is no conict of interest.