The forces and stresses are converged to 10 −3 a.u. In all calculations, complete relaxation of both forces and stress is required. The band gap calculation with the B3LYP 10 and PBE0 11 exchange-correlation functionals was performed with a norm-conserving pseudopotential and an energy cutoff of 80 Ry. The plane-wave expansion cutoff energies are 40 Ry and 200 Ry for wavefunctions and for density and potential, respectively. The numerical parameters were chosen to converge the energy to 10 −4 Ry per atom. The exchange-correlation functional is approximated by the Perdew-Burke-Ernzerhof (PBE) general gradient approximation 8.ĭensity-functional-perturbation-theory was employed for phonon calculations 9. The pseudopotential is from the Garrity, Bennett, Rabe, and Vanderbilt data set 7. The calculations were performed within the plane-wave formulation of density-functional theory (DFT) with ultra-soft pseudopotentials as implemented in the Quantum-Espresso simulation package 6. In this study, we employ ab initio methods to examine the mechanical and energetic stability, atomic structure, phonon dispersion curve, and band structure of graphullerene. The role of Mg atoms in stabilizing the structure and their effect on the material properties remain to be determined. A computational study of graphullerene in the absence of Mg was reported 5, indicating that the material is meta-stable. Specifically, its structure was deduced indirectly, while its electronic properties have only been probed. This two-dimensional structure has been termed graphullerene, and its corresponding three-dimensional van der Waals crystal, graphullerite 3.Īlthough graphullerene has been synthesized, it has only been partially characterized. Thus, some carbon atoms in this configuration are in sp 2, and others in sp 3 hybridization states. In this crystal, some of the carbon atoms bond with three nearest neighbors, and some, those that connect two neighboring molecules, have four nearest neighbor bonds. Subsequently, it was shown that the magnesium atoms of this two-dimensional crystal could be removed to form a pure allotrope of carbon with a C 60 molecule occupying each hexagonal lattice point 3. Recently, C 60 molecules were synthesized with magnesium to create a monolayer of a two-dimensional hexagonal periodic structure (Mg 4C 60) n 3, 4. The carbon ball consists of hexagons and pentagons of carbon atoms, such that each atom bonds to its three nearest neighbors 2 in an sp 2 hybridization. The C 60 molecule is a carbon ball similar in shape to a football, with an atom in each corner. However, although carbon is similar to silicon and germanium in its chemical bonding and electronic structure, none of the common allotropes of carbon, diamond, graphite or graphene are semiconductors. The recognition that the layered structure of graphite could be cleaved to form a two-dimensional carbon allotrope, graphene, was a significant development in condensed matter physics 1. In contrast, graphite is a layered structure characterized by an sp 2 hybridization between each atom and its three nearest neighbors in a given layer and van der Waals interactions between layers. Diamond is a three-dimensional network of carbon atoms each atom bonds with its four nearest neighbors within sp 3 hybridization. As a pure element, carbon has two well-known, extended allotropes: graphite and diamond, each with distinct properties. It can bond within molecules in different electronic configurations: sp, sp 2, and sp 3. Similar content being viewed by othersĬarbon is one of the essential elements in nature, as it participates in most of the complex organic structures that allow life. In addition, symmetry breaking of the C 60 molecules results in a distribution of bond lengths and creates vibrational modes that serve as a signature of graphullerene. Phonon spectrum calculations confirm the dynamical stability of the material and yield its in- and out-of-plane sound velocities. In the absence of Mg, this allotrope is a pure carbon semiconductor with an indirect band gap. However, the inclusion of Mg atoms transforms the cohesion energy from negative to positive values by forming additional C-Mg bonds, creating an energetically stable material. We find this structure to be meta-stable, owing to the strain produced by the covalent bonding of the molecules. Each of these molecules is connected to six neighbors in a hexagonal network with a total of eight chemical bonds. Structurally, graphullerene is composed of strained C 60 molecules. Ab initio calculations are employed to examine the structure and properties of this material. It has been synthesized in the form (C 60Mg 4) n and subsequently transformed into (C 60) n by removal of the Mg atoms. Graphullerene is a recently discovered, two-dimensional allotrope of carbon formed from C 60 molecules.
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