Applied Surface Science 598 (2022) 153844

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Theoretical proposal of a revolutionary water-splitting photocatalyst: The
monolayer of boron phosphide
Tatsuo Suzuki (鈴木達夫)
Tokyo Metropolitan College of Industrial Technology, 8-17-1, Minami-Senju, Arakawa-ku, Tokyo 116-8523, JapanA R T I C L E I N F O

A B S T R A C T

Keywords:
Water-splitting photocatalyst
Monolayer
Boron phosphide
Density-functional theory calculations
Hydrogen and oxygen
HSE06

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, photocatalytichydrogen generation is currently inefficient. This paper proposes the monolayer of boron phosphide as a stablehighly-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 fromwater 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.

1. 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. Photocatalytichydrogen-generation systems are much simpler, cheaper, and easier toscale up than the coupled systems of electrolysis and solar cells, windpower generation, etc. Recently, Nishiyama et al. [2] reported solarhydrogen production from water on a 100 m2-scale using an aluminumdoped strontium titanate particulate photocatalyst. They demonstrated
that safe, large-sale photocatalytic water splitting and gas collection andseparation were possible; however, the hydrogen production was inef­
ficient. 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 300 W Xe lamp irradiation, 195 times higher than that ofbulk ZnSe. Similarly, the efficiency of SnS2 single layers is 72 times
higher than bulk SnS2 [4], and SnS monolayers is 104 times higher thanbulk SnS [5]. These reports reveal that two-dimensional materials can behighly-efficient water-splitting photocatalysts. The possible reason is asfollows. In the case of bulk photocatalysts, light penetrates deep inside
the photocatalyst, where it generates electron-hole 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 orions 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 reactwith atoms or ions adsorbed on the surface with little movement because
two-dimensional photocatalysts are surface-only materials. Since Sun’sreports, many two-dimensional photocatalysts have been developed,
and details are found in review articles [6,7,8].
2. Proposal
This paper theoretically proposes the monolayer of boron phosphide(BP) as a stable highly-efficient water-splitting photocatalyst (cf. Fig. 1(a)). As a result of searching for various two-dimensional materials byhigh-precision density-functional theory (DFT) calculations, the revo­
lutionary property of the BP monolayer was discovered. At present,

E-mail address: dr.tatsuosuzuki@gmail.com.
https://doi.org/10.1016/j.apsusc.2022.153844
Received 5 April 2022; Received in revised form 24 May 2022; Accepted 27 May 2022
Available online 2 June 2022
0169-4332/© 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

T. Suzuki

Applied Surface Science 598 (2022) 153844

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◦
C through a solid state reaction route, graphite-like layers with thelattice 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 zincblend 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 typeorbital (GTO) basis calculation using all electrons. The PW basis calcu­
lation 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 reliablecalculation methods, and the error between the calculated energy gaps
and the experimental values is less than 10% [13].

2 H2 O → O2 + 4 H+ + 4 e−(E◦ = +1.229 V vs. SHE)

(4))
kB T (
ln pO2 ⋅[H+ ]4 = − 5.662 + 0.0592 pH (eV)
4e
(6)

2
3 atm

and pO2 = 13 atm, respectively. The theoretical limit Δlimit =EH+ /H2 − EO2 /H2 O = 1.217 eV.

4. Reviews of previous researchesFirst, we review the bulk crystal of BP, which has a cubic zinc-blend
structure. The cubic zinc-blend BP is quite chemically stable and isresistant to chemical corrosion. It is not attacked by hot concentrated
mineral acids or aqueous alkali solution [14]. It is also resistant tooxidation in air up to about 800–1000 ◦ C [15]. The cubic zinc-blend BP
is an indirect transition semiconductor with an energy gap of 2.0 eV, andfunctions 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 condi­
tions [14]. These durable properties of the cubic zinc-blend BP originate
in the strong covalent bonds between elements B and P. This durability

And, Δlimit of (d) is the redox potential difference; that is,(2)

Eg = EC − EV ⩾ Δlimit = EH+ /H2 − EO2 /H2 O(3)From the definition of the Nernst equation, EH+ /H2 and EO2 /H2 O are thepotential energies of the electron in the BP monolayer, not the potential
energies in the solution. The origin of these equations is the vacuum
level, and − 4.44 eV is the energy level of SHE relative to the vacuum
level. kB , e, and [H+] are Boltzmann constant, elementary charge, andthe molar concentration of H+ ions, respectively. Temperature T =298.15 K, and pH = − log10 [H+ ]. The reaction vessel is filled withgenerated gas; therefore, the partial pressures of H2 and O2 are pH2 =(1)

EO2 /H2 O ⩾EV

0.000 V vs. SHE)

EO2 /H2 O = − 4.44 − 1.229 −First, we confirm four important conditions that two-dimensional
photocatalysts must satisfy for large-scale practical use; (a) stable inwater against long exposure to strong sunlight, (b) made from earthabundant elements, (c) one-step excitation using a single semi­
conductor 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 thecomplexity of equipment, and (d) a direct allowed transition semi­
conductor with an energy gap Eg that is larger than the theoretical limit
Δlimit but as small as possible. In order to achieve one-step excitation of(c), band edges (i.e., conduction band minimum EC and valence band
maximum EV ) should straddle water redox potentials EH+ /H2 and EO2 /H2 O ;that is,
and

(E◦ =

Water molecules H2O and hydrogen ions H+ adsorbed on the surface of
the BP monolayer are transformed into various intermediates on thesurface (cf. Fig. 1(b)–(h)), and are finally decomposed into hydrogenmolecules H2 and oxygen molecules O2, as described in detail below.
Here, E◦ is the standard electrode potential relative to the standardhydrogen electrode (SHE). EH+ /H2 and EO2 /H2 O are expressed by the
Nernst equation in Eqs. (5) and (6), respectively.
)(
kB T[H+ ]2
EH+ /H2 = − 4.44 −= − 4.445 + 0.0592 pH (eV)
(5)
ln
2e
p H2

3. Important conditions

EC ⩾EH+ /H2

2 H+ + 2 e− → H2

Next, we confirm redox potentials EH+ /H2 and EO2 /H2 O . The hydrogen
evolution reaction (HER) and the oxygen evolution reaction (OER) are
expressed in Eqs. (3) and (4), respectively.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Fig. 1. Optimized structures of (a) BP monolayer, (b) O*, (c) OH*, (d) OOH*, (e) H*0, (f) H*1, (g) H*2, and (h) H*3. Black, green, red, and blue balls are boron,
phosphorus, oxygen, and hydrogen atoms, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version ofthis article.)2

T. Suzuki

Applied Surface Science 598 (2022) 153844

will be carried over to BP monolayers. Recently, Li et al. [17] preparedcubic zinc-blend BP nanosheets with a thickness of about 4 nm, anddemonstrated that the BP nanosheets were well dispersed in water witha concentration of 0.2 mg/mL. Liang et al. [18] synthesized cubic zincblend BP single crystals larger than 1 mm, and evaluated their excellent
thermal stability up to 1200 ◦ C.
Next, we review BP monolayers. The most stable structure of a BP
monolayer is a hexagonal planar structure like a graphene or a h-BNmonolayer (cf. Fig. 1(a)) [19]. Şahin et al. [20] performed DFT calcu­
lations using a PW basis and local-density approximation, and reported
the bond length d = 1.83 Å and the direct energy gap Eg = 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, andconfirmed the dynamical stability of a BP monolayer. Suzuki & Yoko­
mizo [21] calculated d = 1.87 Å and Eg = 1.912 eV using a GTO basis
and a B3LYP/6-31G(d) functional. After that, the high-precision calcu­
lation method using a HSE06 functional became widespread. Zhuang &Hennig [22] calculated d = 1.855 Å and Eg = 1.36 eV using a PW basis
and a HSE06 functional. Wang & Wu [23] calculated the band edges of a
BP monolayer in a vacuum using a PW basis and a HSE06 functional: d =1.855 Å, EC = − 3.96 eV, and EV = − 5.33 eV; and 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 theNosé-Hoover method at 2500 K 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, andCO2. 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 Eg = 1.833 eV. Therefore, the intrinsic high-efficiency of BP mono­
layers 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 [25–28]. Wu et al. [29] per­formed DFT calculations combined with ab initio molecular dynamics(AIMD) simulations, and demonstrated that the physical and chemical
stabilities of BP monolayers in a vacuum, and in oxygen, water, andoxygen-water environment.

6. Results and considerations
This paper shows three types of calculated results: (a) PWsol using a
PW basis with a solvent effect, (b) PWvac using a PW basis in a vacuum,and (c) GTOvac using a GTO basis in a vacuum.
First, we consider the shapes of BP monolayers after structural op­
timizations. The bond lengths of PWsol, PWvac, and GTOvac are 1.845,
1.846, and 1.854 Å, respectively. Comparing PWsol and PWvac, thebond lengths are almost the same with and without a solvent effect.
Comparing 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. V(z) is the potential whichis averaged within the unit cell.
∫∫V (x, y, z) dx dy∫∫ sol(7)
V(z) = unit celldx dyunit cell
where Vsol (x, y, z) is the entire local potential (ionic plus Hartree plus
exchange correlation) with the solvent effect. The potential value at the
midpoint of the spacer is vacuum level, and it is aligned with the originof energy; that is, V(z = 9) = 0. n(z) is the averaged number density ofvalence electrons of the BP monolayer with the solvent effect, and nb (z)is the averaged bound charge density of water. Drawn for comparison,
Vvac (z) is the averaged potential of PWvac, i.e., the averaged potential
without the solvent effect. Vvac (z) at the midpoint of the spacer is alsoaligned with the origin of energy; that is, Vvac (z = 9) = 0. We define
Vd (z) ≡ V(z) − Vvac (z), which is the potential difference caused by thepolarization of water. Here, we notice that Vd (z) is the vacuum level
when the solvent effect exists; that is, Vd (z) corresponds to the vacuum
level of Anderson model [37] which explains the energy band profiles ofsemiconductor heterostructures. Therefore, VH ≡ Vd (z = 0) = 0.21 eV isthe electrical double layer voltage. EC = − 3.85 eV and EV = − 5.17 eV
are band edges with the solvent effect. EH+ /H2 = − 3.90eV andEO2 /H2 O = − 5.12eV are the redox potentials in Eqs. (5) and (6) at pH =9.2. Here, EH+ /H2 and EO2 /H2 O are based on the vacuum level Vd (z > 3)
outside the electric double layer. Under the condition in this figure, theband edges straddle the redox potentials, and Eqs. (1) and (2) aresatisfied.
Then, we consider energy bands in the left panel of Fig. 3. Here, theenergy bands of PWsol and PWvac are drawn under the same condition
that V(z = 9) = Vvac (z = 9) = 0, as in Fig. 2. The energy bands ofGTOvac are also drawn so that the vacuum level is the origin of energy.
First, we compare PWsol and PWvac. The energy gaps of PWsol and
PWvac are 1.32 and 1.34 eV, respectively. We understand that the dif­ference of energy gaps between with and without the solvent effect issmall. The energy gap of PWvac is in good agreement with previous
researches [22,23]. The band edges (EC , EV ) of PWsol and PWvac are(− 3.85, − 5.17) and (− 4.06, − 5.39) eV, respectively. (EC , EV ) are shifted
only by the electrical double layer voltage VH = 0.21 eV. Next, we
compare PWvac and GTOvac. The energy gap of GTOvac is 1.47 eV,
which is 10% larger than PWvac. This discrepancy is due only to thedifferent calculation methods. (EC , EV ) of GTOvac is (− 4.13, − 5.60) eV.
Despite the different calculation methods, the band edges (EC , EV ) arelocated at almost the same energy levels, which are in good agreementwith a previous research [23].
Then, we consider the relationship between band edges and redox
potentials. The band edges in this paper are calculated under the con­dition that the BP monolayer is not charged, i.e., the pH of the solution isat the point of zero charge pHpzc. It is unclear how the band edges of the
BP monolayer depend on pH; that is, whether the band edges show a
Nernstian dependence of 0.059 eV/pH like semiconducting metal oxides(e.g. TiO2) [38], or are pH-independent like a hydrogen-terminateddiamond [39]. Therefore, we cannot estimate pHpzc. In the right panelof Fig. 3, the redox potentials are drawn according to Eqs. (5) and (6). If

5. Calculation methods
PW basis calculations use a plane-wave basis set, the projector
augmented wave (PAW) potentials [30,31], a HSE06 functional, a 27 ×
27 × 1 Monkhorst-Pack k-point mesh, the super-cell width of 18 Å, thecutoff energy of 800 eV for the PW basis, and VASP 5.4.1 package[32,33]. The convergence criteria of electronic self-consistent calcula­tions and ionic relaxations are 10− 6 and 10− 5 eV, respectively. A solvent
effect by the polarization of water is implemented as an implicit solva­
tion model based on the Poisson-Boltzmann equation, and is performedby using VASPsol package [34,35]. GTO basis calculations use a
Gaussian type orbital 6–311G(d,p) basis set and a HSE06 functional
under the periodic boundary condition. A pseudo-potential is not usedbecause of all-electron calculations. About 2000 k-points are requested
in a unit cell. The convergences of electronic self-consistent calculations
are that the maximum and the root mean square (RMS) of the variationsof the density matrix are less than 10− 5 and 10− 7, respectively, and thatthe variation of the total-energy is less than 10− 5 Hartree. The conver­gences of ionic relaxations are that the maximum and RMS of force areless than 2 × 10− 6 and 10− 6 Hartree/Bohr, respectively, and that the
maximum and RMS of displacement are less than 6 × 10− 6 and 4 × 10− 6
Bohr, respectively. The GTO basis calculation is performed by using
Gaussian 09 package [36].

3

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Applied Surface Science 598 (2022) 153844

Fig. 4. Gibbs free energy change ΔG in each pathway. Here, a0 means a re­action with a H*0 adsorbed-proton. a1, a2, …, c3 are similar.

Fig. 2. Potentials, charge densities, and band edges vs. a z-coordinate. The
inset is an overall view.

dissolve as ions. Therefore, the BP monolayer will not be charged verymuch.
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]. HER pathways considered are (a) H+ + e− + * → H*, (b) H+ + e−
+ H* → H2(g) + *, and (c) 2H* → H2(g) + 2 *. OER pathways are (d)H2O(l) + * → OH* + H+ + e− , (e) OH* → O* + H+ + e− , (f) 2OH* → H2O(l) + O* + *, (g) H2O(l) + O* → OOH* + H+ + e− , (h) OOH* → O2(g) + *+ H+ + e− , and (i) 2OOH* → O2(g) + 2O* + 2H+ + 2 e− . Here, * denotes
an adsorb-site on the BP monolayer. In the following, temperature T =298.15 K. The Gibbs free energies per molecule of hydrogen gas andoxygen gas are GH2 (g) = G0H2 (g) + kBeT lnpH2 and GO2 (g) = G0O2 (g) + kBeT lnpO2 ,the pHpzc of PWsol is in the range of 8.4–10.0, the BP monolayer func­
tions as a photocatalyst because it satisfies Eq. (1). However, even if thepHpzc is out of this range, the BP monolayer still functions as a photo­catalyst. This is because the band edges EC and EV are very close to theredox potentials EH+ /H2 and EO2 /H2 O , respectively; then, either band edge
is pinned to the corresponding redox potential. The basis for this idea isthe experiments by Chakrapani et al. [39]. They added hydrogenterminated diamond particles into aqueous solutions and measured
the changes in pH and oxygen concentrations. Their experiments showthat electron exchange systematically occurs between diamond and theoxygen redox couple; that is, the electrochemical potential (Fermi en­ergy) of the diamond is pinned by the oxygen redox potential. By theway, 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 adepletion layer like bulk semiconductors. Furthermore, the covalentbonds between elements B and P are so strong that B or P does notwhere G0 is the Gibbs free energy at standard conditions. The Gibbs freeenergies of water is GH2 O(l) = G0H2 O(l) = G0H2 O(g) − 0.088 eV [44].
0
ZPE
0
0
G0 H2 (g) = EDFT
H2 (g) + EH2 (g) + ΔH H2 (g) (0→T) − TSH2 (g) , and G H2 O(g) =Fig. 3. (Left panel) energy bands. (Right panel) band edges and redox poten­
tials vs. pH.

Fig. 5. Calculated energy gaps, solar radiation spectrum (air mass 1.5 global),and photon flux vs. wavelength.
4

T. Suzuki

Applied Surface Science 598 (2022) 153844

7. Conclusions

0
ZPE
0
DFT
DFT
EDFT
H2 O(g) + EH2 O(g) + ΔHH2 O(g) (0→T) − TSH2 O(g) . Here, EH2 (g) and EH2 O(g) are

ZPE
1
the total energies calculated by DFT. EZPE
H2 (g) = 2e hνH2 (g),1 and EH2 O(g) =∑3
1i=1 hνH2 O(g),i are the zero-point energies; where h is Plank’s constant,2eand νH2 (g),1 and νH2 O(g), i are the calculated frequencies of the normal

This paper theoretically proposes the BP monolayer as a highlyefficient water-splitting photocatalyst. It is a stable semiconductor
with a direct allowed energy gap of about 1.4 eV, and functions as a onestep excitation photocatalyst. It absorbs sunlight with wavelengths
below about 890 nm (ultraviolet, visible, and near-infrared light) andproduces 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.

mode. The enthalpy changes ΔH0 H2 (g) (0K→T), ΔH0 H2 O(g) (0K→T) andthe standard entropies S0H2 (g) , S0H2 O(g) are taken from the Ref. [44].

G0O2 (g) = 2G0H2 O(l) − 2G0H2 (g) + 4 × 1.229 eV which is E◦ of OER. The sumof Gibbs free energies of a proton and an electron is GH+ + Ge− =1
2

G0H2 (g) −kB Te ln10⋅pH + Ve + 4.44 eV; where Ve is the potential energy ofthe electron in the BP monolayer relative to the vacuum level, and 4.44
eV is the difference between SHE and the vacuum level. The Gibbs freeenergy of O* is calculated by GO* = EDFT
EZPE
O* +
O* +

Declaration of Competing Interest

DFT
DFT
ΔU0O* (0→T) − TS0O* − EDFT
are the total energies by* . Here EO* and E*

00
DFT. EZPE
O* , ΔUO* (0→T), and SO* are the zero-point energy, the internalenergy change, and the standard entropy, respectively. EZPE
O*) }={(∑
hνO*,i0
kB T ∑
01.
and ΔUO* (0→T) − TSO* =ln 1 − exp − kB Te
2e i hνO*,i ,The author declares that he has no known competing financial in­terests or personal relationships that could have appeared to influence
the work reported in this paper.

Similarly, GOH* , GOOH* , and GH* are calculated; however, for GH* weconsider four types: GH*0 , GH*1 , GH*2 , and GH*3 . H*0 is a proton adsorbedon the pure surface of the BP monolayer. H*1, H*2, and H*3 are protons
adsorbed on the back surface of O*, OH*, and OOH*, respectively (cf.
Fig. 1). Spin-polarized calculations were performed by using VASP 5.4.4
package, PAW potentials, a PBE functional [45], a DFT-D3 method for
vdW interactions [46], and the cutoff energy of 520 eV for the PW basis.
The convergence criteria of self-consistent calculations and ionic re­laxations were 10− 5 and 10− 4 eV, respectively. The adsorbed atoms were
calculated with a 2 × 2 × 1 supercell, a 7 × 7 × 1 Monkhorst-Pack kpoint mesh, and the super-cell width of 18 Å. H2(g) and H2O(g) were
calculated in a box of 20 Å×20 Å×20 Å at Γ k-point. As a result, GH2 (g) ,GO2 (g) , GH2 O(l) , GO* , GOH* , GOOH* , GH*0 , GH*1 , GH*2 , GH*3 and GH+ +Ge− are− 6.827, − 9.911, − 14.216, − 6.403, − 9.938, − 15.932, − 2.557, − 2.703,− 3.862, − 4.324, and 1.032 − 0.0592 pH + Ve eV, respectively (see thesupplementary information for computational details). For each reac­tion (a)–(i), we calculate the Gibbs free energy change ΔG. Because thereaction does not proceed unless ΔG < 0, we find the threshold potential
Ve,th when ΔG = 0. The difference between this threshold potential andthe redox potential is defined as η; that is, η = Ve,th − EH+ /H2 for HER andη = EO2 /H2 O − Ve,th for OER. Note that η is pH independent because thethreshold potential and the redox potential are the same pH dependent.
For all reactions included in a pathway, the maximum value of those η isthe overpotential ηHER or ηOER . Fig. 4 shows Gibbs free energy change ΔG
in each pathway. Therefore, ηHER = 0.45 eV along a pathway (a and b)
with a H*2 adsorbed-proton; and ηOER = 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 Eg − Δlimit are 0.10, 0.12, and 0.25 eV for
PWsol, PWvac, and GTOvac, respectively. Although these values are alittle smaller than ηHER + ηOER , the BP monolayer will function well as aphotocatalyst under sunlight. The reason is as follows. When a photonwith an energy larger than the energy gap is absorbed, an electron withan energy larger than EC and a hole with an energy smaller than EV 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 andthe hole recombine or form an exciton, the electron and the hole canreact with atoms or ions adsorbed on the surface of the BP monolayer
because the BP monolayer is a surface-only material. This is a greatfeature that is different from bulk photocatalysts.
And finally, Fig. 5 shows the calculated energy gaps of BP mono­
layers 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 withwavelengths below about 890 nm (ultraviolet, visible, and near-infrared
light), and uses about 48% of the photon flux from the sun effectively.

AcknowledgementsiThis work was partially supported by Tokyo Metropolitan College ofIndustrial Technology.
Appendix A. Supplementary material
Supplementary data to this article can be found online at https://doi.
org/10.1016/j.apsusc.2022.153844.
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6

Supplementary Information
Theoretical proposal of a revolutionary water-splitting photocatalyst:
The monolayer of boron phosphide
Tatsuo Suzuki (鈴木 達夫)
Tokyo Metropolitan College of Industrial Technology
TABLE I. Calculated results: Gibbs free energy 𝐺, total energy calculated by DFT 𝐸 DFT , zeropoint energy calculated by DFT 𝐸 ZPE , internal energy change ∆𝑈 0 (0K → 𝑇), enthalpy change∆𝐻 0 (0K → 𝑇), standard entropy 𝑆 0 , and Gibbs free energy at standard conditions 𝐺 0 . The unit
is eV.

𝐺
*

𝐸 DFT

𝐸 ZPE

∆𝑈 0 (0K → 𝑇) − 𝑇𝑆 0
or
∆𝐻 0 (0K → 𝑇) − 𝑇𝑆 0

𝐺0

-49.059

O*-6.403-55.5450.094-0.011OH*-9.938-59.3350.374-0.036

OOH*-15.932-65.375

0.439-0.055H*0-2.557-51.8500.235-0.001H*1-2.703-58.494

0.247-0.001

H*2-3.862-63.4270.232-0.002H*3-4.324-69.9400.243-0.001

H2(g)-6.827-6.771

0.271-0.316-6.816-14.2190.572-0.481-14.128

H2O(g)
H2O(l)-14.216-14.216O2(g)-9.911-9.883

H+ + e-1.032 − 0.0592 𝑝𝐻 + 𝑉e

1

TABLE II. Gibbs free energy change ∆𝐺 and the difference 𝜂 between the threshold potential andthe redox potential. The unit is eV.

HER pathways(a0) H+ + e- + * → H*0(b0) H+ + e- + H*0 → H2(g) + *(c0) 2 H*0 → H2(g) + 2 *.

∆𝐺 = −3.589 + 0.0592 𝑝𝐻 − 𝑉e
∆𝐺 = −5.302 + 0.0592 𝑝𝐻 − 𝑉e
∆𝐺 = −1.713

𝜂 = 0.856
𝜂 = −0.856(a1) H+ + e- + * → H*1(b1) H+ + e- + H*1 → H2(g) + *(c1) 2 H*1 → H2(g) + 2 *.

∆𝐺 = −3.735 + 0.0592 𝑝𝐻 − 𝑉e
∆𝐺 = −5.156 + 0.0592 𝑝𝐻 − 𝑉e
∆𝐺 = −1.421

𝜂 = 0.711
𝜂 = −0.711(a2) H+ + e- + * → H*2(b2) H+ + e- + H*2 → H2(g) + *(c2) 2 H*2 → H2(g) + 2 *.

∆𝐺 = −4.894 + 0.0592 𝑝𝐻 − 𝑉e
∆𝐺 = −3.997 + 0.0592 𝑝𝐻 − 𝑉e
∆𝐺 = 0.897

𝜂 = −0.448
𝜂 = 0.448(a3) H+ + e- + * → H*3(b3) H+ + e- + H*3 → H2(g) + *(c3) 2 H*3 → H2(g) + 2 *.

∆𝐺 = −5.356 + 0.0592 𝑝𝐻 − 𝑉e
∆𝐺 = −3.535 + 0.0592 𝑝𝐻 − 𝑉e
∆𝐺 = 1.821

𝜂 = −0.910
𝜂 = 0.910(d) H2O(l) + * → OH* + H+ + e-

∆𝐺 = 5.309 − 0.0592 𝑝𝐻 + 𝑉e

𝜂 = −0.353(e) OH* → O* + H+ + e-

∆𝐺 = 4.568 − 0.0592 𝑝𝐻 + 𝑉e

𝜂 = −1.094(f) 2 OH* → H2O(l) + O* + *∆𝐺 = −0.741

OER pathways(g) H2O(l) + O* → OOH* + H+ + e- ∆𝐺 = 5.718 − 0.0592 𝑝𝐻 + 𝑉e

𝜂 = 0.056(h) OOH* → O2(g) + * + H+ + e-

∆𝐺 = 7.053 − 0.0592 𝑝𝐻 + 𝑉e

𝜂 = 1.391(i) 2 OOH* → O2(g) + 2 O* + 2 H+ + 2 e∆𝐺 = 11.211 + 2(−0.0592 𝑝𝐻 + 𝑉e )

𝜂 = −0.056

2