Valence bond multiple excitation RVB calculations on the singlet ground states of some carbon fullerenes Cn with 20⩽n⩽60

A detailed analysis of the nature of the π-VB singlet ground state in terms of multiply excited resonance valence bond (RVB) wavefunctions is presented for some carbon fullerenes in the range from 20 to 60 atoms by comparison to exact solutions of the Heisenberg model for fullerenes of up to 30 atoms. It is found that singlet pair excitations over an odd number of bonds are more important than those over even ones. By far the most important contributions to the ground-state energies besides the non-excited Kekulé RVB space come from those RVB functions containing singlet pair excitations over three carbon bonds.