Theoretical proposal of a revolutionary water-splitting photocatalyst: The monolayer of boron phosphide

Recently, hydrogen generation by water-splitting photocatalysts is attracting attention as a sustainable and clean energy resource. Photocatalytic hydrogen-generation systems are much simpler, cheaper, and easier to scale up than the coupled systems of electrolysis and solar cells, wind-power generation, etc. However, photocatalytic hydrogen generation is currently inefficient. This paper proposes the monolayer of boron phosphide as a stable highly-efficient water-splitting photocatalyst by high-precision density-functional theory calculations using a HSE06 functional with a solvent effect. The monolayer of boron phosphide has a direct allowed energy gap of about 1.4 eV, and functions as a one-step excitation photocatalyst. It absorbs sunlight with wavelengths below about 890 nm (ultraviolet, visible, and near-infrared light) and produces both hydrogen gas and oxygen gas from water at a suitable pH condition. By calculating the overpotentials of hydrogen and oxygen evolution reactions, its photocatalytic effectiveness was confirmed. The monolayers of boron phosphide will realize green hydrogen revolution.


Introduction
Fossil fuels cause global warming and will dry up in the future. Nuclear fuel has a risk of radioactive contamination such as Fukushima or Chernobyl. Recently, hydrogen generation by water-splitting photocatalysts 1 is attracting attention as a sustainable and clean energy resource to replace fossil fuels and nuclear fuel. Photocatalytic hydrogen-generation systems are much simpler, cheaper, and easier to scale up than the coupled systems of electrolysis and solar cells, wind-power generation, etc. Recently, Nishiyama et al. 2 reported solar hydrogen production from water on a 100 m 2 -scale using an aluminum-doped strontium titanate particulate photocatalyst. They demonstrated that safe, large-sale photocatalytic water splitting and gas collection and separation were possible; however, the hydrogen production was inefficient.
Finding a stable highly-efficient photocatalyst is an urgent task for humankind to realize green hydrogen revolution.
In 2012, Sun et al. 3 reported the fabrication of large-area freestanding single layers of ZnSe with four-atomic thickness, which have an enhanced water-splitting efficiency and photostability.
The ZnSe single layers exhibit a photocurrent density of 2.14 mA cm −2 at 0.72 V versus Ag/AgCl under 300W Xe lamp irradiation, 195 times higher than that of bulk ZnSe. Similarly, the efficiency of SnS2 single layers is 72 times higher than bulk SnS2 4 , and SnS monolayers is 104 times higher than bulk SnS 5 . These reports reveal that two-dimensional materials can be highly-efficient water-splitting photocatalysts. The possible reason is as follows. In the case of bulk photocatalysts, light penetrates deep inside the photocatalyst, where it generates electronhole pairs. The generated electrons and holes must move to the surface of the photocatalysts against the mutual Coulomb attraction in order to react with atoms or ions adsorbed on the surface. Therefore, bulk photocatalysts require mechanisms such as depletion layers or heterojunctions to separate electrons and holes; nevertheless, the electrons and holes still recombine, resulting in energy loss. However, in the case of two-dimensional photocatalysts, the generated electrons and holes can instantly react with atoms or ions adsorbed on the surface with little movement because two-dimensional photocatalysts are surface-only materials. Since Sun's reports, many two-dimensional photocatalysts have been developed, and details are found in review articles. 6

Proposal
This paper theoretically proposes the monolayer of boron phosphide (BP) as a stable highlyefficient water-splitting photocatalyst (cf. Fig. 1(a)). As a result of searching for various twodimensional materials by high-precision density-functional theory (DFT) calculations, the revolutionary property of the BP monolayer was discovered. At present, there are no reports that BP monolayers were synthesized. However, in 2019, on the surface of a cubic zinc-blend BP nanocrystal grown at 1250 ºC through a solid state reaction route, graphite-like layers with the lattice spacing of 0.35 nm were observed in high-resolution TEM images. 9 These layers may become the precursors of BP monolayers. In 2020, Hernández et al. 10 theoretically proposed that BP monolayers can be exfoliated by incorporating arsenic in the (1 1 1) surface of a cubic zinc-blend BP.
Below, we investigate the property of the BP monolayer as a photocatalyst by two types of high-precision DFT calculations: a plane-wave (PW) basis calculation using a pseudo-potential and a Gaussian type orbital (GTO) basis calculation using all electrons. The PW basis calculation also include a solvent effect, i.e., a water polarization effect by an implicit solvation model based on the Poisson-Boltzmann equation. All calculations use Heyd-Scuseria-Ernzerhof (HSE06) hybrid density functionals 11 12 for both structural optimizations and energy bands calculations because the HSE06 functional is one of the most reliable calculation methods, and the error between the calculated energy gaps and the experimental values is less than 10%. 13

Important conditions
First, we confirm four important conditions that two-dimensional photocatalysts must satisfy for large-scale practical use; (a) stable in water against long exposure to strong sunlight, (b) made from earth-abundant elements, (c) one-step excitation using a single semiconductor because Z-scheme using two connected semiconductors requires double photons of one-step excitation, and PEC water splitting using two electrodes is difficult to deploy on a large scale due to the complexity of equipment, and (d) a direct allowed transition semiconductor with an energy gap g that is larger than the theoretical limit ∆ limit but as small as possible. In order to achieve one-step excitation of (c), band edges (i.e., conduction band minimum C and valence band maximum V ) should straddle water redox potentials H + /H 2 and O 2 /H 2 O ; that is, (1) And, ∆ limit of (d) is the redox potential difference; that is, Water molecules H2O and hydrogen ions H + adsorbed on the surface of the BP monolayer are transformed into various intermediates on the surface (cf. Fig. 1(b)-(h)), and are finally decomposed into hydrogen molecules H2 and oxygen molecules O2, as described in detail below.
Here, ° is the standard electrode potential relative to the standard hydrogen electrode (SHE).

Reviews of previous researches
First, we review the bulk crystal of BP, which has a cubic zinc-blend structure. The cubic zinc-blend BP is quite chemically stable and is resistant to chemical corrosion. It is not attacked by hot concentrated mineral acids or aqueous alkali solution. 14 It is also resistant to oxidation in air up to about 800-1000 ºC. 15 The cubic zinc-blend BP is an indirect transition semiconductor with an energy gap of 2.0 eV, and functions as a photocatalyst for H2 evolution. 9 14 16 The photocatalytic H2 evolution reactions continue even in strong acid or strong alkaline, and the BP photocatalyst is stable under these extreme conditions. 14  Next, we review BP monolayers. The most stable structure of a BP monolayer is a hexagonal planar structure like a graphene or a h-BN monolayer (cf. Fig. 1(a)). 19 Şahin et al. 20 performed DFT calculations using a PW basis and local-density approximation, and reported the bond length = 1.83 Å and the direct energy gap g = 0.82 eV or 1.81 eV which is corrected by frequency-dependent GW0 calculations. They calculated the phonon dispersion of a BP monolayer also, and confirmed the dynamical stability of a BP monolayer. Suzuki & Yokomizo 21 calculated =1.87Å and g = 1.912 eV using a GTO basis and a B3LYP/6-31G(d) functional.
After that, the high-precision calculation method using a HSE06 functional became widespread. showed that the optical absorption of a BP monolayer was strong over a wide energy range between 1.37 and 4 eV. They performed a BOMD simulation by using the Nosé-Hoover method at 2500K for 5 ps, and indicated the high thermal stability of BP monolayers. Furthermore, they reported the chemical stability of BP monolayers in environment, such as N2, O2, H2O, H2, and 7 CO2. However, they did not mention the photocatalytic application of BP monolayers. Shu et al. 24 stated that BP monolayers were suitable for a water-splitting photocatalyst based on their calculations using a PW basis, a PBE functional, and the extrapolation of G0W0 method.
However, their low-precision calculation overestimated the energy gap as g = 1.833 eV.
Therefore, the intrinsic high-efficiency of BP monolayers was not reported correctly, and the photocatalytic effectiveness of BP monolayers has been buried. There are no other papers reporting photocatalytic applications of BP monolayers, except for van der Waals heterostructures with other monolayers. 25

Calculation methods
PW basis calculations use a plane-wave basis set, the projector augmented wave (PAW) potentials, 30  PWvac and GTOvac, there is 0.4% difference in bond lengths due to the different calculation methods. These bond lengths are in good agreement with previous researches. 22 23 Next, we consider the results of PWsol in Fig. 2. An infinitely wide BP monolayer is placed on the x-y plane at z=0. ( ) is the potential which is averaged within the unit cell.
where Their experiments show that electron exchange systematically occurs between diamond and the oxygen redox couple; that is, the electrochemical potential (Fermi energy) of the diamond is pinned by the oxygen redox potential. By the way, on the BP monolayer side of water-solid interface there is little charge to compensate for ions adsorbed on the water side because the BP monolayer does not have free electrons like metals nor does it form a depletion layer like bulk semiconductors. Furthermore, the covalent bonds between elements B and P are so strong that B or P does not dissolve as ions. Therefore, the BP monolayer will not be charged very much.
Then, we calculate the overpotentials of HER and OER by Nørskov approach. 40 41 42 Here, we consider an acidic reaction involving H + ; however, the results are the same for the alkaline reaction involving OH -. 43  For each reaction (a)-(i), we calculate the Gibbs free energy change ∆ . Because the reaction does not proceed unless ∆ < 0, we find the threshold potential e,th when ∆ = 0. The difference between this threshold potential and the redox potential is defined as ; that is, = e,th − H + /H 2 for HER and = O 2 /H 2 O − e,th for OER. Note that is pH independent because the threshold potential and the redox potential are the same pH dependent. For all reactions included in a pathway, the maximum value of those is the overpotential HER or OER . Fig. 4 shows Gibbs free energy change ∆ in each pathway. Therefore, HER =0.45 eV along a pathway (a and b) with a H*2 adsorbed-proton; and OER = 0.06 eV along a pathway (d, e, g, and i) or (d, f, g, and i). By the way, the difference between the energy gap and the theoretical limit g − ∆ limit are 0.10, 0.12, and 0.25 eV for PWsol, PWvac, and GTOvac, respectively.
Although these values are a little smaller than HER + OER , the BP monolayer will function well as a photocatalyst under sunlight. The reason is as follows. When a photon with an energy larger than the energy gap is absorbed, an electron with an energy larger than C and a hole with an energy smaller than V are generated. Before the electron falls to the bottom of the conduction band, the hole rises to the top of the valence band, or the electron and the hole recombine or form an exciton, the electron and the hole can react with atoms or ions adsorbed on the surface of the BP monolayer because the BP monolayer is a surface-only material. This is a great feature that is different from bulk photocatalysts.
And finally, Fig. 5 shows the calculated energy gaps of BP monolayers and solar radiation spectrum (air mass 1.5 global). 47 The BP monolayer has an energy gap of about 1.4 eV. It absorbs sunlight with wavelengths below about 890 nm (ultraviolet, visible, and near-infrared light), and uses about 48% of the photon flux from the sun effectively.

Conclusions
This paper theoretically proposes the BP monolayer as a highly-efficient water-splitting photocatalyst. It is a stable semiconductor with a direct allowed energy gap of about 1.4 eV, and functions as a one-step excitation photocatalyst. It absorbs sunlight with wavelengths below about 890 nm (ultraviolet, visible, and near-infrared light) and produces both H2 and O2 from water at a suitable pH condition. By calculating the overpotentials of hydrogen and oxygen evolution reactions, its photocatalytic effectiveness was confirmed. BP monolayers will realize the hydrogen economy as a sustainable and clean energy resource; therefore, we hope that BP monolayers will be synthesized.

Supplementary Information
Theoretical proposal of a revolutionary water-splitting photocatalyst: The monolayer of boron phosphide Tatsuo Suzuki (鈴木 達夫)