Effects of exchange-correlation potentials on the density-functional description of ${\mathrm{C}}_{60}$ versus ${\mathrm{C}}_{240}$ photoionization

We study the photoionization properties of the ${\mathrm{C}}_{60}$ versus ${\mathrm{C}}_{240}$ molecule in a spherical jellium frame of the density-functional method. Two prototypical approximations of the exchange-correlation (xc) functional are used: (i) the Gunnarsson-Lundqvist parametrization [Gunnarsson and Lundqvist, Phys. Rev. B 13, 4274 (1976)] with a correction for the electron self-interaction (SIC) introduced artificially from the outset and (ii) a gradient-dependent augmentation of approximation (i) using the van Leeuwen and Baerends model potential [van Leeuwen and Baerends, Phys. Rev. A 49, 2421 (1994)], in lieu of SIC, that restores electrons' asymptotic properties intrinsically within the formalism. Ground-state results from the two schemes for both molecules show differences in the shapes of mean-field potentials and bound-level properties. The choice of an xc scheme also significantly alters the dipole single-photoionization cross sections obtained by an ab initio method that incorporates linear-response dynamical correlations. Differences in the structures and ionization responses between ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{240}$ uncover the effect of molecular size on the underlying physics. Analysis indicates that the collective plasmon resonances with the gradient-based xc option produce results noticeably closer to the experimental data available for ${\mathrm{C}}_{60}$.

Figure 1

(a) Ground-state radial wave functions for ${\mathrm{C}}_{60}$ HOMO (H) levels and both ${\mathrm{C}}_{240}$ HOMO and HOMO-1 levels calculated in SIC and LB94. (b) Corresponding radial potentials are shown. Shell widths are identified. Energy bands of $\sigma$ and $\pi$ characters (see text), obtained only in LB94, are illustrated.

Figure 2

Photoionization cross sections for the HOMO level calculated in SIC and LB94 for (a) ${\mathrm{C}}_{60}$ and (b) ${\mathrm{C}}_{240}$.

Figure 3

Photoionization cross sections for the HOMO-1 level calculated in SIC and LB94 for (a) ${\mathrm{C}}_{60}$ and (b) ${\mathrm{C}}_{240}$.

Figure 4

Total cross sections calculated in SIC and LB94 for (a) ${\mathrm{C}}_{60}$ and (b) ${\mathrm{C}}_{240}$. The corresponding single-electron (LDA) results using LB94 are also shown.

Figure 5

Total $\pi$-band cross sections in SIC and LB94 for (a) ${\mathrm{C}}_{60}$ and (b) ${\mathrm{C}}_{240}$. Curves are scaled at higher energies to illustrate a strong minimum (see text). The total cross sections are also displayed for comparisons.

Figure 6

Total $\sigma$-band cross sections in SIC and LB94 for (a) ${\mathrm{C}}_{60}$ and (b) ${\mathrm{C}}_{240}$. The total cross sections are also displayed for comparisons.

Figure 7

Lorentzian fits to the total cross sections (also shown) obtained from LB94. These are compared with the fits of the corresponding SIC results. Two sets of experimental data [13, 20], appropriately redshifted, are included to aid the comparison between plasmonic responses obtained via two xc schemes.