Structure and Properties of the Nonface-Spiral Fullerenes T-C₃₈₀, D₃-C₃₈₄, D₃-C₄₄₀, and D₃-C₆₇₂ and Their Halma and Leapfrog Transforms

Abstract

The structure and properties of the three smallest nonface-spiral (NS) fullerenes NS-T-C₃₈₀, NS-D₃-C₃₈₄, NS-D₃-C₄₄₀, and the first isolated pentagon NS-fullerene, NS-D₃-C₆₇₂, are investigated in detail. They are constructed by either a generalized face-spiral algorithm or by vertex insertions followed by a force-field optimization using the recently introduced program Fullerene. The obtained structures were then further optimized at the density functional level of theory and their stability analyzed with reference to Ih-C₆₀. The large number of hexagons results in a higher stability of the NS-fullerenes compared to C60, but, as expected, in a lower stability than most stable isomers. None of the many investigated halma transforms on nonspiral fullerenes, NS-T-C₃₈₀, NS-D₃-C₃₈₄, NS-D₃-C₄₄₀, and NS-D₃-C₆₇₂, admit any spirals, and we conjecture that all halma transforms of NS-fullerenes belong to the class of NS-fullerenes. A similar result was found to not hold for the related leapfrog transformation. We also show that the first known NS-fullerene with isolated pentagons, NS-D₃-C₆₇₂, is a halma transform of D3-C₁₆₈.

Novel hollow all-carbon structures

“…For the moment we do not distinguish between single, double or triple bonding in the polyhedral graph. 35,39 Here, we use the fact that simple insertions (deletions) of divalent vertices into edges (edge subdivisions) of a graph G results in a graph G ′ (which is homeomorphic to G) with a larger vertex set. 35 The classification of (non-regular) polytopes is currently an open problem.…”

From small fullerenes to the graphene limit: A harmonic force‐field method for fullerenes and a comparison to density functional calculations for Goldberg–Coxeter fullerenes up to C980

“…As the original Wu force field was developed for C 60 ‐ I h only, bonds adjacent to two pentagons were treated in the same way as bonds adjacent to one pentagon and one hexagon in the program Fullerene . The geometry can then be optimized using for example a Fletcher–Reeves–Polak–Ribiere geometry optimization with analytical gradients, which is very computer time efficient even for larger fullerenes containing thousands of carbon atoms …”

Fullerene Stability by Geometrical Thermodynamics

“…Subsequently, it was thought that all stable fullerenes could be decomposed into a single spiral of edge‐connected faces, but this turned out not to be true; in fact, C 380 and C 384 are the two smallest “unspirallable” fullerenes . However, it turns out that that these so‐called “nonface‐spiral” (NS) fullerenes are extremely rare so that the IUPAC recommendation for fullerene numbering based on “spirallability” remains reasonable. However, there are other numbering schemes that are more efficient, more elegant and exception‐free …”