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

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.