Progress towards a realistic theoretical description of ${\text{C}}_{60}$ photoelectron-momentum imaging experiments using time-dependent density-functional theory

We have studied theoretical photoelectron-momentum distributions of ${\mathrm{C}}_{60}$ using time-dependent density functional theory (TDDFT) in real time and including a self-interaction correction. Our calculations furthermore account for a proper orientation averaging allowing a direct comparison with experimental results. To illustrate the capabilities of this direct (microscopic and time-dependent) approach, two very different photo-excitation conditions are considered: excitation with a high-frequency XUV light at 20 eV and with a low-frequency IR femtosecond pulse at 1.55 eV. The interaction with the XUV light leads to one-photon transitions and a linear ionization regime. In that situation, the spectrum of occupied single-electron states in ${\mathrm{C}}_{60}$ is directly mapped to the photoelectron spectrum. On the contrary, the IR pulse leads to multiphoton ionization in which only the two least-bound states contribute to the process. In both dynamical regimes (mono- and multiphoton), calculated and experimental angle-resolved photoelectron spectra compare reasonably well. The observed discrepancies can be understood by the theoretical underestimation of higher-order many-body interaction processes such as electron-electron scattering and by the fact that experiments are performed at finite temperature. These results pave the way to a multiscale description of the ${\mathrm{C}}_{60}$ ionization mechanisms that is required to render justice to the variety of processes observed experimentally for fullerene molecules.

Figure 1

Combined PES and PAD of ${\mathrm{C}}_{60}$ obtained at ${\omega }_{\mathrm{las}}=20$ eV given by (a) our calculations $(I=7.8\times {10}^9$ $\mathrm{W}/{\mathrm{cm}}^2$, duration of 60 fs, and orientation averaged) and (b) our experimental measurements using synchrotron radiation. The two-dimensional projections of the Newton sphere (VMI-like raw image) in panel (a) and of the synchrotron raw VMI image in panel (b) are plotted in panels (c) and (d), respectively. The laser polarization is vertical.

Figure 2

Top panel: Theoretical (blue thin line) and experimental (red thick line) photoelectron spectra under the conditions of Fig. 1 (one-photon regime). The vertical bars indicate the static single-particle density of states upshifted by the laser frequency and downshifted by 0.3 eV to account for the Coulomb shift due to a final ionization of 0.1. Middle and bottom panels: Corresponding angle-resolved distributions obtained from Legendre polynomial fits of the HOMO (middle panel) and HOMO-1 (bottom panel) levels. The shaded areas take into account the error bars in ${\beta }_2$ (0.25 for the experiment, in dark gray, and 0.1 for the theory, in light gray); see text for detail.

Figure 3

Multiphoton excitation of ${\text{C}}_{60}$ with a laser of ${\omega }_{\mathrm{las}}=1.55$ eV, a duration of $T_{\mathrm{pulse}}=60$ fs, and an intensity of about $1.25\times {10}^{13}$ $\mathrm{W}/{\mathrm{cm}}^2$. Top panel: Comparison of theoretical (blue thin line) and experimental (red thick curve) photoelectron spectra in logarithmic scale. Bottom panel: Calculated depletions (blue solid) of single-particle states, compared with a density-of-states depletion from all orbitals (green dots). The single-particle energies have been downshifted by 0.2 eV to account for a Coulomb shift due to a total ionization of 0.06.

Figure 4

Experimental photoangular distribution from HOMO and HOMO-1 states (red dashed curve) of ${\mathrm{C}}_{60}$ in the same multiphoton regime as in Fig. 3, compared with total theoretical PADs, one taking into account only direct electronic emission (blue thin line) and the other one including in addition thermal fluctuations due to electronic temperature (green thick line).