Prediction of low-energy isomers of large fullerenes from C132 to C160

Hybrid ADFT Study of the C104 and C106 IPR Isomers

This work presents a hybrid auxiliary density functional theory (ADFT) study of the neutral and hexaanionic C₁₀₄ and C₁₀₆ fullerenes with the aim to determine their ground state structures. To this end, all C₁₀₄ and C₁₀₆ fullerene structures that obey the isolated pentagon rule (IPR) were optimized with the Perdew-Burke-Ernzerhof generalized gradient approximation followed by a single-point energy calculation with the PBE0 hybrid functional. Our studies show that this composite approach yields relative energies of giant fullerenes that are accurate to around 1 kcal/mol. As a result, the ground states of C₁₀₄, C₁₀₄^6-, and C₁₀₆^6- can be assigned to the isomers 234:C_s, 821:D₂, and 891:C_s, respectively. On the other hand, the energetically lowest lying IPR isomers of C₁₀₆, 331:C_s, 1194:C₂, 534:C₁ are separated by less than 1 kcal/mol which makes an unequivocal ground state assignment by hybrid DFT methods impossible. To guide future experiments, we also report the simulated IR and Raman spectra of the most stable neutral and hexaanionic C₁₀₄ and C₁₀₆ fullerenes.

Generalized structural motif model for studying the thermodynamic stability of fullerenes: from C60to graphene passing through giant fullerenes

A generalized motif model to describe the stability of neutral fullerenes, covering the full range of cage sizes, starting from C₆₀, going through giant fullerenes, and ultimately leading to graphene.

Giant Spherical Cluster with I-C140 Fullerene Topology

We report on an effective cluster expansion of CuBr-linked aggregates by the increase of the steric bulk of the Cp^R ligand in the pentatopic molecules [Cp^RFe(η⁵-P₅)]. Using [Cp^BIGFe(η⁵-P₅)] (Cp^BIG=C₅(4-nBuC₆H₄)₅), the novel multishell aggregate [{Cp^BIGFe(η^{5:2:1:1:1:1:1}-P₅)}₁₂(CuBr)₉₂] is obtained. It shows topological analogy to the theoretically predicted I-C₁₄₀ fullerene molecule. The spherical cluster was comprehensively characterized by various methods in solution and in the solid state.

The topology of fullerenes

Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar graphs and fullerene graphs has grown since they were studied by Goldberg, Coxeter, and others in the early 20th century, and many mathematical properties of fullerenes have found simple and beautiful solutions. Yet many interesting chemical and mathematical problems in the field remain open. In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems. WIREs Comput Mol Sci 2015, 5:96-145. doi: 10.1002/wcms.1207 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website.