Predictions on Structural and Electronic Properties to Synthesize Bismuth-Carbon Compounds in Different Periodicities

This work was carried out to explore the compounds of bismuth with carbon using density functional theory (DFT)-based computations. The structures of the compounds BiC, BiC2, BiC3, Bi2C3, BiC5, and Bi2C5 were predicted at a generalized gradient approximation (GGA-PBE) level of theory. The calculations were carried out on the structures in unit cell and supercell geometries in slab and bulk periodicities. The structural and electronic properties of the mentioned compounds were investigated in detail. The calculations of the structures revealed lattice constants of the compounds for cubic unit cell as 212.2 pm for BiC, 176.9 pm for BiC2, 240.5 pm for BiC3, 232.4 pm for Bi2C3, and 354.5 pm for Bi2C5. The compounds BiC, BiC2, BiC3, BiC5, and Bi2C5 were found to be metallic, whereas Bi2C3 exhibited semiconducting character with a band gap of 0.305 eV. This work provides an initial framework for preparing new 2D materials from BixCy.


Introduction
The theoretical predictions to synthesize new materials have been on prime focus in computational material science [1][2][3][4][5][6][7]. The preparation of metal-carbon compounds has recently attained significant research interest, due to their far-reaching applications [8,9]. There are several compounds of Bi that have been reported and found suitable for different applications. An orthorhombic crystal system Bi 2 S 3 in one dimension has been reported to be an n-type semiconductor material with a band gap of 1.2 eV and found suitable for optoelectronic devices [10]. Bi 2 Se 3 is a 2D material belonging to the P-3m1 space group having a band gap of 1.42 eV and, hence, can be used for optoelectronic, photo catalytic, and photovoltaic applications [11]. Bi 2 Se 3 shows the topological insulating behavior, which can be tuned by strain in the structure [12]. The bulk BiI 3 with hexagonal structure has been reported with a band gap 1.57 eV [13]. BiP is a 2D material with a band gap of 0.92 eV having applications in ferro-electric gadgets [14]. BiP 3 is also a 2D material having monoclinic and trigonal symmetries with a band gap of 1.36 eV, which is favorable for photo-catalytic usage [15]. InBi is a 2D material with a band gap 0.35 eV, whose structural symmetry shows a resemblance to hexagonal lattice [16]. BiOX (X = Br, I, Cl) is a class of materials in which BiOI and BiOCl are 3D, while BiOBr has 2D periodicity with band gap in ranges from 1.85 eV to 3.44 eV [17]. PdBi 2 is a 2D material that has a tetragonal symmetry with a band gap of 1.53 eV and was found suitable for catalytic application [18]. The series

Computational Detail
The entire calculations were based on DFT computations, which were carried out using the linear combination atomic orbital (LCAO) scheme employed in ADF-BAND code [37]. The Bi-C compounds reported herein have not been reported yet, due to which, no structure files are available. These structures were manually prepared starting from simple BiC unit cell to successively extending to increase in Bi and C atoms in the structures by allowing for complete structural relaxation. The unit cell of BiC contains one Bi and one C atom, while the 2 × 2 super cell of BiC contains four Bi atoms and four C atoms. The unit of BiC 2 contains 1 Bi atom and 2 C atoms, while the 2 × 2 super cell slab of BiC 2 contains 8 Bi atoms and 16 C atoms. The unit of BiC 3 contains 1 Bi atom and 3 C atoms, while 3 × 3 super cell of BiC 3 contains 8 Bi atoms and 24 C atoms. The unit of Bi 2 C 3 contains 2 Bi atoms and 3 C atoms, while the 2 × 2 super cell of Bi 2 C 3 contains 8 Bi atoms and 12 C atoms. The unit of Bi 2 C 5 contains 2 Bi atoms and 5 C atoms, while the 3 × 3 super cell of Bi 2 C 5 contains 18 Bi atoms and 45 C atoms. The 2 × 2 super cell of BiC 5 contains 9 Bi atoms and 45 C atoms.
The geometries of the unit cells and supercells were fully optimized to obtain relaxed structures. The maximum Cartesian step allowed for the convergence of geometry is 1 × 10 −3 Å. The convergence criteria for energy was 10 −5 eV. The maximum RMS gradient allowed was 6.66 × 10 −4 Hartree/Å. For the optimizations of structure, the quasi-Newton model was used. The optimized parameter considered in this method is the Hessian update method, which is based on the BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm. All the basic functions were confined to a radius of 10 Bohr. The calculations were carried out at a generalized gradient approximation with Perdew-Burke-Ernzerhof (GGA-PBE) level of theory [38] and triple zeta polarization (TZP) basis sets were employed. In order to investigate the bi-layered materials, D3 correction offered by Grimme was included to count the interlayer van der Waals interactions [39]. Considering presence of Bi, the scalar relativistic effects ZORA (zeroth order regular approximations) were included.

Results and Discussion
The results obtained to investigate the structural and electronic properties of the entire series of Bi-C compounds are described below.

Structural Properties (A) Unit Cell of BiC
The converged geometry of the BiC unit cells in 2D slab and 3D bulk periodicity is given in Figure 1. In case of 2D structure, the Bi-C bond length appeared as 212.2 pm, whereas the bond energy was equal to −6.41 eV. The Hirshfeld charge analysis revealed that the net atomic charge on Bi was 0.321 e, and on C it was −0.321 e. On the other hand, the bond length Bi-C for 3D structure was found to be 212.1 pm. The computed results reveal that bond energy was −6.39 eV, the Hirshfeld charge on Bi was 0.316 e and on C was −0.316 e. The computed values pointed out that the charge on Bi appeared positive, whereas it was negative on C atoms. This finding points to the fact that Bi appeared cationic, whereas C was anionic in nature in the Bi x C y compounds, which agrees with the literature [40]. The transfer of charge from the Bi to C atoms, in the case of Bi-doped graphene, has been reported [41].

(B) Super Cell of BiC
The optimized geometry of the BiC supercell is shown in Figure 1. In the case of 2D, the values of the bond lengths Bi = Bi and Bi-C appeared as 300 pm and 212.2 pm, respectively, whereas the dihedral angles C-Bi-C or Bi-C-Bi were 90 • and Bi-Bi-C is 45 • . The bond energy for this material was −81.66 eV, whereas the Hirshfeld charges on Bi and C were 0.214 e and −0.214 e, respectively. On the other hand, in the case of the 3D supercell of BiC, the values of the bond lengths appeared as Bi=Bi at 300 pm in the intra-layer with bond order 2.0 and Bi-Bi at 359 pm for the interlayer. The bond length Bi-C was 226.3 pm with bond orders of 1 and 1.5, pointing to an aromatic bond, whereas the C-C bond length was 331.2 pm. The value of the dihedral bond angle varied from 89.7 • to 89.8 • for the Bi-C-Bi arrangement of atoms. The bond energy for this material was −52.29 eV, and the Hirshfeld charges on Bi and C were 0.327 e and −0.327 e, respectively. The computed values pointed out that the charge on Bi appeared to be positive, whereas it was negative on the C atoms. This finding points to the fact that Bi appeared to be cationic, whereas C was anionic in nature, which agrees with the literature [40].

(B) Super Cell of BiC
The optimized geometry of the BiC supercell is shown in Figure 1. In the case of 2D, the values of the bond lengths Bi = Bi and Bi-C appeared as 300 pm and 212.2 pm, respectively, whereas the dihedral angles C-Bi-C or Bi-C-Bi were 90° and Bi-Bi-C is 45°. The bond energy for this material was −81.66 eV, whereas the Hirshfeld charges on Bi and C were 0.214 e and −0.214 e, respectively. On the other hand, in the case of the 3D supercell of BiC, the values of the bond lengths appeared as Bi=Bi at 300 pm in the intra-layer with bond order 2.0 and Bi-Bi at 359 pm for the interlayer. The bond length Bi-C was 226.3 pm with bond orders of 1 and 1.5, pointing to an aromatic bond, whereas the C-C bond length was 331.2 pm. The value of the dihedral bond angle varied from 89.7° to 89.8° for the Bi-C-Bi arrangement of atoms. The bond energy for this material was −52.29 eV, and the Hirshfeld charges on Bi and C were 0.327 e and −0.327 e, respectively. The computed values pointed out that the charge on Bi appeared to be positive, whereas it was negative on the C atoms. This finding points to the fact that Bi appeared to be cationic, whereas C was anionic in nature, which agrees with the literature [40].

(C) Unit Cell of BiC2 in 2D and 3D
The unit cell of BiC2 is shown in Figure 1. The computed values of bond length Bi-C for the 2D unit cell was between 176.9 pm for one carbon atom and 254.4 pm for the other. The bond angle between the Bi and C in arrangement of Bi-C-Bi was 93.8°. The Hirshfeld charge analysis showed that the net atomic charge on Bi was 0.515, and it was −0.257 e on both C atoms. In case of the BiC2 unit cell in the 3D the bond length, Bi-C was 176.7 pm for one carbon and 254.6 pm for the other one. The bond angles in arrangements such as C-Bi-C and Bi-C-Bi were 90.5° and 53.8°, respectively. The Hirshfeld charge analysis show that the net charge on Bi was 0.510, while on every C atom its value was −0.255 e. The

(C) Unit Cell of BiC 2 in 2D and 3D
The unit cell of BiC 2 is shown in Figure 1. The computed values of bond length Bi-C for the 2D unit cell was between 176.9 pm for one carbon atom and 254.4 pm for the other. The bond angle between the Bi and C in arrangement of Bi-C-Bi was 93.8 • . The Hirshfeld charge analysis showed that the net atomic charge on Bi was 0.515, and it was −0.257 e on both C atoms. In case of the BiC 2 unit cell in the 3D the bond length, Bi-C was 176.7 pm for one carbon and 254.6 pm for the other one. The bond angles in arrangements such as C-Bi-C and Bi-C-Bi were 90.5 • and 53.8 • , respectively. The Hirshfeld charge analysis show that the net charge on Bi was 0.510, while on every C atom its value was −0.255 e. The computed values pointed out that the charge on Bi appeared positive, whereas it appeared negative on C atoms. This finding points to the fact that Bi appeared cationic, whereas C was anionic in nature, which agrees with the literature [40].

(D) Super Cell of BiC 2 in 2D and 3D
We designed multiple super cells of BiC 2 as 2 × 2 slab, 2 × 2 bilayer-slab, 4 × 4 monolayer slab, and 4 × 4 bilayer slab. The computed results revealed that the bond length Bi=Bi was 300 pm, with bond orders of 2.0 and 3.0, whereas the values of the bond lengths of C-C were 145.4 pm and 150 pm, with a bond order 1.0. The bond length Bi-C is in range 409-409.2 pm, whereas dihedral bond angles of Bi-Bi-Bi and C-C-C were 90 • and its 79.4 • , respectively. In the case of an optimized structure of a BiC 2 super cell, the results show that the bond length Bi-Bi was 300 pm with bond order 1.0, whereas Bi-C was 254.8 pm with the bond order 1.0. The bond angle of Bi-Bi-Bi was 90 • , and Bi-C-Bi was 45.8 • . The Hirshfeld charges on the Bi and all C atoms were 0.541 e and −0.270 e, respectively. The computed values pointed out that charge on Bi appeared positive, whereas it was negative on C atoms. This finding points to the fact that Bi appeared cationic, whereas C was anionic in nature, which agrees with the literature [40].
In case of the 4 × 4 monolayers in 2D and 3D, the values of the bond lengths, bond orders, and bond angles appeared to be the same. The bond angle of the Bi-Bi was 300 pm with bond order 1.0, whereas the bond lengths of Bi-C were 177.2 pm and 245.6 pm. The bond length C-C was 111 pm with bond order 1.0. The bond angle Bi-C-Bi was 115.7 • , whereas the bond angle Bi-C-C or C-C-Bi was found to be 122.2 • . The bond angle Bi-Bi-C or C-Bi-Bi was 32.2 • . The Hirshfeld charge on Bi and C was 0.549 e, and C was −0.274 e. The computed values pointed out that charge on Bi appeared positive, whereas it was negative on the C atoms. This finding points to the fact that Bi appeared cationic, whereas C was anionic in nature.
In the case of the 4 × 4 bilayer, the bond angle Bi-Bi was 300 pm with the bond orders 1, 1.5, and 2. The bond length Bi-Bi was also 524.8 pm, whereas Bi-C appeared as 177.2 pm and 245.6 pm. The bond length C-C was 111.4 pm with bond order 1.0. The bond angle of Bi-Bi-Bi was 90 • , whereas its value for Bi-C-C or C-C-Bi appeared as 122.2 • . The bond angle also had a value of 57.8 • in the Bi-C-C arrangement.
In case of the 4 × 4 bilayer in the slab, the bond angle, bond order, and bond angle were almost same for both layers. The bond of Bi-Bi was 300 pm with bond orders such as 1.5, 2, and 3. The bond lengths for Bi-Bi were found to be 714.2 pm and 804.5 pm, while the bond lengths for Bi-C were 285.2 pm and 286.3 pm with a bond order of 1.5. The bond lengths between C-C were 157.5 pm and 142.5 pm with bond order 1.5. The bond angle Bi-Bi-Bi was 90 • , while its values for Bi-C-C or C-C-Bi were found to be 73.6 • , 105.9 • , and 106.1 • . The bond energy of the 4 × 4 bilayer slab material was −532.49 eV.

(E) Unit cell of BiC 3
The optimized structure of the unit cell of BiC 3 is given in Figure 1. The unit cell of BiC 3 in 2D exhibited bond lengths for Bi-C of 240.5 pm and for C-C of 143.5 pm. The bond angle between the Bi and C in the arrangement of Bi-C-C was 131.1 • , and for C-C-C the bond angle was 57.2 • . The bond energy for this material was −24.53 eV, whereas Hirshfeld charge analysis revealed that the net atomic charge on Bi was 0.132 e, while on one C its value was −0.142 e. The computed values pointed out that the charge on Bi appeared to be positive, whereas it was negative on C atoms. This finding points to the fact that Bi appeared cationic, whereas C was anionic in nature, which agrees with the literature [40,41]. In the case of the BiC 3 unit cell in 3D, the bond length Bi-C was 226.6 pm, with a bond order of 1.0, while a bond length of C-C was 133.3 pm. The bond angles Bi-C-C had values of 84.3 • and 120.1 • , while the bond angle of C-C-C was 90.9 • . The bond energy of the material was −84.61 eV.

(F) Super Cell of BiC 3
We designed multiple super cells of BiC 3

(G) Unit Cell of Bi 2 C 3
The unit cell of Bi 2 C 3 was modeled in 2D and 3D. In the case of the 2D unit cell, Bi-C had bond lengths values of 218.9 pm and 232.4 pm. The bond length C-C was 134.8 pm for one C atom and 170.4 pm the other C atom. The bond angles Bi-C-Bi had two values, 110.5 • and 136.7 • , while C-C-C had a value of 115 • . The bond energy was −28.45 eV, whereas the Hirshfeld charges on two Bi atoms were 0.121 e and 0.161 e, while on C, the charge values were −0.018 e, −0.091 e, and −0.173 e. The computed values pointed out that charge on Bi appeared positive, whereas it appeared negative on the C atoms. This finding points to the fact that Bi appeared cationic, whereas C was anionic in nature. In the case of the 3D unit cell of Bi 2 C 3 , the value of bond length Bi-Bi was 212.6 pm, while bond length Bi-C had five different values, i.e., 180.1 pm, 198 pm, 198.1 pm, 226.7 pm, and 283.1 pm. The bond length C-C was 179.7 pm with the bond order 1.0. The bond angle Bi-Bi-C had three values, 66.9 • , 91.9 • , and 120.9 • . The bond angle for C-C-Bi had a value of 63 • , while its value for Bi-C-C was 56.1 • . The Hirshfeld charge analysis shows that the net atomic charge on two Bi were the same, i.e., 0.464 e, and two C atoms had the same charge, i.e., −0.313. e, and on the third carbon, it was −0.302 e.

(H) Super Cell of Bi 2 C 3
The optimized structure of a super cell of Bi 2 C 3 in 2D is shown in Figure 1 The computed values pointed out that the charge on Bi appeared to be positive, whereas it appeared to be negative on the C atoms. This finding points to the fact that Bi appeared cationic, whereas C was anionic in nature, which agrees with the literature [40,41].
The super cell of Bi 2 C 3 was also optimized in 2D for monolayer and bilayer slabs. The computed results revealed that the bond length of Bi-Bi was 394.1 pm. The bond length of Bi-C had four values, which were 218. The computed values pointed out that the charge on Bi appeared to be positive, whereas it appeared to be negative on C atoms. This finding points to the fact that Bi appeared cationic, whereas C was anionic in nature. Now, we discuss the 10 × 10 mono-layered and bi-layered slabs of Bi 2 C 3 in 2D. First, we discuss the 10 × 10 slab of Bi 2 C 3 , for which the computed results revealed the bond length of Bi-Bi as 300 pm, with bond orders of 1. The computed values pointed out that the charge on Bi appeared positive, whereas the charge appeared negative on C atoms. This finding points to the fact that Bi appeared cationic, whereas C appeared anionic in nature.

(J) Unit Cell of Bi 2 C 5
The unit cell of Bi 2 C 5 was optimized in 2D and 3D. In the case of the 2D unit cell of

(K) Super Cell of Bi 2 C 5 in 2D
The super cell of Bi 2 C 5 was optimized in 2D, as shown in Figure 1 atoms. This finding point to the fact that Bi appeared cationic, whereas C was anionic in nature, which agrees with the literature [40,41]. The optimized values of the lattice constant, angles, area of slabs, volume of bulk cells, and structural symmetry of the studied compounds are given in Table 1.

Electronics Properties (A) Unit Cell of BiC
The total density of states (TDOS) and partial density of states (PDOS) calculated for BiC unit cell in 2D periodicity are given in Figure 2.
The analysis of TDOS indicated the major contribution of the Bi states in the formation of valence band maxima (VBM), conduction band minima (CBM), and conduction band (CB), whereas the lower and deep parts of the valence band (VB) comprised the main involvement of the C states. Bi and C, with the respective valence shell configurations 6s 2 6p 3 and 2s 2 2p 2 , are responsible for electronic structure of their compounds. Considering the electronic configurations, the calculated partial DOS involving the s and p states of the compounds are shown and analyzed. The observation of the s-DOS near the Fermi level revealed the greater contribution of Bi-s states in the valence band (VB), as well as in the conduction band (CB), in comparison to that of than of C-s states. However, in the case of the p-states, the trend was different, as the contribution of the Bi-p states dominated in CB, whereas those of the C-p states were higher in the VB. The involvement of both Bi-p, with C-p as the majority, and Bi-s, with C-s as the minority, states at the Fermi level were found, which points to the role of the sp hybrid states in the transport properties of compound BiC. The mentioned electronic structure indicated the metallic nature of BiC. The unit cell of BiC was periodically extended in 3D to examine the electronic properties of the materials. The calculated DOS are given in Figure 2. , in comparison to that of than of C-s states. However, in the case of the p-states, the trend was different, as the contribution of the Bi-p states dominated in CB, whereas those of the C-p states were higher in the VB. The involvement of both Bi-p, with C-p as the majority, and Bi-s, with C-s as the minority, states at the Fermi level were found, which points to the role of the sp hybrid states in the transport properties of compound BiC. The mentioned electronic structure indicated the metallic nature of BiC. The unit cell of BiC was periodically extended in 3D to examine the electronic properties of the materials. The calculated DOS are given in Figure 2. Now, we are going to discuss the electronic properties of the BiC unit cell in 3D, as per calculated DOS given in Figure 2. The material remained metallic in nature; however, the composition of the states in the formation of the electronic structure changed. The observation of the s-DOS indicated that the Bi-s states dominated in CB, but the C-s states showed a comparatively major contribution in the VB. Contrary to the 2D case, the comparison of p-DOS revealed that the C-p states showed a greater contribution in VB, near the Fermi level and in the top portion of the CB. The comparison of TDOS indicated major parts of the C states in the formation of VB and CBM, as well as a Fermi level opposite of the 2D unit cell of BiC. However, the presence of sp hybrid states at the Fermi level were still observed in this case.
The TDOS of 2 × 2 supercell in 2D (Figure 3) indicated the dominance of the C states in VB, Fermi level, and CBM, whereas the Bi states mainly contributed to the formation of deep CB, which showed deviation in behavior, when compared with the 2D unit cell of the material. The partial DOS points to major contribution of the C-p states and minor role of the Bi-p states, whereas the involvement of the s-states was very small. The material remained metallic in nature, with the involvement of sp hybrid states at the Fermi level. The 2 × 2 × 2 supercell of the material in 3D still showed a metallic nature, with major contributions of C-p states in the formation of VB at Fermi level and CBM, whereas the Bi-p states were dominant in the CB. states in VB, Fermi level, and CBM, whereas the Bi states mainly contributed to the formation of deep CB, which showed deviation in behavior, when compared with the 2D unit cell of the material. The partial DOS points to major contribution of the C-p states and minor role of the Bi-p states, whereas the involvement of the s-states was very small. The material remained metallic in nature, with the involvement of sp hybrid states at the Fermi level. The 2 × 2 × 2 supercell of the material in 3D still showed a metallic nature, with major contributions of C-p states in the formation of VB at Fermi level and CBM, whereas the Bi-p states were dominant in the CB.

(B) Unit Cell of BiC 2
The TDOS and PDOS calculated for unit cell of BiC 2 in 2D are given in Figure 4. The comparison of s-PDOS revealed the major contribution of the Bi-s states in the formation of VBM at Fermi level and the CB. On the other hand, the Bi-p states dominated, in comparison to that of C-p states, when TDOS or all PDOS were taken into account. The material was metallic in nature, with the sp hybrid states at the Fermi level. In the case of the BiC 2 unit cell in 3D, the material was still metallic, with a comparative DOS and dominance of the p-states from both the Bi and C at the Fermi level. The contribution of the Bi-p states was rich in deep CB and deep VB, whereas the C-p states were bit higher at the Fermi level, as well as for VBM and CBM. The calculated DOS for the 2 × 2 supercell of BiC 2 indicated the dominance of the p states in the electronic structure of the material, in such a way that the Bi-p states and the C-p states were rich in VBM ( Figure 5). Both the Bi-p and C-p states equally contributed at the Fermi level, whereas the role of the Bi-s and C-s states were negligibly small. at the Fermi level, as well as for VBM and CBM. The calculated DOS for the 2 × 2 supercell of BiC2 indicated the dominance of the p states in the electronic structure of the material, in such a way that the Bi-p states and the C-p states were rich in VBM ( Figure 5). Both the Bi-p and C-p states equally contributed at the Fermi level, whereas the role of the Bi-s and C-s states were negligibly small.

(C) Unit Cell of BiC3
In case of BiC3, the s-PDOS for the unit cell in 2D indicated a comparative contribution from the Bi-s and C-s states in VB and CB, but both equally contributed at

(C) Unit Cell of BiC 3
In case of BiC 3 , the s-PDOS for the unit cell in 2D indicated a comparative contribution from the Bi-s and C-s states in VB and CB, but both equally contributed at the Fermi level ( Figure 6). The survey of TDOS revealed nearly the same contribution from the Bi and C atoms in VB, but the dominant part of the Bi states in the CB, whereas both equally contributed at the Fermi level. The material was metallic in nature, with the sp hybrid orbitals taking part in the transport mechanism. The 3D unit cell of BiC3 exhibited the rich involvement of the Bi-p and C-p states, in comparison to the s-states. The s-PDOS showed C-s rich states in VB; it showed Bi-s rich states in VB, whereas the Bi-s states were slightly higher at the Fermi level. On the other hand, the analysis of p-PDOS indicated the major contribution of the C-p states in VB and at the Fermi level, as well as and at the CBM, whereas the Bi-p states dominated in the deeper part of the VB. The situation of TDOS remains the same as those of the p-states, as mentioned earlier. The material was still metallic in nature.
The 2D supercell of BiC3 exhibited a similar electronic structure, but the contribution of the p-states were comparatively higher. The s-PDOS and p-PDOS revealed the dominant role of the Bi-s and Bi-p states, respectively. The states at the Fermi level were very low, which indicated that the material may be a narrow gap semiconductor, but in the current computational details, we assigned a metallic nature to BiC3. In the case of the 3D supercell of BiC3, the analysis of s-PDOS and p-PDOS pointed to the dominance of Bip states and the metallic nature of the material. The 2D supercell of BiC 3 exhibited a similar electronic structure, but the contribution of the p-states were comparatively higher. The s-PDOS and p-PDOS revealed the dominant role of the Bi-s and Bi-p states, respectively. The states at the Fermi level were very low, which indicated that the material may be a narrow gap semiconductor, but in the current computational details, we assigned a metallic nature to BiC 3 . In the case of the 3D supercell of BiC 3 , the analysis of s-PDOS and p-PDOS pointed to the dominance of Bi-p states and the metallic nature of the material.

(D) Unit cell and Supercell of Bi 2 C 3
The electronic properties of Bi 2 C 3 were also studied by preparing its unit cells and supercells in 2D and 3D. The PDOS and TDOS calculated for 2D unit cell of Bi 2 C 3 are given in Figure 7, which shows the dominant nature of the Bi-p and C-p states in the electronic structure of the material. The s-PDOS showed the dominance of the Bi-s states over the C-s states throughout. On the other hand, the p-PDOS and TDOS exhibited the major contribution of Bi-p in CBM and that of C-p in the formation of VBM. The material was metallic in nature, with sp hybrid states at the Fermi level.  In the case of the 3D unit cell of Bi2C3, s-PDOS and p-PDOS showed nearly the same DOS of the s and p states of Bi and C ( Figure 8). However, the comparison of s-PDOS revealed that the Bi-s states were richer than the C-s states, whereas the comparison of p-PDOS indicated that the C-p states were higher than those of the Bi-p states. The comparison of the TDOS exhibited nearly the same contribution of the Bi-and C-related states. Bi2C3 exhibited a semiconducting nature with a band gap of 0.305 eV, which was close to the reported values [43]. The analysis of partial DOS indicated that VBM In the case of the 3D unit cell of Bi 2 C 3 , s-PDOS and p-PDOS showed nearly the same DOS of the s and p states of Bi and C ( Figure 8). However, the comparison of s-PDOS revealed that the Bi-s states were richer than the C-s states, whereas the comparison of p-PDOS indicated that the C-p states were higher than those of the Bi-p states. The comparison of the TDOS exhibited nearly the same contribution of the Bi-and C-related states. Bi 2 C 3 exhibited a semiconducting nature with a band gap of 0.305 eV, which was close to the reported values [43]. The analysis of partial DOS indicated that VBM comprised Bi-p states hybridized with C-p states. On the other hand, CBM was dominated by the C-p states, with a smaller contribution from the Bi-p states. These findings agree with the reported electronic properties of metal carbides [8,44].

(E) Super Cell of BiC5
The calculated TDOS, SDOS, and PDOS of 3×3 super cells of BiC5 are shown in Figure  9. In the case of the s-DOS near the Fermi level, we observed that the major contributions in VB, as well as in CB, were due to the C4 atom, and they were minor for the C3 atom. While observing the graph of PDOS and TDOS, the major contribution in VB, as well as CB, was due to Bi atom, and it was minor for the C3 atom. From observing the TDOS, SDOS, and PDOS graphs, it is clear that total contribution in VB and CB was due to the Bi-p subshell. From the graphs, we indicated that there were no maximum and minima; additionally, overlapping occurred in VB and CB. Thus, the material is metallic.

(E) Super Cell of BiC 5
The calculated TDOS, SDOS, and PDOS of 3 × 3 super cells of BiC 5 are shown in Figure 9. In the case of the s-DOS near the Fermi level, we observed that the major contributions in VB, as well as in CB, were due to the C4 atom, and they were minor for the C3 atom. While observing the graph of PDOS and TDOS, the major contribution in VB, as well as CB, was due to Bi atom, and it was minor for the C3 atom. From observing the TDOS, SDOS, and PDOS graphs, it is clear that total contribution in VB and CB was due to the Bi-p subshell. From the graphs, we indicated that there were no maximum and minima; additionally, overlapping occurred in VB and CB. Thus, the material is metallic.

(F) Unit cell of Bi 2 C 5
The comparison of s-PDOS and p-PDOS calculated for the 2D unit cell points to the fact that the p-states dominated to define the electronic structure of Bi 2 C 5 in such a way that the C-related states were found to be rich at the Fermi level. The analysis of s-PDOS indicated a richness of the C-s states in the formation of VB and CB, whereas the p-PDOS and TDOS revealed the dominance of the C-p states in the principal bands. In the case of the 3D unit cell of Bi 2 C 5 , the Bi-related states highly dominated, and the C states were suppressed in the electronic structures of the materials that appeared metallic in nature ( Figure 10). The analysis of s-PDOS, in the case of the 2D Bi 2 C 5 supercell, showed a major contribution of the Bi-s states in VB and CB, but the C-s states dominated at the Fermi level. However, the entire electronic structure of the material revealed the richness of the Bi-p states and metallic nature. 9. In the case of the s-DOS near the Fermi level, we observed that the major contributions in VB, as well as in CB, were due to the C4 atom, and they were minor for the C3 atom. While observing the graph of PDOS and TDOS, the major contribution in VB, as well as CB, was due to Bi atom, and it was minor for the C3 atom. From observing the TDOS, SDOS, and PDOS graphs, it is clear that total contribution in VB and CB was due to the Bi-p subshell. From the graphs, we indicated that there were no maximum and minima; additionally, overlapping occurred in VB and CB. Thus, the material is metallic.

(F) Unit cell of Bi2C5
The comparison of s-PDOS and p-PDOS calculated for the 2D unit cell points to the fact that the p-states dominated to define the electronic structure of Bi2C5 in such a way that the C-related states were found to be rich at the Fermi level. The analysis of s-PDOS indicated a richness of the C-s states in the formation of VB and CB, whereas the p-PDOS and TDOS revealed the dominance of the C-p states in the principal bands. In the case of the 3D unit cell of Bi2C5, the Bi-related states highly dominated, and the C states were suppressed in the electronic structures of the materials that appeared metallic in nature ( Figure 10). The analysis of s-PDOS, in the case of the 2D Bi2C5 supercell, showed a major contribution of the Bi-s states in VB and CB, but the C-s states dominated at the Fermi level. However, the entire electronic structure of the material revealed the richness of the Bi-p states and metallic nature.

(G) Unit cell of BiC5
From observing the TDOS, SDOS, and PDOS graphs, it is clear that total contribution in the VB and CB was due to the Bi-p subshell, and the material was found to be metallic [43].

(G) Unit cell of BiC 5
From observing the TDOS, SDOS, and PDOS graphs, it is clear that total contribution in the VB and CB was due to the Bi-p subshell, and the material was found to be metallic [43].

Summary
The first principle calculations were performed to predict a series of compounds of Bi and C in the form of unit cell and super cell models of BiC, BiC 2 , BiC 3 , Bi 2 C 3 , BiC 5 , and Bi 2 C 5 in two and three dimensions. The structural and electronic properties of the compounds were studied. The survey of the structural properties indicated that the bond length Bi-Bi remained almost the same for all compounds, whereas the bond lengths and orders for Bi-C and C-C showed variation. The symmetry of the materials appeared cubic. On the basis of charge analysis, it was found that Bi was cationic, whereas C was anionic. The entire materials were metallic, except 2D Bi 2 C 3 , which exhibited a semiconducting nature with a band gap of 0.305 eV. The mentioned Bi-C structures were reported, for the first time, in this paper; however, further investigations are required to investigate other possible structures in the series. Thus, this study is far from a complete structural search, and the prospects of more Bi x C y compounds in different crystal structures are yet an open research area.