Introduction

Graphitic carbon nitride (g-C3N4) has been paid much attention because of its low cost, easy preparation, excellent biocompatibility, outstanding chemical and thermal stability, etc.[1, 2]. Nevertheless, the photocatalytic efficiency of g-C3N4 is restricted by its low light absorption efficiency, slow charge mobility and fast electron–hole recombination rate [3]. Doping is an effective way to organize the electronic features of semiconductors [1]. Experimentally, the 3d transition metal (TM) elements (Ti [4, 5], V [6], Cr [7], Mn [8], Fe [1, 8,9,10,11,12,13,14,15,16,17], Co [8, 13, 15, 18,19,20], Ni [21], Cu [8, 9, 15, 22, 23] and Zn [8, 16, 24, 25]) have been extensively explored over years [4]. Theoretically, Ghosh et al. [26] have calculated the structures and electronic and magnetic attributes of the 3d TM substituting for g-C3N4 sheet. However, precise identification of the available active sites of g-C3N4 has not been explored [27] because E. Kroke have revealed gh-C3N4 is more stable than gt-C3N4 by the density functional theory (DFT) [28]. In the current work, the primitive cell (C6N8) of the gh-C3N4 is abstract and then the 3d TM atom substituting the C atoms of the C6N8 clusters is considered. Ma et al. [29] have revealed that metal doping could reduce the energy gap of g-C3N4 by DFT calculations. If 3d TM substituted will reduce the energy gap of the C6N8 clusters? The TM atom substituting can modulate the electronic and magnetic properties of materials. It plays a crucial role in the diluted magnetic semiconductors [30]. So the structures, stability and electronic and spin properties of the TMC5N8 clusters are calculated by using DFT. It is very important to prepare the novel C3N4-based materials.

Computational details

The C6N8 clusters are abstract by the primitive cell of gh-C3N4 in Ref. [28]. And then, the TMC5N8 clusters are created by substituting a C atom for the C6N8 clusters by a TM atom. Hypothetical constructions of the TMC5N8 clusters must be optimized. The optimized process and properties calculations are performed by DFT which are embedded in the DMol3 package. The Perdew–Burke–Ernzerhof (PBE) functional (including a semiempirical van der Waals (vdW) correction) within the generalized gradient approximation (GGA) is selected for the exchange–correlation [26, 31]. Due to the strong interaction between the TM atoms and the N atoms [32], Coulomb exclusion U must be considered [33]. To avoid missing the lowest-energy structures, symmetry unconstraints must be adopted [34, 35]. All electron relativistic treatments are selected due to the electron relativity effects of the TM atoms [36]. Spin polarization is chosen because certain TM atoms possess high spin values [35]. Double numerical plus polarization (DNP) is adopted [37]. Furthermore, the Mülliken population analysis is executed to get the electronic and spin characteristics of the TMC5N8 clusters [35].

In order to confirm whether the substituting can improve the structural stabilities of the TMC5N8 clusters, the average binding energy (Eb) of them was calculated [35]:

$$E_{b1} = [E({\text{TM}}) + 5E({\text{C}}) + 8E({\text{N}}) - E({\text{TMC}}_{5} {\text{N}}_{8} )]/14$$
(1)

where E(TM), E(C) and E(N) present the energy of the single TM, C and N atoms, respectively. E(TMC5N8) is the total energy of the TMC5N8 clusters.

To determine the feasibility of the PBE functional considered, the calculated distance (6.840 Å) between two nitride pores is compared with the experimental result (6.81 Å) [38]. And the calculated lattice constant (7.138 Å) of gh-C3N4 agrees well with the computational values (7.13 Å [39] and 7.14 Å [40]) and the experimental result (7.13 Å [41]). Therefore, the PBE functional is adopted to analyze the TMC5N8 clusters.

Results and discussion

Structures

Optimized configurations of the TMC5N8 clusters are shown in Fig. 1. The C atoms are described as gray balls, the N atoms are described as blue balls, and the TM atoms are described as other balls. As for the TMC5N8 clusters, the planar structure of the C6N8 clusters is distorted to different degrees. It is derived that the TM atoms can increase the coupling between the unoccupied molecular orbitals (UMOs) with occupied molecular orbitals (OMOs), which leads to pseudo-Jahn–Teller (PJT) distortion and the characteristic buckling [42]. 3d atoms prefer to substitute the C atom which is farthest away from the biasing N atom. However, TM atoms substitute the C atom which approaches the biasing N atom of the C6N8 clusters. The isomers (c) are the most unstable structures. All the structures of the TMC5N8 clusters inherit those of the C6N8 clusters except for the ZnC5N8 clusters. The radius of the TM atoms are larger than that of the substituted C atoms. It results in the C1 symmetry. As for significant distortion of the ZnC5N8 clusters, it derives from the d-p repulsion interaction between the 3d orbital electrons of the Zn atom and the 2p orbital electrons of the N atoms [24]. Wang et al. [2] have pointed out the pore diameter of Zn doped C3N4 has increased compared with g-C3N4 by the BET analysis. It attributes to the aggregate effect of Zn-N bond [2]. Our calculated TMC5N8 clusters indeed undergo an obvious deformation.

Fig. 1
figure 1

Structures and charges of the C6N8 and TMC5N8 clusters. (Color figure online)

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Stability

The average binding energies Eb of the TMC5N8 clusters are plotted in Fig. 2. The chemical element symbols which are corresponding to the abscissa are shown in Fig. 2. Due to the more negative binding energy, the more stable the structure, compare the average binding energy Eb of the C6N8 clusters, it can be found that all the TM substituting reduces the structural stability of the C6N8 clusters except for ScC5N8, TiC5N8 and VC5N8. It means that the TM atoms prefer to segregate and then aggregate TM clusters [26]. From Fig. 2, it can also be found that the ground-state TMC5N8 clusters have slightly more structural stability than the other isomers. Oh et al. [15] have pointed out C3N4 is thermally stable up to 500 °C by the thermogravimetric analysis. However, once the temperature is further increased, the binding will weaken because of thermal fluctuation [43]. As for the TMC5N8 clusters, the abnormal stretching in the C6N8 clusters due to the TM substituting will cause the fracture of the C-N bond at a lower temperature. TM atoms will promote the transition of the quasi-planar structures into 3D-cluster-like structures [44]. Xiong et al. [45] have found the nano-structural transformation from graphitic-like CNx to fullerene-like β-C3N4 with the increase in the temperature by TEM observation and blue-shift photoluminescence peaks. However, the cross-link effect of Zn between inter-layers obstructs the exfoliation of g-C3N4 [2].

Fig. 2
figure 2

Average binding energies of the TMC5N8 clusters

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The energy gaps between the highest occupied molecular orbital (HOMO) states and the lowest unoccupied molecular orbital (LUMO) states of the TMC5N8 clusters which can analyze the chemical reaction process are shown in Fig. 3. The calculated HOMO–LUMO gap (0.694 eV) of the C6N8 clusters is much narrower than the experimental value (2.7 eV) of C3N4. Zhu et al. [39] have also revealed that the band gap (1.24 eV) in monolayer CN is smaller than the experimental value above. It is not only the well-known shortcomings (the lower exchange correlation between electrons) of the GGA functional, but also the difference between the systems. The larger HOMO-LUMO gap, the higher kinetic stability. Compare the energy gap of the ground-state TMC5N8 clusters, it indicates that the TM substituting can improve the kinetic stability of the C6N8 cluster except for Ti, Cr and Cu. Ding et al. [4] have found a slightly red shift from 465 to 467 nm due to Ti-doped the pristine C3N4 by the photoluminescence emission spectrum, which confirm to the narrowed band-gap by Ti doping. As for the isomers (a), only the Sc, Fe, Co and Ni substituting can improve the kinetic stability of the C6N8 clusters. Zhu et al. [39] have pointed out the 3d electrons of the doped Co have an excellent contribution to the reduction in the band gap of Co-CN by the characterization and density functional theory (DFT). As for the isomers (b), only the Sc, Fe, Ni and Zn substituting will improve the kinetic stability of the C6N8 clusters. Oh et al. [15] have observed that Fe has a relatively stronger coordination interaction with g-C3N4 than Co and Cu by the XRD peak shifting. As for the isomers (c), only the Sc, Mn and Zn substituting will increase the kinetic stability of the C6N8 clusters. It is derived that these TM atoms are quite appropriate for the “nitrogen pots” characteristic which possesses six lone-pair electrons [1]. From another perspective, the Ti, Cr and Cu substituting significantly improves the kinetic activity of the C6N8 clusters. As for the isomers (a), only the Ti, Mn and Cu substituting improves the kinetic activity of the C6N8 clusters. As for the isomers (b), only the Ti, Cr, Co and Cu substituting improves the kinetic activity of the C6N8 clusters. As for the isomers (c), only the Ti, Cr, Fe and Cu substituting improves the kinetic activity of the C6N8 clusters. It is because of the hybridization between d orbitals of the TM atoms and p orbitals of the C6N8 clusters [26]. Further, the TM atoms lead to the strengthening of the vibronic coupling in the OMO-UMO pairs. The vibrational instability leads to the planar C6N8 clusters transfer to the puckered TMC5N8 structures [42]. The TMC5N8 clusters which possess metal-like dense electronic density of states will lead to non-adiabatic instability for the C3N4 [46].

Fig. 3
figure 3

The HOMO–LUMO gaps of the TMC5N8 clusters

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To further understand the effect of the TM atom substituting for the C6N8 clusters, the HOMO and LUMO states of the ground-state TMC5N8 clusters are demonstrated in Table 1. The blue regions prefer to trap electrons, and the yellow regions prefer to release electrons. It is shown that for the majority of the TMC5N8 clusters, the HOMO and LUMO states have evident hybridization between the 3d orbital electrons of the TM atoms and the 2p orbital electrons of the N atoms, while for the ZnC5N8 clusters, the hybridization effect is rare because the Zn atoms are the 3d10 systems which contain all paired d orbital electrons [26].

Table 1 The HOMO and LUMO orbitals of the ground-state TMC5N8 clusters
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Electronic properties

The net charges of the TM atoms for the TMC5N8 clusters are displayed in Fig. 4; it can be found that for the ground-state TMC5N8 clusters, the TM atoms loss a small amount of electrons within the scope of 0.375 |e| and 0.931 |e| except for Sc loss 1.150 |e|. Charge transfer of Co and CN molecules has been confirmed by Raman enhancement factors [39]. Zhu et al. [39] have also found that the three N atoms gain 1.03|e| on average, while Co atom loses 0.94|e| through the Bader analysis. As for the differences in the net charges of TM atoms for the TMC5N8 isomers in Fig. 4 and the Mülliken charges of the C and N atoms for the TMC5N8 clusters in Fig. 1, it is derived that the atomic coordination number [47] and atomic arrangements [48] of the TMC5N8 clusters affect the electron transferred at a certain level.

Fig. 4
figure 4

The net charges of the TM atoms for the TMC5N8 clusters

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The natural electron configurations of the ground-states TMC5N8 clusters are included in Table 2. Comparing the natural electron configurations (Sc: 3d14s2, Ti: 3d24s2, V: 3d34s2, Cr: 3d54s1, Mn: 3d54s2, Fe: 3d64s2, Co: 3d74s2, Ni: 3d84s2 Cu: 3d104s1 and Zn: 3d104s2) of the isolated TM atoms with those of the TM atoms for the TMC5N8 clusters in Table 2, it can be found that the 3d and 4p orbitals of the TM atoms acquire a few electrons. In contrary, the 4s orbital of the TM atoms loses a small amount of electrons. It further confirms the hybridization mechanism of the sp orbital electrons of the TM atoms in the TMC5N8 clusters. Zhu et al. [39] have found that the 3d electrons of the Co atom and 2p electrons from the nearest neighboring N are hybrid by the XPS analysis.

Table 2 Natural electron configurations of the TM atoms for the ground-state TMC5N8 clusters
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Magnetic properties

Incorporation of spin-polarized 3d TM atoms in the g-C3N4 systems is an effective method to adjust spin moment [26]. The spin values of TM atoms in the TMC5N8 clusters are shown in Fig. 5. It can be found that for the TM atoms in the TMC5N8 clusters, all the spin densities are lower than those for isolated TM atoms in Ref. [36], and it is mainly derived from the origin of different kinds of magnetic couplings in these planar sheets can be understood by considering the spatial arrangement of interacting magnetic orbitals [26]. And the spin directions of the N atoms are opposite to that of the TM atoms [26]. As for the ground-state TMC5N8 clusters, the maximum spin values of the TM atoms occurred in Mn and Ni. It is derived that the 3d orbitals of Mn display strong spin exchange splitting εd [49], while for Cu and Zn atoms they display the non-magnetic states due to the all paired d orbital structures [26]. As for SpinMn > SpinFe > SpinNi > SpinCo, it is derived that the minority spin gaps Emin decreased as the numbers of 3d electrons increased [49]. As for the discrete spin values of these TMC5N8 isomers, it derives from the spatial arrangements of interacting magnetic orbitals [26]. D. Ghosh et al. [26] have also pointed out that the V, Cr and Fe atoms interact with the g-C3N4, which exhibits ferromagnetic states.

Fig. 5
figure 5

The spins of the TM atoms for the TMC5N8 clusters

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Conclusions

In summary, the structures and electronic and spin properties of the 3d TMC5N8 clusters have been calculated by using first-principles. The results reveal that the Zn atoms can significantly distort the C6N8 clusters. 3d TM atoms prefer to substitute the C atom which is farthest away from the biasing N atom except for ScC5N8, TiC5N8 and VC5N8 by the average binding energy. The TM substituting significantly reduces the structural stability of the C6N8 clusters by the average binding energy. As for the ground-state TMC5N8 clusters, the TM substituting improves the kinetic stability of the C6N8 clusters except for Ti, Cr and Cu by the HOMO–LUMO gaps. From the net-charge distribution of the TMC5N8 clusters, it can be found that the TM atoms loss a certain amount of electrons and a few 4s orbital electrons of TM atoms transferred to the N atoms. The maximum spin values of the TM atoms occur at Mn and Ni for the TMC5N8 clusters by the Mülliken population analysis.