**Screening of promising candidates.** Figure 1(a) shows the top and side views of primitive cell of the MoSi2N4 monolayer with a septuple-atomic-layer structure, where the MN2 layer is sandwiched by the top and down Si-N bilayers. The optimized lattice constant of MoSi2N4 monolayer is 2.90 Å, consistent with the value reported by the previous experiments. Based on the sandwich architecture of MoSi2N4 monolayer, we construct 2D MSi2N2XY (M = Mo, W; X/Y = N, P, As, S, Se, Te; X ≠ Y) compounds by a intercalation design principle, that is, inserting a Janus MXY layer into the Si2N2 layer. The atomic arrangements and our studied element compositions of MSi2N2XY monolayers are shown in Fig. 1(b), where M represents group-VI transition-metal elements (M = Mo, W), X and Y correspond to group-V and -VI elements (X, Y = N, P, As, S, Se, Te; X ≠ Y). The asymmetric geometry of MXY layer results in the crystalline symmetry breaking of MSi2N2XY monolayers, which leads to spontaneous polarization along the out-of-plane direction. Through the stochastic combination of element compositions, 30 possible configurations for 2D MSi2N2XY materials are initially identified. Then, all these predicted structures are fully relaxed to obtain their corresponding stable configurations.

To explore the potential application of MSi2N2XY monolayers in water splitting, we present a multilevel workflow combining several key criteria to screen stable, and highly efficient candidate photocatalysts, as shown in Fig. 1(c). In general, the external potential provided by photogenerated electrons (and holes) should be large enough to overcome the overpotential of HER (and OER), so that the whole process of water splitting can proceed spontaneously. Moreover, the STH efficiency can be used to evaluate the energy conversion efficiency of photocatalytic materials quantitatively. Therefore, we introduced the energy cost and STH efficiency as determining descriptors to characterize the photocatalytic activity of MSi2N2XY monolayers.

Following this screening strategy, the structural properties of MSi2N2XY monolayers are studied first. Detailed structural parameters are listed in Tables S1. It is found that some predicted structures display a lattice stretching along the *z*-direction after geometry optimizations due to the enlarged bond length between Si and X (Y) atoms *d*Si−X (*d*Si−Y). Excessive distance stretching between MXY layer and SiN layer means the structural distortions of MSi2N2XY monolayers. We define a threshold value of 3.0 Å for *d*Si−X (*d*Si−Y) to assess the distortion degree of MSi2N2XY monolayers, and find that 22 candidates are within this threshold range, indicating that these structures possess good structural strength.

After that, we perform a series of stability confirmation calculations to further screen stable and synthesizable candidates, as shown in Fig. S1. First, we calculated the enthalpies of formation of MSi2N2XY monolayers by \({E}_{\text{f}}=\left\{{{E}_{\text{t}\text{o}\text{t}}-(E}_{\text{M}}+{2E}_{\text{S}\text{i}}+{2E}_{\text{N}}+{E}_{\text{X}}+{E}_{\text{Y}})\right\}/7\), where \({E}_{\text{t}\text{o}\text{t}}\) represents the total energy of the system, and \({E}_{\text{M}}\), \({E}_{\text{S}\text{i}}\) \({E}_{\text{N}}\), \({E}_{\text{X}}\) and \({E}_{\text{Y}}\) are the energies of separate M, Si, N, X and Y atoms, respectively. As shown in Fig. S2, we found that the enthalpies of formation of 22 selected MSi2N2XY monolayers are within the range of -0.73 eV to -2.74 eV, demonstrating the energetics. Then, we explore their dynamical stability by calculating the phonon dispersion, for which the results are shown in Fig. 2 and S3. Our calculations suggest that only four candidates, that is, MoSi2N3P, MoSi2N3As, WSi2N3P and WSi2N3As are dynamically stable, while the others 18 compounds are discarded since they exhibit imaginary frequencies. The AIMD simulations are conducted to further confirm the thermal stabilities of four selected structures (Fig. 2). After 5ps of heating at room temperature, the fluctuation range of energy and temperature is small, and no large structural deformation occurs, attesting high thermal stability. Additionally, four independent elastic constants \({C}_{11}\), \({C}_{22}\), \({C}_{12}\) and \({C}_{66}\) of MSi2N2XY monolayers are obtained, which fulfills the Born-Huang criteria38 for mechanically stable 2D systems. (see the details in the Supporting Information and Table S2). Furthermore, Young’s modulus *Y*(*θ*) and Poisson’s ratio *υ*(*θ*) demonstrate their isotropic mechanical behaviors (Fig. S4). Especially, the calculated *Y*(*θ*) for MoSi2N3P and WSi2N3P reach to 312.8 N/m and 324.6, respectively, which is comparable to graphene (342.2 N/m)39 and MoS2 (330.0 N/m)40.

On the basis of the stability evaluation, four kinds of MSi2N2XY monolayers, namely, MoSi2N3P, MoSi2N3As, WSi2N3P and WSi2N3As, are screened out with excellent stabilities. Their band structures predicted by HSE06 functional are shown in the left column of Fig. 3. It can be seen that all the four candidates exhibit semiconducting characters with the band gaps of 0.96 eV, 0.46 eV, 0.79 eV and 0.45 eV for MoSi2N3P, MoSi2N3As, WSi2N3P and WSi2N3As, respectively. Intriguingly, MSi2N3Y monolayers can transform from indirect to direct band gap semiconductors, when the Y component varies from P to As because the valence band maximum (VBM) moves from K to the Γ point. Consequently, the narrow band gaps of 2D MSi2N3Y in the range of 0.45–0.96 eV means that they can expand the light absorption into visible or even infrared regions, implying efficient utilization of solar energy.

**Photocatalytic performance of MSi** **2** **N** **2** **Y**. As is well-known, a prerequisite for water splitting of semiconducting materials is that the band edges enclose the hydrogen reduction potential (-4.44 eV at pH = 0) and water oxidation potential (-5.67 eV at pH = 0)41. For conventional photocatalysts without intrinsic polarization, the reduction/oxidation potential is aligned with respect to the conduction/valence band edge according to the same vacuum level, and thus, the band gap required for water splitting should be larger than 1.23 eV. Owing to the broken out-of-plane symmetry, the intrinsic diploes are introduced into MSi2N3Y monolayers (Table 1), which generates an internal electric field perpendicular to the layer. The presence of internal electric field results in a vacuum level difference between the two sides of MSi2N3Y monolayers, which is characterized by the electrostatic potential curves in the middle column of Fig. 3. The internal electric field points from the bottom surface near Y component to the top surface, and the potential differences between the two surfaces are 2.12 eV, 2.55 eV, 2.00 eV and 2.46 eV for MoSi2N3P, MoSi2N3As, WSi2N3P and WSi2N3As, respectively. Driven by the internal electric field, the photogenerated electrons and holes aggregate on the bottom and top surfaces of MSi2N3Y monolayers respectively, ensuring that the HER and OER occurs on the two respective regions. In this case, the water redox potentials of MSi2N3Y monolayers are determined with respect to the vacuum energy levels of the bottom and top surfaces respectively, thus breaking the band gap limitation (1.23 eV) for overall water splitting.

Considering the different vacuum levels, the band edge positions of MSi2N3Y monolayers are shown in the right column of Fig. 3. Obviously, the conduction band maximum (CBM) of all four candidates lies above the hydrogen reduction potential ( \({E}_{{\text{H}}^{+}/{\text{H}}_{2}}^{\text{r}\text{e}\text{d}}\)) and the VBM lies below the water oxidation potential (\({E}_{{\text{O}}_{2}/{\text{H}}_{2\text{O}}}^{\text{o}\text{x}\text{i}}\)), fulling the band edge requirements for water splitting. Importantly, the energy difference between the \({E}_{{\text{H}}^{+}/{\text{H}}_{2}}^{\text{r}\text{e}\text{d}}\) and the CBM (or VBM) represent the redox capacities of photogenerated electrons (or holes), which is denoted as *U*e (*U*h) (Fig. 3). The detailed *U*e at the bottom surface and *U*h at the top surface for MSi2N3Y monolayers are listed in Table 1. It is found that all four structures satisfy the screening criterion: *U*e > 0 eV and *U*h > 1.23 eV, suggesting their sufficient redox capacities for both HER and OER. As a result, MSi2N3Y monolayers are preliminarily identified as potential structures for overall water splitting.

In general, the photogenerated electrons and holes distributed at different locations of one material benefits to reducing their recombination probability. To explore the spatial distribution of photogenerated carriers, we examined the partial charge densities at the CBM and VBM for both MSi2N3Y and MSi2N4 monolayers, which is shown in Fig. S5. For the MSi2N4 monolayers, both the charge densities of the CBM and VBM are mainly distributed at the MN2 layer, which is consistent with previous reports. In contrast, for the case of MSi2N3Y monolayers, the charge density of the CBM is mostly localized at the Si-N layer while that of VBM is localized at the MXY layer, resulting in good separation between photogenerated electrons and holes. Such charge distribution can significantly decrease the possibility of recombination of photogenerated electrons and holes, and ensure the high efficiency of photocatalytic reactions.

Above, we have confirmed that MSi2N3Y monolayers possess suitable band edge positions with sufficient redox potentials. Therein, we further investigated the mechanism of the half-reaction of both water oxidation and hydrogen reduction by calculating their reaction free energies at a neutral condition (Computational details can be obtained in supplementary materials). For HER, there are only two reaction steps (reaction (1) and (2)). Therefore, the reaction barrier (𝐸*barrier*) could be obtained as follows:

$${E}_{barrier-HER}=\left\{\begin{array}{c}\text{max}\left({\varDelta G}_{1},{\varDelta G}_{2}\right) \text{max}\left({\varDelta G}_{1},{\varDelta G}_{2}\right)>0\\ 0\text{ max}\left({\varDelta G}_{1},{\varDelta G}_{2}\right)<0\end{array}\right.$$

1

While the OER follows four elementary steps (reaction (3), (4), (5) and (6)). The 𝐸*barrier* of OER is determined by:

$${E}_{barrier-OER}=\left\{\begin{array}{c}\text{max}\left({\varDelta G}_{3},{\varDelta G}_{4},{\varDelta G}_{5},{\varDelta G}_{6}\right) \text{max}\left({\varDelta G}_{3},{\varDelta G}_{4},{\varDelta G}_{5},{\varDelta G}_{6}\right)>0\\ 0\text{ max}\left({\varDelta G}_{3},{\varDelta G}_{4},{\varDelta G}_{5},{\varDelta G}_{6}\right)<0\end{array}\right.$$

2

When the 𝐸*barrier* for HER and OER equals to 0, which means that the redox reactions of overall water splitting can proceed spontaneously. The corresponding free-energy profiles for MSi2N3Y monolayers are shown in Fig. 4. In the dark environment, the 𝐸*barrier*s of HER and OER for MoSi2N3P monolayer are calculated to be 0.55 eV and 0.56 eV, respectively, requiring additional energies for photocatalytic reactions. At light irradiation condition, *U*e and *U*h can act as the driving forces of photogenerated electrons and holes to decrease the 𝐸*barrier*s of HER and OER, respectively, thereby directly promoting the full water-splitting process. Accordingly, we find that the free energies for HER and OER decrease in each step with the external potential of *U*e = 0.96 V and *U*h = 2.12 V under illumination, implying that MoSi2N3P monolayer can catalyze water to produce hydrogen and oxygen spontaneously. Similar to the case of monolayer MoSi2N3P, the other three structures show the different values of 𝐸*barrier* at the absence of any light irradiation, but they all can satisfy the screening criterion: 𝐸*barrier−HER* = 𝐸*barrier−OER* = 0 eV under illumination.

**Solar-to-hydrogen efficiency**. Excellent optical response is of great significance to produce more photogenerated carriers under photon absorption. To evaluate the performance of MSi2N3Y monolayers in harvesting sunlight, we calculated their optical absorption spectra by using the HSE06 functional. As shown in Fig. S6, compared with MSi2N4 monolayer, a red-shift of the spectrum is observed for MSi2N3Y monolayers, supporting its utilization of visible light. Moreover, we obtain the peak intensity of up to 2×105 cm− 1 for MoSi2N3As monolayer, which is higher than that of previously reported 2D MSiGeN442. Hence, the MSi2N3Y monolayers can effectively harvest sunlight, improving the efficiency of light absorption as a photocatalyst for water splitting. As listed in Table S6, the light absorption efficiency of MSi2N3Y monolayers exceed 90%. Meanwhile, the intrinsic electric field of MSi2N3Y monolayers affects the carrier dynamics, enhancing the carrier utilization efficiency. The improvement of energy conversion efficiency is the ultimate target in the pursuit of solar energy utilization. Supposing that the efficiency of catalytic reaction is 100%, the corrected STH efficiencies of MoSi2N3P、MoSi2N3As、WSi2N3P and WSi2N3As monolayers are predicted to be 30.57%, 29.84%, 32.93% and 30.51%, respectively, which are larger than that of previously reported Janus WSSe (11.68%)43, P4O2 (17.2%)44 and AgBiP2Se6 (10.04%)45. Note that these predicted values surpass the conventional theoretical limit of 18%22. It is thus conclusive that MSi2N3Y monolayers can act as an effective candidate for photocatalytic water splitting with high stability and STH efficiency.