Ab-initio study of ReCN in the bulk and as a new two dimensional material

First principles total energy calculations have been applied to describe the ReCN bulk structure and the formation of ReCN monolayers and bilayers. Results demonstrate a strong structural rearrangement in the monolayer due to a reduced dimension effect: an increase in the lattice parameter, accompanied with the contraction of the distance between the C and N planes. On the other hand, a ReCN bilayer has structural parameters similar to those of the bulk. Surface formation energies show that the monolayer is more stable than bilayer geometries. Although bulk ReCN shows a semiconductor behavior, the monolayer ReCN presents a metallic behavior. This metallic character of the ReCN monolayer is mainly due to the d-orbitals of Re atoms.

energy. Vanderbilt ultra-soft pseudopotentials were used to replace the effect of core electrons. To evaluate the Brillouin zone integrations we have used a k-points mesh of 4 × 4 × 1 32 .
To begin with the calculations, we have optimized the ReCN bulk structure in a tetragonal structure, with space group P63mc (186) 29 . The monolayer has been simulated by taking only a Re-C-N unit with an empty space large enough (~15 Å) to account for the surface effects in the 2D system as well as to eliminate undesirable interactions between adjacent monolayers. A similar procedure has been used to simulate the bilayers, with two different configurations.

Results and Discussion
ReCN bulk structure. Previous calculations of bulk ReCN have found a stable tetragonal structure with lattice parameters: a = 2.897 Å and c = 7.851 Å 29 , and a semiconductor behavior with a calculated energy gap of ~0.6 eV 29 . Before studying the ReCN 2D system, we have reproduced the ReCN bulk structure, as shown in Fig. 1(a). Our fully optimized lattice parameters are: a = 2.896 Å and c = 7.844 Å ( Fig. 1(b)), which indicates good agreement with previous calculations 29 . The Re-C, Re-N, and C-N distances were found also in agreement with previously reported data, as seen in Table 1. Figure 1(a) shows that in the ReCN structure, besides the C-N bonds formed by atoms of different tri-layer units, it is possible that the carbon and nitrogen atoms separated by a Re layer could be bonding. However, the atomic distance between C and N planes is 2.509 Å, indicating that the carbon and nitrogen atoms of those layers are not interacting directly.

ReCN monolayer.
We have next studied the properties of a single ReCN monolayer. Since surface effects may generate structural changes, we have fully optimized the atomic structure of the monolayer. Figure 2(a) depicts the energy as function of the lattice parameter. Note that this tri-layer system presents a behavior similar to silicene, in which there is a high buckling metastable configuration and a more stable low buckling structure. In this case, the metastable structure has a lattice parameter (a = 3.071 Å) characterized by a C and N planes distance of 2.016 Å. In the low buckling structure, the lattice parameter has a value of 3.176 Å, which is around 9.67% larger than the lattice parameter in the bulk ( Fig. 1(b)). With this modification in the lattice constant, the atomic distances change too. The Re-C and Re-N bonds decrease with respect to the values in the bulk by ~0.1 Å and ~0.05 Å, respectively (See Fig. 2(b)).
Different from bulk, in the ReCN monolayer there are no C-N bonds between atoms belonging to different tri-layer units, since in this case there in one monolayer only. However, the large structural changes in the monolayer reduce the distance between the C and N planes to 1.748 Å, a distance in which carbon and nitrogen atoms may be forming bonds.

ReCN bilayers.
To analyze how two monolayers interact when they are near each other, we have plotted the interaction energy as function of the inter layer separation distance. Two different configurations were considered. In Fig. 3(a) the alignment of the monolayers is bulk like, while in Fig. 3(b) the two tri-layer units are on top of each other.
The behavior is similar in the two cases. At very small separation distances, there is a large repulsion, making the system unstable (as expected). As the monolayer-monolayer distance increases, the bilayer becomes stable in    a structure with a C-N distance similar to the one in the bulk. Increasing the distance between monolayers, the separation becomes so large that there is no interaction between them and they behave as isolated monolayers. At the most stable interaction distance, we have carried out a new structural optimization of the equilibrium lattice parameter. It is clear from Fig. 4 that the lattice parameter (a bulk-like = a on-top = 2.938 Å) decreases following a trend that should reach the bulk limit when the number of monolayers increase. It is also interesting to see that the bulk-like arrangement of the monolayers is slightly more stable than the on-top configuration.

Structure d Re-C (Å) d Re-N (Å) d C-N (Å)
A summary of the structural parameters of both geometries is presented in Table 2. From these results, we can see that both structures are structurally similar, and they differ only by the Re layer alignment. Also, the C and N planes distance (~2.380 Å) is the same in both configurations.

Stability analysis.
We have considered several possible configurations with different number of atoms. To compare their relative stability, we use the surface formation energy formalism that depends on the chemical potential of each species of the system. It has the following form 33,34 : where E model is the energy of the system under study, E reference is the reference energy, in this case, the one of a single ReCN monolayer, n i is the number of extra atoms and µ i the chemical potential of each species. Under this formalism, we can calculate the chemical potential as the total energy per atom of the most stable bulk structure. Then, µ Re is obtained from a hexagonal lattice. As carbon has two allotropes, diamond and graphite, we have calculated the chemical potential of both structures. Finally, the N chemical potential is determined from an isolated N 2 molecule. It is found that the monolayer configuration is more stable than any of the two bilayer configuration. This behavior is the same for both allotropes of carbon, as seen in Table 3.
Electronic properties. In this section, we report on the electronic properties of the different configurations that we have studied. Figure 5 shows the total density of states of bulk ReCN. A clear semiconductor behavior can be observed, with a calculated band gap of ~0.51 eV, in agreement with previous calculations 29 .
Monolayer and bilayer density of states. Figure 6 shows the total density of states of an optimized single monolayer of ReCN. In this case, a high population of states is concentrated around the Fermi level, indicating a    Table 3. Calculated formation energies in eV/ReCN monolayer. metallic behavior. Since bulk ReCN is semiconductor, we can say that the metallic behavior is due to the decrease in dimensionality. The total density of states of the two bilayers in an on top and bulk-like configurations are shown in Fig. 7(a) and (b) respectively. A clearly metallic behavior can be observed in both of them, with a peak at the Fermi level, indicating an electronic instability.

Structure d Re-C (Å) d Re-N (Å) d C-N (Å)
Projected density of states of the stable ReCN monolayer. We now concentrate in the stable ReCN monolayer system. In order to describe the orbitals which generate the metallic behavior in this structure, we plot the projected density of states (Fig. 8). It is clear that the Re-d orbitals have the most important contribution around the Fermi energy, being the main factor of the metallic behavior. The Re-p, Re-s, C-s, and N-s orbitals have a very small contribution to the density of states. On the other hand, the N-p and C-p orbitals have slightly contributions around the Fermi level. Their main contributions are for more negative and positive energies, as seen in Fig. 8.
Since the Re-d, C-p and N-p orbitals have the largest contributions to the density of states, we resolve them in to their components. In Fig. 9(a), we depict the resolved p orbitals of the N atom. In this case the N-p z orbital has the main contribution around the Fermi level, with important contributions for more negative and positive energies too. The N-p x and N-p y orbitals are degenerated in all the range of energy. Figure 9 , and Re-d xy orbitals are degenerated. Finally, the C-p z orbital and the degenerated C-p x , and C-p y orbitals have contributions for more negative and positive energies (Fig. 9(c)), with little contribution around the Fermi level. The degeneration of the orbitals in all atoms is a strong indicative of a highly symmetric and stable 2D structure.
Charge density of the stable ReCN monolayer. To gain a better understanding of the Re-N, Re-C interactions and the possible bond formation between the C and N atoms, we plot the charge density in some preferential planes. Figure 10(a) depicts the charge density at the average height of the Re and N atoms. A large charge accumulation can be noted at the Re and N atoms position. It is also clear that Re and N atoms are sharing charge, forming covalent bonds. A similar behavior is observed between the Re and C atoms, but in this case the   Re atoms have a larger charge accumulation than C atoms, indicating a polar covalent character (see Fig. 10(b)). Now, to analyze the possible formation of a C-N bond in the monolayer, we plot the charge density in the (010) plane. As mentioned in the previous section, the inter-atomic carbon nitrogen distances make it possible for the two atoms to form a bond. Figure 10(c) shows a strong interaction with a covalent character. Since N atoms are more electronegative than carbon atoms, there is more charge around the nitrogen atoms. This charge difference may be the driving force to the decrease in the distance between the C and N planes.

Conclusions
Applying first principles calculations, we have described the structural and electronic properties of ReCN in the bulk, as a monolayer and as a bilayer. Results show an increase in the lattice parameter when a single ReCN monolayer is optimized. This effect is generated by the contraction of the distance between the C and N planes of the monolayer along the perpendicular direction. In the case of a bilayer two different layer stacking are possible. The lattice parameters of both of them are similar to the one of bulk. Surface formation energies show that the monolayer is more stable than the bilayer models. A semiconductor behavior has been found in bulk, whereas the monolayer and bilayer ReCN present metallic behavior, mainly induced by the d-orbitals of Re atoms. Charge density plots confirm the Re-N, Re-C and C-N covalent bonds driving to a strong electronic stability in the monolayer. This new single ReCN monolayer could be used to form heterostructures with other 2D materials such as graphene or phosphorene in new generation electronic devices. We hope our study motivate experimental studies of the ReCN monolayer.