## 1. Introduction

Two problems have plagued people for a long time—the energy crisis and environmental pollution. Scientists have put much effort into solving these two problems. The development of hydrogen energy is promising [

1]. If we can obtain much hydrogen, we can solve these two problems effectively.

Water-splitting to produce hydrogen using a photocatalyst is a feasible method [

2]. In 1972, Honda and Fujishima first produced H

_{2} by photochemical water-splitting using TiO

_{2} [

3]. With development of technology, there are increasing kinds of photocatalysts, including various oxides, sulfides, oxynitride semiconductors, etc. [

4,

5,

6,

7,

8,

9,

10,

11,

12], which belong to inorganic materials. Inorganic photocatalysts materials have some drawbacks, for example limited concentration of active sites and heavy metal toxicity [

13,

14,

15]. However, organic photocatalysts have some merits, for example low cost, ease of fabrication and mechanical flexibility [

16,

17]. Therefore, research of metal-free organic high-efficiency photocatalysts is very important.

Since the exfoliation of monolayer graphene, two-dimensional materials have attracted comprehensive research for excellent properties [

18,

19,

20,

21,

22,

23,

24,

25]. It is increasingly important to study and regulate the properties of two-dimensional materials [

26,

27,

28]. Wang et al. first considered graphene-like carbon nitride (g–C

_{3}N

_{4}) as a photocatalyst. They predicted that the g–C

_{3}N

_{4} photocatalyst exhibits interesting electronic properties that can decompose water to produce hydrogen [

29]. Subsequently, many studies were carried out on the application of graphene-like carbon nitride in photocatalysis [

30,

31,

32,

33,

34,

35,

36].

In this work, we propose a graphene-like carbon nitride structure with a primitive cell that consists of eight carbon atoms and six nitrogen atoms. Hence, we call this structure g–C_{8}N_{6}. First using basic calculations, we analyzed the electronic structure of g–C_{8}N_{6} and compared its band edge position with the redox potential of water. At the same time, we calculated its optical properties and considered it as a suitable photocatalyst material.

## 2. Results and Discussion

The structure of the g–C

_{8}N

_{6} supercell (3 × 3 × 1) is shown as

Figure 1a. The primitive cell is marked using the yellow shaded area. The lattice constant is 7.177 Å, and the lengths of two types C–N bonds are 1.35 Å and 1.34 Å, respectively. Unlike many carbon nitrides, the s-heptazines in g–C

_{8}N

_{6} is connected by C–C bonds, rather than C–N bonds. The lengths of the C–C bonds in the s-heptazines are 1.426 Å, however the length of C–C bonds between two connected s-heptazines are 1.439 Å. It has a very uniform hexagonal symmetry structure; which angles are all 120°. Because it has many holes, it has enough contact with water when it is used as a photocatalyst.

Many similar carbon nitride structures have been synthesized [

37,

38,

39], so perhaps a carbon-rich g–C

_{8}N

_{6} layered structure may exhibit sufficient stability to be synthesized in future. We checked the stability of the structure theoretically through two methods. First, the force constant theory tested kinetic stability of the g–C

_{8}N

_{6} through the phonon spectrum. A large (2 × 2) supercell was optimized in the calculation. The phonon spectral dispersion diagram along the highly symmetric direction in Brillouin zone is shown in

Figure 1b. Obviously, the phonon spectral dispersion has no imaginary frequency, indicating that g–C

_{8}N

_{6} framework is kinetically stable. This is similar to the phonon spectra of g–C

_{13}N

_{13} [

28], C

_{2} N-

h2D [

40].

Second, the dynamic stability was checked with molecular dynamics simulations. The 126 atoms of the 3 × 3 supercell were simulated using a Nosé–Hoover thermostat at 300 K. The structure remained well after 5 ps, indicating its stability at room temperature. Temperature and total energy varied slightly with time, but the geometry of g–C_{8}N_{6} remained stable.

Next, the electronic structures were analyzed. The energy-band structure distributions and electron density of states (DOS) by PBE method of g–C

_{8}N

_{6} are shown in

Figure 2a,b. It can be obtained that this material is a 2.13-eV band-gap semiconductor without magnetism. The conduction band minimum (CBM) is situated on K point and the valence band maximum (VBM) is situated on M point, which shows that g–C

_{8}N

_{6} is an indirect band-gap semiconductor.

According to electronic structure of the material, we analyzed whether it is suitable for splitting water as a photocatalyst. The band of a photocatalyst should be greater than 1.23 eV, which is the difference between the water reduction potential and water oxidation potential. The positions of the conduction and valence band edges should straddle the redox potentials for water photolysis. The optical absorption properties should show that it can absorb partial visible light [

41].

The band-edge potential affects whether it can be a photocatalyst. The CBM minus the Fermi energy and then minus the vacuum energy level is the conduction band edge. The VBM minus the Fermi energy and then minus the vacuum energy level is the valence band edge. The redox potentials of water are −4.5 eV and −5.73 eV, respectively. The conduction band edge of a suitable photocatalyst should be above the energy corresponding to the water reduction potential [ϕ(H

^{+}/H

_{2})]. At the same time, the valence band edge of a suitable photocatalyst should be below the energy of the water oxidation potential [ϕ(O

_{2} /H

_{2}O)]. As shown in

Figure 3a, band gap of the g–C

_{8}N

_{6} is 2.89 eV, which has ideal positions of the CBM and the VBM (E

_{CBM} = 1.22 eV and E

_{VBM} = 0.44 eV vs the normal hydrogen electrode, pH = 0). In other words, the electrons in the lowest unoccupied molecular orbital (LUMO) have sufficient reactivity to reduce water to hydrogen, whereas holes in the highest occupied molecular orbital (HOMO) have sufficient reduction potential to oxidize water to oxygen.

In order to analyze optical absorption properties of g–C

_{8}N

_{6}, we calculated the frequency-dependent dielectric matrix using hybrid HSE06 function and expanded a 10 × 10 × 1 k-point mesh. The random phase approximation was used during the calculation of the frequency dependent dielectric tensor. The complex dielectric constants at a given frequency can be defined as:

The expression for the absorption coefficient

$I(\omega )$ is given as [

42]:

where

c is the speed of light, and

n is the index of refraction:

According to the above equation, the light absorption property can be obtained mainly from the value of the imaginary part, and slightly from the value of the real part. The absorption coefficient was above zero, when only if the imaginary part:

The imaginary part is determined by the summation on the empty state. The following equation can be used:

where the indices c and v represent the conduction and valence band states and

${u}_{c\overrightarrow{k}}$ is the cell periodic part of the orbitals at the k point. The summation of Equation (4) includes a large number of empty conduction band states. The number of empty conduction band states is almost twice the number of valence bands.

According to the theory described above, frequency-dependent dielectric function of g–C

_{8}N

_{6} was calculated by the hybrid HSE06 function.

Figure 3b shows the absorption coefficient and

Figure 3c shows imaginary part of dielectric function of g–C

_{8}N

_{6}. From

Figure 3b,c, the solar spectral range which can be absorbed is from 60 nm to 600 nm. Hence, it is obvious that g–C

_{8}N

_{6} can be used as a photocatalyst for splitting water.

The recombination rate of electron–hole is an important aspect affecting the photocatalytic performance. In the process of photocatalytic water-splitting, after electronic transition, electrons and holes will decompose water into hydrogen and oxygen. However, there are many electrons that will go back to original orbitals and recombine with holes. If recombination rate of electrons and holes is relatively low, then there will be more electrons involved in the redox reaction process, and the catalytic performance will be improved.

Figure 4a is the charge density of the conduction band minimum (CBM), which is situated on K point of the 32nd energy band.

Figure 4b is the charge density of the valence band maximum (VBM), which is located on M point of the 31st energy band. Comparing

Figure 4a,b, we can find that there are few overlapping parts in the distribution of charge density, that is, the recombination rate of electrons and holes is relatively low. This result indicates that g–C

_{8}N

_{6} may exhibit long-lived electrons and holes that can improve its photocatalytic performance.

The g–C_{8}N_{6} is a semiconductor with a suitable band gap. Its band edge position relative to the redox potential of water is ideal and can absorb a part of visible light. More valuable, the recombination rate of its electron holes is relatively low. In summary, it has characteristics of photocatalyst and can be used for water-splitting.

Next, we analyze whether there are some ways to improve its performance. As we all know, tensile strain can regulate electronic structure of material and thus improves its properties [

28,

38,

43]. Hence, we applied tensile strain to g–C

_{8}N

_{6} to observe its band-gap change. Tensile strain is defined as:

where

${l}_{0}$ is length of original supercell structure, and

$l$ is length of supercell under tensile strain.

Figure 5 is the case of band-gap changes as the tensile force changes with PBE functional. The color of the squares in figure represents the color of the solar spectrum that can be absorbed. With the increase of tensile force, the length of C–C bonds and C–N bonds gradually increases, indicating that the orbitals binding ability of these bonds is weakened. At the same time, the splitting of bonding and antibonding decreases, resulting in narrow band gap, so absorption range of sunlight extends to green region. In contrast, when compressive stress is applied, the splitting of bonding and antibonding increases, thus widened the band gap, and the absorption of sunlight moves to red region. To sum up these two cases, tensile force can be used to capture a wider spectrum of the sun.

Multilayer stacking can also adjust electronic structure of material, thus improving its performance [

44]. The multilayer structure is AA stacking. Work functions and energy-band gap of two-, three-, four-, five- and six-layer g–C

_{8}N

_{6} calculated are listed in

Table 1 with HSE06 functional. This is particularly important for layered structures as the interlayer interaction depends on the van der Waals interaction [

45,

46]. The results of

Table 1 and

Figure 6 were calculated using van der Waals force. Although the number of layers is increasing gradually, the work function maintain stability. In sharp contrast band gap decreases gradually with increase of the number of layers. Similar to the monolayer, all multilayer g–C

_{8}N

_{6} remain an indirect gap semiconductor. When the number of layers is 2–6, the band gap is 2.50–2.35 eV. As number of layers increases, properties of the material gradually approach the bulk material with a gap of 2.35 eV. Compared with single-layer, multilayer stacking reduced the band gap by 0.54 eV.

To study the photocatalytic capacity of multilayer g–C

_{8}N

_{6}, the band alignment are shown in

Figure 6. Compared with the monolayer, the VBM of the bilayer structure increased, while the CBM of the bilayer structure decreased. The other multilayer g–C

_{8}N

_{6} systems were similar to the bilayer structure. The multilayered g–C

_{8}N

_{6} system had ideal band edges that could decompose water to produce hydrogen and oxygen.