Stability of subnanometer MoS wires under realistic environment

We carried out first-principles density functional theory calculations of hydrogen and oxygen adsorption and diffusion on subnanometer MoS nanowires. The nanowires are robust against adsorption of hydrogen. On the other hand, interaction with oxygen shows that the nanowires can oxidize with a small barrier. Our results open the path for understanding the behavior of MoS nanowires under realistic environment.


Introduction
The discovery of graphene has attracted the interest of the scientific community in other lowdimensional materials, such as transition-metal dichalcogenides (TMDCs), which exhibit novel physical and chemical properties with promising applications in nanotechnology. [1][2][3] In particular, single-layered MoS 2 posses a sizebale electronic band gap of 1.8 eV, which may be useful for applications in high-end electronics, spintronics, optoelectronics, energyharvesting, flexible electronics, and biomedicine . [4][5][6] Recently transition metal chalcogenide (TMC) subnanometer nanowires have been fabricated by ion and electron beam techniques in MoS 2 layers . 7,8 Contrary to single-layered MoS 2 , MoS nanowires show metalic behavior . 9 Such wires under tensile strain undergo a phase transformation is observed in the MoS NWs which results in tension-induced hardening in their tensile modulus . 10 Furthermore, topological states in one-dimensional MoS nanowires have been proposed . 11 For several nanoscale applications, the interaction of nanostructures with the environment is very important, since it provides information on their stability against degradation.
Usually two-dimensional MoS 2 exhibits unique surface effects but the interaction with hydrogen is limited by the amount of active sites . 12 Although hydrogen molecules diffuse on MoS 2 monolayers with a high energy barrier of 6.56 eV, their diffusion can be facilitated by applying strain which then reduces the diffusion barrier to 0.57 eV . 13 Reactivity can further be improved via doping with transition metals . 14 More recent results claim that oxygen strongly interacts with defective MoS 2 layers, enhancing their photoluminescence properties due to dissociation of O 2 on sulphur vacancies . 15 Although the interaction of MoS 2 monolayers with oxygen and hydrogen has been largely explored, investigations of MoS nanowires under realistic environments are still missing. In this paper we perfrom first-principles calculations density functional theory calculations of hydrogen and oxygen adsorption and difusion on subnanometer MoS nanowires. We show that the nanowires have sizeable interaction with atomic hydrogen. However, dissociation of hydrogen molecules is hindered by a high enegy barrier and unfavourable orientation of orbitals. On the other hand, oxidation of MoS wires may take place with a small diffusion barrier of oxygen atoms.

Computational details
The calculations are performed using density-functional theory (DFT) , 16,17 as implemented in the Vienna ab initio simulation package (VASP) , 18 The electron-ion interactions are taken into account using the Projector Augmented Wave (PAW) method. We employ the generalized gradient approximation (GGA-PBE) 19 to describe the interaction between valence electrons. The Kohn-Sham orbitals are expanded in a plane wave basis set with an energy cutoff of 500 eV. The Brillouin Zone is sampled according to the Monkhorst-Pack method using a (1×1×8) k-points mesh. In order to determine the diffusion and reaction barriers we have performed CI-NEB 20,21 calculations with seven images to search the minimum-energy reaction paths and saddle points between the initial state and final state configurations.

Pristine nanowires
Mo and S atoms in pristine MoS nanowires are arranged by stacking of triangular layers rotated 180 o along the nanowire axial direction, with three S atoms located at the vertices of the triangles and three Mo atoms located between the S atoms, as seen in Fig. 1. The calculated equilibrium lattice parameter along the axis wire is 4.39 Å. Contrary to single-layered MoS 2 , pristine MoS nanowires show metallic behavior, as seen in Fig. 1(a). At Γ point the states with character d x 2 cross the Fermi level. Localized states with d z 2 character lie around 0.25 eV above the Fermi level, as seen in Fig. 1(b). In Fig. 1(c1) and (c2) (empty states) and (c3) and (c4) (occupied states) we show the orbital projected charge density in pristine wires. The empty states lie along the wire growth direction. We discuss the importance of orbital orientation later on. In order to understand the strength between MoS wires and hydrogen/oxygen we have calculated the adsorption energy according to: where E MoS−ad and E MoS are the total energies of the MoS supercell with and without the adsorbate (hydrogen or oxygen). N i and µ i are the number and chemical potencial of hydrogen and oxygen in gas phase.  Fig. 2(a). Atomic hydrogen prefers to be at ontop position, with the nanowire structure barely affected by the hydrogen atom. Charge density difference calculated according to Fig. 2(b) with the nanowire structure barely affected by the hydrogen atom. Total charge density with views along and perpendicular to the wire growth direction is shown in Fig. 2(c) and (d).
To corroborate with this picture we show the band structure of atomic hydrogen adsorbed    Table 1 shows that contrary to atomic hydrogen, the adsorption energy of molecular hydrogen is only 6.00 meV. Furthermore, negligible difference is found for hydrogen concentrations of 1 /24 and 1 /12 ML. In order to further understand this behavior, we have calculated the dissociation barrier of hydrogen along the path shown in Fig. 5(a)-(i). Barrier of 1.10 eV. The band structure of the most stable state in Fig. 6(a) is shown in Fig. 6(b).  Fig. 7(a)) is shown in Fig. 8(j).
At 1 /12 ML oxygen concentration as shown in Fig. 8 a) side view) and b) top view we have an endothermic reaction, as seen from Table 1. Interestingly enough, by decreasing the oxygen concentration to 1 /24 ML, the reaction turns out to be exothermic. The band structure is shown in Fig. 10(c). The more stable structure for an oxygen molecule shows a small magnetic moment due to outwards relaxation of nearby Mo atoms. The presence

Conclusion
In this paper we perfrom first-principles calculations density functional theory calculations of hydrogen and oxygen adsorption and difusion on subnanometer MoS nanowires. We show that the nanowires have sizeable interaction with atomic hydrogen, but little with hydrogen molecules. Furthemore, oxidation of MoS nanowires is feasible and occurs with a small barrier.