A Simple Model for Relative Energies of All Fullerenes Reveals the Interplay between Intrinsic Resonance and Structural Deformation Effects in Medium-Sized Fullerenes

Fullerenes are sheets
of sp2 carbon
atoms wrapped around to form spheres. With this simple consideration,
we have in the present study devised and (with over 3600 DFT data
points) successfully validated a simple model, termed R+D, for estimating
the relative energies of fullerenes. This model contains a resonance
component to account for the intrinsic differences between the π-energies
of different fullerenes, and a deformation component for treating
the distortions from planarity. Notably, we find that both terms (and
they alone) are required to obtain good relative energies, which lends
support to the formulation of the R+D model. An interesting finding
is that for some medium-sized IPR fullerenes, their isomers show similar
variations in the two components. We deduce that these fullerenes
may represent a good opportunity for tuning molecular properties for
practical applications. We hope that the promising results of the
present study will encourage further investigations into fullerenes
from a fundamental perspective.