# Computational Atomistic Modeling in Carbon Flatland and Other 2D Nanomaterials
## 4 Electronic Structure and Vibrational Properties of MXenes  
Among the recently discovered 2D systems, the emerging family of 2D transition metal carbides and nitrides, known as MXenes [65; 66; 67], stands out because of the wide chemical diversity allowing for materials property tuning. In contrast to graphite-like layered materials which can be mechanically exfoliated to obtain 2D flakes, MXenes are obtained from the chemical treatment of three-dimensional MAX phases [65]. MAX phases are layered ceramics with the general formula M\({}_{n+1}\)AX\({}_{n}\), where M represents an early transition metal, A an element from groups 13 to 16, X either a carbon or a nitrogen atom, and \(n\) varies from 1 to 3 [68; 69]. Due to the use of etching agents, MXenes are always terminated with functional surface groups, such as -F, =O, and -OH, that are randomly distributed [67]. Since the discovery of the first MXene, Ti\({}_{3}\)C\({}_{2}\)T\({}_{z}\), at Drexel University in 2011 [65], more than 30 MXenes have been synthesized, and the stability and properties of dozens more have been investigated using _ab initio_ calculations [70]. The exploration of new MAX phases and derivative MXenes is of great interest to further control materials properties and highlight potential applications, such as catalysis, energy storage and related electrochemical applications [70]. Up to now, most of the research has been devoted to the first MXene Ti\({}_{3}\)C\({}_{2}\)T\({}_{z}\) and consists in experimental works [70]. However, given the wide chemical versatility on both M and T sites, _ab initio_ calculations are powerful to investigate the structural and functional properties of the resulting huge variety of MXenes compositions. The geometries and electronic properties of the V\({}_{2}\)CT\({}_{z}\) systems are investigated using DFT calculations. The ground-state structure of the pristine V\({}_{2}\)C shows a hexagonal lattice with the \(P\overline{3}m1\) space group (Figure 7a). Based on the unit cell of V\({}_{2}\)C, functionalized V\({}_{2}\)CT\({}_{z}\) MXene structures with terminations are constructed. Two types of hollow sites on the surface of V\({}_{2}\)C can be distinguished (Figure 7a), leading to different functionalization models [71]. The energetically favorable model for functionalized V\({}_{2}\)CT\({}_{z}\) corresponds to MD2 where the two functional groups are located on fcc sites for which no C atom is present under the V atom (Figure 7b). Similarly to graphene and other 2D materials with hexagonal symmetry, an armchair direction and a zigzag direction can be identified, as depicted in Figure 7c. Moreover, moving to the reciprocal space, the \(\Gamma\)-M and \(\Gamma\)-K high-symmetry paths in the Brillouin zone respectively correspond to the armchair and zigzag direction (Figure 7c). Figure 6: Optical Hall conductivity \(\sigma_{xy}\) of unstrained and 8% strained graphene along armchair (\(\theta=0^{\circ}\)) and zigzag (\(\theta=90^{\circ}\)) direction for incoming light polarized obliquely (\(\phi=45^{\circ}\)). Inset: Sketch illustrating the Faraday rotation mechanism of linearly polarized light (red and blue lines) in uniaxially strained graphene (green line). Visible (UV) light rotates (anti-)clockwise when strain is applied along the armchair direction. The electronic band structure of pristine V\({}_{2}\)C and fully-terminated V\({}_{2}\)CT\({}_{2}\) with T = -F and/or -OH are presented in Figure 8. The metallic character of V\({}_{2}\)C is ensured by the presence of V-\(3d\) orbitals at the Fermi level, and is not affected by any kind of terminations [72]. This is not always verified since [PERSON] et al. showed that the metallic pristine Ti\({}_{2}\)C could turn into a semiconductor upon functionalization, depending on the nature of the terminal groups [71]. In general, all pristine MXenes are metallic, while terminated MXenes can be either metallic or semiconducting, depending on the configuration and nature of the terminal groups.