Structural Motifs and the Stability of Fullerenes

Abstract

Full geometry optimization has been performed within the semiempirical QCFFPI model for the 18 12 fullerene structural isomers of c 6 0 formed by 12 pentagons and 20 hexagons. All are local minima on the potential energy hypersurface. Correlations of total enery with many structural motifs yield highly scattered diagrams, but some exhibit linear trends. Penalty and merit functions can be assigned to certain motifs: inclusion of a fused pentagon pair entails an average penalty of 11 1 kJ mol-'; a generic hexagon triple costs 23 kJ mol-';a triple (open or fused) comprising a pentagon between two hexagonal neighbors gives a stabilization of 19 kJ mol-'. These results can be understood in terms of the curved nature of fullerene molecules: pentagons should be isolated to avoid sharp local curvature, hexagon triples are costly because they enforce local planarity and hence imply high curvature in another part of the fullerene surface, but hexagon-pentagon-hexagon triples allow the surface to distribute steric strain by warping. The best linear fit is found for H, the second moment of the hexagon-neighbor-index signature, which fits the total energies with a standard deviation of only 53 kJ mol-' and must be minimized for stability; this index too can be interpreted in terms of curvature.

Archetypal energy landscapes

“…Excluding enantiomers, there are 1,812 different isomers for C 60 with 12 pentagonal and 20 hexagonal faces, and following Austin et al 31 we have performed geometry optimizations for all these minima. Austin et al 32 have also investigated the connectivity of the same set of minima under a generic rearrangement mechanism proposed by Stone and Wales 33 .…”

Strain Energies Due to Nonplanar Distortion of Fullerenes and Their Dependence on Structural Motifs

“…13 Their results are reasonable in terms of the curved nature of fullerene molecules: pentagons should be isolated to avoid sharp local curvature; moreover, hexagon triples are costly because they enforce local planarity and hence imply high curvature in another part of the fullerene surface, but hexagonpentagon-hexagon triples allow the surface to distribute steric strain by warping. 13 In a similar way, this methodology was applied to the study of the standard heats of formation (∆H f 0 ) of fullerenes by Cioslowski et al 11 Due to the absence of abutting pentagons, hexagons in fullerenes possess only five distinct first neighborhoods and this arrangement of rings gives rise to 30 possible structural motifs. 11 Furthermore, the values of ∆H f 0 calculated from B3LYP/6-31G(d) can be reproduced within 3 kcal/mol by a simple scheme based upon counts of these motifs.…”

Structure and Electronic Properties of Fullerenes C52q+: Is C522+ an Exception to the Pentagon Adjacency Penalty Rule?

“…This parameter was introduced to quantify the steric strain in the fullerene and has been found to correlate roughly linearly with the relative energies for a large series of fullerene isomers, [25,45] and it has only a partially predictive value. [46] Structure 4 deserves a separate discussion since it is the only isomer considered in this work that presents a nonclassical structure.…”

“…Isomer 2, despite À1 ] at different levels of theory. The structural properties are characterised using the following parameters: symmetry of the neutral before geometry optimisation (the parentheses indicate the number given to the isomer in the CAGE [43] program), structural properties (C4 AP, C3 AP, 2 AP and S refer to chain of four adjacent pentagons, chain of three adjacent pentagons, two adjacent pentagons and square ring, respectively), number of adjacent pentagons (NAP), hexagon neighbour signature, h k , [25,45] (see text), normalised second moment of the hexagon signature, H, [25] (see text the absence of symmetry, also presents a low value of SP. As shown in Table 2, the value of SP tends to decrease for all the structures when the fullerene charge increases.…”