D. Mitchell

BORON-NITROGEN ANALOGUES OF THE FULLERENES : ELECTRONIC AND STRUCTURAL PROPERTIES

Abstract 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 B 12 N 12 , B 16 N 16 and B 28 N 28 are “magic” (i.e. anomalously stable) clusters. The infrared spectrum of B 12 N 12 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.

Increasing cost of pentagon adjacency for larger fullerenes

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.

Boron–nitrogen analogues of the fullerenes: the isolated-square rule

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.

Energetics of fullerenes with heptagonal rings

The energetic costs of widening the fullerene definition to include carbon cages with heptagonal as well as pentagonal and hexagonal faces are investigated theoretically. Relative energies of all 426 hypothetical C40 cages that can be assembled from pentagonal, hexagonal and heptagonal faces are calculated within two independent semi-empirical 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 heptagons is of lower energy than the best classical C40 fullerene, but that many such cases are more stable than many C40 fullerenes. All one-heptagon C40 cages are predicted to lie within the range of energies spanned by the classical fullerene isomers. Energy penalties of 90–150 kJ mol–1 per heptagon are suggested by the DFTB calculations, and penalties about half as large again by the QCFF/PI model. The energy variation across the range of fullerenes and pseudo-fullerenes is rationalised by an extension of the isolated-pentagon rule: when heptagons are present, structures of low energy are those that maximise the number of pentagon–heptagon contacts subject to prior minimisation of the number of pentagon–pentagon adjacencies.

Structures and energetics of dimeric fullerene and fullerene oxide derivatives

Semi-empirical models confirm the stability of bridged dimer structures assigned in the literature to C120, C120O and C120O2, interpreting all three as additions across formal double bonds of the C60 monomers. Analogous structures are proposed and compared for C60/C70 dimers C130, C130O, C130O2, C140, C140O and C140O2.

Energetics of Fullerenes with Octagonal Rings

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

A generalized Stone - Wales map: energetics and isomerizations of carbon cages

The generalization of the Stone - Wales (SW) rearrangement to act on any edge of a carbon polyhedron is discussed. Nine such polyhedral Stone - Wales (PSW) transformations are possible for a fullerene. Energies and geometric structures are obtained within the semi-empirical QCFF/PI (quantum consistent force field/) model for all non-fullerene cages (935 in total) that can be reached in one PSW step from a classical fullerene. Many have lower energies than at least some fullerenes. An isomerization map can be constructed using only SW and PSW links that connect all 40 classical fullerenes and involves only intermediates within the fullerene energy range.

A sum rule for symmetries and isomer counts of trivalent polyhedra

The trivalent polyhedra on v 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, ni, of isomers belonging to groups with gi symmetry operations to an analytical function of the vertex count, giving a useful check on isomer enumeration and symmetry assignment.

ELECTRONIC AND STERIC FACTORS IN THE STABILITY OF A PROTOFULLERENE FRAMEWORK : INDACENOID ISOMERS OF C30H12

Semiempirical all-valence-electron calculations on the 45 indacenoid isomers of C3&2 show a strong correlation between low curvature and high overall stability, with topological n 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.