Six different levels of theory agree in predicting a C 62 cage with one heptagonal, 13 pentagonal, and 19 hexagonal rings to be of lower total energy than all 2385 "classical" 12-pentagon fullerene isomers. At the LDA level of density functional theory the nonclassical structure, which uniquely has three pentagon-pentagon and five pentagon-heptagon edges, is more stable than its nearest fullerene rival by 36 kJ mol -1 .
The energetic cost of introducing square faces to fullerenes with
adjacent pentagons is investigated theoretically.
Relative energies of all 1735 hypothetical C40 cages
that can be assembled from square, pentagonal, and
hexagonal faces are calculated within two independent semiempirical
models. All isomers are found to lie
in local minima on the potential surface. The QCFF/PI (quantum
consistent force field/π) and DFTB (density
functional tight binding) approaches agree in predicting that no cage
with one or more squares is of lower
energy than the best classical C40 fullerene but that many
such cages are more stable than many C40
fullerenes.
Energy penalties of 160−200 kJ mol-1 per square
are suggested by the DFTB calculations, and penalties of
about twice this size by the QCFF/PI model. The energy variation
across the range of fullerenes and
pseudofullerenes is steric in origin and correlates well with the
normalized second moment of the hexagon
neighbor signature: aggregation of hexagons in one part of the cage
surface is incompatible with even
distribution of curvature and implies crowding of defects elsewhere.
QCFF/PI calculations for selected isomers
of C62 to C68 also show that though cages with
squares may again be more stable than some fullerenes,
they
are all bettered in energy by the best classical fullerene at each
nuclearity.
Trivalent polyhedra with six square and (x -4) hexagonal faces are candidates for fully alternating (BN), 'inorganic fullerene' cages. Systematic density-functional tight-binding calculations for 4 d x d 30 show that the most stable isomer of this type will have isolated squares, whenever mathematically possible. This rule of thumb for (BN), cages is the counterpart of the powerful isolated-pentagon rule for the all-carbon fullerenes.
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