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Whether planar or corrugated graphitic carbon nitride combined with titanium dioxide exhibits better photocatalytic performance?

The density functional theory method was performed to study the electronic structures of planar (pGN), corrugated (cGN) graphitic carbon nitride and their interactions with titanium dioxide cluster (TiO2)7. The transfer of photoinduced electrons was analyzed and electronic excitations were calculated. The obtained results show that cGN is thermodynamically more stable than pGN. cGN chemically interacts with titanium dioxide clusters, while the interaction between pGN and the cluster is assigned to physical nature. The combination of cGN and pGN with (TiO2)7 reduces the energy of the first excited states compared to that of the pure substances. The photocatalytic activities were estimated based on hypotheses on the location of the reduction and oxidation sites, the distance between the photoinduced holes and electrons and the electron density of molecular orbitals involved in the excitation. cGN/TiO2 is predicted to have a higher photocatalytic activity than pGN/TiO2.


Introduction
Graphitic carbon nitride (g-C 3 N 4 ) is a relatively new type of carbon-based material that is being researched in the last few decades. g-C 3 N 4 possesses many unique properties such as non-toxicity, high thermal and chemical stability, simplicity of fabrication techniques, moderate band gap, which make it a promising candidate in electronic, catalytic and energetic applications. 1,2 In particular since Wang and his co-workers rst discovered the photocatalytic H 2 and O 2 evolution by water splitting over g-C 3 N 4 in 2009, 3 g-C 3 N 4 has gained tremendous attention as an organic semiconductor metal-free photocatalyst. Recently, g-C 3 N 4 has been widely investigated for the photodegradation of organic pollutants, 4-6 water splitting, 7,8 CO 2 conversion, [9][10][11] etc. However, high electron-hole pair recombination rate and insufficient visible absorption are principal drawbacks of g-C 3 N 4 . Many efforts have been devoted to overcoming these two deciencies by modifying the electronic band structure of g-C 3 N 4 through methods such as metal ion doping, 12 non-metal doping, 13 noble metalloading 9,14 or creating heterojunction structures with other semiconductors. 10,11,15,16 The latter has been shown to be an effective method for improving photocatalytic performance through better charge separation at the interface between two semiconductors since valence and conduction bands (VB and CB) of one semiconductor are located at higher energy levels compared to those of other coupling semiconductors. The popular semiconductor widely used for coupling with g-C 3 N 4 is a traditional photocatalysttitanium dioxide (TiO 2 ). The combination of g-C 3 N 4 and TiO 2 (g-C 3 N 4 /TiO 2 ) has shown to exhibit higher photocatalytic activity compared to that of pure materials in many reactions due to the efficient separation of the photogenerated electron-hole pairs. 15,[17][18][19][20][21][22] However, the inside mechanism of electron transfer in the g-C 3 N 4 /TiO 2 combination and the interaction between components are still rarely discussed in the literature. Wang et al. studied TiO 2 -C 3 N 4 hybrid microspheres 21 and found that this hybrid material exhibited superior photocatalytic activity compared to TiO 2 -C 3 N 4 composites prepared by traditional physical mixing methods. In the FTIR spectrum of the hybrid material, some location shis of C 3 N 4 characteristic bands were observed, suggesting the presence of chemical interaction or a synergistic effect between TiO 2 and C 3 N 4 . Fagan et al. studied photocatalytic properties of g-C 3 N 4 /TiO 2 heterojunctions 22 and reported a substantial up-eld shi in Raman spectra upon the addition of g-C 3 N 4 to TiO 2 , indicating the formation of new bonds or bond modications. Therefore, the authors suggested that g-C 3 N 4 was probably incorporated into the TiO 2 system rather than existing as a component of the mixture of the two. 19 The structural and optical properties of the g-C 3 N 4 /TiO 2 system have also been intensively investigated in various theoretical studies. 15,19,20,23,24 Lin et al. studied the electronic and optical properties of g-C 3 N 4 /TiO 2 (101) heterostructure using spin-polarized DFT+U calculations. 15 Based on the calculated equilibrium distance between g-C 3 N 4 and anatase TiO 2 (101) (1.94Å) and the binding energy (24 meVÅ À2 ), the g-C 3 N 4 / TiO 2 (101) composite material was assigned to the van der Waals heterostructure. The authors also noticed that the electrons can migrate from the g-C 3 N 4 monolayer to anatase TiO 2 (101) surface, which leads to oxidation and redox reactions occurring on g-C 3 N 4 and TiO 2 , respectively. A similar charge transfer was reported in the work of Liu et al. 20 The interaction between TiO 2 and g-C 3 N 4 results in the formation of a built-in electric eld at the interface, which encourages the separation of electron-hole pairs. 15,19,20 Gao et al. suggested that electron transition from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO) promoted the separation of electrons and holes. 19 Obviously, the interaction between TiO 2 and g-C 3 N 4 plays a crucial role in the photocatalytic performance of the combined material. It is also has been reported in various studies that the structure of the material, including decient structures of g-C 3 N 4 , signicantly inuences its catalytic activity. [25][26][27][28] Lei et al. studied a TiO 2 /g-C 3 N 4 composite photocatalyst with an inverse opal structure and heterojunction 28 and showed that the inverse opal TiO 2 /g-C 3 N 4 degraded Rhodamine B 2.7 times faster than the normal TiO 2 /g-C 3 N 4, owing to the interaction between inverse opal g-C 3 N 4 and TiO 2 creating more interfaces for the efficient transfer of photogenerated electron-hole pairs. 29 Ren et al. studied stabilities, electronic properties, and nitrogen reduction activity of planar and corrugated conformations of g-C 3 N 4 (ref. 25) and showed the distortion conformation could activate more n / p* transitions of g-C 3 N 4 , promoting separation efficiency of photoinduced carriers in g-C 3 N 4 . The stability of the corrugated geometry of g-C 3 N 4 compared to the planar geometry was highlighted in several theoretical studies. The corrugation was proved to minimize the electronic repulsion experienced by the N lone pairs located in their structural holes. 29,30 It was suggested that the corrugation enhances the catalytic performance of g-C 3 N 4 for the selective production of CO/CH 3 OH. 30 In this work, we investigate the interaction between the planar and corrugated g-C 3 N 4 with titanium dioxide cluster and clarify the mechanism of the transfer of photogenerated electrons using a combination of different theoretical methods.

Models and computational methods
Models. It is well known that the two main forms of g-C 3 N 4 are triazine and heptazine (tri-s-triazines), which can simultaneously exist. 31 This work focuses on triazine-based g-C 3 N 4 , which is used to build corrugated (denoted as cGN) and in planar (denoted as pGN) forms. The idea of studying the corrugated and planar forms of g-C 3 N 4 is because the synthesized g-C 3 N 4 has a multilayer structure. The surface of g-C 3 N 4 can be considered corrugated if the material has a thin structure. In contrast, if the thickness of g-C 3 N 4 is thick enough, the surface can be considered planar.
In both, constructed corrugated and planar models, the peripheral atoms were saturated by hydrogen atoms. cGN and pGN consist of 200 atoms and have a molecular formula of C 75 N 100 H 20 . Titanium dioxide cluster (TiO 2 ) 7 was chosen due to the comparable stability among small (TiO 2 ) n clusters (n ¼ 1-9) in terms of cluster formation energy per TiO 2 unit. 32 The initial geometry of the (TiO 2 ) 7 cluster was created from the anatase structure of the bulk.
Computational methods. All optimization and energy calculations were performed using the DFT approach in the generalized gradient approximation (GGA). The PBE (Perdew, Burke, and Ernzerhof) gradient-corrected function was used to calculate the exchange-correlation energy. 33 The double zeta basis plus polarization orbitals (DZP) was used for valence electrons, while core electrons were treated by using normconserving pseudopotentials in its fully nonlocal (Kleinman-Bylander) form. 34 The spin-polarized function, which performs a calculation with collinear spin was applied in all calculations, and, thus, the total spin polarization for an optimized structure was automatically determined for the structure with the lowest energy. The calculations have been performed using the SIESTA code. 35 UV-Vis spectra were calculated using time-dependentdensity functional theory (TD-DFT) at CAM-B3LYP/6-31G(d,p) level of theory. This method is implemented in the ORCA code. 36,37 The energy threshold up to which conguration state functions (CSFs) included is 8 eV.

Results and discussions
Electronic structures of cGN, pGN and (TiO 2 ) 7 cGN and pGN. The optimized structures of cGN and pGN are presented in Fig. 1.
The calculated results show that cGN has an energy of 9.2 eV, lower than that of pGN. In other words, cGN is more stable than pGN in terms of the formation energy. The corrugation in the structure of cGN is attributed to the strong repulsion between nitrogen atoms, which are in the sp 2 hybridization state and contain valence electron pairs in the xOy plane. 30 This nding is consistent with previous studies. 29,30 Analysis of HOMO and LUMO provides useful information about the photogenerated electrons. Fig. 2 illustrates HOMO and LUMO of cGN and pGN. Notably, the multiplicity of both cGN and pGN is 1, implying that the systems do not have unpaired electrons.
The distribution of HOMO and LUMO of cGN and pGN is very similar. In cGN, as well as in pGN, HOMO is mainly located on the nitrogen atoms in the triazine heterocycles (denoted as N1 atoms), while the three-coordinated (linked) nitrogen atoms (denoted as N2 atoms) almost do not contribute to HOMO. The LUMO is primarily supported by N1 and carbon atoms in the heterocycles. It is noted that LUMO is perpendicular to the molecular plane.
When a molecule absorbs light with appropriate energy, electrons can be excited from the occupied molecular orbitals (H) to the unoccupied molecular orbitals (L) to form photogenerated holes (h + ) and electrons (e*), as illustrated in the following scheme: L + e / e* (1b)   The h + -e* pair will play the critical role of an oxidant and a reductant in photocatalysis reactions.
An effective photocatalyst is a material that satises the following two requirements: (i) the recombination rate of h + and e* is low and (ii) h + and e* can be generated under visible light irradiation.
Starting from the rst requirement, we propose three hypotheses for the explanation of an effective separation of h + and e*: (i-a): The reduction and oxidation sites are located separately to facilitate photocatalytic reactions, (i-b): The greater the distance between h + and e* is, the more efficient the separation is, (i-c): The electron density of H (where h + is formed) as well as L (where e* is generated) in narrow space results in high densities of h + and e*, which would be more effective for the electron transfer process.
The HOMO and LUMO of the cGN system (Fig. 2) are located in different spatial areas and spread across many atoms. As a result, the photogenerated electrons and holes are far apart from each other, leading to their efficient separation and slow recombination. A similar picture is observed for the pGN system. These specic structural features along with the moderate band gap properly contribute to the photocatalytic activity of g-C 3 N 4 .
To study the nature of the excitation of g-C 3 N 4 , TD-DFT calculations were performed. The results are summarized in Table 1. Fig. 3 and 4 illustrate molecular orbitals involved in the rst excitation of cGN and pGN. The excitation energy of the rst excited state was used instead of the bandgap to evaluate the photocatalytic activity. In principle, a photocatalytic process is initiated with the photon absorption of the photocatalyst to generate the rst excited state. The calculation results show that cGN has 2070 roots (excitations) and pGN has 2190 roots. The excitation energies of the rst excited states of gCN and pCN were determined to be 4.185 eV and 3.769 eV, respectively. It is also noted that the theoretical band gap is strongly dependent on the model size due to the quantum connement effect. 38,39 Hence, using the energy of the rst excited state is meaningful for the same size of the g-C 3 N 4 model used.
H and L involved in the rst excitation of cGN are distributed in a narrower space than those of pGN. Although the excitation energy of the rst excited state of cGN is slightly larger than that of pGN, according to the above-proposed hypothesis (i-c), cGN form is predicted to have higher photocatalytic activities than the pGN form. This nding is consistent with the previous studies. 25,30 To estimate the photoexcitation probability, fractional occupation density (FOD) was calculated and analyzed. The FOD analysis provides meaningful information about the static correlated electrons, viz. active electrons in a molecule. 40,41 The fractional occupation number weighted electron density (rFOD) at r position is dened as: where 4 i are molecular spin orbitals, f i is the fractional orbital occupation number (0 # f i # 1) and the sum is taken over all electronic single-particle levels in the system. The fractional occupation number f i is calculated as: where E F is the Fermi energy level, T el is the electron temperature. The constants d 1 and d 2 are chosen to be unity if the level is lower than E F , while they are zero and À1, respectively, for levels higher than E F . 40,41 The larger the FOD of an atom is, the more active is the atom considered. From the results of FOD calculations for cGN at T el ¼ 12500 K, it can be seen that the nitrogen and carbon atoms in the triazine heterocycles are more active with FOD equal to 0.32 and 0.20 e per bohr 3 , respectively. Meanwhile, the linked three coordinated nitrogen atoms outside the ring have a FOD value of only about 0.10 e per bohr 3 . These results are consistent with the above-discussed contribution of atoms of g-C 3 N 4 into HOMOs and LUMOs. Thus, photoinduced electrons are likely to come from N and C atoms in the heterocycles.
Titanium dioxide (TiO 2 ) 7 . Fig. 5 illustrates the HOMO and LUMO of the (TiO 2 ) 7 cluster. Obviously, the HOMO of (TiO 2 ) 7  cluster is mainly supported by 2p z orbitals of oxygen atoms with the sum of the squares of the coefficients in the wavefunction's equation was determined to be 0.84. In contrast, the LUMO of (TiO 2 ) 7 cluster was primarily contributed by 3d orbitals of titanium atoms with the sum of the squares of the coefficients in the LUMO's equation equal to 0.70 (considering only 3d orbitals with coefficients larger than 0.10).
Thus, when TiO 2 absorbs photons, electrons will transfer from O atoms contributing to HOMO to Ti atoms, contributing to LUMO. It is noted that in the Frontier HOMO and LUMO of the TiO 2 cluster, contributions of O atoms at different positions to HOMO (and similarly for Ti atoms to LUMO) are different, which is attributed to the different mobility of the atoms.
The excitation energy of the rst excited state of (TiO 2 ) 7 is 4.738 eV. The calculation results for the rst excited state of (TiO 2 ) 7 are tabulated in Table 2.
Thus, for the (TiO 2 ) 7 cluster, the transition from HOMO to LUMO primarily contributes to the rst excitation. Unlike g-C 3 N 4 , TiO 2 is typically considered chemically inert, i.e., it does not react with other substances and is, therefore, a stable substance that can be used in many different industries and in a variety of applications. This is an important property contributing to the broad practical application of TiO 2 . However, the drawback of using anatase in photocatalytic applications lies in its large bandgap. Therefore, the combination of TiO 2 with g-C 3 N 4 is expected to decrease the band gap compared to that in pure substances.

Combination of g-C 3 N 4 and TiO 2
Interaction between cGN and pGN with (TiO 2 ) 7 . When (TiO 2 ) 7 is placed onto the g-C 3 N 4 structure, there are a number of possible congurations. In this work, the most favorable congurations for g-C 3 N 4 /TiO 2 systems were preliminarily determined using the iMTD-GC algorithm, which makes use of extensive metadynamic sampling (MTD), with an additional genetic z-matrix crossing (GC) step at the end. iMTD-GC is implemented in the GFN-xTB (short for "Geometries, Frequencies, and Noncovalent interactions-extended TightBinding") package. [42][43][44] The generated favorable congurations from iMTD-GC calculations were then fully optimized at GGA-PBE/ DZP level of theory. Fig. 6 illustrates the most favorable congurations of cGN and pGN combined with the (TiO 2 ) 7 cluster, which are denoted as cGN/TiO 2 and pGN/TiO 2 , respectively.
The interaction between cGN and pGN with (TiO 2 ) 7 cluster is characterized by the interaction energy (D int E), which is dened as follows: The interaction energy determined for cGN/TiO 2 and pGN/ TiO 2 was À355.9 kJ mol À1 and À185.0 kJ mol À1 , respectively. Thus, the formation of g-C 3 N 4 /TiO 2 systems is energetically favorable. To evaluate the nature of the interaction between g-C 3 N 4 and TiO 2 cluster, Mayer bond order (BO) was calculated and analyzed using the following denition: BOðABÞ ¼ X m˛A X m˛B ½ðPSÞ mn þ ðPSÞ nm þ ðRSÞ mn ðRSÞ nm where, P is the total electron density matrix, R is the spin-density matrix and S is the overlap matrix.
The computed BO, distances between atoms (d) and Hirshfeld net atomic charge (q) for cGN/TiO 2 and pGN/TiO 2 are presented in Table 3.
It can be seen that, for the cGN/TiO 2 combination, the distances between Ti and N atoms are slightly larger than the sum of the atomic radius of Ti and N (2.05Å). This nding is consistent with the reasonable values of BO between Ti atoms and N atoms, which are smaller than 1. A signicant charge transfer from cGN to (TiO 2 ) 7 is observed. Thus, the interaction between cGN and TiO 2 clusters is considered to have a chemical nature. Table 2 The parameters of the first excitation of (TiO 2 ) 7

Excitation energy (eV)
Oscillator strength f Â 10 4 The amplitude of MO transition (TiO 2 )    For the pGN/TiO 2 combination, the minimum distance between Ti atoms of the TiO 2 cluster and N atoms of g-C 3 N 4 was determined to be 3.2Å, which is signicantly larger than the sum of the atomic radii of Ti and N. The BO between Ti and N atoms is quite small and ranges from 0.015 to 0.071 and the total BO between Ti and N atoms is only 0.183. The charge transfer from pGN to (TiO 2 ) 7 is less than from cGN to (TiO 2 ) 7 . Therefore, it can be suggested that the interaction between the TiO 2 cluster and pGN is primarily governed by physical interactions. These ndings are in good agreement with the work of Lin et al., who reported that the interaction between g-C 3 N 4 and anatase TiO 2 (101) is assigned to the van der Waals heterostructure. 15 This can make the photocatalytic performance of pGN/TiO 2 very different compared to that of the cGN/TiO 2 combination.
Electronic excitation. The excitation energies of the rst excited states are 3.712 eV and 2.206 eV for cGN/TiO 2 and pGN/ TiO 2 , respectively. Table 4 and Fig. 7 illustrate the contribution of molecular orbitals transition to the rst excitation of cGN/ TiO 2 and pGN/TiO 2 .
The calculation results show that the rst excitation of cGN/ TiO 2 is primarily determined by the transfer of photogenerated electrons from the HOMOs (HOMO, HOMOÀ7, HOMOÀ6), mainly located on g-C 3 N 4 to the LUMO+1 orbital principally contributed from d orbitals of Ti and 2p z orbitals of N atoms. Electrons from cGN/TiO 2 could be photogenerated by photons with an energy of 3.712 eV, which is much lower than the case of pure cGN and the TiO 2 clusters. Moreover, HOMOs and LUMO+1 orbitals of cGN/TiO 2 are distributed in different spatial areas. When photogenerated electrons are assigned to TiO 2 , their density is higher as compared to the distribution of these electrons on the large cGN surface and, thus, makes the electron transfer process more favorable.
The calculated HOMO and LUMO energy levels are À10.575 and À2.406 eV, and, À7.964 and À1.054 eV for the TiO 2 cluster and cGN, respectively. There is an important issue that will be claried: how do electrons transfer from g-C 3 N 4 to TiO 2 when photogenerated? If the interaction between g-C 3 N 4 and TiO 2 is just physical, electrons cannot migrate because both g-C 3 N 4 and TiO 2 are non-metal. If there is a strong chemical interaction, the electronic structure of each substance will be changed, leading to photocatalytic deactivity.
For the cGN/TiO 2 system, the interaction between TiO 2 and cGN is considered as a weak chemical interaction expressed through a small BO and the atomic distances and, thus, the LUMO+1 orbital of the cGN/TiO 2 system contains both 2p z orbitals of N atoms and 3d orbitals of Ti atoms. Therefore, the electron transition in cGN/TiO 2 can be described as follows: cGN, due to the lower energy of the rst excited state as compared to TiO 2 , when photogenerated, electrons transfer from the hybrid orbitals containing electron pairs of the N atoms in HOMOs (H) to the 2p z orbitals of N atoms in (LUMO+1) orbitals. This transition is the same as described for g-C 3 N 4 (Fig. 2), but the difference is that electrons transfer only to 2p z orbitals of N atoms bound to Ti atoms. Both the 2p z orbitals of N atoms and the 3d orbitals of Ti atoms are involved in the (LUMO+1) orbital, so in this case, the electron transition is almost instantaneous. For the pGN/TiO 2 system, the LUMO system consists of only orbitals of the TiO 2 cluster. Because there is no chemical interaction between pGN and the TiO 2 cluster, there is no electron transfer from pGN to TiO 2 . Thus, for the pGN/TiO 2 system, although the energy of the rst excited state is reduced, the photocatalytic efficiency of the combined system is not signicantly improved compared to the pure substances.
The calculated UV-Vis spectra for (TiO 2 ) 7 , cGN, pGN compared with UV-Vis of cGN/TiO 2 and pGN/TiO 2 are illustrated in Fig. 8. The relative total peak areas (S) in the photon energy region of 2-5 eV for the studied systems are shown in Table 5.
The UV-Vis of pGN/TiO 2 is not different from the parent pGN, proving that there is no chemical interaction between (TiO 2 ) 7 and pGN. Meanwhile, the spectrum of cGN/TiO 2 has a signicant shi to the lower energy photon region. This is attributed to the above-mentioned interaction between (TiO 2 ) 7 and cGN. Besides, cGN/TiO 2 exhibits a larger total peak area than that of the pure components and thus, more transitions are appearing in the photon energy region of 2-5 eV. The combination between TiO 2 and cGN improved the light absorption ability of the component due to the synergistic effect. Concerning the idea of using corrugated and planar models of g-C 3 N 4 that characterize the thickness of the material (see section Models), our calculation results conrm that exfoliated g-C 3 N 4 nanosheets exhibit higher photocatalytic performance than bulk C 3 N 4 . These ndings are in good agreement with the experimental study of Gao et al. on the enhancement of the photocatalytic activity of ZnO/g-C 3 N 4 composites by regulating the stacked thickness of g-C 3 N 4 nanosheets. 45 Their results showed that ZnO/g-C 3 N 4 with the middle thickness shows the highest photocatalytic performance.

Conclusions
The interactions between planar g-C 3 N 4 (pGN) and corrugated g-C 3 N 4 (cGN) with the (TiO 2 ) 7 cluster were investigated using the DFT method. The obtained ndings show that the cGN chemically interacts with the titanium cluster, while the interaction between pGN and the cluster is assigned to physical nature. The combination of both cGN and pGN with (TiO 2 ) 7 reduces the energy of the rst excited state. The photocatalytic activities were estimated based on hypotheses on the location of the reduction and oxidation sites, the distance between the photoinduced holes and electrons and the electron density of the molecular orbitals involved during excitation. cGN/TiO 2 is predicted to have a higher photocatalytic activity than pGN/TiO 2 due to the synergistic effect.

Conflicts of interest
There are no conicts to declare.