Aromaticity, Coulomb repulsion, π delocalization or strain: who is who in endohedral metallofullerene stability?

Endohedral metallofullerenes (EMFs) synthetized in the laboratory are known to often violate the isolated pentagon and pentagon adjacency penalty rules that successfully describe the relative stability of pristine fullerene isomers. To explain these anomalies, several models have been proposed. In this work, we have systematically investigated the performance of the widely used IPSI (inverse pentagon separation index), ALA (additive local aromaticity) and CSI (charge stabilization index) models in predicting the relative stability of a large number of EMF isomers with cages ranging from C28 to C104 and charge states of 4- and 6-. By explicitly comparing with existing experiments and quantum chemistry calculations, we show that the predictive power of the ALA and CSI models is similarly good, with CSI being slightly superior though computationally much less involved. IPSI's performance is generally worse though still acceptable in a wide range of cage sizes, except for the higher charge states in the C62 to C82 size interval. From our analysis, we conclude that neither Coulomb electronic repulsion (IPSI) nor aromaticity (ALA) are the sole parameters governing the relative stability of EMF isomers. Electron delocalization in the π shell in combination with minimum strain (CSI) provides a more realistic description of the relative stabilities observed experimentally, as the former can compensate an unfavorable Coulomb repulsion and account for stabilizing binding effects that do not necessarily translate into aromaticity.