Prediction of a Stable Organic Metal-Free Porous Material as a Catalyst for Water-Splitting

: It is of practical signiﬁcance to ﬁnd organic metal-free catalyst materials. We propose a new graphene-like carbon nitride structure, which was able to meet these requirements well. Its primitive cell consists of eight carbon atoms and six nitrogen atoms. Hence, we called this structure g–C 8 N 6 . The stability of the structure was veriﬁed by phonon spectroscopy and molecular dynamics simulations. Then its electronic structure was calculated, and its band edge position was compared with the redox potential of water. We analyzed its optical properties and electron–hole recombination rate. After the above analysis, it is predicted that it is a suitable photocatalyst material. To improve its photocatalytic performance, two methods were proposed: applied tensile force and multilayer stacking. Our research is instructive for the photocatalytic application of this kind of materials.


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.
Next, the electronic structures were analyzed. The energy-band structure distributions and electron density of states (DOS) by PBE method of g-C8N6 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-C8N6 is an indirect band-gap semiconductor. (a) Atomic structure of g-C 8 N 6 supercell (3 × 3 × 1), the primitive cell is marked using the yellow shaded area, brown atoms are C and gray atoms are N; (b) phonon spectral dispersion diagram of g-C 8 N 6 supercell (2 × 2 × 1).
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. Figure 1. (a) Atomic structure of g-C8N6 supercell (3 × 3 × 1), the primitive cell is marked using the yellow shaded area, brown atoms are C and gray atoms are N; (b) phonon spectral dispersion diagram of g-C8N6 supercell (2 × 2 × 1).
Next, the electronic structures were analyzed. The energy-band structure distributions and electron density of states (DOS) by PBE method of g-C8N6 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-C8N6 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. eV, which has ideal positions of the CBM and the VBM (ECBM = 1.22 eV and EVBM = 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(ω) is given as [42]: where c is the speed of light, and n is the index of refraction: Catalysts 2020, 10, 836 5 of 10 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 → 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. The g-C8N6 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-C8N6 to observe its band-gap change. Tensile strain is defined as: where 0 l 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-C8N6 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-C8N6 remain an indirect gap semiconductor. When the number of layers 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.
Catalysts 2020, 10, 836 7 of 10 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. Table 1. Work function (WF) and band gap (Eg) of two-, three-, four-, five-and six-layer 2D g-C 8 N 6 computed with HSE06 functional. The band-gap differences (∆Eg) between the multilayers and mono-layer g-C 8 N 6 are shown.  Figure 6. Band-edge potentials of multilayer g-C8N6 compare to standard water redox potentials.

Method and Computational Details
The calculations were carried out within the framework of density functional theory (DFT), which was implemented in the Vienna ab initio simulation package known as VASP [47][48][49]. The electron-electron interactions were handled by exchange correlation functions with Perde-Burke-Ernzerhof (PBE) in the form of generalized gradient approximation (GGA) [50]. Energy cutoff value for plane wave expansion of electron wave function is set to 600 eV. Projector-augmented wave (PAW) potentials were used to describe electron-ion interactions [51,52]. Valence electrons include four electrons of carbon (2s22p2) and five electrons of nitrogen (2s22p3). A vacuum region was set to 15 Å. The Brillouin zone was divided into 9 × 9 × 1 k points. Structural optimization was performed by conjugate gradient (CG) method until the residual force of each atom was less than 0.001 eV/Å. A more accurate Heyd-Scuseria-Ernzerhof (HSE) screening potential method [53,54] was used to calculate band gap. Optical absorption spectra of the two dimension covalent triazine frameworks (CTFs) were computed from the dielectric function by Kramers-Kronig dispersion relation [55]. Work function means the minimum energy that must be provided for an electron to escape immediately from the surface of the material. The work function can be calculated by: and EF are the electrostatic potential in a vacuum region far from the neutral surface and the Fermi energy of the neutral surface system, respectively. 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.

Method and Computational Details
The calculations were carried out within the framework of density functional theory (DFT), which was implemented in the Vienna ab initio simulation package known as VASP [47][48][49]. The electron-electron interactions were handled by exchange correlation functions with Perde-Burke-Ernzerhof (PBE) in the form of generalized gradient approximation (GGA) [50]. Energy cutoff value for plane wave expansion of electron wave function is set to 600 eV. Projector-augmented wave (PAW) potentials were used to describe electron-ion interactions [51,52]. Valence electrons include four electrons of carbon (2s22p2) and five electrons of nitrogen (2s22p3). A vacuum region was set to 15 Å. The Brillouin zone was divided into 9 × 9 × 1 k points. Structural optimization was performed by conjugate gradient (CG) method until the residual force of each atom was less than 0.001 eV/Å. A more accurate Heyd-Scuseria-Ernzerhof (HSE) screening potential method [53,54] was used to calculate band gap. Optical absorption spectra of the two dimension covalent triazine frameworks (CTFs) were computed from the dielectric function by Kramers-Kronig dispersion relation [55]. Work function means the minimum energy that must be provided for an electron to escape immediately from the surface of the material. The work function can be calculated by: ϕ = V(∞) − E F , where V(∞) and E F are the electrostatic potential in a vacuum region far from the neutral surface and the Fermi energy of the neutral surface system, respectively.

Conclusions
We propose a new graphene-like carbon nitride structure g-C 8 N 6 , the stability of the structure of which was verified by phonon spectroscopy and molecular dynamics simulations. Then its electronic structure was calculated, and its band edge position was compared with the redox potential of water. We analyzed its optical properties and electron-hole recombination rate. After the above analysis, it is theoretically a suitable water-splitting photocatalyst material. To improve its photocatalytic performance, two methods were proposed: applied tensile force and multilayer stacking. Our research is instructive for the photocatalytic application of this kind of materials.

Conflicts of Interest:
The authors declare no conflict of interest.