Six different levels of theory agree in predicting a C62 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.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

A combination of topological and quantum mechanical techniques is used to predict the energetically favored isomer set for the experimentally detected but as yet uncharacterized C-116 fullerene. A systematic search and calculation at the QCFF/PI (quantum-consistent force field/pi) semiempirical level of the energies of the 6063 isomers of C-116 that satisfy the isolated-pentagon rule (IPR) find that the isomers in the most stable group have low degrees of eccentricity and are predicted by the highly discriminating hexagon-neighbor rule (HNR), for which a more generally applicable formulation is proposed.

The Stone−Wales rearrangement is analyzed using a newly developed continuous chirality measure. In enantiomerization reactions of chiral fullerenes we find an approximately linear correlation between π-energy and the chirality content of the molecule. These correlations show that the sensitivity to chirality change increases for larger fullerenes. We show its predictive properties and provide an explanation for it on the basis of another observation; namely, that the chirality value decreases monotonically with fullerene size. Comparison of the enantiomerization to other isomerizations of fullerenes is made.

On the basis of a systematic density functional tight-binding study of boron-nitrogen polyhedra (BN)x composed entirely of four- and six-membered rings, it is predicted that octahedron-like structures B12N12, B16N16 and B28N28 are “magic” (i.e. anomalously stable) clusters. The infrared spectrum of B12N12 is predicted. The similarities and differences between these “inorganic fullerenes” and the carbon-based equivalents are outlined. Ahigh stability of the (BN)x clusters is found to correlate with a large HOMO-LUMO gap.

Model semiempirical studies using quantum consistent force field/pi (QCFF/PI) and density functional tight binding (DFTB) methods show the C-20 dodecahedral fullerene to have the lowest energy of all 7595 mathematically possible 20-vertex trivalent polyhedral cages by a substantial margin (estimated at 521 (QCFF/PI) or 125 (DFTB) kJ mol(-1)). A topological invariant based on the distribution of face sizes is used to correlate the energies and predict the best polyhedral structure for C-22, which must be a nonfullerene cage. With 1 square, 10 pentagonal, and 2 hexagonal faces, this structure is verified to be more stable (by 259 (QCFF/PI), 60 (DFTB) kJ mol(-1)) than its nearest trivalent polyhedral rival.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

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).

Abstract The energetic costs of widening the classical fullerene definition to include carbon cages with octagonal as well as pentagonal and hexagonal faces are investigated theoretically. Relative energies of all 16 C40 and 620 C48 cages that can be assembled with one face octagonal, 14 pentagonal and all others hexagonal are calculated within two independent semi-empirical models and compared with the 295 C40 and 2664 C48 one-square, one-heptagon and classical-fullerene cages. All isomers are lo-cal minima on the potential surface, and many non-classical structures fall within the energy range spanned by the classical fullerenes. Penalties for introduction of a single non-classical face increase in the order heptagon < square < octagon, estimated for C48 as 58–123, 108–236, and 329–450 kJ mo−1, respectively, depending on model. The energy variation across the range of classical and non-classical structures is rationalised by extension of the isolated-pentagon rule: when 1

The trivalent polyhedra on upsilon vertices can be classified according to the maximal point-group symmetries of their graphs. A sum rule based on early work by Tutte relates the numbers, n(i), of isomers belonging to groups with g(i) symmetry operations to an analytical function of the vertex count, giving a useful check on isomer enumeration and symmetry assignment.

The energetic cost of introducing square faces to fullerenes with adjacent pentagons is investigated theoretically. Relative energies of all 1735 hypothetical C-40 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/pi) 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 C-40 fullerene but that many such cages are more stable than many C-40 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 C-62 to C-68 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.

Semi-empirical all-valence-electron calculations on polycyclic hydrocarbons with 2, 3 and 4 pentagons show a strong correlation between low curvature and high overall stability, with topological pi stabilisation playing only a minor role. 284 isomers of C30H12 and 51 Of C58H16 are considered. As with the fullerenes themselves, the energies of these protofullerene patches generally follow an isolated-pentagon rule, but a more important requirement for stability in the patch is that both pentagons should lie on its perimeter.

The cost of a pentagon adjacency in a fullerene cage grows linearly from 72 kJ mol−1 for C30 to 111 kJ mol−1 for C60, according to systematic QCFF/PI model calculations on a set of 2624 structural isomers.

Trivalent polyhedra with six square and (x– 4) hexagonal faces are candidates for fully alternating (BN)x'inorganic fullerene' cages. Systematic density-functional tight-binding calculations for 4 ⩽x⩽ 30 show that the most stable isomer of this type will have isolated squares, whenever mathematically possible. This rule of thumb for (BN)x cages is the counterpart of the powerful isolated-pentagon rule for the all-carbon fullerenes.

Semiempirical all-valence-electron calculations on the 45 indacenoid isomers of C30H12 show a strong correlation between low curvature and high overall stability, with topological pi stabilization playing only a minor role. As with the fullerenes themselves, the energies of these protofullerene patches generally follow an isolated-pentagon rule, but a more important requirement for stability in the patch is that both pentagons should lie on its perimeter.