## 1 Introduction  
Since the first successful preparation of graphene in 2004 [1], two-dimensional (2D) materials have attracted great attention owing to their unique properties and potential applications in areas such as energy storage, catalysis, and electronics [2; 3; 4]. In 2011, [PERSON], [PERSON] and other researchers [5] introduced a novel group of 2D transition metal carbides, nitrides, and carbon nitrides known as MXenes, which has rapidly spurred the exploration of new 2D materials in the field of materials science. In general, MXenes have been synthesized by using strong acid or alkali solutions [6] and exfoliating their A-layers in the MAX phases [7; 8], where M is an early transition metal (M: Mo, Ti, Zr, Cr, W,...), A is a group element (A: Si, Ga, Al,...), and X is a carbon and/or nitrogen atom (X: C, N). This formed transition metal carbides and nitrides with the M\({}_{n+1}\)X\({}_{n}\)T\({}_{x}\) formula, where T represents functional groups such as F, H, O, or OH and n = 1, 2, 3, or 4 [9; 10]. To date, over 70 different synthesized MAX phases have been reported [11]. Thus far, the addition of termination groups (T) on the MXene surface has resulted in more than 30 distinct MXenes structures being experimentally obtained and theoretically predicted [12; 13].  
In recent years, 2D MXenes, including Ti\({}_{3}\)C\({}_{2}\)T\({}_{x}\), Nb\({}_{2}\)CT\({}_{x}\), Mo\({}_{2}\)CT\({}_{x}\)[14; 15; 16], etc., have been explored in every possible field, with particular attention paid to energy storage applications, mainly due to their good electrical conductivity and ability to host of cations (e.g., Li\({}^{+}\) and Na\({}^{+}\)). Compared with the common MXenes, Mo\({}_{2}\)C-MXenes are new and stand out from various MXenes. They were successfully obtained by the selective etching of Ga layers from Mo\({}_{2}\)Ga\({}_{2}\)C MAX phases using hydrofluoric acid [16; 17; 18]. The current studies show that Mo\({}_{2}\)C-structures have high storage capacity, excellent electrical conductivity, chemical stability, and other properties, making them potential electrocatalysts [19], photocatalysts for photocatalytic H\({}_{2}\) production [20; 21], anode materials in batteries [9], and materials for electromagnetic interference shielding [22]. Interestingly, among 35 different functionalized MXenes, Mo\({}_{2}\)CT\({}_{x}\) functionalized with fluoride (F) has been reported to have an excellent thermoelectric power factor [23]. Generally, the etching solution used in the synthesis process is directly related to the type of surface termination. Therefore, the electronic and optical properties of MXenes are strongly dependent on the interaction between the outer metal layer and the surface functional groups (F, OH, O, Cl, etc.). However, there is a lack of information about the dependence of the electronic, optical, and thermoelectric properties of Mo\({}_{2}\)C-based MXenes materials on the surface termination groups and the number of layers. As a material with a small bandgap, knowing how the number of layers affects the electronic, optical, and thermoelectric properties will greatly enhance its potential. Therefore, we investigated these properties for three kinds of Mo-based MXenes, namely, Mo\({}_{2}\)CF\({}_{2}\), Mo\({}_{2}\)C(OH)\({}_{2}\), and Mo\({}_{2}\)CO\({}_{2}\), with different structures, from monolayer to multilayer. Knowledge of the properties of Mo\({}_{2}\)C-MXenes resulting from this work will guide experiments and the development of new applications using Mo\({}_{2}\)C-MXenes.