Isomers of the C84 fullerene: A theoretical consideration within energetic,structural, and topological approaches

Currently, there is no common conception on the stability and achievability of fullerene isomers under the arc-discharge synthesis conditions. Different approaches operate with energetic, structural, and topological parameters of the fullerene molecules to explain why some fullerene isomers are more preferable than the others. In the present work, we have selected the most appropriate approaches based on topological roundness, information entropy, nuclear volumes, and sphericities and compared their predictions with the relevant experimental data on the C₈₄ fullerene isomers (obeying the isolated pentagon rule) and density functional theory estimates of their stability. We have found that the molecules of most stable (and most abundant) C₈₄ isomers have the minimal extremal roundness, maximal sphericity, and largest volume and vice versa. In the case of the information entropy, no correlation is observed. Interestingly, the found correlation between the volume and the stability of the C₈₄ isomers is unexpectedly inverse, i.e. more stable C₈₄ isomers have larger inner cavities inside, though traditionally large volume is associated with instability of hollow framework molecules. We assume that the large volumes allows enhancing the sphericity of the fullerene cages as we found the last one favoring the stability and the unstable C₈₄ fullerene cages having low volumes are far from the spherical shape. We think that the results obtained may be extrapolated to other fullerene isomeric sets and contribute to the understanding the grounds of the interconnection in the triad “topology – structure – energy” underlying structural chemistry.