Estimates of Effective Hubbard Model Parameters for C20 isomers

We report on an effective Hubbard Hamiltonian approach for the study of electronic correlations in C$_{20}$ isomers, cage, bowl and ring, with quantum Monte Carlo and exact diagonalization methods. The tight-binding hopping parameter, $t$, in the effective Hamiltonian is determined by a fit to density functional theory calculations, and the on-site Coulomb interaction, $U/t$, is determined by calculating the isomers' affinity energies, which are compared to experimental values. For the C$_{20}$ fullerene cage we estimate $t_{\rm cage}\simeq 0.68-1.36$ eV and $(U/t)_{\rm cage} \simeq 7.1-12.2$. The resulting effective Hamiltonian is then used to study the shift of spectral peaks in the density of states of neutral and one-electron-doped C$_{20}$ isomers. Energy gaps are also extracted for possible future comparison with experiments.