24 IPR isomers of fullerene C₈₄: Cage deformation as geometrical characteristic of local strains

Abstract

The structures of 24 IPR-isomers of C 84 fullerene with distributed single, double and delocalized bonds are presented. Obtained results are fully supported by DFT quantum-chemical calculations of electronic and geometrical structures of these isomers. Two reasons of instability of fullerene molecules are their radical origin and/or high local strain. Distortion of pentagons as well as hexagons with alternating single and double bonds is the most significant geometrical parameter reflecting local strain of a molecule. These distortions are measured as maximal dihedral angles of those cycles and reach 20 degrees in mostly deformed hexagons and pentagons. In contrast high values of dihedral angles in hexagons with delocalized p-bonds are typical for stable isomers. Other geometric parameters such as valence angles, sums of valence angles and dihedral angles between approximate planes of fused rings have no marked influence on stability. The development of strain-related criteria for fullerene stability will be helpful in the prediction which isomers might potentially be observable in experiment.

Substructural Approach for Assessing the Stability of Higher Fullerenes

“…Indeed, a similar analysis of the bond distribution in higher fullerenes C 72 –C 90 , C 104 [ 33 , 34 , 35 , 36 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 69 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 ], including non-IPR [ 87 , 88 , 89 , 90 , 91 ] and small fullerenes C n (n < 60) [ 92 , 93 , 94 ], confirmed that the instability of fullerenes may depend on two most important factors: (i) the presence of unpaired electrons in a molecule (i.e., an open electron shell), (ii) the excessive local strain of the molecule due to its topology.…”

“…For example, eleven isomers of C 84 have already been isolated and identified. According to the calculations [ 78 , 79 , 127 , 128 ], all of them are located in the range between 0 and 25 kcal/mol (relative to the most favorable by energy IPR isomer 23 (D 2d )). Assuming that this interval, which includes the values of relative total energies of all synthesized isomers and is equal to 25 kcal/mol, can be taken as some criterion of stability and transferred to other higher fullerenes, it turns out that the number of energetically stable fullerenes from C 70 to C 84 should be much greater because the difference between the relative total energies of stable and unstable isomers of other fullerenes is much smaller.…”

“…As a couple of examples, one can cite a theoretical study of endohedral fullerene C 84 with methane molecule inside CH 4 @C 84 , isomer 20 (T d ) [ 119 ], or an experimental attempt to synthesize the same isomer of fullerene C 84 [ 118 ]. It was convincingly shown that the synthesis of this isomer cannot be successful due to its instability resulted from significant local strains in this molecule [ 78 , 79 , 127 ]. Therefore, it can be assumed that the generalized analysis of the electronic structure of already obtained (isolated and characterized) fullerenes from this point of view will reveal general regularities in their structure and, in particular, identify substructures that do not lead to destabilization of the entire molecule.…”

Accurate Thermochemical and Kinetic Stabilities of C84 Isomers

“…Subsequent attempts to assign these two C s isomers have produced conflicting results; a combined electrochemical and DFT (BLYP/6-31G) study assigned C s (b) to be isomer 16 [ C s (V)] and C s (a) to be isomer 14 [ C s (III)], while a B3LYP/6-31G 13 C NMR spectrum indicates the reverse assignment, consistent with single-crystal XRD experiments and a number of independent theoretical and semiempirical investigations. − Moreover, while two C 2 symmetry isomers have been isolated, , to date only one of them has been characterized (i.e., 11 [ C 2 (IV)]) by confirming experimental NMR chemical shifts with those calculated using DFT (B3LYP/6-31G*) . Additional DFT studies ,,, confirmed 11 [ C 2 (IV)] to be the lowest-energy C 2 isomer. It is possible that the other C 2 isomer isolated experimentally is 13 [ C 2 (IV)] as B3LYP/6-31G energies indicate it to be the next most stable.…”

“…Additional DFT studies ,,, confirmed 11 [ C 2 (IV)] to be the lowest-energy C 2 isomer. It is possible that the other C 2 isomer isolated experimentally is 13 [ C 2 (IV)] as B3LYP/6-31G energies indicate it to be the next most stable. However, this has never been proven experimentally.…”