Effects of orbital angles on the modeling of conjugated systems with curvature

The remaining p orbitals of carbon atoms form some conjugated systems, such as fullerenes. The non-parallel p orbitals of fullerene conjugated systems dominate their stability. In this work, a model is proposed with a good correlation between model outputs and relative energies of fullerenes. The model is built from the extended Hückel molecular orbital theory and geometrical features, especially the orbital axial angle characteristics. The extended charge stability index (XCSI) proposed in this paper offers a good representation of the stability from small cage to at least C₇₀. The axial angle feature is no longer necessary in large carbon cages, which is similar to previous models based on fullerene deformation factors. In addition, a deep learning model based on spatial orientation features containing spherical harmonic functions yields surprising transferring results on the stability of charged fullerenes. We hope this work will assist in building more general models dealing with problems related to conjugated systems.