Tuning near-gap electronic structure, interface charge transfer and visible light response of hybrid doped graphene and Ag3PO4 composite: Dopant effects

The enhanced photocatalytic performance of doped graphene (GR)/semiconductor nanocomposites have recently been widely observed, but an understanding of the underlying mechanisms behind it is still out of reach. As a model system to study the dopant effects, we investigate the electronic structures and optical properties of doped GR/Ag3PO4 nanocomposites using the first-principles calculations, demonstrating that the band gap, near-gap electronic structure and interface charge transfer of the doped GR/Ag3PO4(100) composite can be tuned by the dopants. Interestingly, the doping atom and C atoms bonded to dopant become active sites for photocatalysis because they are positively or negatively charged due to the charge redistribution caused by interaction. The dopants can enhance the visible light absorption and photoinduced electron transfer. We propose that the N atom may be one of the most appropriate dopants for the GR/Ag3PO4 photocatalyst. This work can rationalize the available experimental results about N-doped GR-semiconductor composites, and enriches our understanding on the dopant effects in the doped GR-based composites for developing high-performance photocatalysts.


Results
Structural properties and formation energy. The representative views of GR/Ag 3 PO 4 (100) composites are shown in Fig. 1. Parts (a) and (b) present the top and side views of the GR/Ag 3 PO 4 (100) interface used in our calculations, respectively. The blue atom is the center C atom of GR sheet, which is replaced by B, N, S, and P in the B C -GR/Ag 3 PO 4 (100), N C -GR/Ag 3 PO 4 (100), S C -GR/Ag 3 PO 4 (100), and, P C + V C -GR/Ag 3 PO 4 (100) composites, respectively. Part (c) of Fig. 1 is given the top view of the P C + V C -GR/Ag 3 PO 4 (100) composite, while part (d) for side view of the S C -GR/Ag 3 PO 4 (100) composite after optimization. Geometry optimization has first been performed for these systems using the conjugate gradient method. The distances from the Ag 3 PO 4 (100) surface to GR/doped GR sheets after optimization for the GR/Ag 3 PO 4 (100) and doped GR/Ag 3 PO 4 (100) composites are listed in Table 1. For the pure GR/Ag 3 PO 4 (100) composite, the farthest and closest distances between the GR sheet and the top of the Ag 3 PO 4 (110) surface is calculated to be 2.65 and 2.61 Å, respectively, which is about equal to those between the GR sheet and other materials (2.65 Å for TiO 2 (110)/GR 51 , 2.422-2.866 Å for ZnO(0001)/GR) 52 . This indicates that the GR sheet is slightly distorted because the forces on different C atoms, caused by the interfacial interaction, are vary, owing to the different arrangement of atoms at the top layer of Ag 3 PO 4 (100) surface.
The dopant effects on the interface distances for GR/Ag 3 PO 4 (100) composites can be clearly seen from Table 1. The variation of interface distances of doped GR/Ag 3 PO 4 (100) composites depends on the impurity atom. The B dopant on the carbon lattice site induces a small increase (about 0.02~0.03 Å) of interface distances between the B-dope GR sheet and Ag 3 PO 4 (100) surface. The same increase of interface distance also happens in the P C + V C -GR/Ag 3 PO 4 (100) composite. Surprisingly, the interface distance between the N-dope GR sheet and Ag 3 PO 4 (100) surface is significantly increased (~0.5 Å) compared to that in pure GR/Ag 3 PO 4 (100) composite. Although the interface distances are changed in these composites, the doped GR sheets are still quite flat, indicating that the interfacial interactions are indeed van der Waals (vdW) rather than covalent, in accordance with previous studies 44 . On the contrary, the S dopant leads to a local distinct deformation of the GR sheet, as shown in Fig. 1(d). This is because the bond length of S-C (1.74 Å) is longer than that of C-C (1.42 Å), while those of B-C and N-C are 1.48 and 1.41 Å, respectively, very close to 1.42 Å. This is the main reason why the doped GR sheet is still flat in the B C /N C -GR/Ag 3 PO 4 (100) composites, whereas the S-doped GR sheet is undulating one, resulting into the farthest and closest distances between the S-doped GR sheet and the top of the Ag 3 PO 4 (110) surface to be 2.71 and 1.73 Å, respectively. The microscopic crumpling around the S dopant can be comparable in size to the suspended GR sheet, which exhibit intrinsic microscopic roughening such that the surface normal varies by several degrees and out-of-plane deformations reach 1 nm 53 . The change of interface distance indicates the variation of interface interaction between doped GR and Ag 3 PO 4 (100) surface, which will result into the change of electron transfer in these composites. Meanwhile, the atoms in the top two layers of Ag 3 PO 4 (100) surface have been rearranged, implying that the electron transfer occurs at the interface, as will be shown below.
To assess the dopant effects on the relative stability of these doped composites, the interface binding energies, ΔE f , of these composites are estimated according to the following equation:

Density of States.
Incorporating impurity atom into semiconductors to engineer their electronic structures and photocatalytic performances have widely been used as an effective strategy. The influence of dopants on the properties of the composites containing two-dimensional layered material has not been explored theoretically so far. To evaluate the dopant effects, it is insightful to analyze the electronic structures of doped-GR-based composites. The density of states (DOSs) of five models are displayed in Fig. 2. As its (100) surface is exposed, Ag 3 PO 4 becomes a direct band gap semiconductor and the band gap, E g , decreases to 2.15 eV from 2.45 eV 44 . The GR/Ag3PO4(100) has an E g of 0.53 eV due to the Fermi level down-shifting by 0.655 eV with respect to the Dirac point of GR, which extends its absorption spectrum covering the entire visible region, even infrared light 44 . Figure 2 shows that, for pure GR/Ag 3 PO 4 (100) composite, the upper part of valence band (VB) consists of the states of GR sheet, whereas the bottom of conduction band (CB) is composed by orbitals from the Ag 3 PO 4 (100) surface. Under light irradiation, electrons in the top VB can be directly excited to the CB of GR/Ag 3 PO 4 (100), producing well-separated electron-hole pairs. The most important feature in Fig. 2 is the band alignment between the doped GR sheet and the Ag 3 PO 4 (100) surface. As shown in the left column of Fig. 2, the main shapes of the calculated DOSs projected on two different components in the doped GR/Ag 3 PO 4 (100) composites are similar to those of the DOSs of isolated doped GR sheets and the Ag 3 PO 4 (100) surface, respectively (note that the DOSs of doped GR sheets are not given here). This is due to larger separation space between them (about 2.6− 3.2 Å), suggesting that the interaction between doped GR and Ag 3 PO 4 (100) surface is weak due to the absence of covalent bonding upon formation between the interfaces. The interaction between the doped GR sheets and Ag 3 PO 4 (100) surface varies with different dopants. From Fig. 2, the VB offset (VBO) and the CB offset (CBO) between GR sheets and Ag 3 PO 4 (100) surface appear in these composites. This kind of the band alignment between the two components demonstrate that a type-II heterojunction is formed, which is key to enhance the photoactivity of the doped GR/Ag 3 PO 4 (100) composites.
Doping can tune the band gap of doped GR/Ag 3 PO 4 (100) composites, as listed in Table 2. The B or S substituting on the C site in the GR sheet will decrease the band gap of the composites. Similarly, the P C + V C -GR/ Ag 3 PO 4 (100) composite has a smaller band gap (0.12 eV), compared to pure GR/Ag 3 PO 4 (100). The decrease of band gap, due to B, S, and P dopants, stems from the negative movement of the CB bottom, relative to the Fermi level ( Fig. 2 (b1,d1,e1)). In contrast, N atom doped into the GR sheet as impurity increases the band gap from 0.53 to 1.44 eV of N C -GR/Ag 3 PO 4 (100) composite. The origin of band gap broaden can be traced by the movement of the VB maximum (VBM) and the CB minimum (CBM). Compared to the Fermi level, there is a significantly raise of the CBM compared to the pure GR/Ag 3 PO 4 (100) composite. Note that the CBM consists mainly of O 2p states from the top layer of the Ag 3 PO 4 (100) surface. The doped N atom has three unpaired electrons with strong N 2p character, similar to its neighboring O 2p states, leading to the hybridization between N and its neighboring O atoms. Fig. 2 (c2,d2) show that the N 2p orbital above the Fermi level is much higher than those of S dopant. Since the N 2p orbital energy is higher than the O 2p orbital energy, the overlap of N 2p and O 2p states at the bottom of CB then elevates the CBM, as well as the donor level to be above the VB. Therefore, doping with N impurity into GR sheet widens the band gap of N C -GR/Ag 3 PO 4 (100) composite, whereas the S dopant reduces the band gap of S C -GR/Ag 3 PO 4 (100) composite. The N dopant can also broaden the band gap of Cu 2 O 54 . The cases of B C -GR/ Ag 3 PO 4 (100) and P C + V C -GR/Ag 3 PO 4 (100) composites are quite different: the B 2p and P 3p states are located at the Fermi level, i.e., to modify the VB edge (p-type doping) (see Fig. 2 (b2,e2)), thus the decrease of band gaps resulting in an upward shift of the VBM (see Figs 2 (b1,e1)). These results indicate that the substitution doping of GR sheet not only tune the band gap, but also change the ingredients of near-gap electronic structure of the doped-GR-based composites, which will influence the light absorption.

Mulliken Population, Charge Transfer and Mechanism Analysis. The interactions between GR and
Ag 3 PO 4 (100) surface would induce the charge distribution fluctuations of GR sheet 44 . To quantitatively analyze the charge variation caused by doping in the doped GR/Ag 3 PO 4 (100) composites, the Mulliken population analysis of the plane-wave pseudopotential calculations has been performed for five composites. Figures 3 and 4 render the results of the Mulliken charges on the atoms near the dopants, in which selected typical values are denoted. Although the C atom in the pure GR has a Mulliken charge of zero electrons, those C atoms in the GR/Ag 3 PO 4 (100) composite have different Mulliken charges because the arrangement of atoms under various C atoms is different ( Fig. 3(a)). The redistribution of charge of doped GR sheet mainly depends on the incorporation of impurity atoms into C lattice. As shown in Fig. 3(b-e), the doped B, N, S, and P atoms have a Mulliken charge of + 0.51, − 0.23, + 0.84, and + 1.06, respectively. Compared Fig. 3(a) with Fig. 3(b-e), one can see that the C atoms bonded to the dopants have much larger Mulliken charges than those in the pure GR/Ag 3 PO 4 (100) composite. Interestingly, the three C atoms bonded to N atom have positive Mulliken charges (+ 0.14, + 0.15), whereas those bonded to B (S, P) atom have negative Mulliken charges. This can be ascribed to the different atomic radiuses, electronegativities, and their bond length with C atom, of these dopants. Moreover, some C atoms become positively charged (not given in Fig. 3), while others are negative in these composites. Those atoms, especially the dopants, with positive effective charge will facilitate the adsorption of some species with negative charges, thus becoming active sites. The dopants in GR sheets also change the charge redistribution of the Ag 3 PO 4 (100) surface, which are shown in Fig. 4. In particular, there are obvious changes of the Mulliken charges of Ag atoms under the dopants. For example, Fig. 4(c) shows that the Mulliken charges of the Ag atoms in the first, second and third layers are reduced from 0.85 to 0.73, 0.56 to 0.51, 0.57 to 0.55, respectively, compared to those in undoped GR/Ag 3 PO 4 (100) composite ( Fig. 4(a)). The value variation is decreased gradually is due to the elongation of the distance between the dopants and the Ag atoms in different layers. However, the electrons of O atoms in the top layer are almost no change. Therefore, incorporating substitutional impurity into the GR sheet is likely to be one effective strategy to improve stability of GR/Ag 3 PO 4 (100) composites.
The rearrangements of atoms near the interface and the strong change of DOSs imply a substantial charge transfer between the involved constituents. This can be visualized (as shown in Figs 5 and 6) by the three-dimensional charge density difference Δρ = ρ − X GR/Ag PO (100) 3 4 − ρ Ag PO (100) 3 4 − ρ − X GR (X = B, N, S, P+ V C ), where ρ − X GR/Ag PO (100) 3 4 , ρ Ag PO (100) 3 4 , and ρ − X GR are the charge densities of the composite, Ag 3 PO 4 (100) surface, and free-standing X-GR in the same configuration, respectively. Similar to the case of undoped composite, the strong charge accumulations in the four doped GR/Ag 3 PO 4 (100) composites are found just above the Ag atoms in the top layer, whereas the regions of charge depletion appear both on the lower side of the doped GR (facing the surface) just above the O atoms in the top layer and on the higher side of the Ag atoms in the top layer in the ground electronic state. It can be clearly seen from Figs 5 and 6 that the effects of dopants on the interface charge transfer are apparent. The relative order of the amount of charge transfer for the doped composites is found to be N C -GR/Ag 3 PO 4 (100) > S C -GR/Ag 3 PO 4 (100) > P C + V C -GR/Ag 3 PO 4 (100) > B C -GR/Ag 3 PO 4 (100). To offer quantitative results of charge redistribution, parts (c) of Figs 5 and 6 plot the planar averaged charge density difference These values are larger than those in the undoped GR/Ag 3 PO 4 (100) composite, indicating that the interaction between doped-GR sheets and Ag 3 PO 4 (100) surface becomes stronger due to doping. This can be further verified by the efficient electron accumulation above the doped GR sheets, which is more than that in the undoped GR/Ag 3 PO 4 (100) composite. A further charge analysis based on the Bader method can give the quantitative results of charge transfer between the two constituents, which are listed in Table 2. One can see that 0.39 electrons transfers from GR sheet to Ag 3 PO 4 (100), in agreement with the previous results 44 . However, the amount of charge transferred at the B C -GR/Ag 3 PO 4 (100) interface is 0.15 electron from B C -doped GR sheet to Ag 3 PO 4 , which is less than that at the GR/Ag 3 PO 4 (100) interface. The decreased amount of charge transferred in B C -GR/ Ag 3 PO 4 (100) is due to the longer average equilibrium distance of Ag 3 PO 4 (100) surface and the B C -doped GR sheet than that between Ag 3 PO 4 (100) surface and pure GR sheet (Table 1). Furthermore, the B atom has smaller electronegativity than C atom, leading to some electron transfers from former to latter in the GR sheet. On the contrary, the amounts of charge transferred in the other three doped GR/Ag 3 PO 4 (100) composite are larger than that in undoped GR/Ag 3 PO 4 (100) one, which may be related to their electronegativities and structural deformation of doped GR sheets. The underlying mechanism for different interface charge redistributions can be traced to the electrostatic potential distribution in the doped GR/Ag 3 PO 4 (100) composites. The profile of the planar averaged self-consistent electrostatic potential for these composite as a function of position in the z-direction is displayed in Figs 5 and 6(a,d). Similar to the case of undoped GR/Ag 3 PO 4 (100) composite, the periodic lattice potential in the Ag 3 PO 4 (100) lattice is clear although it has some distortion due to the atoms in the upper layers having a slight movement compared to their positions in bulk Ag 3 PO 4 . The higher potential near the doped GR sheets leads to a potential well formed at interfaces. The appearance of such a large built-in potential well can effectively hinder the recombination of photogenerated charge carriers in the doped GR/Ag 3 PO 4 (100) composite. During the photocatalytic process, photogenerated electrons migrated to the Ag 3 PO 4 (100) surface could be pumped to the doped GR sheets, resulting in the net efficient electrons accumulation at doped GR sheets, because the built-in potential is large enough to drive efficient charge separation in the composites. Among these dopants, substitutional N doping can push the plane of largest potential at the GR sheet to the Ag 3 PO 4 (100) surface, as shown in Fig. 5(d). The closer the largest potential gets to the Ag 3 PO 4 (100) surface, the higher the migration efficiency of electrons at the Ag 3 PO 4 (100) surface. These results partly offer a physical interpretation for the enhanced photocatslytic activities of the N-doped GR/semiconductor composites synthesized by experiments 13-18,21,22,24-26,55,56 . Optical Properties. To investigate the influence of dopants on the optical properties, we have calculated the absorption spectra of the undoped and doped GR/Ag 3 PO 4 (100)composites, as shown in Fig. 7. One can see, the undoped GR/Ag 3 PO 4 (100) composite has a significant absorption at a wide region from 300 to 800 nm. The remarkable feature of its absorption curve is three resonant-like peaks at about 300, 440, and 780 nm, which has been discussed previously 44 . As the impurity atom is doped into the GR sheet in the composites, the absorption curves have more than one resonant-like peak (three peaks for B C -and P C + V C -GR/Ag 3 PO 4 (100), four peaks for N C -and S C -GR/Ag 3 PO 4 (100) composites), due to the transitions between different energy levels. Compared to the undoped GR/Ag 3 PO 4 (100) composite, the weaker absorption intensity of the doped GR/Ag 3 PO 4 (100) composite at long wavelength range (λ > 600 nm) can be attributed to the change of the near-gap electronic structures caused by the dopants. Fortunately, the doped GR/Ag 3 PO 4 (100) composites have strong absorption in the UV and vis-light range (ranging from 300 to 600 nm) which is more importantly for the photocatalysis. In particular, the higher resonant-like peaks at about 400~440 nm, due to doping, are especially beneficial to enhance the photocatalytic performance of the doped GR/Ag 3 PO 4 (100) composites, according to the fact that the light with wavelength of ~440 nm might be the most appropriate visible light for generation of radical species in the GR/Ag 3 PO 4 (100) composite 39,44 . Figure 7 illuminates that the N C -GR/Ag 3 PO 4 (100) composite has excellent absorption, followed by P C + V C -GR/Ag 3 PO 4 (100) composite. Therefore, it can be concluded that doping with substitutional impurities into the GR sheet is an effective strategy to enhance the photocatalytic performance of the GR/Ag 3 PO 4 (100) composites.
We now propose, based on the above results, that the N atom may be one of the most appropriate dopants for the GR/Ag 3 PO 4 photocatalyst. Firstly, the N C -GR/Ag 3 PO 4 (100) composite can be easily prepared due to its lower formation energy (− 5.48 eV). Secondly, the N dopant results in the more stronger absorption in the UV and vis-light range, especially from 350-600 nm, which is one of the important factors for a high-efficiency photocatalyst. Thirdly, the C atoms bonded to N dopant become positively charged while the N dopant is negative in the N C -GR/Ag 3 PO 4 (100) composites. Those C atoms (the N dopant) with positive (negative) effective charge, as active sites, will facilitate the adsorption of some species with negative (positive) charges, thus enhancing the photocatalytic activity. Most importantly, the photocatalytic activity and stability of the GR/Ag 3 PO 4 (100) composite can be greatly improved by doping N atom in the GR sheet, owing to the fact that the highest potential plane will be pushed away from the GR sheet to the interface, thus promoting the migration of photogenerated electrons at the Ag 3 PO 4 surface. Fortunately, this proposal here can be largely demonstrated by the available experimental results about N-doped GR-semiconductor composites 13  Discussions Graphene has attracted considerable attention and has been the object of extensive study since its first successful synthesis in 2004 57-60 . We have first performed the first ab initio DFT calculations to explore the effects of dopants on the structural, electronic and optical properties, charge transfer at the interface formed between the B C -, N C -, S C -, and P C + V C -GR sheets and a Ag 3 PO 4 (100) surface in the context of stable vis-light photocatalyst. The band gap, near-gap electronic structure and interface charge transfer of the doped GR/Ag 3 PO 4 (100) composite can be tuned by the dopants. Moreover, the substitutional doping in the GR sheet plays an essential role in the absorption of vis-light, in the promotion of electrons to the CB, and in photoinduced electrons transfer to reducible adsorbates of doped GR/Ag 3 PO 4 (100) composites. We propose that the N atom may be one of the most appropriate dopants for the GR/Ag 3 PO 4 photocatalyst. This work provides the theoretical results to rationalize the available experimental results about N-doped GR-semiconductor composites, and enriches our understanding on the effect of dopants in the doped GR-based composites for developing high-performance photocatalysts.

Methods
Theoretical model. We construct a supercell (12.01 × 12.25 × 18 Å 3 ) of GR/Ag 3 PO 4 (100), a 5 × 6 single GR layer containing 60 carbon atoms sits on a 2 × 2 seven atomic layer stoichiometric Ag 3 PO 4 (100) surface (i.e., the most stable one among the low index surfaces) slab containing 64 atoms with three bottom layers fixed at bulk position. A 15 Å thick vacuum layer is above the GR sheet to avoid artificial interaction. The whole system (a,d) are for B C -and N C -GR/Ag 3 PO 4 (100) composites, respectively. The higher potential near the doped GR sheets leads to a potential well formed at interfaces. 3D charge density difference with an isovalue of 0.006 e/Å 3 : (b,e) are for B C -and N C -GR/Ag 3 PO 4 (100) composites, respectively. Blue and yellow is surfaces represent charge accumulation and depletion in the space. Planar averaged charge density difference as a function of position in the -direction: (c,f) are for B C -and N C -GR/Ag 3 PO 4 (100) composites, respectively. The charge difference shows that charge transfer occurs inversely from the Ag 3 PO 4 surface to GR and induces the electrostatic potential inverse at the interface.
contains totally 124 atoms with 736 valence electrons. To explore the dopant effects in the heterojunction, four substitutional dopants, B, C, S, and P, are chosen to substitute C atom of GR sheet. It should be pointed out that when one C atom is substituted by only a P atom, the deformation of doped GR sheet is very large, the vertical displacement of P atom more than 1.0 nm relative to the GR plane. This can be eliminated by removing one nearest neighbor C atom. Four doped GR/Ag 3 PO 4 (100) composites are: B C -GR/Ag 3 PO 4 (100) (B atom substituting C atom of GR), N C -GR/Ag 3 PO 4 (100) (N atom substituting C atom of GR), S C -GR/Ag 3 PO 4 (100) (S atom substituting C atom of GR), and P C + V C -GR/Ag 3 PO 4 (100) (P atom substituting C atom of GR and one neighbor C atom removed ). For comparison, undoped GR/Ag 3 PO 4 (100) composite are also studied.
Electronic structure calculation. The calculations are performed using the CASTEP code 61 based on first-principles DFT. The local density approximation (LDA) with inclusion of the vdW interaction is chosen because long-range vdW interactions are expected to be significant in these complexes. However, LDA has been known generally to underestimate the energy gap of semiconductor, resulting into an overestimate for photoinduced electrons transfer in photocatalytic process. To correct this band gap problem, all of the theoretical calculations are performed using the DFT/LDA+ U method implemented in the plane wave basis CASTEP code. We have performed extensive tests to determine the appropriate U parameters for Ag 4d states, which reproduced the Figure 6. Planar averaged self-consistent electrostatic potential as a function of position in the -direction: (a,d) are for S C -and P C + V C -GR/Ag 3 PO 4 (100) composites, respectively. The higher potential near the doped GR sheets leads to a potential well formed at interfaces. 3D charge density difference with an isovalue of 0.006 e/Å 3 : (b,e) are for S C -and P C + V C -GR/Ag 3 PO 4 (100) composites, respectively. Blue and yellow is surfaces represent charge accumulation and depletion in the space. Planar averaged charge density difference as a function of position in the -direction: (c,f) are for S C -and P C + V C -GR/Ag 3 PO 4 (100) composites, respectively. The charge difference shows that charge transfer occurs inversely from the Ag 3 PO 4 surface to GR and induces the electrostatic potential inverse at the interface.
Scientific RepoRts | 6:22267 | DOI: 10.1038/srep22267 correct energy gap (2.48 eV) for cubic Ag 3 PO 4 . The appropriate Hubbard U values for Ag 4d, O 2p, and P 3p are 7.2, 7.0, and 7.0 eV, respectively. The states of O: 2s 2 2p 4 , Ag: 4d 10 5s 1 , C: 2s 2 2p 2 , P: 3s 2 3p 4 , S: 3s 2 3p 4 , N: 2s 2 2p 3 , B: 2s 2 2p 1 , are treated as valence states. The plane wave cut off is set to 400 eV. The k mesh of 2 × 2 × 1 and 4 × 4 × 1 is respectively used for geometry optimizations and for calculating density of states using the Monkhorst-Pack scheme. In the geometrical optimization, the maximum ionic displacement is within 0.002 Å, and the total stress tensor is reduced to the order of 0.1 GPa. All geometry structures are fully relaxed until the convergence criteria of energy and force are less than 10 −6 eV/atom and 0.01 eV/Å, respectively.
Optical response. The strong light absorption is one fundamental premise for a high-efficiency photocatalyst except for a low recombination rate of photogenerated charge carriers and suitable redox potentials. For the semiconductor material, the dielectric function is mainly connected with the electronic response. The imaginary part ɛ 2 of the dielectric function ɛ is calculated from the momentum matrix elements between the occupied and unoccupied wave functions, given by 62 : where Ω, ω, u, ν, and c are the unit-cell volume, photon frequency, the vector defining the polarization of the incident electric field, valence bands, and conduction bands, respectively. The real part ε 1 of the dielectric function ε is evaluated from the imaginary part ε 2 by Kramer-Kronig transformation. The absorption coefficient ω I ( ) can be derived from ε 1 and ε 2 , as following: which depends on ε 1 and ε 2 and thus on the energy. All other optical constants can also be obtained. The relations above are the theoretical basis of band structure and optical properties, which reflected the mechanism of luminescence spectral caused by electronic transition between various energy levels. The inset of shows that the N C -and S C -GR/Ag 3 PO 4 (100) composites display strong absorption in the range 550 to 750 nm. The higher resonant-like peaks at about 400~440 nm, due to doping, are especially beneficial to enhance the photocatalytic performance of the doped GR/Ag 3 PO 4 (100) composites, according to the fact that the light with wavelength of ~440 nm might be the most appropriate visible light for generation of radical species in the GR/Ag 3 PO 4 (100) composite. The N atom may be one of the most appropriate dopants for the GR/Ag 3 PO 4 photocatalyst.