Engineering 2D Materials for Photocatalytic Water-Splitting from a Theoretical Perspective

Splitting of water with the help of photocatalysts has gained a strong interest in the scientific community for producing clean energy, thus requiring novel semiconductor materials to achieve high-yield hydrogen production. The emergence of 2D nanoscale materials with remarkable electronic and optical properties has received much attention in this field. Owing to the recent developments in high-end computation and advanced electronic structure theories, first principles studies offer powerful tools to screen photocatalytic systems reliably and efficiently. This review is organized to highlight the essential properties of 2D photocatalysts and the recent advances in the theoretical engineering of 2D materials for the improvement in photocatalytic overall water-splitting. The advancement in the strategies including (i) single-atom catalysts, (ii) defect engineering, (iii) strain engineering, (iv) Janus structures, (v) type-II heterostructures (vi) Z-scheme heterostructures (vii) multilayer configurations (viii) edge-modification in nanoribbons and (ix) the effect of pH in overall water-splitting are summarized to improve the existing problems for a photocatalytic catalytic reaction such as overcoming large overpotential to trigger the water-splitting reactions without using cocatalysts. This review could serve as a bridge between theoretical and experimental research on next-generation 2D photocatalysts.


Introduction
Developing clean and renewable energy resources is critical in today's world to meet the enormous difficulties posed by global energy and environmental crises. With the long-term utilization of fossil fuels, the exhaustion of energy sources will severely affect sustainable development. Meanwhile, massive CO 2 emissions have dramatically raised CO 2 concentrations in the atmosphere, causing severe environmental issues such as global warming and rising sea levels. As an alternative, solar energy is becoming the ultimate energy source for all life on our planet [1][2][3][4].
Although the total solar energy incident on the earth in one hour is greater than the annual global energy consumption, the most pressing difficulty remains the gathering and storing of the diffused form of energy to ensure a feasible and continuous fuel supply [5]. Among the different technologies, photocatalytic process or artificial photosynthesis is a more appealing method of harnessing solar energy has piqued interest due to three key benefits (i) ability to generate O 2 and H 2 at different electrodes, removing the separation issue; (ii) the ability to operate in ambient circumstances; and (iii) the ability to build a system using only stable and abundant inorganic materials [6]. It is well known that solar energy is being used to run thermodynamic uphill reactions to split the water into hydrogen and oxygen [7,8]. It appears to be a straightforward method that combines water, semiconductor material, and solar light. However, each of these elements has a role in the

Overall Water Splitting
The water-splitting reaction is endothermic in which water is broken down into oxygen and hydrogen: Splitting water into hydrogen is an uphill chemical process with a corresponding rise in Gibbs free energy (∆G • = 237 kJ mol −1 ) [64].
In general, the overall water-splitting photocatalysis at the semiconductor catalyst interface has three significant steps: (i) photons with adequate energy absorption (which is larger than the bandgap) on the surface of a photocatalyst, which can accelerate excited electrons and holes for subsequent redox reactions, (ii) the separation and migration of charges on the photocatalyst's surface in a brief period, and (iii) surface reactions, such as HER (i.e., hydrogen evolution reaction) and OER (i.e., oxygen evolution reaction) for water reduction (Equation (2)) and oxidation (Equation (3)) on the surface of photocatalysts, respectively.
2H Significant potential losses are expected ("interfacial loss"), resulting from entropy contributions of electrons and potential interfacial barriers caused by poor alignment [65,66]. The efficient electron/hole transport to the photocatalyst adjusts the potentials either negatively or positively at short time scales of milliseconds to seconds. It then maintains steady-state potentials that allow steady-state electrochemical redox processes to produce H 2 and O 2 [12].
However, the photocatalytic reactions follow a complex competing sequence for multistep processes. Lighting the preceding physical features determine which factor(s) dominates the net photocatalytic activity. This emphasizes the significance of comprehending the kinetics and dynamics of a catalytic reaction to build realistic methodologies for the rapid development of photocatalysis in the future.

Thermodynamic Requirements
The photocatalytic materials, typically consisting of metal oxide semiconductors, efficiently absorb visible light irradiation up to a wavelength of 520 nm to achieve around 10% solar to hydrogen (STH) efficiency [67,68]. Such semiconductors must meet the thermodynamic conditions for driving water breakdown into H 2 and O 2 [9]. The photocatalysis mechanism can generally be characterized by the electronic band structure, as shown in Figure 1. A photon with an energy higher than the bandgap excites an electron from a filled valence band state to an empty conduction band. After photo-excitation, the ability of a photoexcited electron (e − ) and hole (h + ) to reduce and oxidize is then determined by the bottom of CB and top of VB in the band structure. Those charge carriers should be thermally relaxed to the bottom of the CB and the top of the VB. At the bottom of CB, the conditions for a photocatalytic reaction should be higher (more positive) than the reactant's reduction potential (P red ). Moreover, photocatalysis may be used to generate both positive and negative ∆G reactions [69,70]. For example, ΔG < 0 is found in the photo-degradation of organic molecules in the presence of oxygen. On the other hand, ΔG > 0 occurs for water splitting [13,15] and CO2 reduction [71] with substantial positive changes in ∆G. The material does not affect the thermodynamics of the process but only modifies the kinetics by generating new reaction pathways through absorption of optical light [72].

Reaction Kinetics
The photocatalytic reaction occurs when a photocatalyst satisfies the thermodynamic The top of VB is suggested to be more positive than the oxidation potential of the reactant to be oxidized (P ox ). Since the difference between P red and P ox corresponds to the total Gibbs energy change (∆G), the ∆G is negative when P red is lower than P ox and vice-versa. Importantly, to drive a chemical reaction, ∆G must be negative in the reduction and oxidation steps by e − and h+, which is the determining factor to initiate a photo redox process. Thus, the photocatalytic processes are regulated by partial ∆Gs, i.e., ∆G e and ∆G h shown in Figure 1.
Moreover, photocatalysis may be used to generate both positive and negative ∆G reactions [69,70]. For example, ∆G < 0 is found in the photo-degradation of organic molecules in the presence of oxygen. On the other hand, ∆G > 0 occurs for water splitting [13,15] and CO 2 reduction [71] with substantial positive changes in ∆G. The material does not affect the thermodynamics of the process but only modifies the kinetics by generating new reaction pathways through absorption of optical light [72].

Reaction Kinetics
The photocatalytic reaction occurs when a photocatalyst satisfies the thermodynamic requirements of a particular redox process. It is possible that the reaction will occur and the chemical reaction rate can be forecast by their kinetics. Various kinetic models have been developed [73]. The production and migration of electron-hole pairs within the surface and recombination of electron-hole pairs followed by the oxidation and reduction reaction with reactants take place on the surface of photocatalyst materials. In general, light irradiation generates electron-hole pairs, where surface defects can trap holes or oxidize the reactant. In contrast, electrons move arbitrarily via a multi-strapping pathway until they come across a recombination centre where they can recombine with holes or an active site, and the surface chemical reaction can be completed [69,70,74].
The elementary steps of calculating the Gibbs free energies (∆G) for catalytic reactions using the standard hydrogen electrode (SHE) model are given by Norskov et al. [75,76]. (4) where ∆E ZPE and T∆S denotes the zero-point energy difference and entropy, respectively, and ∆E is the intermediates absorption energy. The relevant electrode potential U is ∆G U = −eU. The ∆G was corrected to H + concentrations and represented by ∆G pH . Two electron paths are involved in the HER process, including a fast proton/electron transfer step and a fast hydrogen release step: * + H + + e − → H * H * + H + + e − → * + H 2 (g) (6) where * and H* represent the catalyst's active site and adsorbed H + ions, respectively. It is well-known that photocatalytic water oxidation for oxygen evolution is complex and challenging. The Norskov group has done substantial theoretical research on the OER mechanism [76][77][78][79][80]. The electrochemical OER's proposed mechanism included four proton-coupled electron transfer (PCET) steps: where * stands for the coordinatively unsaturated sites where the reaction takes place and OH*, O*, and OOH* denote the adsorbed intermediates. Each step must be supplied with enough energy to drive the process, which is fulfilled by the external electrode energy according to Norskov's calculations. The energy term qU was used to empirically reflect this process, which derives from the electrons' higher energy, arising from the applied voltage. The OER processes for a given applied voltage bias can be produced energetically and thermodynamically favourable (∆G < 0). The reaction may contain kinetic barriers associated with each step and be excluded from the reaction-free energy calculations. According to first-principles estimates, the rate-determining step can vary based on chemical circumstances, calculation methods, and substrate composition [81]. Theoretical calculations and spectroscopic measurements for detecting intermediates during catalytic reactions are informative and helpful in determining the mechanism of photocatalytic water-splitting.

Quantification of Essential Photocatalytic Water Splitting Properties
Apart from the significance of the kinetics and dynamics of a photocatalytic reaction, many other vital parameters involved in the process of photocatalytic reactions are (i) potential of the reaction, (ii) exciton separation, and (iii) Solar-to-Hydrogen (STH) efficiency, which depicts the photocatalytic water-splitting process sequentially occurring at different time scales.

Overpotential
The HER and the OER require an external energy source such as solar radiation, which generates an electric current involving electrons and holes. The electrode potential (U) represents the external energy in an electrochemical cell, which reduces the free energy barrier and causes thermodynamic and kinetic transformations. Norskov's group investigated the OER's thermodynamics by estimating the free energy change (∆G) of the products and reactants in each step using one-by-one electron transfer steps as shown in a typical free energy diagram ( Figure 2).

Band Alignments and Overpotentials of 2D Materials
The calculated band edge position of VBM (valence band maxima) and CBM (conduction band minima) for some typical 2D materials concerning the water reduction and oxidation potentials for photocatalytic water-splitting is shown in Figure 3. The overpotential and required extra potential to trigger photocatalytic water-splitting OER and HER reactions employing 2D materials are listed in Tables 1 and 2, respectively.
Note that the presence of appropriate band edge positions does not always assure that the material will be an effective photocatalyst for overall water-splitting. We do not know whether photo-generated electrons and holes in the monolayer provides sufficient driving force to activate overall water-splitting. Due to the energy loss during the photogenerated carriers' migration between different materials [83], the overpotential is a crucial element for evaluating the performance of photocatalysts for water splitting [84]. To this end, further research into the processes of both the HER and OER is required to better Water oxidation E 0 O 2 /H 2 O has a standard electrochemical potential of 1.23 eV versus NHE. This value corresponds to the red dashed lines in Figure 2, representing the ideal free energy profile for a 4-e oxidation process. Each of the four consecutive steps in this idealistic scenario continues with a constant ∆G equal to the usual electrochemical potential. As defined by Equations (7)-(10), the various steps of the OER have distinct free energy change values in the entire system (solid red lines in Figure 2). These aberrations can be associated with the conformational and electronic changes of the reacting subsystem and how such reactions impact the surroundings, such as the solvent and substrate. The third step given by Equation (9) is the rate-limiting step with 1.60 eV potential. As a result, the electrode potential (1.23 eV) is inadequate to allow the thermodynamic oxidation process to occur (solid blue line). At U = 1.23 V, the energy diagram flattens out ( Figure 2, dotted blue line) and permits all steps to be thermodynamically feasible. The minimum voltage supplied to the electrode requires at least 1.60 V, which is the highest ∆G in the reaction pathway (rate-limiting potential). The 0.37 V external voltage is required for the optimal procedure (1.60 V − 1.23 V = 0.37 V). This extra voltage is called the overpotential (η). The theoretically estimated overpotential for TiO 2 ranges from 0.76 to 0.78 V [76], close to the experimental results of 0.9-1.1 V [82].

Band Alignments and Overpotentials of 2D Materials
The calculated band edge position of VBM (valence band maxima) and CBM (conduction band minima) for some typical 2D materials concerning the water reduction and oxidation potentials for photocatalytic water-splitting is shown in Figure 3. The overpotential and required extra potential to trigger photocatalytic water-splitting OER and HER reactions employing 2D materials are listed in Tables 1 and 2  . Band alignments and required extra potential of some typical 2D materials concerning the water reduction and oxidation potential for photocatalytic water-splitting.
The potential provided by the photogenerated holes (Uh: the difference in energy between the VBM and the hydrogen reduction potential) cannot overcome the high overpotentials, resulting in high required external potential (>1 V) to proceed with the oxygen evolution reaction for water splitting (Tables 1 and 2). While g-CN, BeN, β-GeSe, C6N7, and Cu2ZnSnS4 (112) required the external potential greater than 0.40 V. The β-PdSe2, Ag-BiP2Se6 (PE), RhTeCl, Cu2ZnSnS4, β-SnSe, and β-AuS monolayers required minimal external potential to process the OER reaction. Remarkably, under the external potential provided by photogenerated holes, the AgBiP2Se6 (FE), SiP2S6, PdSeO3, SiP2, and SiAS2 monolayers can proceed OER without using sacrificial reagents or cocatalysts.  . Band alignments and required extra potential of some typical 2D materials concerning the water reduction and oxidation potential for photocatalytic water-splitting.
Note that the presence of appropriate band edge positions does not always assure that the material will be an effective photocatalyst for overall water-splitting. We do not know whether photo-generated electrons and holes in the monolayer provides sufficient driving force to activate overall water-splitting. Due to the energy loss during the photogenerated carriers' migration between different materials [83], the overpotential is a crucial element for evaluating the performance of photocatalysts for water splitting [84]. To this end, further research into the processes of both the HER and OER is required to better understand the monolayer's photocatalytic activity. For example, monolayers of C 3 S, CuCl (111), CuCl, g-C 3 N 4 , and Pd 3 P 2 S 8 exhibit a very high overpotential (rate-limiting potential) in the oxygen evolution half-reaction ( Table 1).
The potential provided by the photogenerated holes (U h : the difference in energy between the VBM and the hydrogen reduction potential) cannot overcome the high overpotentials, resulting in high required external potential (>1 V) to proceed with the oxygen evolution reaction for water splitting (Tables 1 and 2). While g-CN, BeN, β-GeSe, C 6 N 7 , and Cu 2 ZnSnS 4 (112) required the external potential greater than 0.40 V. The β-PdSe 2 , AgBiP 2 Se 6 (PE), RhTeCl, Cu 2 ZnSnS 4 , β-SnSe, and β-AuS monolayers required minimal external potential to process the OER reaction. Remarkably, under the external potential provided by photogenerated holes, the AgBiP 2 Se 6 (FE), SiP 2 S 6 , PdSeO 3 , SiP 2 , and SiAS 2 monolayers can proceed OER without using sacrificial reagents or cocatalysts.  For HER, the monolayer AgBiP 2 Se 6 (FE) and AgBiP 2 Se 6 (PE), overpotential cannot be overcome by the potential provided by the photogenerated electrons (U e : the difference in energy between the hydrogen reduction potential and the CBM) as shown in Table 1. Therefore, these materials required a potential >1 to trigger the reduction reaction. The monolayer SiP 2 and AgBiP 2 Se 6 (FE) efficiently activate only the oxidation reaction. In contrast, the Cu 2 ZnSnS 4 , C 3 N 5 (2L) GaAs monolayer can trigger only the reduction reaction without the help of additional cocatalysts. Notably, very few monolayers (Penta-SiAs 2 , PdSeO 3 , SiP 2 S 6 , LiGaS 2 (2L)) can be used as a high-performance photocatalyst for overall water-splitting, triggering both oxidation and reduction reaction without using any cocatalysts due to the sufficient external potential provided by photogenerated carriers.

Exciton Binding Energy
The electron-hole pairs will be formed as the photon is absorbed, and they must be separated appropriately to ensure adequate free photoexcited carriers for the subsequent water redox reactions. The exciton binding energy plays a vital role in examining the carrier separation induced by photo-excitation, and it is defined as: E b = E QP − E OPT , where E OPT and E QP stand for the energy at the first optical absorption peak and quasiparticle bandgap, respectively. The smaller the value of E b , the easier it is to separate the carrier. The minimum energy needed to ionize an exciton from its lowest energy state is given by E b [12,120]. The effective masses and dielectric constant are two crucial parameters that influence the values of the exciton binding energy.
Currently, DFT calculations and beyond can accurately predict exciton binding energies, effective masses, and different crystal orientations. The significant distortion causes an anisotropic electronic field during exciton formation, facilitating charge separation [121]. Furthermore, these quasiparticles are sensitive to a range of external stimuli, which may be used to alter 2D materials' intrinsic optical and optoelectronic properties, making them intriguing candidates for novel optoelectronic applications.
A representative scheme of exciton binding energy for various 2D responsive materials is shown in Figure 4. In the chalcogen-based 2D materials, the exciton binding weakens as the chalcogen becomes heavier, explaining the enhanced dielectric screening provided by heavier chalcogens' to diffuse more orbitals. The amplitude of the spin-orbit splitting is directly related to the exciton splitting in these materials, and the exciton splitting in WX 2 compounds is substantially higher than in MoX 2 compounds. Excitation energies for Molybdenum and Tungsten dichalcogenides materials are predicted to range from 1 to 2 eV, suggesting potential applications in the near-IR to the red regime [122]. As seen in Figure 4, the E b of Janus, WSSe is less than monolayer WS 2 and WSe 2 due to the built-in electric field directed from the Se layer to the S layer [108,122]. Moreover, the excitation energies of C 2 N/WS 2 heterobilayer are less than their monolayer counterparts [118]. may be used to alter 2D materials' intrinsic optical and optoelectronic properties, making them intriguing candidates for novel optoelectronic applications. A representative scheme of exciton binding energy for various 2D responsive materials is shown in Figure 4. In the chalcogen-based 2D materials, the exciton binding weakens as the chalcogen becomes heavier, explaining the enhanced dielectric screening provided by heavier chalcogens' to diffuse more orbitals. The amplitude of the spin-orbit splitting is directly related to the exciton splitting in these materials, and the exciton splitting in WX2 compounds is substantially higher than in MoX2 compounds. Excitation energies for Molybdenum and Tungsten dichalcogenides materials are predicted to range from 1 to 2 eV, suggesting potential applications in the near-IR to the red regime [122]. As seen in Figure 4, the E of Janus, WSSe is less than monolayer WS2 and WSe2 due to the built-in electric field directed from the Se layer to the S layer [108,122]. Moreover, the excitation energies of C2N/WS2 heterobilayer are less than their monolayer counterparts [118].

Solar-to-Hydrogen (STH) Efficiency
STH efficiency is an important characteristic that can be used as a realistic standard for measuring the performance of photocatalysts. The STH efficiency has been estimated to evaluate the photocatalytic performance of the monolayer, assuming 100% efficiency of the catalytic reaction [123,124]. The STH efficiency (QSTH) for the semiconductor can be determined by [84,111]:

Solar-to-Hydrogen (STH) Efficiency
STH efficiency is an important characteristic that can be used as a realistic standard for measuring the performance of photocatalysts. The STH efficiency has been estimated to evaluate the photocatalytic performance of the monolayer, assuming 100% efficiency of the catalytic reaction [123,124]. The STH efficiency (Q STH ) for the semiconductor can be determined by [84,111]: where ∆G = 1.23 eV and P(hω) represents the potential difference for water splitting and the AM1.5 solar energy flux at the photon energy of hω, respectively.
The ultra-violet (UV) photocatalysts perform better than visible light photocatalysts for hydrogen generation via solar water splitting because UV light has higher photonic energy than visible light. Most of the described photocatalysts are only active when exposed to UV light. However, ultraviolet light (400 nm) accounts for only 4%, while visible light (400-800 nm) and infrared light (>800 nm) contribute about 53% and 43%, respectively, of total solar energy. Since UV light accounts for only a small amount of solar energy, it is vital to rationally design and build photocatalysts that can harvest more visible or infrared light, effectively boosting the low STH conversion efficiency throughout a broad spectral range. Thus, a less efficient photocatalyst that absorbs visible light is preferred than a more efficient photocatalyst that absorbs only UV light [12,125,126].
Moreover, heterostructures are created by stacking light absorbers with various bandgaps on top of one another, enhancing photo potential and exploiting a more significant portion of the solar spectrum. These systems can create more photo potential with a broader range of solar absorption, resulting in more excellent STH conversion efficiencies [125,126]. The light absorption efficiency is strongly dependent on the bandgap. A representative scheme of STH for various 2D responsive materials is shown in Figure 5, where the STH range for mostly 2D materials is from 4-20%. In contrast, Janus Pd 4 S 3 Se 3 shows the highest STH of 30.01%. The ultra-violet (UV) photocatalysts perform better than visible light photocatalysts for hydrogen generation via solar water splitting because UV light has higher photonic energy than visible light. Most of the described photocatalysts are only active when exposed to UV light. However, ultraviolet light (400 nm) accounts for only 4%, while visible light (400-800 nm) and infrared light (>800 nm) contribute about 53% and 43%, respectively, of total solar energy. Since UV light accounts for only a small amount of solar energy, it is vital to rationally design and build photocatalysts that can harvest more visible or infrared light, effectively boosting the low STH conversion efficiency throughout a broad spectral range. Thus, a less efficient photocatalyst that absorbs visible light is preferred than a more efficient photocatalyst that absorbs only UV light [12,125,126].
Moreover, heterostructures are created by stacking light absorbers with various bandgaps on top of one another, enhancing photo potential and exploiting a more significant portion of the solar spectrum. These systems can create more photo potential with a broader range of solar absorption, resulting in more excellent STH conversion efficiencies [125,126]. The light absorption efficiency is strongly dependent on the bandgap. A representative scheme of STH for various 2D responsive materials is shown in Figure 5, where the STH range for mostly 2D materials is from 4-20%. In contrast, Janus Pd4S3Se3 shows the highest STH of 30.01%. Figure 5. Solar-to-hydrogen (STH) efficiency for 2D materials.

Single-Atom Catalysts (SACs)
SACs have shown tremendous promise in photocatalytic water-splitting because of distinctive geometric and electronic configurations that enhance mass and charge transfer

Single-Atom Catalysts (SACs)
SACs have shown tremendous promise in photocatalytic water-splitting because of distinctive geometric and electronic configurations that enhance mass and charge transfer during the photocatalytic process. The interaction of the single metal atom with the pedestal layer can affect the photocatalytic pathways and catalytic performances [127]. First-principles calculations [128] have recently demonstrated that the 2D metal-organic frameworks (MOFs) containing transition metal (TM = Cr-Zn, Ru-Ag, Ir, and Pt) atoms and tetraaza annulene (TAA) [14] can act as multi-functional photocatalysts. As illustrated in Figure 6a,b, the unit cell of two-dimensional TM-TAA MOFs has three equivalent TM atoms; each bind to four N-atoms to create nitrogen-coordinated metal macrocycles (TM-N4). The VBM and CBM of these TM-TAA MOFs estimated using the HSE06 functional were aligned relative to the vacuum level with hydrogen reduction and water oxidation ( Figure 6c). were aligned relative to the vacuum level with hydrogen reduction and water oxidation ( Figure 6c). Moreover, the calculated catalytic performance of TMTAA MOFs with TM = Ru-Ag, Ir, Pt predict them to be an efficient catalyst for OER with the overpotential of 0.45 V [128]. While Rh-TAA MOF can catalyze OER with the overpotential of 0.40 V. These values are comparable or even lower than that of the best catalysts for water splitting (Pt/RuO2) [129][130][131]. Remarkably, under visible light irradiation, the Ir-TAA and Rh-TAA MOF monolayers could operate like very effective photocatalysts for overall water-splitting.
However, the g-C3N4 has good solar utilization and redox potentials, and it has poor carrier separation because the VBM and CBM are positioned in the closed N and C atoms [132]. We note that the recombination rate of photogenerated electron-hole pairs and overpotentials in OER and HER must be controlled to obtain high catalytic efficiency. For the above purpose, the single-atom embedded g-C3N4 has recently displayed a unique charm in oxidation [133,134] and water splitting [135] in both experiment and theory due to the high utilization rate and selectivity of SACs [136][137][138].  [128]. Copyright 2021 RSC. (d) The relationships of the calculated overpotentials (ΔηOER and ΔηHER) with the differences between the redox potentials of specimens and water oxidation/H+ reduction (Δηox and Δηred). (e) The free energy charges of HER at sites 1 and 2 of specimens. Reprinted with permission from ref. [104]. Copyright 2018 Elsevier.
The absorption energy of OH, O, OOH, and H intermediates on different sites of catalysis surface is also an essential factor to determine the catalytic efficiency. TM1/g-C3N4 specimen shows that the adsorption energies of intermediates decrease significantly compared to pristine g-C3N4. A relationship of the overpotential with the difference between the water oxidation/H + reduction and redox potential of the specimen (Figure 6d) shows that the ΔG*H values are negative at site 1 (the centre of the triangular pore) and positive at site 2 (top of TM1 atom), suggesting a preference of adsorption of H atom on-site 1 [104]. A similar variation tendency is found for the overpotential for HER (ΔηHER). Comparing the ΔηHER with the differences of reduction potentials between H + reduction (Δηred) and specimens (see Figure 6e), the Δηred of Pd1/and Pt1/g-C3N4 are equal or more significant  [128]. Copyright 2021 RSC. (d) The relationships of the calculated overpotentials (∆η OER and ∆η HER ) with the differences between the redox potentials of specimens and water oxidation/H+ reduction (∆η ox and ∆η red ). (e) The free energy charges of HER at sites 1 and 2 of specimens. Reprinted with permission from ref. [104]. Copyright 2018 Elsevier.
Moreover, the calculated catalytic performance of TMTAA MOFs with TM = Ru-Ag, Ir, Pt predict them to be an efficient catalyst for OER with the overpotential of 0.45 V [128]. While Rh-TAA MOF can catalyze OER with the overpotential of 0.40 V. These values are comparable or even lower than that of the best catalysts for water splitting (Pt/RuO 2 ) [129][130][131]. Remarkably, under visible light irradiation, the Ir-TAA and Rh-TAA MOF monolayers could operate like very effective photocatalysts for overall water-splitting.
However, the g-C 3 N 4 has good solar utilization and redox potentials, and it has poor carrier separation because the VBM and CBM are positioned in the closed N and C atoms [132]. We note that the recombination rate of photogenerated electron-hole pairs and overpotentials in OER and HER must be controlled to obtain high catalytic efficiency. For the above purpose, the single-atom embedded g-C 3 N 4 has recently displayed a unique charm in oxidation [133,134] and water splitting [135] in both experiment and theory due to the high utilization rate and selectivity of SACs [136][137][138].
The absorption energy of OH, O, OOH, and H intermediates on different sites of catalysis surface is also an essential factor to determine the catalytic efficiency. TM 1 /g-C 3 N 4 specimen shows that the adsorption energies of intermediates decrease significantly compared to pristine g-C 3 N 4 . A relationship of the overpotential with the difference between the water oxidation/H + reduction and redox potential of the specimen (Figure 6d) shows that the ∆G *H values are negative at site 1 (the centre of the triangular pore) and positive at site 2 (top of TM 1 atom), suggesting a preference of adsorption of H atom on-site 1 [104]. A similar variation tendency is found for the overpotential for HER (∆η HER ). Comparing the ∆η HER with the differences of reduction potentials between H + reduction (∆η red ) and specimens (see Figure 6e), the ∆η red of Pd 1 /and Pt 1 /g-C 3 N 4 are equal or more significant than the ∆η HER of them at both absorption sites. As a result, the Pd 1 /and Pt 1 /g-C 3 N 4 catalysts can be used to produce hydrogen [104].
In conclusion, the interaction of single metal atoms with a 2D surface impacts photocatalytic pathways and catalytic performance [127]. For example, metal atoms interacting with the g-C 3 N 4 surface can change the material's inherent band structure, affecting light absorption, charge carrier separation, and reaction kinetics. The development of atomically dispersed active sites is attributed to the contact between an isolated metal atom and the surface, improving the catalytic activity and stability of SACs for photocatalytic water-splitting [104,139].

Defects Engineering
Engineering the morphologies of photocatalysts by constructing defects, heteroatom doping, and surface/interface building is a promising strategy for improving photocatalytic performance [140][141][142][143][144][145][146]. Material with defects may be relatively more conducive to photocarrier separation, allowing more photoelectrons and holes to engage in the reduction and oxidation reactions [142]. Defects are also important in photocatalysis because they provide active sites for reaction participation, which improves light harvesting and charge carrier concentration with better charge separation [140].
Zheng et al. [147] induced the intrinsic point defects (selenium vacancy (V Se ), diselenium vacancy (V Se2 ), platinum vacancy (V Pt ), diplatinum vacancy (V Pt2 ), and anti-site defects with a Se atom substituting a Pt atom (Se Pt )) in ultrathin PtSe 2 layers using firstprinciples computations and STM/STS (Scanning Tunneling Microscopy/Scanning Tunneling Spectroscopy) [148], which can improve the photocatalytic water-splitting efficiency of PtSe 2 monolayers [147]. Moreover, on the other side, Ma et al. [149] recently introduced Pd dopant and vacancies into PtSe 2 to boost the basal plane for the HER. They constructed five (V Se , V Pt , V Se2 , V Pt2 , and Se Pt ) and nine (VSe, V Se2 , V Pt , V Pd , V Pt2 , V Pd2 , V PdPt , Se Pt , Se Pd .) intrinsic defect in PtSe 2 and PdPtSe 4 monolayer, respectively (Figure 7a). The divacancy sites (V Se2 and V Pt2 ) in pristine PtSe 2 monolayers, as well as the vacancy (V Se , V Pd ) and divacancy sites (V Pt2 , V PdPt ) in PdPtSe 4 monolayers, significantly boost catalytic activity comparable to that of Pt [149]. More excitingly, the defect engineering significantly reduces the overpotentials of the HER and the OER to levels exclusively provided by photogenerated carriers [151][152][153][154]. For example, the overpotential of HER according to free energy calculations on the InGaSSe bilayer is about 2.16 V (Figure 7b). This calculated value is higher than photogenerated electrons potential (Ue = 0.68 V), implying that HER cannot be activated solely by photo-generated electrons in the InGaSSe bilayer. To improve the InGaSSe's monolayer performance, the surface defects, including Ga vacancy, are introduced, leading to a decrement of HER overpotential to −0.21 V. Therefore, the results suggest that HER can be carried out by photogenerated electrons under photogenerated potential, as shown in Figure 7c. On the other hand, OER for the defective InGaSSe bilayer, the free energy profile More excitingly, the defect engineering significantly reduces the overpotentials of the HER and the OER to levels exclusively provided by photogenerated carriers [151][152][153][154]. For example, the overpotential of HER according to free energy calculations on the InGaSSe bilayer is about 2.16 V (Figure 7b). This calculated value is higher than photogenerated electrons potential (U e = 0.68 V), implying that HER cannot be activated solely by photo-generated electrons in the InGaSSe bilayer. To improve the InGaSSe's monolayer performance, the surface defects, including Ga vacancy, are introduced, leading to a decrement of HER overpotential to −0.21 V. Therefore, the results suggest that HER can be carried out by photogenerated electrons under photogenerated potential, as shown in Figure 7c. On the other hand, OER for the defective InGaSSe bilayer, the free energy profile becomes favourable with ∆G < 0 under the external potential provided by the photogenerated holes, indicating that the OER can proceed under these conditions (Figure 7d). As a result, vacancy defects can lower the HER and OER overpotentials of 2D semiconductors to the levels generated by photogenerated carriers, allowing overall water-splitting without reagent sacrifice.

Strain Engineering
By varying the distances between surface atoms, lattice using either tensile or compressive strain can fine-tune the electronic structure of surfaces [155,156]. Since the applied strain usually varies with the ions' specific bonding and local symmetry, there are no general rules for the strain effect on the material's electronic structure. Single-layer materials can sustain high mechanical strain [157,158]. For example, graphene can endure a 25% uniaxial strain [159], while phosphorene can sustain a 30% uniaxial strain [160]. This gives much flexibility when it comes to electronic structure engineering. This surface tuning strategy is another practical way to manipulate the catalytic reaction activity by changing the overlap of orbitals of catalysts [161].
The bandgap, as well as indirect-to-direct transition, can be modulated by strain engineering [179]. For example, when subjected to uniaxial and biaxial strains (compressive and tensile) in hexagonal AlN (h-AlN) monolayer, its bandgap and band edge alignment perfectly match with the water-splitting energy levels (Figure 8a-c) [179]. Besides the suitable band gap and appropriate band alignment of the h-AlN monolayer, the optical absorption capability can also be modified by strain engineering [51-54]. Figure 8d shows that the optical absorption peak of strained th-AlN has different absorption energies than the pristine th-AlN monolayer. In addition, the optical properties can also be tuned with strain engineering [152,180,181]. Importantly, Zhao et al. [182] demonstrated that applied tensile strains (0-2%) improve the HER activity of the h-B 2 O monolayer, resulting in ∆G* being close to 0 eV at low hydrogen coverage, as shown in Figure 8e. Also, the imposed compressive strain (−2 to 0%) may increase hydrogen bonding, resulting in lower ∆G* (Figure 8e). Furthermore, the uniaxial strain (−8% to +8%) can also improve the HER activity of the α-Sb monolayer [182]. For Cu-doped α-Sb monolayer, the value of ∆G H* decreases with both tensile and compressive strain (Figure 8f). This observation indicates that the HER catalytic performance of the monolayer can be promoted by applying a uniaxial strain. Besides HER, OER catalytic performance is also boosted with strain engineering for the photocatalytic process. The values of the EDF (electrochemical driving forces) at pH = 0 are more than the PDS (potential determining step) for 2% and 4% uniaxial strain. The −2%, −4% uniaxial and −2% biaxial strained WS 2 /BlueP heterostructures are thermodynamically feasible at pH = 0 for photocatalytic water-splitting (Figure 8g). In contrast, at pH = 7, all the strained heterostructures are feasible [166]. Reprinted with permission from ref. [182]. Copyright 2020 ACS. (f) The hydrogen adsorption free energy of Cu@Sb under strain from −8% to 8%. Reprinted with permission from ref. [165]. Copyright 2020 Elsevier. (g) The EDF and PDS of uniaxial and biaxial strained WS2/BlueP during OER at PH = 0 and PH = 7. Reprinted with permission from ref. [166]. Copyright 2021 RSC.

Intrinsic Electric Fields
An electric field can modify the photocatalyst bandgap requirement of 1.23 eV in the reaction mechanism of water splitting. Yang and colleagues first introduced a new way to breach the 1.23 eV limit and significantly boosted solar energy efficiency [84]. When an external electric field is introduced in the interface between two identical photocatalysts, all energy levels bend in the same direction, leading to the development of a nano-heterojunction with the charge distribution of the VB on one surface (001) and the CB on the other (001) surface.
In contrast, the reduction potential on the (001) surface should be below the CBM, according to this newly proposed principle. Furthermore, the internal electric field prevents excited electrons on the (001) surface from returning to the (001), encouraging the spatial separation of the photogenerated electron-hole pair [84]. Here, we discuss many designing techniques such as Janus structure, type-II heterostructure, and Z-scheme heterostructure, which can have a self-induced internal electric field, reducing the HER and OER overpotentials of 2D semiconductor to the levels that the photogenerated carriers can provide.

Janus Structures
Researchers recently became more interested in Janus structures, a new class of 2D materials with unique properties induced by symmetry breaking and intrinsic out-ofplane polarization [183][184][185]. Because of their inherent out-of-plane mirror asymmetry, Reprinted with permission from ref. [182]. Copyright 2020 ACS. (f) The hydrogen adsorption free energy of Cu@Sb under strain from −8% to 8%. Reprinted with permission from ref. [165]. Copyright 2020 Elsevier. (g) The EDF and PDS of uniaxial and biaxial strained WS2/BlueP during OER at PH = 0 and PH = 7. Reprinted with permission from ref. [166]. Copyright 2021 RSC.

Intrinsic Electric Fields
An electric field can modify the photocatalyst bandgap requirement of 1.23 eV in the reaction mechanism of water splitting. Yang and colleagues first introduced a new way to breach the 1.23 eV limit and significantly boosted solar energy efficiency [84]. When an external electric field is introduced in the interface between two identical photocatalysts, all energy levels bend in the same direction, leading to the development of a nano-heterojunction with the charge distribution of the VB on one surface (001) and the CB on the other (001) surface.
In contrast, the reduction potential on the (001) surface should be below the CBM, according to this newly proposed principle. Furthermore, the internal electric field prevents excited electrons on the (001) surface from returning to the (001), encouraging the spatial separation of the photogenerated electron-hole pair [84]. Here, we discuss many designing techniques such as Janus structure, type-II heterostructure, and Z-scheme heterostructure, which can have a self-induced internal electric field, reducing the HER and OER overpotentials of 2D semiconductor to the levels that the photogenerated carriers can provide.

Janus Structures
Researchers recently became more interested in Janus structures, a new class of 2D materials with unique properties induced by symmetry breaking and intrinsic out-of-plane polarization [183][184][185]. Because of their inherent out-of-plane mirror asymmetry, Janus monolayers have been proposed to be effective photocatalysts for water splitting and piezoelectric materials in device applications.
The recently synthesized asymmetric Janus TMDCs (Transition-metal dichalcogenides) inherit the advantages of two H-phase TMDCs while also providing an additional degree of flexibility to boost photocatalytic performance [184]. Figure 9a depicts the typical structure of an MX monolayer's atomic structure, composed of two layers of vertically bonded metal atoms sandwiched between two layers of chalcogen atoms. A Janus M 2 XY monolayer is formed by substituting the bottom layer of chalcogen atoms with another chalcogen atom, as shown in Figure 9b [186]. The Janus M 2 XY and parent MX monolayers possess negative formation energies, indicating that they can be formed stably as investigated by DFT computations. Furthermore, MX and Janus M 2 XY monolayers exhibit suitable band alignments (Figure 9c), with a robust optical absorption coefficient (~3 × 10 4 /cm) in visible light and an even higher absorption coefficient (~10 5 /cm) in the near UV range (Figure 9d,e) [186].
The WSSe monolayer's driving force for the photoexcited carriers has been investigated by Kou et al. using DFT calculation [108].
Step 2 (∆G O *) has a positive free energy change, indicating that the water oxidation half-reaction on the S side cannot proceed in the dark medium. During the reaction, ∆G O * is the maximum, termed the OER barrier (rate-limiting potential). When the WSSe monolayer is exposed to light, photogenerated holes provide sufficient light. U h , which grows with increasing pH value, contrasts the situation of ∆G O *. Surprisingly, all of the steps in the half-reaction of water oxidation are favourable (∆G < 0) at pH = 1-7, as shown in Figure 9f. In other words, in a light environment, the H 2 O molecules could spontaneously oxidize into O 2 on the Janus monolayer WSSe at neutral or even acidic media (1-7 pH) [108].
On the other hand, the hydrogen reduction at pH = 0−7 cannot proceed spontaneously on the Se side without light irradiation. When U e is evaluated at pH = 0, both steps are energetically favorable (∆G < 0), indicating that the HER might occur spontaneously on the Se side in an acid media (0-5 pH) under U = 0.93 V (Figure 9g). At pH = 3, the WSSe monolayer shows optimal work conditions for catalytic reaction due to the competitive correlation between the pH requirements for limiting the catalytic reaction barriers [108].

Heterojunctions
Heterojunctions have been developed as a new technique to design high-performance photocatalysts for water splitting [195,196]. There are two types of heterojunctions for photocatalytic water-splitting systems, namely type-II [197] and Z-scheme [198][199][200] heterojunctions. This proposed strategy can enhance the separation efficiency of photogenerated electrons and holes and catalytic reaction activity by occurring on different surfaces of materials. monolayer is formed by substituting the bottom layer of chalcogen atoms with another chalcogen atom, as shown in Figure 9b [186]. The Janus M2XY and parent MX monolayers possess negative formation energies, indicating that they can be formed stably as investigated by DFT computations. Furthermore, MX and Janus M2XY monolayers exhibit suitable band alignments (Figure 9c), with a robust optical absorption coefficient (~3 × 10 4 /cm) in visible light and an even higher absorption coefficient (~10 5 /cm) in the near UV range (Figure 9d,e) [186]. The WSSe monolayer's driving force for the photoexcited carriers has been investigated by Kou et al. using DFT calculation [108].
Step 2 (ΔGO*) has a positive free energy change, indicating that the water oxidation half-reaction on the S side cannot proceed in the dark medium. During the reaction, ΔGO* is the maximum, termed the OER barrier (rate-limiting potential). When the WSSe monolayer is exposed to light, photogenerated

Type-II van der Waals Heterostructures (vdWH)
Type-II vdWH can be constructed by layering monolayers on top of other monolayers [201][202][203]. The photogenerated electrons and holes are trapped independently in various building blocks; thus, lowering the recombination rate with more active sites. Therefore, type-II heterojunctions photocatalysis is very useful to split water photo catalytically since it avoids the unwanted surface back reactions to a large extent [40,195,196,204]. Therefore, there are three essential criteria to construct type-II heterojunctions: (i) The gap between CBM and VBM in two types of monolayers must be slightly overlapped to assure the separation of holes and electrons. (ii) Photocatalytic activity for water splitting should be present in both types of monolayers within a specific pH range. (3) The lattice parameters of two different types of monolayers must be similar enough to reduce strain and distortion in their lattices while also improving stability. A matched lattice can also be designed by combining supercells with various numbers of unit cells, for example, a 2 × 2 supercell with a 3 × 3 supercell.
Various type-II heterojunctions have been reported with different materials interface stacking to show charge separation as photocatalysts for splitting water [205][206][207][208][209][210][211][212][213][214][215]. A novel SiH/CeO 2 (111) type-II heterojunction with the six stacking modes was constructed with optimized structures (Figure 10a) having a slight lattice mismatch of less than 1% [216]. The electron and hole accumulation regions formed at the heterostructure interface due to the vdW interaction between SiH and the CeO 2 (111) layer, separating the photoexcited electron-hole pairs. The band edge potentials of pristine SiH monolayer, CeO 2 (111), and SiH/CeO 2 (111) heterojunction with respect to the 4.5 eV NHE are shown in Figure 10b. All of their VBM (CBM) potentials are greater (lower) than the oxygen reduction (proton reduction) potential, suggesting that the catalytic reaction may be successfully executed under light-driven conditions [216].
SiH monolayers, respectively, thereby delaying photogenerated carrier recombination. As a result, OER and HER reactions may be carried out efficiently on various monolayers [216].
Without any light irradiation (U = 0), the SeGe@SSn heterostructure carried out the OER reaction, which resulted in a rate-determining step of 1.94 eV (Figure 10d). While the photogenerated holes of SeGe@SSn offer the additional potential (U = 2.11 V) for the irradiated sample in the neutral solution [119]. All steps are energetically favorable (ΔG < 0), implying that under light irradiation at pH = 7, all oxidation reactions can proceed spontaneously without any barriers, which is highly appealing for practical applications. On the other hand, only two hydrogen reduction processes are required, as shown in Figure  10e. The fact that the extrinsic potential provided by photogenerated electrons (U = 0.89 V) can be generated under light irradiation makes both of these steps exothermic. Thus, it is reasonable to assume SeGe@SSn to be capable of photocatalytic water-splitting without using a sacrificial agent when exposed to light [119]. In addition, the computed ΔG for the OER process at U = 1.23 V for the InSe/g-C3N4 heterostructure are illustrated in Figure 10f. The third reaction step has the maximum ΔG of 0.433 eV on the g-C3N4 side, while the highest ΔG value of 1.057 eV on the InSe side and 0.596 eV at the InSe/g-C3N4 interface, respectively, for the dissociation of H2O to OH*. The  (111) heterojunction layers. Reprinted with permission from ref. [216]. Copyright 2021 RSC. The free energy steps for (d) OER and (e) HER in SeGe@SSn for potential U = 2.11 V and U = 0.89 V at pH = 7. Reprinted with permission from ref. [119]. Copyright 2019 RSC. (f) The ∆G profiles of the OER (pH 0, U = 1.23 V) on the InSe surface, the g-C 3 N 4 surface, and the interlayer of InSe/g-C 3 N 4 . Reprinted with permission from ref. [217]. Copyright 2019 ACS.
In addition, Figure 10c shows a schematic model of charge transfer between SiH/CeO 2 (111) heterojunction layers, which clarifies the mechanism of photocatalytic water-splitting. Firstly, light excites VB electrons to CB of the SiH and CeO 2 (111) layers, while holes stay in VB. Photogenerated electrons and holes tend to gather on the CeO 2 (111) and SiH monolayers, respectively, thereby delaying photogenerated carrier recombination. As a result, OER and HER reactions may be carried out efficiently on various monolayers [216].
Without any light irradiation (U = 0), the SeGe@SSn heterostructure carried out the OER reaction, which resulted in a rate-determining step of 1.94 eV (Figure 10d). While the photogenerated holes of SeGe@SSn offer the additional potential (U = 2.11 V) for the irradiated sample in the neutral solution [119]. All steps are energetically favorable (∆G < 0), implying that under light irradiation at pH = 7, all oxidation reactions can proceed spontaneously without any barriers, which is highly appealing for practical applications. On the other hand, only two hydrogen reduction processes are required, as shown in Figure 10e. The fact that the extrinsic potential provided by photogenerated electrons (U = 0.89 V) can be generated under light irradiation makes both of these steps exothermic.
Thus, it is reasonable to assume SeGe@SSn to be capable of photocatalytic water-splitting without using a sacrificial agent when exposed to light [119].
In addition, the computed ∆G for the OER process at U = 1.23 V for the InSe/g-C 3 N 4 heterostructure are illustrated in Figure 10f. The third reaction step has the maximum ∆G of 0.433 eV on the g-C 3 N 4 side, while the highest ∆G value of 1.057 eV on the InSe side and 0.596 eV at the InSe/g-C 3 N 4 interface, respectively, for the dissociation of H 2 O to OH*. The increasing trend of ∆G value for the H 2 O to OH* step reveals that the InSe/g-C 3 N 4 heterojunction catalyst has a high active water adsorption energy on all three sides, preventing water dissociation OH* intermediates species, resulting in slow OER kinetics [217]. Due to the separation of photogenerated electron-hole pairs, reaction kinetics, and optical absorption, the heterostructure is widely thought to be a viable solution to large overpotential for HER and OER. As a result, numerous 2D Janus vdW heterojunctions have been designed, such as MoSTe/C 3 N 4 [218], ZnO/WSSe [219], MoSSe/SiC [220], GeC/MoSSe [221], GaS0.5Se0.5/Arsenene [222], MoSSe/AlN [223], MoSSe/GaN [223], GeC/WSSe [221], WSSe-SiC [220], MoSSe/WSSe [224], MoSSe/C 3 N 4 [218], and ZnO/MoSSe [219] heterostructures for photocatalytic water-splitting.

Z-Scheme Heterostructures
In contrast to one-step excitation, the Z-scheme photocatalytic mechanism [198,200] is a two-step excitation system motivated by natural photosynthesis in green plants [225]. The ideal Z-scheme photocatalysts comprise three components as two different photosystems are connected by the acceptor/donor pair (shuttle redox mediator), as schematically illustrated in Figure 11a. In contrast, the separate components of these Z-scheme photocatalysts systems for the catalytic reaction are inappropriate for overall water decomposition. On the other hand, redox mediators in Z-scheme photocatalysts may cause unwanted reverse reactions and prevent optical absorption [226]. Therefore, as schematically illustrated in Figure 11b, mediator-free systems are direct Z-scheme systems. Hence, direct Z-scheme photocatalysts for overall water breakdown have sparked much interest because of their remarkable redox capability and effective separation of photogenerated electron-hole pairs [227][228][229][230][231][232][233][234][235][236][237][238].
The charge redistribution and generation of the built-in electric field across the heterostructure interface are driven by the difference in work function (W) between the adjacent monolayers [239]. Figure 11c depicts the photocatalytic mechanism of pure, Cr, B doped, and co-doped g-C 3 N 4 /BiVO 4 interfaces [227]. The face-to-face g-C 3 N 4 /BiVO 4 2D materials of g-C 3 N 4 and BiVO 4 (010) surface can initiate an electric field, encouraging interface charge transfer and preventing electron-hole pair recombination resulting in a negative charge on the g-C 3 N 4 monolayer and a positive charge on the BiVO 4 (010) surface. Figure 11d is a schematic diagram of the photo-excitation and charge transfer mechanism at the MoSSe/WSeTe interface [240]. In theory, if process 1 has a longer lifetime than process 2, photoexcited electrons at MoSSe's CBM tend to recombine with holes at WSeTe's VBM, generating a Z-scheme path. While process 2 has a longer lifetime than process 1, the photoexcited electrons and holes split fast and remain at MoSSe and WSeTe, respectively, operating as a conventional type II channel.
The electron transfer, hole transfer, and e-h recombination dynamics of MoSSe/WSeTe hetero-structure with Te-Se and Te-S stacking are shown in Figure 11e [241,242]. The rapid charge separation demonstrated that the charge transfer in Te-Se stacking follows the typical type-II path. At the same time, the e-h recombination makes the charge transfer facilitation in the Z-scheme path for the Te-S stacking [240]. In addition, the type II path for Te-Se stacking and the Z-scheme pathway for Te-S stacking is also confirmed by the averaged nonadiabatic coupling (NAC) (Figure 11f). The Z-scheme mechanism benefits from the enormous long carrier lifetime and photoinduced charge density to increase the reduction and oxidation reaction rates. For example, the PtS 2 /Arsenene vdW heterostructure can split the water into hydrogen and oxygen by direct Z-scheme [110]. Figure 11g shows the ∆G H is as low as -0.487 eV, with the most stable adsorption site for HER on the arsenene layer. As a result, the PtS 2 /Arsenene vdW heterostructure is an intriguing HER catalyst candidate. In OER, under U = 0, the rate-limiting step (2 eV) is the production of OH* by H 2 O adsorption on the PtS 2 layer. The ∆G steps for OER change for this reaction step are decreased at an external potential of 1.23 V, as represented by cyan lines in Figure 11h. Moreover, all reaction steps are energetically favorable (∆G < 0) in free energy under 2.10 V potential field, as shown by yellow lines (Figure 11h), indicating that OER has a lower exothermic reaction than other 2D photocatalysts [97].  [110]. Copyright 2020 RSC.
The electron transfer, hole transfer, and e-h recombination dynamics of MoSSe/WSeTe hetero-structure with Te-Se and Te-S stacking are shown in Figure 11e [241,242]. The rapid charge separation demonstrated that the charge transfer in Te-Se stacking follows the typical type-II path. At the same time, the e-h recombination makes the charge transfer facilitation in the Z-scheme path for the Te-S stacking [240]. In addition, the type II path for Te-Se stacking and the Z-scheme pathway for Te-S stacking is also confirmed by the averaged nonadiabatic coupling (NAC) (Figure 11f). The Z-scheme mechanism benefits from the enormous long carrier lifetime and photoinduced charge density to increase the reduction and oxidation reaction rates. For example, the PtS2/Arsenene vdW heterostructure can split the water into hydrogen and oxygen by direct Z-scheme [110]. Figure 11g shows the ΔGH is as low as -0.487 eV, with the most stable adsorption site for HER on the arsenene layer. As a result, the PtS2/Arsenene vdW heterostructure is an intriguing HER catalyst candidate. In OER, under U = 0, the rate-limiting step (2 eV) is the production of OH* by H2O adsorption on the PtS2 layer. The ΔG steps Figure 11. Schematic illustrations of (a) ideal Z-scheme system and (b) direct Z-scheme system. Reprinted with permission from ref. [226]. Copyright 2015 Wiley-VCH. (c) Schematic illustrations of the reaction mechanism for photocatalytic water-splitting and photocatalytic mechanism. Reprinted with permission from ref. [227]. Copyright 2020 Elsevier. (d) Schematic diagram of the photoexcitation and charge transfer dynamics at the MoSSe/WSeTe interface (e) The electron transfer, hole transfer, and e-h recombination dynamics of MoSSe/WSeTe heterostructure with Te-Se and Te-S stacking. (f) Averaged values of NAC between different states for Te-Se and Te-S stacking. Reprinted with permission from ref. [240]. Copyright 2019 RSC. (g) ∆G H as a function of reaction coordinate on Are layer in the PtS 2 /Are vdW heterostructure. (h) The free energy diagram for OER on PtS 2 layer in the heterostructure at U = 0 V, 1.23 V, 2.10 V potential. Reprinted with permission from ref. [110]. Copyright 2020 RSC.

Multilayer Configurations
The thickness heavily influences the electronic structures of 2D layered semiconductors [243][244][245][246][247]. The thickness-dependent electronic characteristics severely limit the potential applications of 2D stacked semiconductors as photocatalysts. For example, the bandgap with conduction and valence band locations shift dramatically from a single layer to a few layers, as seen in MoS 2 and phosphorene layers [248][249][250]. As a result, it is critical to find 2D photocatalysts with appropriate thickness-independent band gaps and band edge alignment with high mobility [36,251]. However, a few single photocatalysts can spontaneously fulfill high solar energy conversion efficiency and photocatalytic redox processes.
Li et al. [252] predict the optoelectronic properties of few-layer P 4 O 2 systems using DFT computation. A three-layer P 4 O 2 with standard (α-3) packing is an attractive option for photocatalytic water-splitting because it facilitates the required optoelectronic properties (Figure 12a-d). The bandgap and band edge positions of monolayers α-2, α-3 and β-2, β-3, surpass the redox potential of water splitting. As a result, they could be good candidates for photocatalysts that do not require an external potential (Figure 12e). More intriguingly, the CBM of α-3 is 0.08 eV larger than the reduction level of H + /H 2 O, whereas the VBM of α-3 is 0.09 eV lower than the oxidation level of O 2 /H 2 O. As a result, α-3 might be considered the most efficient photocatalysts for overall water-splitting processes [252]. Furthermore, all five systems have significant optical absorption in visible and UV spectral regions (Figure 12h). The absorption coefficients of α-3 and β-3 are substantially more effective than those of the other three systems due to interlayer interaction [252].

Edge-Modification in Nanoribbons
Due to the quantum confinement, nanostructures that lower the dimensionality of 2D materials to nanoribbons and quantum dots have tunable electronic properties [253][254][255][256][257][258]. Designing nanoribbons (NRs) for photocatalytic water-splitting by modifying their edges is a new technique for enhancing photocatalytic efficiency [259,260]. According to a quantitative analysis of the Gibbs free energy of hydrogen (H*) adsorption/desorption, edges play a dominating role in triggering the photocatalytic process [261][262][263]. Yang et Furthermore, Qi et al. [97] proposed experimentally feasible 2D LiMX2 (M = Al, Ga, In; X = S, Se, Te) bilayers to be ideal for photocatalytic water-splitting using first-principles calculations. The hydrogen atom prefers to bind to the S site, as seen in Figure 12f. However, after hydrogen desorption, such a deformed surface will be restored to its original structure. As shown in Figure 12i, free energy change calculations demonstrate that H adsorption on the LiGaS 2 bilayer at U e = 0 is uphill with ∆G =1.15 eV. So, it cannot proceed spontaneously.
Interestingly, all HER steps become exothermic reactions when exposed to the potential (U e = 1.59 V) produced by photogenerated electrons (Figure 12i). On the other hand, Figure 12g depicts the photocatalytic mechanism for OER corresponding with their free energy at U h = 0 (Figure 12j). The first step is the rate-limiting step, with a ∆G barrier of 2.08 eV. The photogenerated hole U h = 2.66 V potential can surpass this step. Therefore, the ∆G plot shows a downward trend at this voltage, indicating that the OER can drive under these conditions. The findings show that the photogenerated carriers in the LiGaS 2 bilayer have sufficient photocatalytic redox potential to drive the catalytic reaction in pure water [97].

Edge-Modification in Nanoribbons
Due to the quantum confinement, nanostructures that lower the dimensionality of 2D materials to nanoribbons and quantum dots have tunable electronic properties [253][254][255][256][257][258]. Designing nanoribbons (NRs) for photocatalytic water-splitting by modifying their edges is a new technique for enhancing photocatalytic efficiency [259,260]. According to a quantitative analysis of the Gibbs free energy of hydrogen (H*) adsorption/desorption, edges play a dominating role in triggering the photocatalytic process [261][262][263]. Yang et al. [264] present a novel approach for edge-modified phosphorene nanoribbons (PNRs) as very effective photocatalysts. They find that pseudo-halogen passivated PNRs have the desired band edge positions urged by the edge electric dipole layer, preserving the intrinsic optoelectronic properties of phosphorene [265,266]. Figure 13a-e shows the armchair (AC) and zigzag (ZZ) PNRs passivated by the CN functional group. It is worth noting that edge passivation can result in polar covalent bonds forming along the edges of PNRs [264]. A potential jump shifts to all single-particle energy levels and the band edge energy levels. As a result, the phosphorene's band edge energy levels can be shifted downward employing polar covalent bonds in the form of P + − X − where X represents the atom or a chemical group. This vital edge decoration affects the CBM and VBM levels of edge-modified PNRs, allowing for the design of efficient photocatalysts [265]. In addition, the PNR heterobilayer is designed, which consists of two different types of edge-modified PNRs, as shown in Figure 13f. Heterobilayer acts as a type-II donor-acceptor interface because of the built-in potential induced by the edge dipole layers. This heterojunction type can promote carrier transport and separation at the heterobilayer interface. VBM and CBM states are anticipated to be localized inside discrete donor and acceptor regions due to such an induced potential. Localization of the VBM and CBM states improves charge separation and allows carrier collection easier [267].
is designed, which consists of two different types of edge-modified PNRs, as shown in Figure 13f. Heterobilayer acts as a type-II donor-acceptor interface because of the built-in potential induced by the edge dipole layers. This heterojunction type can promote carrier transport and separation at the heterobilayer interface. VBM and CBM states are anticipated to be localized inside discrete donor and acceptor regions due to such an induced potential. Localization of the VBM and CBM states improves charge separation and allows carrier collection easier [267].  [265]. Copyright 2017 ACS. (g) Photocatalytic hydrogen generation and collection scheme. Reprinted with permission from ref. [268]. Copyright 2019 ACS. (h) Reaction mechanism for two possible mechanisms of the OER via single-site or dual-site reactions on F-10BN_ZZ-GDYNR1 (GDYNR stands for graphdiyne nanoribbons). Reaction energy pathways of (i) the OER following the AEM mechanism, (j) the OER through the O-O coupling mechanism, and (k) the HER on F-10BN_ZZ-GDYNR1 under different electrode potentials U relative to SHE at pH = 7. Reprinted with permission from ref. [269]. Copyright 2020 RSC.
Moreover, Yang et al. [268] designed a photocatalytic hydrogen generating system using carbon nanotube (CNT) and carbon-nitride double-walled nanotube systems (CNNT), in which CNNT is caged in CNT (Figure 13g). To improve water dissociation, they used mono dispersed TMN3 (TM = Fe/Co/Ni/Cu/Zn) sites embedded in CNT, abbreviated as CNTFCNNT. Figure 13g depicts the photocatalytic hydrogen generation and collection scheme: (i) electrons in CNNT and holes in CNT, (ii) water decomposes into a proton and oxygen-containing groups due to energetic holes, (iii) when protons arrive at CNNT, they are converted to hydrogen atoms and (iv) H2 production can be entirely isolated from oxygen-containing species, thanks to CNT's selective permeability of protons. Finally, H2 molecules should diffuse in the gap between two nanotubes, allowing safe delivery [268].
On the other hand, doping of graphdiyne nanoribbons (GDYNRs) with BN pairs can result in an appropriate band structure for accelerating catalytic reactions [270,271]. The F-10BN ZZ-GDYNR1 and F-8BN ACGDYNR1 explore the thermodynamics of the OER  [265]. Copyright 2017 ACS. (g) Photocatalytic hydrogen generation and collection scheme. Reprinted with permission from ref. [268]. Copyright 2019 ACS. (h) Reaction mechanism for two possible mechanisms of the OER via single-site or dual-site reactions on F-10BN_ZZ-GDYNR1 (GDYNR stands for graphdiyne nanoribbons). Reaction energy pathways of (i) the OER following the AEM mechanism, (j) the OER through the O-O coupling mechanism, and (k) the HER on F-10BN_ZZ-GDYNR1 under different electrode potentials U relative to SHE at pH = 7. Reprinted with permission from ref. [269]. Copyright 2020 RSC.
Moreover, Yang et al. [268] designed a photocatalytic hydrogen generating system using carbon nanotube (CNT) and carbon-nitride double-walled nanotube systems (CNNT), in which CNNT is caged in CNT (Figure 13g). To improve water dissociation, they used mono dispersed TMN3 (TM = Fe/Co/Ni/Cu/Zn) sites embedded in CNT, abbreviated as CNTFCNNT. Figure 13g depicts the photocatalytic hydrogen generation and collection scheme: (i) electrons in CNNT and holes in CNT, (ii) water decomposes into a proton and oxygen-containing groups due to energetic holes, (iii) when protons arrive at CNNT, they are converted to hydrogen atoms and (iv) H 2 production can be entirely isolated from oxygen-containing species, thanks to CNT's selective permeability of protons. Finally, H 2 molecules should diffuse in the gap between two nanotubes, allowing safe delivery [268].
On the other hand, doping of graphdiyne nanoribbons (GDYNRs) with BN pairs can result in an appropriate band structure for accelerating catalytic reactions [270,271]. The F-10BN ZZ-GDYNR1 and F-8BN ACGDYNR1 explore the thermodynamics of the OER half-reaction, followed by the adsorbate evolution mechanism (AEM), O-O coupling, and the HER mechanisms (Figure 13h).
Alternatively, the OER can continue via the O-O coupling pathway and other OH* formed by the second dissociation of H 2 O, which couples with a co-adsorbed O* at a nearby site (Figure 13i). It led to an OO* species formation and releasing an (H+-e) pair with a ∆G of 1.65 eV. The desorption of OO* creates an O 2 gaseous molecule in the last stage because the rate-determining phase has a greater negative ∆G. The O-O the coupling mechanism is significantly more likely to occur than the AEM mechanism (Figure 13j) [269]. Therefore, the F-10BN ZZ-GDYNR1 photocatalyst possesses an unfavourable ∆G at pH = 7. At U = 0, ∆G for the production of H 2 molecules from the H* species is 0.19 eV for the HER, as illustrated in Figure 13k. After shifting the energy by an external potential given by photogenerated electrons (i.e., Ue = 1.35 V), the HER's elementary steps become gradually smaller than zero. The results presented by Xu et al. demonstrate that F-10BN_ZZ-GDYNR1 is a viable candidate for use as a metal-free photocatalyst in overall water [269].

The Effect of pH in Overall Water Splitting
It has been shown that altering the redox potential of water splitting can improve the photocatalytic activity of semiconductors (generally by changing the pH) [272,273]. The catalytic reaction mechanism is highly dependent on environmental conditions [274]. In acidic and alkaline environments, the half-reaction on the surface for water oxidation is different. The mechanism of OER under acidic environments has been extensively studied using first-principles studies [89,118,275,276]. The ∆G of H + + e − at a pH other than 0 can be formally addressed using the computational hydrogen electrode (CHE) approach established by Bagger et al. [277] by using the reversible hydrogen electrode (RHE) as the reference electrode and standard hydrogen electrode (SHE) for pH = 0. The two reference potentials U RHE and U SHE can be linked as eU RHE = eU SHE − k B Tlna H + = eU SHE + k B T × pH × ln 10. The a H + is the activity of the H + ions in solution at T = 298.15 K [278,279]. Notably, fewer DFT studies for water oxidation in the alkaline medium were reported in the literature [279][280][281]. The reduction and oxidation potential for water splitting under the influence of pH of the medium is given as [105] E H + /H 2 = −4.44 eV + pH − 0.059 eV (12) Li et al. [282] have investigated the effect of pH on the photocatalytic activity of SnC and As monolayers, as well as the SnC/As heterojunction [282]. The reduction and oxidation potentials are between the band edges of the As monolayer, with a pH (0 to 14) function, as illustrated in Figure 14a. As a result, the As-monolayer meets the fundamental criteria of photocatalytic total water splitting, but SnC fails to meet this condition (Figure 14b). Furthermore, the alkaline conditions are appropriate for photocatalytic water-splitting in H1 configuration of SnC/As heterojunction (Figure 14c).

Catalysis in Acidic Media
Our group has recently demonstrated that the overall water-splitting can occur simultaneously and spontaneously on β-PdSe 2 monolayer in all media conditions [105]. Figure 14d depicts the four-electron (4e) reaction pathway, followed by adsorbed intermediates forming on a β-PdSe 2 monolayer. At U = 0 V, the first step of the β-PdSe 2 monolayer combines with a proton and electron to produce a H* intermediate with uphill ∆G of 1.54 eV (Figure 14e). In contrast, with U = 1.23 V, the first step is uphill, and the second step is downhill. While at U = 1.55 V, the free energy diagram demonstrated that all reaction steps were downhill. As a result, the calculated HER overpotential (η HER ) for a β-PdSe 2 monolayer at pH = 0 is 0.31 V (Figure 14f) [105].
In an acidic medium, the ΔG of elementary steps in the dark (U = 0) and light (U = 1.23 eV, 2.01 eV) radiated conditions show that two reaction steps are uphill and the other two steps are downhill at the equilibrium potential (1.23 V) for pH = 0 to 7. While at U = 2.01 V, the free energy profile revealed all reaction steps exergonic for pH = 0 to 7. As a result, the computed OER overpotential (η OER ) for a β-PdSe2 monolayer at pH = 0 was 0.77 V, as shown in Figure 14g. Figure 14. The band edge alignment of (a) As, (b) SnC, and (c) SnC/As heterostructure with the redox potentials of water splitting as a function of pH. Reprinted with permission from ref. [282]. Copyright 2020 RSC. Proposed photocatalytic pathways and the atomic configuration of absorbed intermediates species during the (d) OER and (e) HER on the β-PdSe2 monolayer in an acidic medium. The free-energy changes of hydrogen reduction at (f) pH = 0 and oxygen evolution at (g) pH = 0 (h) pH = 3 (i) pH = 7 on the β-PdSe2 monolayer. Reprinted with permission from ref. [105]. Copyright 2021 RSC. Figure 14. The band edge alignment of (a) As, (b) SnC, and (c) SnC/As heterostructure with the redox potentials of water splitting as a function of pH. Reprinted with permission from ref. [282]. Copyright 2020 RSC. Proposed photocatalytic pathways and the atomic configuration of absorbed intermediates species during the (d) OER and (e) HER on the β-PdSe 2 monolayer in an acidic medium. The free-energy changes of hydrogen reduction at (f) pH = 0 and oxygen evolution at (g) pH = 0 (h) pH = 3 (i) pH = 7 on the β-PdSe 2 monolayer. Reprinted with permission from ref. [105]. Copyright 2021 RSC.
In an acidic medium, the ∆G of elementary steps in the dark (U = 0) and light (U = 1.23 eV, 2.01 eV) radiated conditions show that two reaction steps are uphill and the other two steps are downhill at the equilibrium potential (1.23 V) for pH = 0 to 7. While at U = 2.01 V, the free energy profile revealed all reaction steps exergonic for pH = 0 to 7. As a result, the computed OER overpotential (η OER ) for a β-PdSe 2 monolayer at pH = 0 was 0.77 V, as shown in Figure 14g.

Conclusions, Perspectives, and Challenges
The emergence of environmental and energy challenges has seriously hindered global development and progress. Photocatalytic water-splitting to produce hydrogen opens up a new way to develop new energy sources. In the last few decades, extensive efforts have been devoted to constructing various photocatalytic 2D semiconductors due to their exceptional optical features and potential uses in the energy and sensing domains. Since first-principles methods can predict the intrinsic photocatalyst properties and be employed to screen the photocatalytic systems reliably and efficiently, this review focuses on the theoretical perspective of photocatalysis with 2D materials, especially the thermodynamics and kinetics aspect involved in the water-splitting mechanism.
We discussed the computational modelling and the reaction kinetic for photocatalytic water-splitting of very recently emerged next-generation 2D materials to show the fundamental principles of reactions occurring on the surface of a photocatalyst. Notably, particular emphasis has been placed on various strategies implemented in specific examples to address issues associated with redox reactions (HER and OER) on the surface of 2D semiconductor photocatalysts. Various effective methods have been adopted to optimize the catalytic performance at the electronic and free energy levels. The defect and Figure 15. Proposed photocatalytic pathways and the atomic configuration of absorbed intermediates species during the (a) OER on the β-PdSe 2 monolayer in an alkaline medium. Free energy diagram for OER at (b) pH = 9 (c) pH = 12 on β-PdSe 2 monolayer. Reprinted with permission from ref. [105]. Copyright 2021 RSC.

Conclusions, Perspectives, and Challenges
The emergence of environmental and energy challenges has seriously hindered global development and progress. Photocatalytic water-splitting to produce hydrogen opens up a new way to develop new energy sources. In the last few decades, extensive efforts have been devoted to constructing various photocatalytic 2D semiconductors due to their exceptional optical features and potential uses in the energy and sensing domains. Since first-principles methods can predict the intrinsic photocatalyst properties and be employed to screen the photocatalytic systems reliably and efficiently, this review focuses on the theoretical perspective of photocatalysis with 2D materials, especially the thermodynamics and kinetics aspect involved in the water-splitting mechanism.
We discussed the computational modelling and the reaction kinetic for photocatalytic water-splitting of very recently emerged next-generation 2D materials to show the fundamental principles of reactions occurring on the surface of a photocatalyst. Notably, particular emphasis has been placed on various strategies implemented in specific examples to address issues associated with redox reactions (HER and OER) on the surface of 2D semiconductor photocatalysts. Various effective methods have been adopted to optimize the catalytic performance at the electronic and free energy levels. The defect and strain engineering can significantly improve catalysts' HER/OER activity to the low reaction energy barrier. The formation of a self-induced internal electric field in Janus structures and heterostructures is another efficient method to improve reaction catalytic performance via accelerated electron transfer. In addition, the photocatalytic performance of 2D materials can also be enhanced by operational conditions such as surface modification and the pH by overcoming large overpotential to trigger the overall water-splitting reactions.
However, challenges still exist, and several crucial bottlenecks must be addressed, including (i) thermodynamics of photocatalytic technique such as energetic requirements and band edge alignment relevant to the HER and OER potential must be thoroughly understood. The migratory behaviors of electrons and holes from substrates receive little attention, even though they considerably impact photocatalytic performance; (ii) photoexcitation of a 2D semiconductor photocatalyst results in photogenerated electrons and holes, inducing the photocatalyst to be excited. The feature of the excited state and the mechanism for the energy barrier lowering by light irradiation remain unknown. As a result, understanding the dynamics of excited electrons is crucial to comprehending the overall photocatalytic process; (iii) many parameters, such as trapping, inelastic and elastic electron-phonon coupling, charge localization, and thermal disorder, influence charge and energy transfer and relaxation processes need to be thoroughly addressed; (iv) additional research in catalyst dependence on pH, edge modification, and multilayer configurations is required to tune the reaction catalyst to improve visible light absorption with minimum charge separation; (v) previously reported theoretical data have been based on the traditional DFT approach, whereas the illumination of photocatalytic kinetic research is still understudied due to its technological complexity. Understanding long-term stability and access to excited state dynamic simulations that could provide kinetic parameters are critical developments needed to comprehend photocatalyst performance.
Because of rapid achievements and a broad understanding of 2D materials in various collaborative research and development sectors in the last decade, it is now an absolute delight to do photocatalysis research on these materials. At the same time, it is possible that utilizing absorbed solar energy might significantly reduce the demand for fossil fuels for human progress while also lowering environmental pollution. Consequently, photocatalysts are becoming increasingly significant, and we must increase the performance of existing photocatalysts and develop new engineering methodologies to exploit innovative photocatalysts in a better way. This review may be helpful to reduce the gap between theory and experiments to understand the photocatalytic performance of 2D materials.