Activating two-dimensional semiconductors for photocatalysis: a cross-dimensional strategy

The emerging two-dimensional (2D) semiconductors substantially extend materials bases for versatile applications such as semiconductor photocatalysis demanding semiconductive matrices and large surface areas. The dimensionality, while endowing 2D semiconductors the unique properties to host photocatalytic functionality of pollutant removal and hydrogen evolution, hurdles the activation paths to form heterogenous photocatalysts where the photochemical processes are normally superior over these on the mono-compositional counterparts. In this perspective, we present a cross-dimensional strategy to employ the nD (n = 0–2) clusters or nanomaterials as activation partners to boost the photocatalytic activities of the 2D semiconductors. The formation principles of heterogenous photocatalysts are illustrated specifically for the 2D matrices, followed by selection criteria of them among the vast 2D database. The computer investigations are illustrated in the density functional theory route and machine learning benefitted from the vast samples in the 2D library. Synthetic realizations and characterizations of the 2D heterogenous systems are introduced with an emphasis on chemical methods and advanced techniques to understand materials and mechanistic studies. The perspective outlooks cross-dimensional activation strategies of the 2D materials for other applications such as CO2 removal, and materials matrices in other dimensions which may inspire incoming research within these fields.


Introduction
Materials have dimensions.Typically, the bulk materials are three-dimensional (3D), with spatial stretches in x-y-z directions.Lowering the dimensionalities will suit materials in confined spaces, yet, defining their dimensions.Following the dimensionalities, the nanomaterials were conventionally grouped into twodimensional (2D) represented by thin films, 1D by nanorods, and 0D by nanoparticles [1].However, in the same year of the publication of the above book, a (re)discovery of monolayer graphene changed the concept of materials dimensionality by realizing a paradoxical 'atomic (0D) crystal (3D)' as a self-standing 2D slab [2].Compared with the 3D bulks, the 2D crystal is advanced in larger surface areas, hosting distinct quantum effects that lead to unique electrical, optical, chemical, and thermal properties [3].Albeit from these advantages, the zero bandgap limits its primary roles in applications demanding semiconductive properties, such as semiconductor photocatalysis utilizing light to accelerate photochemical processes in hydrogen generations and pollutant removals [4].
The realizations of monolayer MoS 2 transistors [5] broadened the materials bases of photocatalysts from 2D graphene to its semiconductor peers.In contrast to semi-metallic graphene, the MoS 2 owns a tunable bandgap energy and types following layer numbers [6].The proper redox potentials and bandgap energy allow the absorption of visible light and the hydrogen evolution on the layered dichalcogenide [7].The semiconductor library [8] further denotes a large number of 2D candidate matrices with their Janus forms further extending applications in sensors, electrochemistry, environmental and biomedical domains [9,10].Thus, varies photocatalysts are expected to be built on 2D semiconductors and their variants.However, the single semiconductor can hardly accomplish practical photocatalysis which requires stringent materials functionalities when using out-of-lab [11].The 2D semiconductors are not exception.Even the MoS 2 with unique physical-chemical features requires dedicated engineering to boost photocatalysis [12].The 2D semiconductors and photocatalysis are seemingly connected but incompatibly apart from each other.
The heterojunctional and heterogenous materials play key roles in photocatalysis, considered as one of the key techniques to mitigate environmental and energy crisis [13].An alternative way to utilize the 2D semiconductors in photocatalysis is to form heterogenous composites which are benefited from the materials properties of the 2D semiconductive matrices and their hetero-partners [14].Despite the materials engineering endeavors to combine other materials into 2D semiconductors, the dimensionality of materials systems is not widely emphasized in engineering strategies.Recently, the 'mixed-dimensional' composites [15][16][17] have demonstrated the impact of combining 2D matrixes to materials of other dimensions on photocatalysis, inspiring the activations and investigations of 2D semiconductors deepening into the dimensionalities.
Herein, a cross-dimensional activation strategy is envisaged to strengthen the dimensionality's impacts in activating 2D semiconductors for photocatalytic applications in pollutant removals and hydrogen evolutions.Apart from mixing materials of dimensionalities for composite construction, the paper is focused on physical and chemical rationales that drive photocatalysis at different hetero-sites, and the photocatalysis crossing hetero-sites of different dimensionalities.It counts on influences given by dimensionality and briefs the influence of the reaction process, following the time which is labeled as the 4th dimension.
The paper is organized as follows.First, we envision the electronic and chemical properties of the heterogenous system, based on which, the constructions of nD@2D (n = 0-2) composites can be latter assumed.The 2D matrixes are constantly enriched computationally and experimentally, with the works detailed successively.The mechanistic studies down to electronic structural levels are described in the 5th part of the paper.Future research within the activation of the 2D semiconductors when crossing dimensions is foreseen in the summary part of the paper.

Band gap and redox potentials of semiconductor candidates
One important parameter to achieve the selective products in the reaction using semiconductors photocatalysis in terms of reaction energy is the positions of conduction band minimum (CBM) and valance band maximum (VBM) present in Figure 1.Band diagram of some common semiconductors and redox potential for the formation of radicals.Reproduced from [23].CC BY 4.0.Reproduced from [24].CC BY 4.0.
the semiconductor [18].Then, the CBM of the semiconductor should present more negative potential than the reduction potential of the reduction reaction, in water-splitting reaction the semiconductor CBM should overpass −4.5 eV at vacuum (H + /H 2 (−4.5 eV at vacuum)).For example, in a water-splitting reaction, the energy of the CBM of the semiconductor should be higher than −4.5 eV at vacuum (H + /H 2 (−4.5 eV at vacuum)).Moreover, the top of the VB must be positioned more positively than the oxidation potential of the oxidation reaction.In the case of water splitting the VBM should be more negative than −5.3 eV at vacuum (H 2 O/O 2 (−5.3 eV at vacuum)) [19,20].There are several 2D semiconductors, such as MoS 2 , and g-C 3 N 4 that CBM and VBM positions are thermodynamically favorable to perform several photocatalytic reactions like water splitting reaction or other remarkable photocatalytic applications such as hydrogen evolution and pollutant abatement, e.g. as demonstrated in figure 1 [21][22][23][24].
Although the CBM and VBM positions may fit photocatalysis, one of the major drawbacks associated with the photocatalytic reactions are the higher band gap of available semiconductor materials, such as TiO 2 [25].This drawback is due to the semiconductor with a high band gap requiring UV light irradiation to carry out the reaction whereas sunlight contains only ∼5% UV radiation [26].In this sense, for example, Fe 2 O 3 is an interesting photocatalyst to perform photocatalytic reactions such as water splitting, since the band gap is adequate to absorb visible light (2.2 eV) and the VB position is adequate to oxidate the water to oxygen (OER).However, the Fe 2 O 3 is not active in water splitting because the CBM position is not energetically favorable to perform the water reduction reaction to produce H 2 (HER) [27] but requires further combinations to form heterojunctional photocatalysts [28].CdS is an adequate material to perform a water-splitting reaction due to this semiconductor's present and suitable band gap (2.4 eV) and CV and VB favorable to perform the water-splitting reaction [29].However, this material presents photocorrosion and fast electro-hole recombination, being the main drawbacks of this material for their applications [30,31].In this sense, to select active 2D materials in photocatalysis, the 2D matrix should have an adequate band gap that adsorbs in the visible range.Moreover, the CBM and VBM should have enough potential to produce the reaction, otherwise, the process will be thermodynamically unfavorable [32,33].Also, the band alignment [34,35] and the intimated contact [36] play an important role in the design of heterostructures materials, that will be explained in this review.The lattice (mis)matches between two semiconductors set another criterion in heterojunction formation from microstructural point of view.This is especially important in vdW heterojunctions constructions [37].An alternative to activate materials that do not have adequate properties is through band gap engineering, dimensionality (tuning the band gap by decreasing the layer number) or heterostructure synthesis [19,38].

Construction of heterojunctional photocatalysts 2D/2D and 1D/2D
Semiconductor heterojunctions, combining two semiconductors into one composite, may well suit the demands to reach both redox potential and light absorption requirements for photocatalysis.Depending on the heterojunction coupling and band alignment of semiconductor/semiconductor (S/S), three types are shown in figure 2 and defined as I (straddling gap), II (staggered gap) and III (broken gap).As for photocatalysis, the most promising one is type-II which can be further viewed from the point of view of directing electron transfer by intermediate material (solid or liquid) or interface internal electric field (IEF).Based on this, type II based heterostructures are categorized by Z-schemes (traditional, all-solid and direct), S-schemes, and p-n junctions.In contrast to S/S contact, the semiconductor/metal (S/M) contact results in Schottky junctions which are also displayed in figure 2.
In type-I heterojunction photocatalyst (figure 2(a)), the CB of the photosystem I (PS I) is higher than that of PS II while the VB of PS I is lower than the VB of PS II.The photoexcited electrons and holes will be shifting and accumulating in the CB and VB of PS II leading to insufficient separation of photoexcited carriers and overall deterioration of the redox capability.Despite that, it has been investigated in the literature, Jabbar et al engineered magnetic silica-coated Ag 2 WO 4 /Ag 2 S type I heterojunction for efficient visible light degradation of Congo red dye [39].They reported that the formation of type I heterojunction improved photocatalytic activity 3.26 and 2.94 times that of pure Ag 2 WO 4 and Ag 2 S NPs, respectively.Another work by Shi and co-workers shed light on photoinduced electron-hole transfer properties in ZnFe 2 O 4 @ZnIn 2 S 4 with different positions of carbon dots (CDs).Two positions of CDs were investigated namely: the exterior and interior of the core-shell structure.It was confirmed that the interior position of CDs in the structure enables swift electron transport and prevents the recombination of electron-hole pairs resulting in the efficient visible-light degradation of tetracycline (TC) with a degradation rate of 87.3% in 120 min [40].
Type II heterojunction or staggered gap (figure 2(b)) represents one of the most efficient band alignments for photocatalysis.The CB and VB of PS II are higher than that of PS I thus enabling effective migration and spatial separation of the photoexcited electrons and holes from one PS to another.Owing to that as well as high redox ability, type II heterojunction is widely used in photocatalytic research for all possible applications.Chen et al prepared 2D/2D boron/g-C 3 N 4 nanosheets by electrostatic self-assembly thermal induction and ultrasoundassisted method for boosting photocatalytic hydrogen production.The optimized composited produced impressing 4.135 mmol h -1 g -1 due to rational band alignment of the bands and subsequent suppression of electrons and holes recombination which was confirmed by photoluminescent (PL) examination [41].A recent study by Ding's group demonstrated the successful preparation of NiAl-LDH/g-C 3 N 4 type II heterojunction using CDs as electron bridges for enhanced photoreduction of CO 2 into CO.The NiAl-LDH/g-C 3 N 4 /CDs were prepared through facile hydrothermal synthesis.The CDs were acting as bridges for photogenerated charge carriers transfer and simultaneously inhibit recombination of electron-hole pairs.The photocatalytic CO 2 reduction under solar simulated irradiation was boosted by using CDs producing a six-fold increase of CO yielding 5.2 µmol g −1 h −1 [42].It is interesting to note that up on contact sides, switchable types between I and II were predicted by using the same components, leading to a 37.5% high solar to hydrogen efficiency [43].
Type III heterostructure or broken type (figure 2(c)) is unsuitable for photocatalytic applications since the staggering gap becomes so huge that the bandgaps do not overlap, and electron-hole migration no longer is possible.Thus, this type is not within the key considerations of the current perspective.
Z-schemes, S-schemes, and p-n junctions are special cases of type II heterojunctions where upon formation of heterojunction, at the interface IEF is formed that drives the separation of electrons and holes more efficiently.The traditional Z-scheme (figure 2(d)) was inspired by natural photosynthesis in plants to improve charge separation and enhance the redox ability of photocatalysts.According to this process, photogenerated holes in the VB of PS II oxidase the electron donors (D), giving the electron acceptors (A) while the photogenerated electrons in the CB of PS I reduce A, yielding D. The photogenerated electrons and holes in the CB of PC II and the VB of PS I respectively, participate in the redox reactions.Wang et al proposed a traditional Z-scheme responsible for improved photocatalytic behavior of Cu 2 O-Pt/SiC/IrO x nanocomposites towards CO 2 reduction and H 2 O oxidation.Employing Fe 3+ /Fe 2+ redox couple they were able to efficiently separate photogenerated charges, highly extend their lifetime, prevent the backward reaction of products, and drive CO 2 reduction reaction to HCOOH (896.7 µmol g −1 h −1 ) and H 2 O oxidation to O 2 (440.7 µmol g −1 h −1 ) [44].
Since the application of the traditional Z-scheme is limited to the liquid phases and the problem with side reactions is present, the all-solid Z-scheme appeared to answer all these issues (figure 2(e)).The working principle is the same as the traditional Z-scheme but instead of the intermediate reaction is substituted by solid conductor materials.Xiao and co-workers demonstrated photocatalytic properties of all-solid Z-scheme 2D-based g-C 3 N 4 @Ag-Bi 2 WO 6 .Using Ag as a mediator between g-C 3 N 4 and Bi 2 WO 6 dramatically improved photocatalytic H 2 generation compared to single-and two-component systems [45].Similar observations were also found in the silver-bridged AgCl and 2D phosphotungstic acid system.The photoinduced charges crossed the interfaces of 2D/0D and 0D/0D and were combined at the 0D Ag buffer [46].In both cases, improved photocatalytic activity was attributed to the all-solid Z-scheme electron pathway and efficient separation of photogenerated species.
Still, dependence on the conductor material within heterojunction is unsatisfying and unreliable.Moreover, from the preparation point of view, the addition of an extra layer in heterojunction could be challenging.Therefore, a direct Z-scheme photocatalyst has been engineered (figure 2(f)).In such a heterojunction, electrons from the CB of PS I directly recombine with holes from the VB of PS II, leaving the electrons and holes of the CB of PS II and the VB of PS I to participate in reduction and oxidation reactions, respectively.A recent finding by Ju and co-workers studied the effect of oxygen vacancies in direct Z-scheme 1D Bi 2 S 3 /2D BiOI heterojunction for bacteria and dye degradation.The result specifies that direct Z-scheme as well as introduced oxygen vacancies improved charge separation and were responsible for the boost photocatalytic activity [47].
As our understanding of transfer mechanisms grows a new concept that describes it clearly has to be introduced.S-scheme (figure 2(g)) is a modern view on the electron-hole transfer in heterojunction.To engineer the S-scheme photocatalyst both reduction and oxidation-type semiconductors are required (RT and OT, respectively).Since the difference in the work function (WF) is huge (smaller WF for RT and higher WF for OT), the spontaneous flow of electrons from RT to OT through their interface occurs, until their Fermi levels reach equilibrium.Naturally, an IEF is formed at the interface, due to the positive charge of RT and the negative charge of OT.That leads to band banding, where the band edges of RT bend upward due to the loss of electrons and the band edge of OT bends downward due to the accumulation of electrons.Under light irradiation, the electrons from CB of OT recombine with holes from VB of RT, leaving electrons and holes in CB of RT and VB of OT, respectively with supreme redox capacity for running photocatalytic reactions.This new concept is a hot topic now and many studies have been conducted [48][49][50][51][52].One of the first examples of the S-scheme was demonstrated by Yu's group.They produced ultrathin 2D/2D WO 3 /g-C 3 N 4 photocatalyst for enhanced H 2 production.The improved activity was attributed to the formation of the S-scheme with the best hydrogen generation of 982 µmol g −1 h −1 [53].
In summary, the key distinction between Z-scheme and S-scheme photocatalysts lies in their electron-hole pair generation mechanism and the electron transfer between semiconductors interfaces.Z-scheme photocatalysts produce electron-hole pairs sequentially using two different semiconductors and shuttles them directly or via mediator, whereas S-scheme photocatalysts generate electron-hole pairs simultaneously through two different semiconductors connected in parallel, which leads to the band bending and swift recombination of electrons and holes.
The p-n heterojunction photocatalyst concept was proposed to address the ultrafast recombination of photogenerated electrons and holes (figure 2(h)).This concept is similar to that of the S-scheme; bringing together p-and n-type semiconductors together, their Fermi levels strive to achieve equilibrium due to the diffusion of electrons from n-type semiconductor to p-type and holes from p-type semiconductor to n-type, eventually creating IEF.Under irradiation with appropriate light, governed by the IEF, the photogenerated electrons and holes in the p-type and n-type semiconductors will migrate to the CB of the n-type semiconductor and the VB of the p-type semiconductor, respectively.This leads to improved separation of the electrons and holes and redox ability compared to type-II heterojunction due to the simultaneous influence of the IEF and the band alignment.Guo et al fabricated p-n heterojunction g-C 3 N 4 /Bi 4 Ti 3 O 12 for the degradation of acid orange-II (AO-7).The enhanced photocatalytic activity was attributed to the p-n heterojunction formation with the strong oxidative ability and efficient charge separation [54].
Finally, besides coupling two semiconductors together, they can be also coupled with conductors (metals and carbon materials).At the interface of the semiconductor and metal, electrons flow from the semiconductor to the metal (from the higher to the lower Fermi level) until Fermi levels reach equilibrium.Upon equilibrium, metal obtains an excess negative charge and the semiconductor has an excess positive charge which results in band banding which calls the Schottky barrier (figure 2(i)).The Schottky barrier acts as an efficient electron trap, preventing electron-hole recombination.Ding et al fabricated 0D/2D g-C 3 N 4 /3NiMoP 2 for highly efficient photocatalytic hydrogen production.Due to the synergy between Ni and Mo, and superior charge separation, the best photocatalyst produced 783 µmol g −1 h −1 under visible light [55].

Nanoparticle, cluster decorations and atom doping in 2D photocatalyst constructions
The above concept of 'heterojunction' mainly applies in the case of semiconductor-semiconductor composites.This may not suit if one part is in the form of nanoparticles or clusters which are conventionally considered as 0D materials [56].Therein bandgap is substituted by local structures of the 0D materials, e.g.HUMO-LUMO energy gaps in the case of clusters [57].In fact, following the reductions of dimensionality, the clear positive effects of reducing the size of the photocatalysts to bidimensional have been emphasized by reducing the dimension to 1D and 0D, and especially developing 1D/2D and 2D/2D composites as shown above and 0D/2D counterparts shown in this section.In this direction, 0D hetero-sites confirmed their advantages such as quantum confinement, edge effect and surface functionality, all beneficial for higher catalytic activity in different 0D/2D heterostructures [58], for example, 2D/2D/0D TiO 2 /C 3 N 4 /Ti 3 C 2 for CO 2 reduction [59] or 2D/0D polymeric g-C 3 N 4 /CeO 2 [60].
Indeed, one can finally reach the point of using ultrasmall metallic aggregates as 0D hetero-sites.Hence, metal clusters and metal single atoms have been drawing attention for their improved catalytic activity compared to their bigger counterparts, i.e., nanoparticles [61,62].By increasing the number of atoms in the aggregates the metallic character increases resulting in a continuum of the electronic energetic levels.While decreasing the atoms number we reach the situation of species possessing well-defined HOMO-LUMO levels, which will directly depend on the number of atoms composing the specie [63] as shown in figure 3.This interesting feature of single atoms and clusters is clearly in line with the characteristics needed in photocatalytic materials.Indeed, the latter will have benefits from the possibility of tuning the 'band-gap' of one of the components by changing the size of the specie and not any other properties [64].The use of metal clusters or single atoms to decorate 2D matrixes will inject new electrons to increase the lifetime of the electron-hole pair in the 2D material (figure 4(a)).In the case of the nanoparticles, the hot electrons may be crated via surface plasmon resonance processes and act as electron donors during photocatalysis [65] (figure 4(b)).The 2D materials will stabilize the nanoparticle, cluster or the single atom, which are highly unlikely to exist as free species.
Overall, the decoration of 2D matrixes by small metallic aggregates, i.e. clusters or single atoms, and more generally the formation of 0D hetero-sites on the matrix are greatly beneficial for the reactions that will be performed.This has been attributed to the possibility of modifying the actual CBs and VBs [66] and performing reactions, somehow 'prohibited' by the redox potentials of the 2D material or by the instability of the metallic specie.Certainly, the uncontrollable synthetic procedure of single atoms and clusters make still difficult for broad photocatalytic applicability of these species.Few examples in the literature propose high activity of single atoms and clusters showing the relevance of this catalytic entity in different photocatalytic applications such as hydrogen evolution [67][68][69], CO 2 reduction [70,71] and drugs photodegradation [72,73].Nanoparticles decorated 2D or layered 2D systems have also been realized and showed enhanced photocatalytic activities in pollutant removal or hydrogen evolution compared to the bare semiconductor matrices [74][75][76].On the other hand, many examples of size-controlled 0D hetero-sites in the literature are computational [77][78][79][80], showing the need for experimental effort in understanding the advantages of these species in photocatalytic applications.
Though scarce especially regarding wide photocatalytic applications, few cross-dimensionally activated heterojunctions of latest works show a wide range of photocatalytic applications and the mechanistic understandings.Recent studies show that the 2D + 0D Co(OH) 2 /Co 3 O 4 heterojunction is capable of visible light photocatalytic hydrogen evolution and microplastics degradations.Facile electron transfers between cobalt components and redox potentials of 2D and 0D counterparts are benefited when crossing two different dimensions [81].Loading CdS nanoparticles onto Ce-MOF microtubes enhances visible light absorption and improves separations of photoinduced charges in the heterostructure, leading to effective heavy metal ion and organic pollutant removals under solar light [82].It is worth mentioning that when lowering the dimensionality of the Ni 3 TeO 6 , visible light photocatalytic water splitting was observed by using the 2D tellurate as a photocatalyst.The distinct HER capability on the 2D slabs is attributed to lower bandgap energy, larger active sites, and more suitable atomic configurations compared to the 3D counterpart [83].
Despite of the aforementioned progresses in mechanistic studies on realized heterojunctional systems, there is a need of exploiting this new class of materials.Indeed, the use of single atoms as 0D hetero-sites was demonstrated by DFT to bring to the 'adjustable' bandgap as shown in figure 5, and certainly to the atom economy of the catalyst itself and larger surface areas, all leading to higher selectivity and catalytic activities [79].
To conclude this chapter, the development of the heterostructures for the photocatalytic application is blooming.However, there are still challenges such as optimizing, improving, and engineering the interface between two semiconductors, as the electron transfer between two semiconductors determine the efficiency of the heterostructure in photocatalytic reaction, their flow must be very efficient, suppressing recombination and providing holes and electrons for the oxidation and reduction reactions.

2D materials database
The concept of quantum confinement due to dimensionality reduction, along with its advantages for materials science, are well-known theoretically [81].Still, one needs to obtain explicit materials with an in-depth understanding of their physical properties.It is of paramount importance to assess photo-catalytic capabilities, as well as for subsequent experimental synthesis and catalytic testing.
While several 2D materials are already known both experimentally [82] and computationally [83], there is still a need to further explore their wide diversity.The discovery of new inorganic 2D materials is a difficult process in experimental research as reaction conditions can be difficult to control (vide infra).Computational approaches do not suffer these limitations, which enable for a very diverse catalogue of 2D materials to be simulated and studied for different applications.They are mainly applied in the frame of density functional theory (DFT), mostly for computational cost reasons.There are several codes to optimize the geometry of materials and calculate their properties such as Vienna Ab initio Simulation Package (VASP) [84], CASTEP [85], Quantum ESPRESSO [86] and SIESTA [87].Herein, we will focus on the computational progresses based on VASP.There are two main methodologies to discover new 2D materials at a competitive speed: high-throughput methods and evolutionary algorithms.
High-throughput methods' core principle is to obtain 2D materials by artificially cleaving different bulk materials and optimizing their geometry as well as assessing their stabilities.The need for a cost-accuracy trade-off forces to lower the accuracy of the results.This is done differently depending on the scheme: cut-off energy is set higher for some [88], the supercell is enlarged for others and the calculation parameters are tailored to the material's composition [89].One consequence of this direction is the risk of obtaining different results when increasing the accuracy for a smaller number of targeted samples while still giving a basis for further screening and material selection.
On the other hand, evolutionary algorithms, such as particle swarm optimization [90] are enabling to increase accuracy while decreasing the computational cost.The basic concept is to start with a set of initial structures to optimize and take shortcuts in geometry optimization by continuously comparing them.These algorithms are quite powerful for structure generation and energy calculations.They come in different forms and strategies [89] are mainly focused on energetic criteria for the calculations.In both cases, computational endeavor in materials science benefits a lot from both strategies, and combinations of evolutionary algorithms with DFT have been reported in literature [91].The amount of data obtained is gigantic, which allows for the researcher to have a large choice of materials to test or screen in different applications [92][93][94].These methods are top-down methods as they usually require a bulk 'substrate' taken from up-stream databases (e.g.OQMD [88,95]), Materials project [96,97], ICSD [89], COD [89,98].Perhaps an even more efficient scheme would be the use of machine learning (ML) to obtain properties from material specific features [99].The main drawback of this scheme is the lack of subsequent database enabling for ab initio calculations and subsequent data extraction.One could take the predicted properties to train another ML model but should take care of the high probability of error propagation.
One important point of computational materials science is the use of approximations to perform the calculations.While they are necessary (as per the cost-accuracy trade-off), they need to be taken into account for the interpretation of computational results as well as for any comparison with experimental results.One of them is the isolated physical state in which most samples are simulated.As experimental endeavor is not yet conducted in outer space, the results produced are always to be considered with caution.To take this computational/experimental gap into account, several criteria are observed to determine the computational stability [100], i.e. the conditions for which a material is indefinitely (thermodynamically) structurally conserved, of the newly simulated materials.

The energy criterion.
The first criterion considered is energetic.Calculation of the exfoliation/decomposition energy of the sample is done and only samples with negative (positive for decomposition) values are considered acceptable.While the negative (positive) exfoliation (decomposition) energy may ensure that it will be stable in other media, one must take into account that the opposite energies are valid only for a material isolated in a vacuum.Moreover, comparison with reference energy is always necessary to have an objective idea of how stable the material is energetically.For slightly opposite energies, one must eliminate a sample that may be somewhat exploitable, bearing in mind that materials are never synthesized in a vacuum as mentioned in previous parts of this perspective.Furthermore, at 0 K, these high-throughput strategies do not take into account the zero-point energy (ZPE), which may play an important role in layered materials.For materials that are simulated using functionals taking into account van der Waals (vdW) interaction (e.g.dispersion-corrected vdW-optB88 exchangecorrelation (XC) functional, vdW-DF2-C09 and revised VV10) [89,97], the potential may change a lot when the atoms of one layer vibrates near another layer, modifying the vdW interactions' contribution to the total energy.This potential variation being taken into account in the calculation of the vibrational frequencies [101], the ZPE may change significantly from many-to mono-layer compounds.This may therefore affect the exfoliation energy of any 2D material coming from layered compounds.Energetic stabilities may therefore be modified to a significant degree by considering the ZPE rather than only the static energy of the layers and some 2D materials may become energetically stable.Gibbs free energy may have an important influence in the energetic stability.ZPE and Gibbs free energy calculations both need the vibrational modes to be taken into account, which is the object of the next part.

Vibrational state criterion.
The second 'filter' is related to the vibrational modes of the material (phonons).For a material to be vibrationally stable, all its vibration modes must have real (positive) frequencies.The imaginary (negative) frequencies can become positive by increasing the size of the supercell studied, which in turn makes the computational cost increase and may be out of the scope of high-throughput methods.
However, several works reported that imaginary frequencies are possible for transition states in the case of molecules [89,97], and several works are associating imaginary frequencies in materials leading to subsequential phase transitions [102,103].These modes are called 'soft modes' [104,105], and are corresponding to saddle points in the potential energy surface (PES).While the general conclusion of the observation of such soft modes is that the material should break down, the only meaning of a saddle point is that the configuration is on a path to a transformation [103].No information is directly given on the stable configuration to be obtained, but an artificial displacive phase transition associated with an exaggeration of the displacement associated with imaginary frequency [105].It is actually sometimes taken into account in high-throughput calculations, in which they exaggerate the displacement as a non-linear strain applied on the material [106].On the other hand, anharmonicity is not taken into account in such 'static' calculations and may also result in imaginary phonon frequencies [104].Those points warrant caution as to whether a material can be deemed unstable or not and pave the way for further in-depth studies.While static material integrity and isolated real vibration frequencies mean possible real conditions stability, it does not take into account the convolution of all these factors.This endeavor is complicated at 0 K but is motivation enough to consider a third criterion: molecular dynamics (MD).

Thermal stability criterion.
The last criterion is called 'thermal' and is related to the 'long-term' conservation of the structure in ab-initio molecular dynamics (AIMD) simulation [100].It relates to the behavior of the structure of the material when anharmonicity is involved and thermal motion is taken into account.AIMD is a good opportunity to follow transformations and reactions, and in the present case to see the material decompose in a short time period (around 5 ps).The system is isolated (vacuum) which makes it difficult to perform a strict comparison with experimental data.However, those costly calculations are considering many things mentioned previously, like ZPE as the system is vibrating constantly, phonon anharmonicity as all modes are simulated at the same time and is enabling to discriminate between phase transition and loss of cohesion of the material [107].Among most of the databases consulted AIMD simulations are overlooked for obvious reasons of computational cost.
More reasonable studies of 2D material with 'static' 0 K methodologies requires assessments in the AIMD simulations, directly ensuring close-toexperimental stability.From these filters and considering their binary states (validated or not), one can classify 2D materials in four categories displayed in figure 6.The first one is the 'perfectly stable' category, in which the formation (exfoliation) energy is negative (positive) the vibration modes all have positive frequencies, and AIMD simulation is yielding a 2D material with its structure left intact.These materials are very good targets for experimental endeavors.The second category is containing the materials that are 'definitely stable' in the sense that the AIMD simulations are leaving them unchanged but some of the other criteria are not validated properly.Those materials may deserve further refinement of the simulation parameters as they 'pass' the most accurate criterion.The class of less realistic materials is then obtained in which AIMD is showing a loss of material cohesion (partial or complete dissociation) which is different from a deformation of the material (e.g.bending, wiggling).Those materials may need to be simulated with a support to be stable which would mean that they can still be synthesized experimentally.The last category corresponds to the 'perfectly unstable' 2D materials that are not passing any of the criteria.They may be used to improve the simulation of the 2D materials but can also be deemed imaginary as not stable whatsoever.By exploring these directions, one may very well find that the realm of exploitable 2D materials is even broader than what is currently being shown.

Density functional predictions
To represent a nD + 2D-structure (n = 0-2) in an atomic-scale model for first-principle calculation, lone component 0D to 2D models are to be joined together.Cases when n = 3 were also briefed in this section to further generalize the overview, though not within the key focus of the present perspective.Keeping in mind the previously discussed, the 0D to 3D models are nowadays readily retrieved from several open-access databases [88,95,97,[108][109][110]. Ordinarily, they foresee periodicity corresponding to their dimensionality.This is typically  achieved by built-in void spaces in inherently 3D supercells if using plane waves.Alternatively, the dimensionality of models can be chosen arbitrarily using Gaussian-type orbitals.Further pros and cons of those different bases were elaborated on by Ulian et al [111].In both cases, the nD + 2D-material models can be constructed variably for all combinations of periodicities of the lone component models.The options involving 3D supercells were suggested schematically in figure 7. Although, a regular demand to achieve a foreseen nD + 2D model is to increase the system size, hence compromising the ease of computation to a certain degree [112].
Carrying out first-principle calculations of nD + 2D-models may have diverse incentives [113][114][115][116][117], one of which is to reveal structure-property-performance relationships.In the context of photocatalysis, the pallet of calculable properties with which photocatalytic performance may be argued has expanded greatly [118][119][120][121].This is because of humanity's long-standing craving for sustainable solar-based energy production and the complexity of photocatalysis itself.Using the diverse ab-initio toolbox, the dimensionality correlated impacts of nD-hetero-sites on 2D-matrices have been revealed in several systems.A selection of advances in the field was touched upon next, simultaneously providing the reader with a glance into the capabilities of first-principle calculation for assessing nD + 2D-photocatalysts.
Using DFT calculations, Chandra et al showed 1D + 2D TiO 2 /g-C 3 N 4 to possess a staggered band structure over a vdW-type heterojunction [122].Thereby favored charge separation was suggested to underpin the experimentally observed photocatalytic ability for H 2 production and benzylamine conversion.Similarly, Ren et al reported staggered bands for the 2D + 2D PtS 2 /arsenene vdW heterostructure [123].Yet in this work, additional calculations of the potential drop and the electron density redistribution allowed the demonstration of a built-in electric field over the heterojunction.Thereby, the preferable Z-scheme carrier flow was argued.Another 1D + 2D structure, CdS/ZnIn 2 S 4 , was modeled in the work of Xu et al for application in photoelectrochemical cells (PECs) [124].Instead of a vdW-type heterojunction, chemical bonding of the 2D ZnIn 2 S 4 nanosheets occurred along the ‹120› axis of the 1D CdS nanowires.This was proclaimed based on bond mismatches acquired by DFT and confirmed by transmission electron microscopy (TEM).Furthermore, the interface states appearing upon CdS/ZnIn 2 S 4 formation positioned inside of the bandgap and were hence suggested to function as carrier transport channels, enhancing PEC performance.
For the study of true 0D + 2D dimensionality, interests may be directed toward the class of rare-earth (RE) doped materials.Due to the lesser dispersity of partially filled 4f-orbitals compared to the filled 5s 2 and 5p 6 subshells of RE dopants, the former will experience a degree of shielding.Consequently, the states tend to remain localized and atomic-like, yet still participate in optoelectronic phenomena as RE-dopants are embedded in 2D matrices [125].Theoretical study of potential RE-doped 0D + 2D photocatalysts remains scarce, nevertheless.In an example by Zhao et al a decrease of the bandgap was calculated from 1.815 eV to 1.466 eV, 1.479 eV and 1.592 eV upon doping a WS 2 monolayer with Er, Tm and Lu atoms, respectively [126].Accordingly, calculated absorption efficiencies in the visible to the near-infrared region increased strongly, hinting at a potential origin for improved photocatalytic performance under solar irradiation.
The few as-mentioned examples point out ongoing interests in ab-initio studies of cross-dimensional structures.Yet, the systems probed therein were not subjected to variations in dimensionality.In contrast, Zan et al investigated nD + 2D SiC/MoS 2 vdW heterostructures (n = 2, 3) by altering the number of SiC layers in the model [127].Changes to the bandgap of the heterostructure were found from 0.92 eV in MoS 2 /single-layer SiC down to zero in MoS 2 /Siterminated SiC composite, expressing metallic behavior.The photocatalytic activity can be tuned by imposing strain on the 2D ZnO/GeC system, resulting from the tuned bandgaps and band alignment [128].In another study, Maji et al probed both 1D + 2D Te/graphene and 1D + 2D Te/MoS 2 heterostructures, where the 1D Te nanoribbons positioned either laterally (figure 7(g)) or vertically (figure 7(j)) on the surface [129].The dimensionality of the heterojunction consequently varied, possessing either 1D or 0D characters.The exciton binding energy of both A and B excitons, derived via time-dependent (TD) DFT calculations, were amongst several material properties discussed in this work.It turned out that compared to the pristine MoS 2 , exciton binding energies increased by ≈200 and 300 meV upon the introduction of lateral and vertical Te nanoribbons, respectively.An increase of the exciton lifetimes was suggested and an impact on photocatalysis may be expected.
The mentioned exciton binding energy is one of many important photocatalysis-related quantities that TD-DFT and other advanced DFT methodologies have become able to derive [130,131], many of which are dynamic, TD properties.Zhu et al were for instance able to report hole transfer and electron-hole recombination times in differently oriented 2D + 2D MoS 2 /WS 2 bilayers using nonadiabatic (NA) MD based on TD-DFT [132].Further, photochemical reaction kinetics could be assessed by computational identification of reaction paths.Although still generally computationally expensive, the mixing of such 4D viewpoints over photocatalysis in nD + 2D systems has thus become within reach of the first-principle approaches.
The above given is merely a notion on the state of the art, yet it should be clear that ab-initio studies on the matter have become plentiful.Despite it, can it be noticed that systematic studies spanning wide ranges of nD + 2D + 4D options, a multitude of materials, and a diversified sets of calculable properties are still lacking.Generalized insights are yet to be elucidated, and may bring invaluable guidelines to synthesis, expose candidate catalyst materials, and inspire smart reallocation of experimental recourses.

Candidate selection for nD/2D systems based on data science
DFT-based studies are extremely powerful to obtain properties of specific groups of materials, they come however with a high computational cost.The pros and cons of high throughput calculations are detailed in a previous part for the 2D materials.Heterostructure properties are even more computationally demanding and suffer computational restrictions, such as the need for calculated counterparts to have similar crystal structures and orientations to avoid simulating extremely large supercells (cost-accuracy trade-off).To circumvent this caveat, and accelerate computational physical chemistry works, ML can be used to obtain different properties of heterostructure samples.Especially for 2D/2D heterostructures, so-called 'van der Waals' heterostructures, that have received a lot of attention [8,133,134].These compounds have been described as 'Lego-like' structures with an amazing potential for combinations, with different stacking arrangements.
In literature, several works have been done about heterostructure property predictions using ML.Different works have been done for different purposes.In this part, the emphasis will be on ML works aiming at helping the selection for heterostructures, focusing on the prediction of different properties such as the heterostructure band gap and interlayer distance [135], the interlayer energies and elastic constants [136], the band alignment and heterojunction type [137], the band diagram [138], band gap and binding energy with lattice constant [139] or the band gap, ionization energies and electron affinity [140].The overall steps to tackle key issues in the ML are summarized in figure 8.
For photocatalysis purposes, one of the most important properties to consider is the band alignment of the two (or more) semiconductors involved in the heterojunction as addressed in section 2.2.The interest of the band alignment comes from the fact that it is directly related to the charge transfer of the samples.In agreement with the current literature related to heterostructures of 2D materials, we will focus on compounds formed by two semiconductors.From the bulk point of view, researchers are using Anderson's rule to predict the band alignment of the heterostructure counterparts.It states that the values of CBM and VBM in the heterostructure are similar to those of the separated semiconductors.The use of Anderson's rule justifies the prediction of the 'heterostructure band gap' as one can obtain the VBM (or CBM) of the composite from the CBM (or VBM) of the isolated counterpart, providing no significant band offsets take place This rule has been used in works, based on separated monolayers [141] or based on the heterostructure band gap prediction as described above, but seems to be too strong an approximation in the case of 2D materials [142].Also, predicting WF and electron affinity can help in indicating which band is more likely to present holes or electrons.It gives valuable information for the comparison of redox potentials, the main descriptors of photocatalytic activity.
Once the research question is defined, that is, for ML works, the property to be predicted or material types to consider.This has been done in the previous part.Then the data collection step starts, a number of cases must be collected in order to train the algorithm and obtain reliable results.

Descriptors-data collection.
The accuracy and generalization of any ML model mainly rely on statistics, i.e. the more data are shown to the algorithm, the more accurate is the prediction going to be.The predictions are also benefiting from the dimensionality of the dataset i.e. the number of features (descriptors) that are associated with one heterostructure.In literature, the data are mainly collected from databases produced with high-throughput methodologies, such as the 2D atlas [83,135], C2DB [88,140], 2DMatPedia [97,136] or ALKEMIE [139,143].Literature search [137] and PyMatgen library [144,145] have also been used the datasets used for predictions range from 31 [137] to 2076 [145].Descriptors are obtained from defined physical properties of the materials [137,140,145], theoretically extracted from material properties, i.e.PLMF or using descriptor-building algorithms, e.g. the SISSO approach [135,136,146].Other work has been taking a very low dimensional dataset with only atoms and bonds [138], compensating for the apparent lack of knowledge about the systems by using a sophisticated model (crystal graph convolutional neural networks (CGCNN), vide infra).
Statistics are also very powerful if the dataset used, i.e. the subset of the targeted population (of molecules, materials, people etc) to be studied is representative of said targeted population.Representativity of a sample is non-trivial to define and is usually assimilated with the generalizability of a model in ML works, which will be discussed in a later part.Any bias in the data collection process is likely to bias the predictions but not invalidate them.Rather, it will effectively refine the question answered by the model but may also lead to misinterpretations of what can be predicted.Bias can also be checked/controlled in the data cleaning step, which is the subject of the next part.

Feature/descriptor selection-cleaning.
After collecting the data, the dataset must be cleaned which corresponds to refining the prediction target.Data cleaning must take place on the features and on the data themselves.While collecting a high-dimensional dataset can give an image of high control of the system to be predicted, it is important to make sure that the descriptors used in the prediction are indeed diverse enough not to give the same type of information.This could bias the prediction by artificially giving more statistical weight to one type of information than to others.Moreover, some algorithms may have trouble predicting well from a high-dimensional dataset.This is why the descriptors to be used must be selected.There are different selection methods to reduce the dimensionality and/or select the descriptors to use for prediction.
The most straightforward one is filtering, i.e. using criteria to screen samples and remove some of them according to different criteria [135,139,140,147,148].It can also intervene in the data collection step.Sometimes screening is indirect, e.g.taking samples from the literature that suffer from applicability, experimental difficulty, readership interest, etc [139].
Correlation coefficients can also be calculated, such as the Pearson coefficient (determination coefficient), or the Spearman coefficient [149,150].While the Pearson coefficient is evaluating linear correlation, the Spearman coefficient is assessing more the monotonic trend in the dataset.The main drawback of these quantities is that they are not measuring the same thing and therefore they give only partial information if used separately or with non-monotonous trends existing in the studied dataset.They are however converging in the case of a low correlation dataset (both coefficients get close to 0).A ranking of the Spearman coefficient for a defined set of descriptors with the labels (prediction targets) can help in selecting the best descriptors for prediction [145].
Feature importance is another way to select features (descriptors) that has been used in heterostructure-related ML works [145].There are two main types of feature importance calculations: the first one is specific to the RF model and is based on the mean impurity decrease [151].The other type of feature importance is algorithm-independent and is called permutation feature importance.It consists in running the model with one descriptor having its values shuffled.It is worth keeping in mind that while it is giving an indication on the correlation between descriptors and labels, it is leaving the prediction results unchanged, i.e. a model predicting with a given score with still predict with the same score value after feature importance analysis [152].Algorithms that are different from the actual estimator can also be used for the selection.At this stage of the study, linear regressions algorithms [137], such as the least absolute shrinkage and selection operation [135][136][137]140] are most used.These algorithms are giving feature importance-like indications in the form of linear coefficients assigned to each feature.
Dimension reduction algorithms can also be used to obtain a low-dimensional dataset, possessing the attribute of all the original descriptors (t-stochastic neighbor embedding (t-SNE)).This unsupervised machine algorithm is meant to reduce dimensionality, based on a probabilistic definition of the similarity between two neighboring points [153].This technique also possesses the advantage of giving an intuitive, visual result.It has been used in heterostructure-related works to select representative samples [145].Other approaches, such as the sure independence screening and sparsifying operator (SISSO) approach [138], have been used.The SISSO approach consists in combining descriptors in a high-dimensional space into fewer, more important descriptors.This approach is using linear regression models at its core to obtain tailor-made descriptors for the dataset.Once the dataset has been cleaned, i.e. the target has been refined, algorithm training and testing can take place.

Algo-training.
For the predictions, several algorithms are trained to obtain the best predictions as well as obtain information on the data studied.The algorithms used have different selection rules and different advantages/ drawbacks.Interpretability is also important: the more complex (not necessarily the stronger) an algorithm is, the less interpretable it may be, literally in the same fashion as it is impossible to know exactly the flow of information in any human being's brain [154].One must bear in mind that the complexity of the model does not mean its strength (high accuracy or low error in prediction) [155].For example, neural networks (NNs) are often giving results similar or inferior to other [135,156], less complex algorithms are sometimes deemed 'weaker', and the most complex architecture could show their advantage towards other low-level models if they cannot be readily detailed (ensemble methods such as random forest [157], stacked ensemble model [158] or XGBoost [159] vs NN.Furthermore, as per the No Free Lunch theorem [160], there is no perfect answer to any question but many very good answers for different questions.This supports the need for using different models to have a global analysis of the dataset [135,140,145] but can also justify the in-depth analysis of one algorithm to understand what type of answer is given [136,138,139].From this part, it can be understood that there is a synergy between data cleaning and model choice to improve predictions.Algorithms have hyperparameters that need to be tuned to ensure the best prediction results.Usually, the test (or a validation) set is used to this aim.The more hyperparameter an algorithm has, the more complex it is.The most utilized method for hyperparameter tuning is grid search.It consists in trying different hyperparameter values combinations, from predefined values.Now that algorithms have been chosen and trained, the evaluation of the obtained model follows and is detailed in the second part.

Scoring functions/scoring fig-evaluation-generalization.
The training and testing values are important as they show information on the trained model, however, they are specific to the test and training sets picked.The most important to assess the usefulness of a model is its generalization power inasmuch as the training/test sets are already well-known and one may need to see how the model performs on a large collection of 'unseen' data.This is usually done by cross-validation procedures.Cross-validation procedures consist in successively splitting the whole dataset in training and testing sets and computing the average scoring function.The number of splitting in the literature varied from 5 [136,140] to 10 [137] in agreement with standard practices.Other works used a subset of the dataset called the verification (or validation) set [136,145].Usually the split is 80:20 (train:test) [145], but other types of splits are possible such as 90:10 [138], 75:25 [136].
To measure the accuracy of a regression, several scoring functions are calculated.For classification works, several indicators are also available, accuracy being deemed the most important in the literature regarding heterostructure predictions [137].With regression works, the final goal is to obtain a value for the research target.Several scoring functions can be used, and the most straightforward score is the mean absolute error, as it directly shows the deviation between the ground truth and the predicted value.Other scoring functions present more of a statistical meaning, e.g.mean squared error and root mean squared error.R 2 and F1 scores have been used.While providing information, it must be kept in mind that the interpretation is not always easy, as different regression curves may have similar R 2 scores for the same collection of points, impairing the selection of the best regression function.From this diversity stems a difficulty in comparing the results of the different works.
The diversity of properties predicted in the literature is interesting, showing the application opportunities of ML in the field of heterostructure prediction.However, the diversity of scoring functions used is preventing performance comparison for the few works predicting similar targets.[22] with permission from the Royal Society of Chemistry.

Theoretical study on the selection for CO 2 removal
The mitigation of energy and environmental crisis cannot circumvent the tackling of CO 2 .Different from photocatalytic pollutant removal and hydrogen evolution on the active 2D semiconductors is CO 2 removal, the products of CO 2 reduction can be simple substances of single carbon atoms or complex organic structures that contain multiple carbon atoms.This complicates the study towards CO 2 reduction but challenges knowhows in photocatalysis.Besides, the reactions that lead to different final products follow different reaction pathways, on which intermediate products may differ.Hence, it needs more effort than other reactions to clearly understand the mechanism of CO 2 reduction on the substrate of interest.
Here we brief the possible track of its removal via similar ways.The research on CO 2 removal has a long history.Dating back to 1979, Inoue and coworkers have studied a variety of powder materials to photoelectrocatalytically synthesize organic matter from CO 2 reduction [161].The main difference between CO 2 removal and water splitting is that the product of CO 2 removal is more than one.Based on the number of carbon atoms that are in the products, they can be classified into C1, C2, and C3, etc which comprise respectively one, two and three carbon atoms.This is because CO 2 has the highest oxidation state of carbon atoms, thus, all the lower oxidation state is viable through its reduction reaction.Due to the same reason, the main challenge is the high bond energy of the C=O bond, which is 750 kJ mol −1 [162], which requires a large input of energy to break.
To select the materials that are suitable for CO 2 removal in a theoretical way, the first step is to test the adsorption behavior of the molecules on the surface.The coordination modes of CO 2 on the surface are typical of three types, oxygen coordination, carbon coordination, and mixed coordination [22].They are demonstrated in figure 9. Depending on the different coordination modes, the reaction pathways and products may vary, leading to distinct selectivity properties.To successfully finish the reduction reaction, the final step of desorption of the product is also important.Li et al has studied the 2D CN/BOS heterojunction by enumerating different C1 intermediates and computing their Gibbs free energy in the reaction [163].This technique has also been used by Ma and Lang in the research of 2D SnO/MoO 3 vdW heterojunctions, which provides a good way to study the surface behavior of CO 2 on low-dimensional material [164].Considering only the reactants and the final products, this process can be simplified to fill the need for screening the candidates for CO 2 removal.With the help of ML, the screening procedure can be accelerated in a certain degree.Wei et al tested different ML models for possible transition-metal-doped chalcogenides electrocatalysts for CO 2 -to-CO reduction [165].Zhu et al successfully used reaction pathways to predict the reactivity and products of CO 2 reduction [166].Moreover, it can also be applied to C2 and C3 products, although the computational cost is increased, the search space is extended.
Similar to the materials and active sites screenings via using available 2D databases in hydrogen evolution reaction, by employing the existing tools such as adsorption modules in PyMatgen [144], CatKit [167], or DockOnSurf [168], the whole process can be automated without any human interference.One difference when moving toward CO 2 removal is that, since the CO 2 molecule is not polarized as water molecules, it will not be adsorbed on the surface of some materials.A method is needed to detect this in order to reduce time on unwanted calculations.ML can also play a role in the study of adsorption and desorption.One example is the work of Deshpande et al [169], in which they have used a genetic algorithm based method to recognize the adsorption configuration.Besides, graph theory and other data structures that are borrowed from computer science have significant potential to play an important part in helping the researcher to design, understand and analyze the process of adsorption structure searching and the recognition and reduction of distinct configurations.The ML-based model to identify the material surfaces that adsorb CO 2 molecules has also been reported [170], yet waiting for more concrete explorations of CO 2 removals beyond its adsorption on surfaces.

Materials preparations and synthesis
In last years the interest of the scientific community for the exploration of 2D materials has exponentially increased, as it was mentioned in the above sections.In this sense, the scientific community has developed novel synthetic strategies, intending to achieve new 2D materials or improve the properties of existing materials [171,172] or to reach advanced photocatalytic activities [14,173].The photocatalytically active 2D materials and their variants have also been reviewed from the theoretical perspective [174].In the synthesis of 2D materials there are two main approaches, see figure 10.The first one in figure 10(a) is the top-down synthesis highlighting the exfoliation [175].The second approach is bottom-up synthesis, where the most relevant methodologies are wet chemical synthesis (co-precipitation, hydrothermal …) and chemical-physical vapor deposition [171,176].The recent advances by combining computational prediction and shape-controlled synthesis have led to success of 2D species realizations to enrich the 2D database, along with the photocatalytic capability in water splitting happening on their 2D pristine forms [177,178].
To improve photocatalytic activities of 2D materials for mitigating environmental and energetic crises [21], various preparation methods have been developed to reach heterogenous forms for the 2D semiconductor slabs.The synthetic methods most used for the synthesis of 2D materials-based heterostructures are manually transfer-assemble, in-situ growth processing and wet chemical methodology, see figure 10 [179, 180].Both manually transfer-assemble and in-situ growth processing is the easy synthetic process, nevertheless, the main drawback is the loss control of the products obtained and in the case of in-situ growth methodology the high temperatures used [181].Then, the wet chemical methodology such as co-precipitation, hydrothermal, templated synthesis … is an interesting alternative to performing 2D materials-based heterostructures [175,182,183].
The bottom-up methodology of hydrothermal synthesis has been developed with special orientations to realize the 2D materials and their heterogenous forms.In figure 10(c), hydrothermal synthesis presents some improvement with respect to another synthetic method, such as control of reaction conditions (temperature, reactant ratio, reaction time and pressure) to generate high product purity and homogeneity with narrow size distributions and lower sintering temperature [184,185] shown in figure 10  A key factor to consider in the synthesis of 2D material-based synthesis is the intimated contact and the interface engineering between the two materials [182,188].Chu et al claimed that the 2D/2D interface engineering is an effective method to design powerful catalysts due to intimate face-to-face contact of two 2D materials (2D/2D MoS 2 /C 3 N 4 heterostructure) that facilitates the strong interfacial electronic interactions.Although this material was tested in electrochemical applications, this approach might be useful in photocatalysis applications due to the strong interfacial electronic interactions [189].Li et al observed that appropriate interfacial contacts and adequate potential can effectively lower overpotential and can also construct an electric field at the interface to increase the separation efficiency of the carriers, increasing the photocatalytic activity [190].Wan et al observed that the Ag 3 PO 4 nanoparticle@MoS 2 catalyst present superior photocatalytic activity due to the intimate and large contact interface, resulting in highly efficient interfacial charge transfer and the separation of photogenerated electrons and holes [191].With this in mind, the develop of novel hydrothermal synthetic routes that produce and control the interface between the heterostructure is curial to obtain suitable material for photocatalysis [183,192,193].

Characterizations of 2D heterogenous photocatalysts
The characterization of activated 2D photocatalysts is crucial to know the interaction between the material, interface contact, and the novel properties of the activated 2D material synthesized [182,193].In this perspective, only the most relevant characterization techniques are cited, focusing on interface characterization techniques, due to there are many reviews describing this topic [182,195,196].In this sense, to study the chemical composition of activated 2D materials the most useful characterization techniques are energy dispersive x-ray spectroscopy, electron energy-loss spectroscopy, x-ray photoelectron spectroscopy etc [197,198].Concerning the physical properties, the most relevant characterization techniques are electron microscopy (atomic force microscopy (AFM), TEM, and SEM), x-ray diffraction, diffuse reflectance spectroscopy, photoluminescence (PL) spectroscopy, electrochemical impedance spectroscopy, thermogravimetric analysis [199][200][201].
Another important property that should be characterized and understood in 2D activated catalysts is the band structure, the most useful techniques nowadays are DFT computational methods, Tauc plot analysis, Kelvin probe force microscopy (KPFM), ultraviolet photoelectron spectroscopy (UPS), and photoelectrochemical methods [196,202,203].Regarding the interface characterization of the activated 2D materials, a powerful technique to probing buried interfaces in 2D materials and vertical heterostructures is cross-sectional TEM [204,205].Also, the AFM technique gives information about the interaction between both materials present in the heterostructure and the thickness of 2D materials [206].Conductivity AFM allows local current-voltage (I-V) measurements to study the electrical properties between the interface of two materials [74,76,207,208].Although optical spectroscopy is not a surface-sensitive technique can be used to understand the interface properties [182].In this sense, Raman shift and peak intensity changes, effectively probe interfacial interactions in 2D vertical heterostructures [209].PL and absorption spectroscopies offer a quick and straightforward characterization of interfacial charge and energy transfer in 2D heterostructures [210].Time-resolved optical spectroscopy such as pump-probe optical spectroscopy is particularly well-suited for the study of interfacial charge and energy transfer dynamics [211].After citing these experimental characterization techniques, it is important to use computational calculations based on DFT to characterization and understand the activation of 2D materials [212,213].This methodology has been used to calculate the Fermi level, and band position and to interpret the charge transfer mechanism [214][215][216].
Photocatalytic organic pollutant removals and hydrogen evolutions are normally assessed via pollutant concentration monitoring and hydrogen quantifications through gas chronometry.The first part can be done more straightforwardly.For instance, by following the characteristic absorption lines or emission lines of the pollutants, optical methods such as UV-Vis spectroscopy have been applied [217,218].In front of transparent or large molecules, the mass spectrometry has been proved as an efficient method, and the degradation paths can be also obtained through the identification of the fragmentants [219].For hydrogen evolution, a dedicated review shows the variation of evolved gas quantifications [220].Recent works as shown above most used both hydrogen evolution rate and the apparent quantum yields to quantify the hydrogen production.The first one serves the quantity at a certain time per unit weight, while the second one takes the fact of incident light absorption into considerations and easier to be compared among photocatalysts.Cyclic tests have also commonly performed to assess the durability of the photocatalysts under the same reaction conditions.The morphologic, microstructural or chemical properties are evaluated before and after cyclic tests with 2D or activated 2D species along with curves to show hydrogen quantifications [76,178].

Synchrotron radiation-based techniques
Along with the above in-house characterizations, the current 2D-heterogeneous systems well benefit from advanced techniques enabled by large-scale facilities, such as synchrotron sources.X-ray absorption spectroscopy (XAS) is a useful tool for providing information about the chemical states of the material, however, it cannot provide the spatial distinction of the different electronic states.Utilizing the techniques has been demonstrated in various conditions such as those reviewed in the literature [221].The non-destructive method is advanced in figuring out the local chemical environment, e.g. in the near-edge structural features [222], and the microstructures through analyzing the extended region of the spectra [223].An advanced version of the XAS can be found as the x-ray spectromicroscopy [224].Within the same methodology, specified attention has been seen in x-ray photoelectron emission microscopy (XPEEM) and soft transmission x-ray microscopy (STXM).Both are able to distinguish the electronic states of the nanoscale materials, i.e. both parts of the heterojunction as well as its interface [74,[225][226][227][228].Unlike regular XAS, synchrotron radiation-based spectromicroscopy does not use area averaging signals which makes it possible to gain insight into heterostructure structure and properties.The use of synchrotron radiation in these methods allows for a high-brilliant, energy-tunable source, uniting microscopy and XAS.Synchrotron-based spectromicroscopic techniques are the most advanced methods of site-selective spatial mapping of topical materials.
In the STXM method, the synchrotron radiation beam in the x-ray region illuminates the Fresnel zone plate which focuses the x-ray beam on the sample.At modern STXM beamlines, the resolution is 10-60 nm and is limited by the illumination spot size [229,230].The analyzed sample is placed at the focal length of the Fresnel zone plate.The scanning occurs with the detection of the transmitted x-rays and the image is recorded using the photomultiplier tube or charge-coupled device.The STXM microscope works in the region of 200-2000 eV and is the least damaging method compared to other microscopic methods such as electron microscopies [226].
Tuneable x-ray radiation from the synchrotron source can be used to improve photoelectron emission microscopy by introducing the distinction of elements on the surface of the sample.This method employs the use of a monochromatic x-ray beam to image the material based on the absorbed x-ray energy and the intensity of secondary electrons.Unlike the STXM method, XPEEM does not require very thin samples, the thickness of which is not small enough for transmission of the x-rays [228,231].A schematic drawing of the PEEM is depicted in figure 11.The method provides information regarding the chemical and electronic environments of the materials, with a resolution of a few tens of nanometers [232].The high spatial resolution under the possibility of tuning incident light enables chemical state analysis of hetero-sites [233] and the mapping of local chemical states [234], as also illustrated in figure 10 on the right.Thus, the method is expected to distinguish the chemical environment of individual elements at nD/2D heterosites and study the homogeneity of the nD material's decorations onto 2D matrices.
On a large scale, to increase the performance of STXM and XPEEM setups the synchrotron facilities are always in pursuit of improved systems.For instance, the implementation of the aberration-corrected optics has improved the spatial resolution of the XPEEM synchrotron-based systems.Only a few of the PEEM beamlines are equipped with aberration correctors, such as the MAXPEEM beamline at MAX IV synchrotron [235] beamline I06 at Diamond Light Sources [236], and select others.In the case of STXM performance improvements, the most important is regarding the efficiency of the scanning.It is mostly related to slow scan rates which are being enhanced by implementing faster motion stages.However, it is apparent that there is still a need for improvement.At this point, the most effective way to get both very good spatial resolution and detection sensitivity is to combine several methods, for example, with in-house TEM measurements for detailed microscopy images.Compared to synchrotron radiation-based spectromicroscopy, the in-house microscopy methods are either very destructive (electron microscopies) or lack resolution (AFM).The latter method, mentioned in section 4.2, does not provide elemental mapping even despite the possibility of modifying the tip.For instance, making the tip sensitive to specific chemical interactions will modify the method to map the surface chemically (chemical force microscopy); using a conductive tip will enable the study of electrical properties (conductive atomic force microscopy).
Recent years show that in situ spectromicroscopic studies are emerging as a promising and rapidly developing method in the field of energy materials.Several works regarding the usage of synchrotron radiation-based spectromicroscopic methods in studies of electrochemical cell electrodes, catalysts, and batteries, both ex situ and in situ.STXM, for example, is already being implemented as a method for in situ catalytic studies, such as Fischer-Tropsch catalytic reactions [237], in situ electrochemical studies [238], etc.In situ spectromicroscopic methods became possible not only due to advances in synchrotron radiation-based methods but also because of the development of cells suitable for these methods.The use of in situ gas cells will make it possible to study the physical and electronic changes of the junctions in heterostructural catalysts and their interfaces during the reaction, e.g. in the atmosphere of water vapor for hydrogen/oxygen evolution and CO 2 reduction, as well as other catalytic processes.Currently, several electrochemical reaction cells have been used in STXM studies [239,240].Additionally, the work on in situ reaction gas cells for STXM has also been undertaken to study the interaction between the metal surface and water vapor [241].
XPEEM systems are compatible strictly with UHV conditions, therefore, a study of the reactions with different gases is impossible at the current stages.The focus of XPEEM in situ studies is the examination of the surface or near-surface reactions of metals and semiconductors, e.g.following changes of temperatures [242].An interesting application of in situ XPEEM has been recorded with the study of organic insulators where if the polymer thickness on a conducting substrate is very low, it is possible to study thin films [243] and the processes therein, such as their growth [244].
It should be noticed that the SR spectroscopic techniques typically involve deep hole photoexcitation and deexcitations, during which the rearrangement of electronic structures may occur [245,246].Combining the x-ray spectroscopic techniques with the other ones, e.g. as described in section 4.2 is expected to give a more concrete understanding of the electronic structures of the heterogenous systems, along with their morphological and microstructural information.The photocatalysts can be spectroscopically characterized in situ, during the chemical reaction through the XAS [247], well benefiting mechanistic studies of photocatalysis happening on the nD/2D heterogeneous systems.It is worth mentioning that the latest progress applying fast x-ray techniques [248] to study electrocatalysis was further empowered by ML treatments of large amount data obtained [249].All of the above techniques will be very beneficial to understand intermediate states of photocatalysts at the catalyst point of view.

Mechanisms in chemical ways: from band diagram to radical pathways
A way for improving and understanding the catalytic activity is the study of the mechanism of the reaction and how the catalyst is involved in the reaction.Especially, photocatalytic mechanisms still need deep studies, due to the difficulties of detecting the radical paths involved in the formation of products.
One route to get acquainted with the mechanism is to look at the chemical reaction pathways and how all the species are taking part in the formation of the products.Before having a real understanding of the chemical routes, it is necessary to study the band diagram of the materials and being able to know which reactions can be performed by them.Different approaches can be used for this, but definitely, the most common ways are UV-Vis spectroscopy for knowing the band gap of the materials [203] and UPS for the valence band edge (E v ) [250,251].By subtracting the value of the E v from the value of the band gap, it is possible to obtain the conduction band edge (E c ) of the material.In the case of heterostructures, this is less straightforward, because two materials are involved in the band diagram.In this case, beforehand the Fermi level is measured by a KPFM [252].Indeed, the Fermi level change in the heterostructure compared with the pure materials will help in understanding the band bending happening on the materials composing the heterostructure and consequently the charge carriers separation (see section 2.2).
Certainly, the band diagram of the heterostructure gives the necessary information to understand the reactions that can be performed by taking into account the redox potentials for the formation of reactants or products.Looking to the degradation of organic molecules, it is crucial for the photocatalyst to have suitable redox capabilities for the formation of the radicals that will generate the cascade processes at the basis of the degradation of the molecules.Indeed, it is well-known that advanced oxidation processes (AOPs) play a key role in the photodegradation of organic molecules of varied nature.AOPs include by definition the formation of highly reactive oxygen species (ROS) (see table 1) which can generate oxidative cascade processes at the basis of the degradation [253].As commented in sections 2.1, the photocatalyst should possess the right CB and VB to form the ROS (figure 1).
A widely used technique for the detection of these radicals is electron paramagnetic resonance (EPR) spectroscopy.Usually, the latter implies the use of the spin trapping agent 5,5-dimethyl-pyrroline N-oxide to form adducts with OH or O 2 − and allow to verify the formation of the two radicals [256].In general, the reconstruction of the band diagram will allow to know which specific radicals can be formed and EPR can identify some of them, but a mechanistic study of the reaction is needed to prove which radicals are really involved in the reaction.Hence, radical scavenger experiments are often used.In this case, a specie that can trap selectively one of the radicals is added at the beginning of the reaction.Well-known species used for this purpose are listed in table 1.By seeing which radical scavengers are decreasing the degradation rate, it is possible to elucidate the mechanism involved in the reaction [257].
Taking into account that we are speaking of the degradation of organic molecules, other studies are needed for understanding the overall mechanism.In the case of contaminants absorbing in the UV-Vis range, preliminary studies might only need the use of UV-Vis spectroscopy to verify the presence and disappearance of the contaminant upon irradiation.Nevertheless, a more comprehensive study would need some techniques capable of separating the different degradation products.Lately, liquid chromatography by itself or coupled with mass spectrometry has brought to a lot of new discoveries in terms of how molecules are getting fragmented by the photocatalytic approach, such as in the degradation of diclofenac [258], sulfanilamide [259] or tetracycline [260].
Finally, these mechanistic studies are opening the way not only for a better understanding of the paths obtained by well-known catalysts but also, they are aiding the chase of better photocatalysts.Additionally, this would be a great advantage for the development of synthetic reactions, which opposite to degrading processes, are used to generate extremely relevant chemical compounds.Photocatalytic synthetic reactions are nowadays applying only homogeneous photocatalysts, hence having a better knowledge of the mechanisms driving the degradation by heterogeneous photocatalysts will certainly uprise the use of heterogeneous systems in this relevant application.

Mechanism derived from the electronic structural level knowledge
Despite that photocatalysis is a typical photochemical process and is mechanistically studied in chemical paths, the physical ground of its origins cannot be neglected.Here, we brief the mechanistic studies via electronic structures given by the DFT, the x-ray spectroscopic determinations and the combinations of them.
The DFT is not only a tool in nD/2D composite prediction, but it also gives critical information for mechanistic investigations.Due to complexity of the photocatalysis and materials structures, many DFT works were constructed and cross-checked with characterizations results.For examples, DFT works in computing the electronic structures of photocatalyst showed the origin of bandgap narrowing, and possible interfacial charge transfers and IEF within the heterogeneous photocatalysts for pollutant removals [217,[261][262][263]. Reaction potential spaces of photocatalytic properties can be fast screened in the DFT studies with similar accuracies of experimental works [264].The hierarchy iodine-doped Bi 2 O 2 CO 3 /Bi 2 WO 6 photocatalysts constituted with 2D flakes were invented for both pollutant removal and hydrogen evolutions.The DFT results were in line with the structural and chemical states identifications from experimental results, and predicted the interfacial charge transfer channels, bandgap type variations, and narrowing at the bismuth composite [265].The charge transfer pathway within the Z-typed 0D/2D photocatalysts has also been identified and attributed to the boosting of hydrogen evolution of the CeO 2 /g-C 3 N 4 [266].The mechanistic studies via DFT itself are dedicated and detailed in a latter section of the paper.
Along with electronic structural information [267] and adsorption tendencies [268], using the DFT studies can fast screen proper 2D matrices in photocatalytic water splitting.In a previous review, four key factors have been listed as the bandgap structures and edges, formation energy and aqueous solubilities [147].Recently, the reaction paths of photocatalytic hydrogen evolution have also been predicted for doped 2D materials [269], extending the mechanistic studies of the photochemical process from static electronic structural levels to thermodynamics.
Spectroscopies have also been widely used to study photocatalysis on 2D heterogeneous materials.Besides ex situ spectroscopic determinations to study the materials of 0D/2D systems, the in situ XAS techniques [247] can apply to study intermediate states of the photocatalysts during the reaction.The spectroscopic results thus are possibly cross-checking predicted results given by the DFT studies.As a competing process to photocatalysis, the optical deexcitation in the form of PL can be timed [268].The time-resolved PL identifies the charge dynamics during photocatalysis [270].Combining the PL mapping and pump-probe method, the fast charge transfer between nD and 2D counterparts can be unveiled [271], to set the time scheme of the photocatalysis involved in the 4th dimensionality.Despite of these spectroscopic progresses, the direct detection of radical creations and timing of photocatalysis remains challenging.Engaged with spectroscopic features and ultrafast processes, the x-ray methodologies enabled by the x-ray free electron laser are promising to accomplish the identification and time the photocatalytic processes happening on the 2D-based heterogeneous materials [272].

Computational mechanistic studies
Heterogeneous (photo)catalysis draws its great interest from the impact that a material's surface has on the reactivity of molecules and the ease of catalyst recovery.It requires the co-existence of a solid and a fluid (liquid or gas).Consequently, to catalyze a chemical reaction, several steps must take place: (1) the diffusion of the reagent to the surface of the solid through the shear plane, (2) the adsorption of the reagent on the surface of the material, (3) the surface reaction of the adsorbed reagent to become the adsorbed product, (4) the desorption of the product, (5) the diffusion of the product through the shear plane.
Computational methods can help in modeling all these steps.Steps 1 and 5 are relevant to flow simulation and can also be simulated with MD simulations as well as multiscale modeling [273].In this part, the emphasis will be on the microscopic steps 2-4, where chemical reactivity is involved.All three steps can be simulated in the frame of heterogeneous catalysis, but their simulation suffers from issues relative to reagent/product configuration, surface hydration state, modeling of the solvent and dynamical evolution of the system, that could be more deeply simulated in current 2D/2D heterostructure works [274][275][276][277][278][279][280][281][282][283], as shown in figure 12 left panel.These caveats are mostly encountered in heterogeneous catalysis systems' simulation.In (heterogeneous) photo catalysis, however, the activation step is added, consisting of the creation of an exciton through light absorption.This gives rise to another succession of events in the catalyst [284].
In our case, the reagent is a molecule, which is easily modeled in a vacuum.For bulk (3D) systems, the simulation of a surface requires a significant amount of work to be properly optimized (number of atomic layers, surface relaxation steps, etc).However, for low dimensional (2D) samples, the work is somehow facilitated by the fact that the materials considered are both the solid and its surface.It is also well mastered in a vacuum, as mentioned in the previous part related to 2D materials databases, and the simulation does not get much more computationally challenging when simulating a 2D/2D heterostructure.The surface complex (product of the adsorption step) also needs to have a defined configuration which requires extensive work.Several methods have been developed to accelerate and/or select the most interesting configurations to try.An efficient way that is implemented by several tools is to employ graph theory for the detection of possible adsorption sites and then to adjust the molecule to a most stable configuration and location [167][168][169]285].The configurations filtered after optimization will be the final results, to be geometrically optimized.One drawback of this method is that the physical and chemical properties of the material are not considered.It is a trade-off between generality and efficiency which leaves room for the use of physico-chemical intuition.

Static calculations, surface hydration and active site identification
To obtain a realistic system, close to the experimental ones (aqueous/solid interface, as shown in figure 12 'Realistic simulation' panel), the solvent and the hydrated surface have to be simulated (figure 12, 'solvent simulation panel' panel).If not done, simulation is closer to a solid/gas interface.It is worth noticing that, even at low relative humidities (≈10%), hydrophilic surfaces are fully covered by water molecules [286,287], triggering surface reactions even at ambient temperature [288].This experimental observation challenges the comparison of any experimental work with experimental works and warrants the outmost caution in interpretation.
From a static, geometry optimization point of view, the solvent can be simulated by implicit, explicit or hybrid methods: implicit implies the use of the dielectric constant of water to mitigate any electrostatic interaction [289], it may be less accurate as the dielectric constant of liquid water may be very different from the water layer close to the surface [290,291].Explicit method raises the question of the 'best' configuration, that is extremely difficult as water molecules are labile species weakly (hydrogen-) bonded to the surface explicit corresponds to the addition of explicit water molecules that would organize around the surface complexes and the surface.Hybrid method corresponds to a mixture of both previous methods: using both explicit solvent molecules (at least for the first water layers) and also implicit solvent at a certain distance of the material's surface.It is also a nice way to go to medium computational cost while keeping a certain accuracy in the system.It is all the more important because protons, that are paramount species for the HER reaction, are now known not to be isolated in a solution [292][293][294].
Beyond static approaches, several works have been performing MD with 2D slabs and showed that water does not interact as strongly with the layer as reported with other systems [295][296][297].The main reasons may be that the main water/solid interfaces studied are water/oxides interfaces, and that several 2D materials, such as transition metal dichalcogenides (TMDs) of which MoS 2 is the most studied, possess no dangling bonds.On the other hand, the cited works show that the band alignment is changed significantly with respect to its isolated (vacuum) state, indicating significant electrostatic interactions [298,299].Furthermore, gap states are appearing without explicit chemisorption of the water molecules, which raises the question of inner-sphere only heterogeneous charge transfer reactivity of water.While inner-sphere, chemisorbed, reaction being the accepted mechanism for heterogeneous reactivity in heterogeneous catalysis, electrochemistry warrants the outer-sphere, physisorbed, electron transfers to be as important [300].
Providing that adsorption can take place on the basal plane, one should bear in mind that the three chemically reactive steps of any (photo)catalytic reaction are mainly used for solids in their fundamental state i.e. with their VB filled and CB empty.This corresponds to a different electronic density and may change the reagent adsorption site configuration, the intermediates and therefore the reaction path.One way to alleviate this issue is to look at the electron density map for the CBM/VBM states and to try and adsorb reagents in locations and configuration favoring the contact with these sites.While they may be energetically less favorable for a slab in its fundamental state, it may also be the most likely configuration to react at the surface of an excited solid, e.g. the CO adsorption on TiO 2 (001) surface [301].
In the frame of chemisorbed surface reactivity, the absence of dangling bond makes it complicated for water (for OER), or protons (for HER), to adsorb easily at the surface, which suggests that point defect in the layer may provide an easier active site for the reaction.Several works indeed report the need for a vacancy in the layer to activate the basal plane [302][303][304].The reactivity of the active site can also be tuned by substitution doping by different heteroatoms [305,306].Of course, vacancies can also be transiently produced with the substitution of a surface atom by an adsorbate, in our case water, which is a typical mechanism found at water/solid interfaces [307][308][309].
The fact that defects are making 2D materials more reactive begs the question whether edges, would be even more reactive than point defects in the basal plane.As surfaces are extended defects for bulk materials, where surface reactivity happens, one can easily see the analogy between edges and basal plane of any bidimensional material.This has also been studied in MoS 2 [310] demonstrating significant improvement of the photocatalytic activity-related descriptors for HER [311].
It is important to see that different works focus on different mechanisms that are, however, very likely to take place at the same time in different proportions.To consider all of them would be extremely valuable in order to obtain a clear image of the material (or composite)'s reactivity towards water splitting.Besides, most of the cited works have been performed on MoS 2 as a prototypical substrate, but still need being studied on other systems as composition changes may give some interesting new properties [298,312] or new preferential mechanisms (basal favored instead of edge, or vice versa).Moreover, these refinements of computational mechanistic studies must also be taken into account in heterostructure calculations, as they have mainly been studied for isolated monolayers and materials until now, leaving many new and exciting study opportunities for 2D/2D heterostructures.While dynamical simulations have been mentioned to simulate the behavior of the solvent, time evolution is still very important for other parts of the photocatalytic process and deserve to be mentioned more in details.

Dynamical evolution of simulated photocatalytic systems
To increase the accuracy of the method used, as well as to obtain simulation results relevant to photocatalysis, the exciton finite lifetime and behavior should be computed (figure 12, 'dynamic simulation' panel).It is not accessible with geometry optimization methods only, that are performed at 0 K.One way to alleviate this drawback of simulation endeavors is to use TD-DFT [313][314][315][316][317][318][319][320][321].
TD-DFT is, as the name suggests, the theory which considers the time factor in the original time-independent Kohn-Sham theory [322].It uses only the approximation of TD XC potentials to predict all the quantities.Most of the TD-DFT calculations use the adiabatic local density approximation (ALDA) as a starting point.Given the XC potential n(r,t), where r is the position and t is the time.ALDA approximates the XC potential as a function of position and time by that of a ground-state uniform electron gas n(r;t), in which it becomes a parameter.This approximation is accurate when the state of the system changes sufficiently slow in time and space.However, it also works surprisingly well for many systems just like local density approximation does for most ground-state systems [323].
TD-DFT plays an important role in the study of excited states and optical response properties of the materials.By employing the Casida equation, the lowest-lying excitations can be extracted to accurately predict the structural properties of the excited states.The more advanced version of TD-DFT is based on the Bethe-Salpeter equation which requires a GW calculation [324][325][326].It gives more accurate XC potentials for complicated systems while being more computationally demanding.BSE is often used to reveal the absorption spectra of the materials in the theoretical study in order to explain the electronic behavior of the material under light [322].
Nevertheless, the calculation of excited modes using TD-DFT is still less accurate than that of ground state when predicting the structure [327].Benchmarks investigating the accuracy of TD-DFT using different hybrid functionals with small to medium molecules has been done.It reveals that, although some XC functionals performs better than others, the accuracy of the calculation also depends on the bond type in the materials of interest [327,328].Hopefully, this problem may be solved by developing more decent approximation of the DFT functionals [329], which takes more complex environmental factors into consideration.
As a theoretical tool, TD-DFT is widely used in photocatalytic research.For example, UV-Vis spectra can be simulated using TD-DFT and have a reasonable correlation with the experimental ones [330,331].Similar benchmarks has been made to compare the performance of various hybrid functionals.Sarkar et al shows that CAM-B3LYP yields excellent results for oscillator strength [332], and Jacquemin et al shows PCM-TD-PBE0 is fast and reliable for simulating UV-Vis spectra of azoalkines [333].After years of development, TD-DFT can not only work well on small to medium sized molecules, but also works on more complex structures.Various optical properties have been calculated for dyes for solar cells [334][335][336], complexes on gas sensors [337], and transition metal-radical ligand complexes [338] etc.To extend the applicability of TD-DFT, memory functionals were invented, which considers the time evolution of the past densities, hence more problem can be solved [329].
AIMD is another way to study the time evolution of materials.Compared to classical MD, AIMD has the advantage of taking into account the electronic changes in the simulation, which is neglected by the former.The difference between them is that the former is based on a number of empirical parameters that define the relative positions and orientations of atoms and molecules, while AIMD relies on the electron densities for all the elements of the system and calculated properties.AIMD can simulate the chemical reaction in which the bond breakage and rebuilding can be clearly seen [103].It provides a great way to investigate the adsorption, thermostability, and phase changes of the materials, as mentioned in a previous part of this perspective.The drawback of AIMD is obvious as it used DFT as the support for all the calculations, therefore, an AIMD simulation usually costs a large amount of computational resources, although in some DFT simulation packages the situation can be relieved by the recently developed on-the-fly ML force field.Unlike the traditional force field simulation, this technique uses the datasets that are obtained from the existing ab-initio calculation to train a force field.The simulation utilizes this on-the fly trained force field whenever the estimated Bayesian error under a threshold.Consequently, the simulation time can be shortened.Another method is NN potential MD [321].It uses a NN that takes the Cartesian coordinates of each atom and output total energy and the forces.
In a photocatalytic process, the process of charge transfer implies the type of cross-dimensional heterostructure.Taking a staggered heterostructure as an example, the generation rate and the recombination rate of the electron-hole pairs are the two quantities that determine whether it is type II or Z-scheme [339].In this process, the NA decay after photoexcitation often involves multiple PESs, with NA transitions among them.It cannot be simply done by TD-DFT because it is based on the Born-Oppenheimer approximation and assumes that the photoexcitation happens on a single PES (associated to one configuration of the nuclei).Hence, NA MD is developed by combining TD-DFT and AIMD.It allows us to identify the crucial photoinduced electron excitation and transfer process, as well as to unravel the pathways of photogenerated charge carriers that drive the reaction [318].By employing the surface hopping technique that allows the state of the system to 'hop' between PESs provided by the AIMD trajectory and implementing the fewest-switches algorithm [340], several codes [316,341] have been written and applied to the study of different photocatalytic materials, and their excited carrier dynamics can be detailly studied [316,318,339].

Challenges and outlook
To summarize, the present paper illustrates the rationales and progresses of utilizing the nD (n = 0-2) hetero-sites to activate the 2D semiconductors for photocatalytic pollutant removals and hydrogen evolution.The dimensional properties of the 2D matrices, as a double-blade sword, facilitate photocatalysis due to quantum confinements but complicate the materials' activations.Cross-dimensionally activating them is given down to the understanding of heterogenous photocatalyst designs, matrices and heterosite selections, characterizations and mechanistic studies.The materials' activations are crossing the dimensionality, that is to say, considering the quantum effects given by the nanomaterials or 0D dopants.The materials characterizations benefit the understanding of the engineered composites and assist the mechanistic studies.Combined with experimental and theoretical efforts, photocatalysis can be elucidated down to electronic structural levels and in situ thermodynamically.
Despite numerous endeavors poured into the development and studies of photocatalysts and cross-dimensionally activated 2D semiconductors photocatalysts, practical solar fuel production is still far from real applications in today's situation.Challenges remain in materials innovations, photocatalytic reactor designs, and various impacts beyond scientific progress [342].Durable and functional materials for solar irradiance conversions into solar fuels are always within key focuses due to their irreplicable importance as the materials bases for photocatalysis.The 2D semiconductors and heterogenous variants provide such a candidacy in the general clean energy and application scenario.However, despite still rather low conversion efficiency (AQE) of the materials, most of the photocatalysis still remain in the lab scale with few in pilot trials [343,344].The photocatalytic reactors that are suitable for 2D heterogeneous systems may require special modifications from these e.g. for TiO 2 -variants [345].Continuous efforts to combine the materials development and engineering innovations of photocatalytic systems are definitely beneficial.
Materials and engineering wise, there are main territories deserving further explorations.Cleavage or thinning of the bulk materials to their 2D forms [346] may result in various thin slab to host the cross-dimensional activation strategies.The constant development of nanotechniques further enables the control the variant of 2D materials at an atomic level [347].Combining them and developing the mass-productions of the 2D-based photocatalysts will bolster materials bases for photocatalytic hydrogen evolution and pollutant removals.Ongoing engineering processes of continuous photocatalytic reactors pose possible applications of them in large-scale and under ambient conditions out of lab [348].Yet, using the 2D-based photocatalysts in these reactors are expected to elevate the photocatalysis into practical applications.
It should be noted that the current cross-dimensional activation strategy may also apply to materials in other dimensions.For instance, the 1D matrices are able to host nanomaterials with lower dimensions in 0D and cluster forms.Typical interface engineering is required to join the external sites to the 1D or flake hosts [349,350].Functionality wise, the applications of the activated 2D slabs are not limited in photocatalysis.Other photonic applications are expected e.g. as luminescent materials where the electron-hole pair recombination at the nD-2D interfaces may result in new functionalities in quantum photonics [351].Other applications can be foreseen, especially these in the transistor designs as originally inspired the researches of the 2D semiconductor studies [5].

Figure 4 .
Figure 4. (a) Supposed energy band diagram of a semiconductor in presence of metal clusters or single atoms.(b) Hot electrons injection from nanoparticles to the CB of a semiconductor.

Figure 5 .
Figure 5. Change of conduction band minimum (CBM) and valence band maximum (VBM) of the host TiO 2 upon the single Pt, Pd, Rh and Ru atom adsorption on anatase TiO 2 (101) surface at the HSE level of theory, with the vacuum level set to zero.Reprinted from [79], Copyright (2017), with permission from Elsevier.

Figure 6 .
Figure 6.Selection criteria for 2D semiconductor matrices and their variants.

Figure 8 .
Figure 8. Summary of the different steps of a data science problem, commented in the text.The colors from red to green indicate the stage of the model, from a large amount of data to a generalizable model.

Figure 9 .
Figure 9. Different coordination modes of CO 2 adsorption: (a) oxygen coordination, (b) carbon coordination, and (c) mixed coordination.Reproduced from[22] with permission from the Royal Society of Chemistry.

Figure 11 .
Figure 11.Schematic drawing of the XPEEM and its microregional analysis of chemical states via x-ray absorption spectroscopy.

Figure 12 .
Figure 12.Illustrative diagram of the different directions proposed to improve the simulation of photocatalytic systems towards experimentally realistic computational simulations.The two rectangles on the bottom represent a 2D/2D heterostructure.