For photocatalytic reactions, the excitation energy required for electron-hole separation is largely decided by the bandgap value of the semiconductor photocatalyst. To make the most use of solar energy, the bandgap of the photocatalysts is expected to be located within the spectrum of sunlight, namely, from the UV to NIR range. In fact, most of the solar energy (nearly 95%) is constituted by visible light (43%) and NIR (52%). To match the Vis-NIR excitation window of sunlight, the bandgap of the candidate photocatalyst is expected to be less than 3.10 eV. And based on the redox potential of water, to drive the water splitting reaction, the bandgap value is projected to be wider than 1.23 eV with the location of VBM lower than the oxidation level of O₂/H₂O and CBM higher than the reduction level of H₂/H⁺. Thus, the bandgap values and band positions of photocatalysts can largely reflect their absorption window toward sunlight, and the relative positions of VBM and CBM with reference to standard hydrogen electrode potential can be used to predict the redox tendency for water splitting.

To evaluate the bandgap matching degree of the TMs-RP, we have first compared the band structure of pristine RP (Figure 1A) with Fe-, Co-, Ni-, Cu-anchored RP, respectively (Figures 1B–E) to reveal the anchoring effect from different TM atoms. For the pristine RP (001) surface, the bandgap is calculated to be 1.86 eV, corresponding to an excitation energy of 667 nm in the red-light range. For Fe-, Co-, and Ni-anchored RP, we find additional TM states generated upper to the valence band maximum (VBM) and below the conduction band minimum (CBM), resulting in a narrowed bandgap of 0.68 eV, 1.15 eV, and 1.29 eV, respectively. Notably, the bandgap of Cu-RP is not affected by Cu single atoms, which still remains 1.87 eV. In particular, owing to the states appeared below CBM in Co-RP (0.81 eV) and Ni-RP (0.79 eV), the excitation energy required for the generation of photon-induced charge carriers has largely shifted to the NIR range (1531 nm–1824 nm), as indicated in Figure 1F. For Cu-RP, there is an obvious downshifting of both VB and CB, which shows only one mid-gap state with a distance of 1.44 eV from the VBM, which reduces the absorption energy to a lower NIR window (861 nm).

Besides band structures, the calculated partial density of states (PDOS) is another important indicator of electronic structures. In Figure 2, we focus on the analysis of the d-orbital property of each TM since the d-band center is also strongly related to the photocatalytic activity and the electron transfer efficiency. (Zhou et al., 2022). The pristine RP shows an evident bandgap between CBM and VBM, which are both dominated by the P-3p orbitals (Figure 2A). For Fe-, Co-, and Ni-anchored RP, the localized d orbitals locate very close to the Fermi level (E_F) and VBM (Figures 2B–D). Especially, Co-RP and Ni-RP both display very sharp 3d orbitals with higher electron density near E_F, exhibiting better performance for electron transmission. In contrast, the 3d orbitals of Cu-RP have significantly moved to a lower position of VB, which is far from the E_F (Figure 2E). This results in a wider gap for the transition of photo-induced charge carriers during photocatalysis. The band edge is mainly contributed by the p-orbitals of P with overlapping of 3d orbitals of TMs, which induces the p-d coupling effect to further facilitate charge-carrier transfer. For all four TMs-RP catalysts, we notice the contribution of s-orbital to the CBM, which serve as a ladder to lower the excitation energy for electron excitation from VB to CB. For Cu-RP, the s-orbital dominates the E_F, which only limitedly compensates for low electron transfer density near the VBM. Overall, the PDOS results have revealed that the single-atom TM anchored in RP, especially Co- and Ni-, brings great improvements in both separations and transportations of photo-generated charge carriers during photocatalysis.

The electron-transition capacity of valence electrons is decided by the energy gap between E_F and vacuum level. (Zhou et al., 2022). Thus, the work function has been treated as a key descriptor for electron transition and charge flow in heterojunction structure, and it can be obtained from the calculated electrostatic potential. (Qin et al., 2020; Ruan et al., 2022). As discussed above, besides the bandgap values, the relative position of the bandgap with a reference to standard hydrogen electrode potential is also critical to predict photocatalytic activity. For the construction of the band alignment diagram (Figure 3), the electrostatic potential for each TM-RP type studied in this work has been calculated to indicate the distance between the Fermi level and vacuum level (Supplementary Figures 2A–E). The thermodynamic driving force for photocatalysis is mainly affected by the relative potential position of CBM and VBM of the semiconductor as well as the redox potential of the corresponding reversible reaction. (Li et al., 2016). More negative CBM means stronger reduction reaction tendency, while more positive VBM potential signifies stronger oxidation reaction driving force. Therefore, besides a bandgap value of more than 1.23 eV, the band edges (both VBM and CBM) of the photocatalyst candidates need to cover both the standard potentials of OER and HER to guarantee the high performances of water-splitting. (Mortazavi et al., 2021).

In the acidic condition (pH = 0 in aqueous solution), the CBM of pristine RP and TM-anchored RP are all located above the reduction level of H₂/H⁺, exhibiting a high hydrogen evolution tendency (Supplementary Figure S3). However, based on the energy gap between CBM and H₂/H⁺ level, the TMs-RP all exhibit a relatively weaker hydrogen evolution tendency than the pristine RP surface except Ni-RP. According to the large gap value from Ni-RP CBM to the H₂/H⁺ level, we propose that the anchoring Ni atom offers a stronger driving force for the hydrogen evolution reaction. Meanwhile, the VBM positions of pristine RP and TM-RP (except Cu-RP) are located above O₂/H₂O level, theoretically indicating the weak capability for oxygen evolution. Previous works have revealed the slight mismatching of bandgaps and work functions between theoretical calculations and experimental data. (Wang et al., 2009; Wang et al., 2012a). By considering the calculated SHE as a reference, the pristine RP and Cu-RP are also able to achieve oxygen evolution in the acidic condition.

Since standard redox potentials of H₂O are sensitive to pH variation, the photocatalytic driving force for HER and OER can be well tuned by the pH manipulation based on the following Nernst equations: (Shojaei et al., 2020; Mortazavi et al., 2021): E H E R H + / H 2 = − 4.44   e V + p H × 0.059   e V (2) E O E R O 2 / H 2 O = − 5.67   e V + p H × 0.059   e V (3)

The pH variation also impacts the band positions, which has been verified in experiments that the slope of E_CB (−0.033 eV/pH) does not follow the Nernstian dependence on pH (−0.059 eV/pH). (Simon et al., 2014). The slope of Nernstian dependence on pH for H₂O redox potentials is steeper. However, in this work, the pH value influences on the corresponding band positions are not included. In our work, the model is built in a vacuum environment with the mainly related elements (H₂O, H, or OH) adsorbed on the catalytic surface in HER. The corresponding band positions are stationary with redox potentials of H₂O in different pH values to reveal the reaction tendency for HER and OER. (Zhang et al., 2021; Yang et al., 2018; Makaremi et al., 2018; da Silva et al., 2019; Shahid et al., 2020). In the neutral condition (pH = 7), the H₂/H⁺ level and O₂/H₂O level move up to a more negative position (with reference to SHE) at −0.41 eV and 0.82 eV, respectively (Supplementary Figure S4). Accordingly, for the pristine RP and TMs-RP photocatalysts, the driving force for HER declines while the tendency for OER increases. RP and Cu-RP still cover both potential levels of HER and OER, indicating their photocatalytic activity towards the full water splitting under neutral conditions. In addition, in the highly alkaline environment (pH = 14), pristine RP and TMs-RP nearly lose their HER capability in terms of thermodynamics (Supplementary Figure S5). Thus, we can predict that in the design of photocatalytic heterojunction, Ni-RP is a possible candidate to serve as an efficient HER photocatalyst in wide pH environments.

Besides thermodynamic driving force, many other factors such as microstructures at the micro or nanoscale, adsorption energy, surface/interface morphological properties, and coupling effects with cocatalyst components also have significant influence on photocatalytic performance. (Li et al., 2015). For a better explanation of the reaction mechanism and the prediction of the catalytic activity of a potential photocatalyst, the adsorption of reactants and the reaction energy should also be included. The complex charge-carrier dynamics as well as surface-reaction interactions should be fully investigated since they can largely affect the apparent quantum efficiency in multi-stage heterogeneous photocatalytic reactions. (Li et al., 2016).

The H₂O adsorption energy has a great influence on interfacial charge transfer, and decides the aggregation extent of H₂O molecules near the catalytic active sites, which further triggers the concentration effect and results in more H* generated from water splitting. (Wang F. et al., 2020). The adsorption strength of H₂O molecules is greatly affected by the structural stability of single atoms anchored catalytic surface. In particular, the interactions between the anchored SA-TMs and supporting P atoms have been investigated regarding the iso-surface of charge density difference (Supplementary Figure S6) and the Mulliken charge (Supplementary Table S1). The RP stabilized SA-atoms have an obvious electron exchange with coordinated P atoms. Notably, we discover that the Fe atoms (0.27 e) have a stronger interaction with surrounding P atoms than those of Co-RP (0.24 e) and Ni-RP (0.18 e) counterparts. The stable anchoring site on the RP surface of SA-Cu is different from the other three TMs-RP, which is not in the center of the hexatomic ring formed by P atoms. SA-Cu shows a relatively larger average net charge loss of 0.30 e. The electron flow between the stabilized SA-TM atoms and supporting atoms indicates the modification of electronic structures on the RP surface, which verifies the feasibility of doping TMs for photocatalytic activity modulation.

From the charge density difference diagram in Figures 4A–E , H₂O molecules have a much stronger interaction with TMs-RP when compared to pristine RP surfaces. We can see the electron loss in active metals SA sites and adsorbed O atoms (from adsorbed H₂O). Then, the electrons aggregate between TM and H₂O with the formation of an obvious adsorption bond. According to the calculated H₂O adsorption energy values in Figure 4F, H₂O adsorption processes in pristine-RP and TMs-RP are all exothermic, indicating spontaneous adsorption trends. By the loading of TMs SA atoms on the RP surface, the water adsorption capacity has been improved remarkably. Among the four TM-based SACs, Fe-RP (−0.61 eV), Co-RP (−0.67 eV), and Ni-RP (−0.60 eV) exhibit better H₂O affinity than Cu-RP (−0.45 eV). If the H₂O adsorption is too strong, the over-adsorption induces poison effects on the catalytic surface. (Sravan Kumar et al., 2020). Overall, the adsorption energies of Fe-, Co-, Ni-, and Cu- RP are not too negative, indicating less possibility for catalyst poisoning effect during the photocatalysis.

Besides the water adsorption comparisons, H adsorption is another determinant factor in HER, where both too negative and too positive values are not beneficial for the HER. Based on the adsorption sites, the calculations for H-adsorption reaction energy change are classified into two different types (Figure 5). One considers that H atoms are adsorbed on the SA-metal atoms (Figure 5A), and the other one demonstrates the adsorption of H atoms on the coordinated P atoms to the SA-metal atom (Figure 5B). To guarantee satisfactory computational accuracy, consistent calculation parameters have been set for all the models. For the situations that H atoms adsorbed on SA-metal atoms (H-TMs), the 4 TM SA (Fe-, Co-, Ni-, and Cu-) anchored RP catalysts all have much smaller energy barriers (0.06 eV, −0.25 eV, 0.30 eV, and −0.29 eV, respectively) than that of pristine RP (1.49 eV). As for H adsorbed on coordinated P atoms (H-P-TMs), it can be discovered that the energy barriers of H-P-TMs are slightly larger than those in H-TMs, 0.33 eV (Fe-RP), 0.35 eV (Co-RP), 0.89 eV (Ni-RP), 0.67 eV (Cu-RP, P₁ site), 0.89 eV (Cu-RP, P₂ site), and 1.27 eV (Cu-RP, P₃ site) respectively, but their calculated ΔE _H values are still much less than that of pristine-RP. To sum up, under an acidic environment, the H* is mainly from H⁺ in the solution, where the adsorption energy of H* on the catalyst surface is the main influence factor for HER. Based on the calculated ΔE _H, in both situations, H adsorbed on TM atoms (Fe-RP < Co-RP < Cu-RP < Ni-RP < RP) or on coordinated P atoms (Fe-RP < Co-RP < H-P₁-Cu < Ni-RP = H-P₂-Cu < H-P₃-Cu < RP), SA TMs-RP have much lower energy barriers than pristine-RP for HER. It is worth noting that in the acidic condition, Fe-RP exhibits the lowest energy HER barrier in both H-adsorption sites discussed above.

For the photocatalytic mechanism in neutral and alkaline environments, H* is mainly from water dissociation. The energy barrier for the dissociation of H₂O molecules and the desorption of OH⁻ are important influence factors in reaction energy changes. As shown in Figures 6A–F, the energy change for the whole reaction towards H₂ generation is compared. For all the catalysts, the water dissociation step requires the largest energy costs as the rate-determining step. We have considered two different situations for water dissociation to compare the reaction energy barriers. For the adsorption of OH and H on TM atoms and neighboring P atoms, respectively, the Co-RP and Ni-RP show an energy barrier of 0.90 eV and 1.20 eV, respectively. Different from other TMs-RP types, the anchored single-atom Cu is not symmetrically located in the hexatomic ring of supporting P atoms, which leads to three possible P sites for water dissociations with a water dissociation energy of 1.50 eV, 1.10 eV, and 1.75 eV, respectively (Figure 6E). For water dissociation, Co-RP, Ni-RP, and Cu-RP exhibit higher energy barriers than that of pristine RP (0.79 eV). Notably, Fe-RP shows the smallest energy barrier (0.66 eV) during water dissociation process among all the candidate catalysts. After H₂O dissociation, if the OH is adsorbed on coordinated P atoms and H is adsorbed on TM atoms, the activation energy barriers needed are relatively higher than the former path discussed above, indicating a lower HER efficiency. While the following desorption of OH⁻ becomes much easier on the TMs-RP surface, which requires much lower energy barriers (<0.28 eV) or even becomes spontaneous. In comparison, the pristine RP exhibits a much higher energy cost for the OH⁻ desorption, which leads to the poisoning effect of active sites and lowers the overall photocatalysis performances. Moreover, only Cu-RP and Co-RP (H adsorbed on Co atoms) show endothermic trends for the direct H₂ formation step while other TMs-RP all show the exothermic trend.

For TMs-RP, the energy barriers for OH* desorption are relatively small. In neutral and alkaline environments, since the H* is mainly from the dissociation products (H* and OH*) of adsorbed H₂O* molecules, the water adsorption energy and dissociation energy are the two main influencing factors for HER. The water adsorption energy follows the order of Co-RP < Fe-RP < Ni-RP < Cu-RP < RP, while the water dissociation energy, which is the largest energy barrier, follows the order of Fe-RP < RP < Co-RP < Cu-RP < Ni-RP. Less H₂O molecules tend to be gathered around the active catalytic sites on pristine RP surface because its adsorption energy is only −0.04 eV. Thus, although pristine-RP has a relatively small energy barrier for water dissociation, its HER activity will be limited due to the inadequate gathering of reactant H₂O molecules on the catalytic surface. The adsorption energies of water molecules on Fe-RP, Co-RP, and Ni-RP are much lower than that of pristine-RP and Cu-RP, leading to more efficient accumulation of H₂O molecules on these three catalyst surfaces, which will benefit the following water dissociation process. Further taking the order of water dissociation energy into consideration, the activation barriers of Ni-RP and Cu-RP are relatively larger. Overall, in neutral and alkaline conditions, the Fe-RP and Co-RP can potentially offer superior HER performance.

Combining the band alignment and reaction energy, we have proposed photocatalyst candidates for different environments. For the acidic solution, Fe-RP, Co-RP, and Cu-RP are the most promising candidates. For the neutral environments, Fe-RP delivers better performances than other TMs-RP, indicating novel selections to achieve even superior performances than the reported Ni-RP catalysts. (Wang et al., 2022; Jia et al., 2023). In a weak alkaline environment, only Ni-RP is possible to satisfy the requirement of band alignments. As we further consider the electronic structure analysis, the much larger bandgap of RP and Cu-RP significantly lowers the charge separation and transfer process after light excitation, which largely affects their photocatalysis performances. Therefore, we propose that Fe-RP and Co-RP are promising candidates for photocatalysis of H₂ generation.