Independent sets and the prediction of addition patterns for higher fullerenes

Abstract

Under the assumptions that no two sp 3 carbon atoms are adjacent in the end product of bromination of a fullerene and that the residual π system is a closed shell, graph theory predicts maximum stoichiometries C 60 Br 24 , C 70 Br 26 , C 76 Br 28 , C 84 Br 32 and rules out all but 58 of the ~10 23 addition patterns conceivable for these molecules.

Perfluoroalkylfullerenes

“…Finally, Clare and Kepert predicted that the most stable structure for C 60 Br 24 has T h symmetry and no cage C(sp 3 )–C(sp 3 ) bonds (24 is the largest number of substituents for which such a restriction is possible). 152 , 154 This isomer corresponds to the experimentally observed structure of C 60 Br 24 . 155 In summary, the seminal computational studies of Clare and Kepert revealed important trends for the addition of Br atom to C 60 , which later proved to be relevant for the prediction of CF 3 additions to fullerenes.…”

Relative Stability of Empty Exohedral Fullerenes: π Delocalization versus Strain and Steric Hindrance

“…However, this is not always the case, as for C 54 Cl 8 , C 64 Cl 8 , and C 50 X 12 (X = H, F, Cl) . Fowler et al , have pointed out that those addition patterns in which there is an odd number of bare carbon atoms isolated by addends have open-shell configurations and should be ruled out. Although this condition reduces the number of possible regioisomers, the reduction is not very important.…”

“…Although this condition reduces the number of possible regioisomers, the reduction is not very important. Also, it has been proposed that bulky addends, such as bromine, should never attach to adjacent carbon atoms on the fullerene cage. Using this assumption in combination with the above-mentioned closed-shell condition, Fowler et al have been able to prescreen the relative stability of many regioisomers solely based on topological information .…”

“…Also, it has been proposed that bulky addends, such as bromine, should never attach to adjacent carbon atoms on the fullerene cage. Using this assumption in combination with the above-mentioned closed-shell condition, Fowler et al have been able to prescreen the relative stability of many regioisomers solely based on topological information . However, the nonadjacent addition assumption is often violated, as for C 60 Br 6 , − C 60 (CF 3 ) 14 , C 60 (CF 3 ) 16 , C 70 (CF 3 ) 18 , C 70 (CF 3 ) 20 , etc.…”

Maximum independent sets of the 120-cell and other regular polytopes

“…For example, sets of codes with increasing d may be seen as templates for addition to an underlying molecular framework by addends of increasing steric demand. Codes have been presented for chemically relevant regular and semi-regular polyhedra [15] and arguments based on d-codes, coupled with spectral information, give useful rationalisations of the extent and symmetry of addition in fullerene chemistry, for example [9,10,11]. Although not invoked in chemistry so far, d-anticodes, defined by the requirement that pairwise distances should not exceed d, would model the opposite regime of attachment to a framework where the added groups cluster under strong inter-addend attraction.…”