## 3 Results and Discussion
### Electronic Properties  
Figure 2 show the energy band structures of monolayer and multilayer Mo\({}_{2}\)CF\({}_{2}\), Mo\({}_{2}\)C(OH)\({}_{2}\), and Mo\({}_{2}\)CO\({}_{2}\). Monolayer Mo\({}_{2}\)CF\({}_{2}\) and Mo\({}_{2}\)CO(OH)\({}_{2}\) are semiconductor materials with indirect band gap energies of 0.278 eV and 0.117 eV, respectively. Meanwhile, monolayer Mo\({}_{2}\)CO\({}_{2}\) behaves like a metal, with no band gap energy. The peaks in the valence bands of Mo\({}_{2}\)CF\({}_{2}\) and Mo\({}_{2}\)C(OH)\({}_{2}\) were shifted to zero energy. The valence band maximum and conduction band minimum of these materials were located at the k point between K and G. Our calculations of the band gap energies for monolayer Mo\({}_{2}\)CF\({}_{2}\) and Mo\({}_{2}\)C(OH)\({}_{2}\) are similar to the previously reported 0.25 eV and 0.11 eV, respectively, which were also calculated using the GGA-PBE function [23; 32]. The calculation results indicate that the band gap energy changed depending on the surface functional group.  
Like the monolayer Mo\({}_{2}\)C-, the energy band structures of multilayer Mo\({}_{2}\)C-MXenes showed similar band shapes, especially for the valence and conduction bands of each material. Bilayer and trilayer Mo\({}_{2}\)CF\({}_{2}\) still exhibited semiconductor properties with band gap energy values of 0.258 eV and 0.249 eV, respectively. A semiconducting-to-metallic behavior was observed in the multilayer Mo\({}_{2}\)C(OH)\({}_{2}\) MXenes when increasing the number of layers of the material. The bandgap changed from about 0.012 eV for the bilayer to 0 eV (no bandgap) for the trilayer Mo\({}_{2}\)C(OH)\({}_{2}\). Our results show a reversal to the band gap energy as the number of layers increased. The band gap energy reduction was related to the coupling between layers, leading to the splitting of the bands [32]. The band splitting had a high dependence on the number of layers. As can be seen in Figure 2, the interlayer coupling was stronger from the monolayer to the trilayer, leading to an increase in the band splitting and a decrease in the band gap energy. This indicates that the band gap of 2D layered Mo\({}_{2}\)C- can be tuned by engineering the number of layers and enhancing this characteristic for electronic device applications. Mo\({}_{2}\)CO\({}_{2}\) still exhibited a metallic behavior in both the bilayer and trilayer structures.  
Figure 1: Structure of monolayer and multilayer for Mo\({}_{2}\)CF\({}_{2}\) (**a**), Mo\({}_{2}\)C(OH)\({}_{2}\) (**b**), and Mo\({}_{2}\)CO\({}_{2}\) (**c**) MXenes.  
The semiconducting or metallic state transition comes from the electron counting rule between the dangling bond states and the additional states created at the Fermi level [33]. Typically, the transition metal d-electrons play an important role in the DOS near the Fermi surface, whereas the p-electrons of the C atoms are composed below the Fermi surface. Additionally, the electronic properties are mainly impacted by the surface terminations bonded to the outer transition metal layers [34; 35]. Therefore, a similar effect could be seen in the surface terminal groups OH- and F-, which accept for only one electron, whereas the O= group receives two electrons from the outer metal layers, representing a different effect. This effect suggests that a new energy band can be formed below the Fermi surface, which can spontaneously reduce the DOS at the Fermi surface (see Figure 3).