The leapfrog principle for boron fullerenes: a theoretical study of structure and stability of B112

Abstract

Two leapfrog isomers of a B(112) boron fullerene are constructed from small C(28) fullerenes (T(d) and D(2) symmetries) by the leapfrog transformation combined with omnicapping of the new hexagons. Their electronic structure is analyzed using the density functional theory at the B3LYP/SVP and BHLYP/SVP levels. Both isomers are characterized as minima on the potential energy hypersurface with a HOMO-LUMO gap at B3LYP/SVP of 1.7 eV and 1.6 eV (3.1 and 3.0 eV at BHLYP/SVP), respectively. The optimized structure of the helical D(2)-leapfrog is asymmetric, due to radial displacements of the capping atoms. The computed cohesive energies amount to -4.2 eV (∼0.04 eV lower than B(80)). The B(112) isomers are isoelectronic to T(d)-C(84) and D(2)-C(84), and HOMO and LUMO orbitals in both isomers closely resemble those of their C(84) homologues. Energetic stability of leapfrog boron fullerenes depends on the isolation of empty hexagon criterion, which is defined by the empty hexagon index based on the total number of empty hexagon pairs and empty hexagon-pentagon fused pairs. The switch of the cap atom to the nearest or farthest empty hexagon destabilizes the cage by 1.6 and 2.7 eV, respectively. The destabilization becomes more enhanced in non-leapfrog structures wherein more caps are displaced.

The Boron Conundrum: Which Principles Underlie the Formation of Large Hollow Boron Cages?

“…Most of the structures have a HOMO-LUMO gap between 0.83 and 1.6 eV and none of them has a HOMO-LUMO gap exceeding that of the leapfrog B 80 , which confirms earlier reports that the leapfrog principle could produce boron nanocages with the largest HOMO-LUMO gaps. [17] In our case, the structure with the largest HOMO-LUMO gap does not have any bound caps, while the most stable isomer in energy at a lower level of theory contains four interacting endo-caps localised on hexagons (Figure 1 d and e). These interactions of caps in B 80 may activate the formation of multiple-shell structures.…”

“…This is not encountered in the leapfrog boron fullerene, in which all caps are sited on hexagons and are oriented either in endohedral or exohedral direction. [17,49]…”

“…Similar indices were used successfully for carbon fullerenes [50] and recently for the boron leapfrog fullerenes. [17] We used pentagon {p 0 ,p 1 ,p 2 ,p 3 ,p 4 ,p 5 } and hexagon {e 0 ,e 1 ,e 2 ,e 3 ,e 4 ,e 5 ,e 6 } signatures to characterise the volleyball isomers. The p k or e i elements of the signatures denote the number of capped pentagons or capped hexagons ,respectively, with k or i capped hexagon neighbours.…”

“…Thus, several hypotheses have been proposed to generate large families of stable boron cages. [11][12][16][17][18][19] One of the most important concepts is the leapfrog principle, [17][18] which underlies the most widely studied large boron cluster, the buckyball B 80 . [20] The actual symmetry of this leapfrog B 80 , I h versus T h , is still controversial depending on the method used, [21] but the energy difference between the two forms is very small.…”

“…[27][28][29] The core-shell clusters are highly coordinated and compact forms of boron build around an inner icosahedral B 12 core and are probably precursors to the solid state. [17] The formation of trivalent cages, such as carbon fullerenes, is not beneficial for boron as it leads to structures with a high electron deficiency. In contrast, boron has the tendency to form triangles, for instance, in the many known polyhedral boranes.…”