- Tungsten and molybdenum dichalcogenides have a layered structure similar to that of graphite. Hollow fullerene-like nanoparticles (inorganic fullerenes (IFs)) and nanotubes (inorganic nanotubes (INTs)) have been synthesized from these inorganic compounds. [1–3] Theoretical investigations provided a basic understanding of the electronic and mechan-ical properties of the INTs. [4–7] These materials are currently being contemplated for numerous applications, in particular, as superior solid lubri-cants and as impact-resistant nanocomposites.  Bulk syn-thesis of the IFs normally yields quasispherical nanoparticles with at least 20 molecular layers and outer diameters of greater than 30 nm. In early work, the formation of hollow MoS 2 clusters with octahedral or tetrahedral shapes was often observed. [2, 9, 10] Laser ablation was used to produce MoS 2 nano-octahedra with diameters of 3–5 nm.  These closed nanocages are the smallest IFs. [11, 12] Herein, the small hollow nano-octahedra and the quasispherical nanoparticles (diameters larger than 30 nm) are termed (inorganic) fullerenes and fullerene-like nanoparticles, respectively. A detailed understanding of their structures and physicochemical properties is still lacking. Structural models of single-layer fullerene-like MoS 2 nanoparticles with squarelike defects were investigated using a universal force field.  These results were used to model high-resolution transmission electron microscopy (HRTEM) images. The geometries of small fullerenes of different shapes were optimized using molecular mechanics, and the electronic spectra of the fullerenes were analyzed using the semiempirical extended Hückel method.  The electronic structures of the "ultrasmall" fullerene cages (MX 2) 48 (M = Ti, Zr, Nb, Mo, X = S; M = Fe, Ni, Cd, X = Cl) were calculated without geometry optimization by using a method based on density functional theory (DFT).  Herein, the results of DFT calculations on MoS 2 ful-lerenes are presented. A detailed investigation of the synthesized nano-octahedra by electron microscopy allowed an instructive comparison with the predicted structures. Moreover, the calculations were extended to larger multi-walled MoS 2 nanoparticles through the use of several approximations. The calculated phase diagram of hollow MoS 2 nanoparticles could be directly compared to the experimentally observed structures. Our study focused on stoichiometric nano-octahedra. A more detailed study includ-ing nonstoichiometric nano-octahedra will follow. As depicted in Figure 1 a, there are two ways to "cut" triangular nanoplatelets from an MoS 2 monolayer. In case I, there are MoÀS bonds perpendicular to the edges of the triangle. In case II, there are MoÀS bonds parallel to the edges of the triangle. The association of these triangular fragments leads to closed stoichiometric polyhedra of octa-hedral shape, in which squarelike defects occur at the corners (Figure 1 b). The edge lengths of the fullerenes are deter-Figure 1. Structures constructed from a hexagonal MoS 2 monolayer with the lattice constant a: triangle faces "cut" in two possible ways (a; I and II), the ideal apex (with a squarelike defect) of a stoichiometric MoS 2 fullerene (b), the DFTB-optimized structure of an (MoS 2) 576 fullerene, which degraded to Mo 576 S 1140 (c), and the structure of the Mo 576 S 1140 fullerene after an MD simulation at 300 K (d). Mo red, S yellow.