Structure and properties of the nonface-spiral fullerenes T-C₃₈₀, D₃-C₃₈₄, D₃-C₄₄₀, and D₃-C₆₇₂ and their halma and leapfrog transforms.

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.