## 4 Conclusions  
Using electronic structure calculations based on Density Functional Theory and Boltzmann transport theory, we investigated the electronic, optical, and thermoelectric properties of the Mo\({}_{2}\)CF\({}_{2}\), Mo\({}_{2}\)C(OH)\({}_{2}\), and Mo\({}_{2}\)CO\({}_{2}\) MXenes from their respective monolayers to multilayers. Our results show that Mo\({}_{2}\)CF\({}_{2}\) and Mo\({}_{2}\)C(OH)\({}_{2}\) are semiconductors with indirect band gap energies of 0.278 eV and 0.117 eV for the monolayers Mo\({}_{2}\)CF\({}_{2}\) and Mo\({}_{2}\)C(OH)\({}_{2}\), respectively. On the other hand, Mo\({}_{2}\)CO\({}_{2}\) behaves like a metal with no band gap energy. Increasing the number of layers results in narrower band gap energy of the 2D layered Mo\({}_{2}\)CF\({}_{2}\) and Mo\({}_{2}\)C(OH)\({}_{2}\) due to interlayer coupling. The band gap energy of the bilayer Mo\({}_{2}\)CF\({}_{2}\) and Mo\({}_{2}\)C(OH)\({}_{2}\) are 0.258 eV and 0.012 eV, respectively. These results indicate that the band gap energy of the Mo\({}_{2}\)C-material can be adjusted by the number of layers.  
For the optical properties of Mo\({}_{2}\)C-sublayers affected by different -F, -OH, and -O functional groups, a higher value of dielectric function was obtained for Mo\({}_{2}\)CO\({}_{2}\) compared to Mo\({}_{2}\)CF\({}_{2}\) and Mo\({}_{2}\)C(OH)\({}_{2}\) (\(\epsilon_{1}(\omega)\) \(\sim\)60 at around 1.48 eV for the trilayer Mo\({}_{2}\)CO\({}_{2}\)), indicating a greater polarizability and visible light absorption. Controlling the band gap energy can manipulate the dielectric constant and optical properties of 2D layered Mo\({}_{2}\)CF\({}_{2}\) and Mo\({}_{2}\)C(OH)\({}_{2}\). This ability makes Mo\({}_{2}\)C- a promising material for applications in the field of electronics.  
Regarding thermoelectric properties, Mo\({}_{2}\)CF\({}_{2}\) showed the best thermoelectric properties among the three types of Mo\({}_{2}\)C-MXenes considered in this study. The remarkable thermoelectric properties of Mo\({}_{2}\)CF\({}_{2}\) are a result of its semiconductor band gap and special band shape near the energy boundaries, which has potential for high-performance thermoelectric devices.  
Opportunities and challenges for Mo\({}_{2}\)C-MXene application coexist, and future efforts should pay more attention to the synthesis and study of other MXenes containing Mo, V, Zr, etc. There is a lack of experimental studies on these materials with different numbers of layers. Therefore, it would be ideal to further study the preparation method of MXenes and combine computational calculations with experiments to enhance the predictions of the characteristics and the properties of these materials. Currently, with the fabrication of materials that control thickness according to the number of layers, research results regarding flexible bandgap energy and high-temperature thermal stability demonstrate the potential of Mo\({}_{2}\)C-MXene for many applications, including energy storage, solar cells, and electrode applications, by optimizing the thin film layer.  
Methodology and validation, M.C.-R. and L.V.M.; formal analysis and investigation, D.T.K.A.; writing--original draft preparation, D.T.K.A. and D.M.H.; writing--review and editing, P.H.M., K.Y., M.C.-R., L.V.M. and N.D.H.; funding acquisition, P.H.M. and M.C.-R.; supervision, P.H.M. All authors have read and agreed to the published version of the manuscript.  
This work is supported by Vietnam Academy of Science and Technology through Project No. NVCC05.03/24-25 and the Osaka University, Institute of Laser Engineering Collaborative Research Fund (2024B1-008).  
Not applicable.  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
On behalf of all authors, the corresponding author states that there are no conflicts of interest.