Estimates of effective Hubbard model parameters for ${\text{C}}_{20}$ isomers

We report on an effective Hubbard Hamiltonian approach for the study of electronic correlations in ${\text{C}}_{20}$ 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 ${\text{C}}_{20}$ fullerene cage we estimate $t_{\text{cage}}\simeq 0.68–1.36\text{eV}$ and ${\left(U/t\right)}_{\text{cage}}\simeq 7.1–12.2$. 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 ${\text{C}}_{20}$ isomers. Energy gaps are also extracted for possible future comparison with experiments.

Figure 1

(Color online) Molecular structures of ${\text{C}}_{20}$ isomers: (a) cage, (b) bowl, and (c) ring.

Figure 2

(Color online) DOS from DFT for neutral cage, bowl, and ring ${\text{C}}_{20}$ isomers. Fermi energy is located at $\omega =0$. Shaded areas are occupied by electrons.

Figure 3

(Color online) Evolution of the DOS with different $U/t$ values for neutral ${\text{C}}_{20}$ isomers: cage, bowl and ring. $U/t=5$ for cage isomer is from exact diagonalization (Ref. 11). Others are from QMC simulations. Fermi energies are located at $\omega =0$.

Figure 4

(Color online) Variation in affinity energy with $U/t$ for the ${\text{C}}_{20}$ cage, bowl, and ring from QMC and ED calculations. The experimental $\text{AE}$ values are shown by the horizontal lines intercepting the $\text{AE}\sim U/t$ curves. The corresponding $U/t$ values are shown by the vertical lines intercepting the curves. Results are shown using the upper bound for $t$ for the cage and bowl.

Figure 5

(Color online) QMC results for the DOS of one-electron-doped ${\text{C}}_{20}$ (solid lines) compared with the neutral molecules (dashed lines). For the bowl, ${\left(U/t\right)}_{\text{bowl}}=4.30$; for the ring, ${\left(U/t\right)}_{\text{ring}}=3.27$. Shaded areas are occupied by electrons. Fermi energies are located at $\omega =0$. Energy units have been converted to eV using $t_{\text{bowl}}=2.36\text{eV}$ and $t_{\text{ring}}=3.16\text{eV}$, respectively. Energy gaps for the neutral molecules and doped ring are shown in the figure.