Correlation between energies of proper fullerenes and their topological invariants. Part 1. Fullerenes with abutting pentagons

For all constitutional isomers of proper fullerenes with N = 50 and 60 carbon atoms, correlations for molecular mechanics-derived energies with r around 0.98 were developed by multilinear regression using four to six molecular descriptors. The descriptors are based on the sizes and disposition of polygons surrounding each edge. By treating separately the 1812 C-60 isomers and the 271 C-50 isomers, standard deviations around 4.2 and 3.3 kcal/mol, respectively, were obtained; if one combines all these isomers and if one includes the number of carbon atoms as an additional descriptor, standard deviations s of about 4.0 kcal/mol result. For systems with N < 50 carbon atoms, the correlations are less good.