Super-atom molecular orbital excited states of fullerenes

Abstract

Super-atom molecular orbitals are orbitals that form diffuse hydrogenic excited electronic states of fullerenes with their electron density centred at the centre of the hollow carbon cage and a significant electron density inside the cage. This is a consequence of the high symmetry and hollow structure of the molecules and distinguishes them from typical low-lying molecular Rydberg states. This review summarizes the current experimental and theoretical studies related to these exotic excited electronic states with emphasis on femtosecond photoelectron spectroscopy experiments on gas-phase fullerenes.This article is part of the themed issue 'Fullerenes: past, present and future, celebrating the 30th anniversary of Buckminster Fullerene'.

Keywords: fullerene; photoelectron angular distributions; super-atom molecular orbitals.

Figure 1.

Cuts in the isocontour amplitudes of the Dyson orbitals (representing the probability density of the electron that is ionized) of the s-, p- and d-SAMO states of C₆₀. Adapted from [3].

Figure 2.

(a) Schematic of VMI/MS apparatus. (b) Sketch of the electron/ion optics from above. (Online version in colour.)

Figure 3.

Schematicillustration of the ‘Rydberg fingerprint spectroscopy’ technique used to probe the SAMO and Rydberg excited states of the fullerenes. (a) Multiphoton excitation is followed by very efficient state couplings and population of a wide range of excited states with varying amounts of vibrational energy. Narrow lines indicate vibrational excitation. Only the first two members of the s-series and the first members of the p- and d-series are shown for clarity. The single-headed arrows indicate two different photon energies. The double-headed arrows indicate the photoelectron kinetic energies. Note that the photon energy corresponding to the red arrow is too low to ionize the lowest-lying s-state. (b) (i) Schematic of the photoelectron spectra that would be observed for the two-photon energies shown in (a). (ii) Corresponding electron binding energies. (Online version in colour.)

Figure 4.

VMI images and the corresponding angle-integrated photoelectron spectra for C₆₀, plotted as a function of electron-binding energy, for ionization with three different laser wavelengths: 545 nm, 514 nm and 400 nm (top to bottom).

Figure 5.

(a) Photoelectron angular distribution for the peak in the 400 nm photoelectron spectrum shown in figure 4 at a binding energy of 1.9 eV. (b) Value of the anisotropy parameter, β, as a function of photoelectron kinetic energyfor the peaks assigned to the first (red, triangles) and second (black, squares) members of the s-SAMO series. The data point corresponding to the plot in (a) appears at an electron kinetic energy of E_kin= hν−E_bind=3.1−1.9=1.2 eV. (Online version in colour.)

Figure 6.

Photoelectron angular distributions (PADs) for (a) s-states, (b) p-states and (c) d-states, characterized by the fitted β-value for experiments on C₆₀ (circles), C₇₀ (squares), C₈₂ (up-triangles) and Sc₃N@C₈₀ (down-triangles). The full lines show the calculated β-values for C₆₀ and C₇₀ at the B3LYP/6-31+G(d) level [8]. The dashed lines are C₆₀ CAM-B3LYP/6-31(+)G(d)-Bq(6-31(6+)G(d)) results [19]. Adapted from [9].

Figure 7.

Photoelectron spectra parallel (black) and perpendicular (blue) to the laser polarizationdirection of (a) C₆₀, 500 nm, 4.7 TW cm⁻², (b) C₇₀, 520 nm, 2.9 TW cm⁻², (c) C₈₂, 519 nm, 2.8 TW cm⁻² and (d) Sc₃N@C₈₀, 506 nm, 4.1 TW cm⁻². Adapted from [9].

Figure 8.

Photoionization widths, Γ, plotted on a logarithmic scale versus the photoelectron kineticenergy. Adapted from [19]. (Online version in colour.)

Figure 9.

Comparisonof relative experimental SAMO peak intensities (squares) and the theoretical photoionization width ratios of SAMO states plotted as a function of laser photon energy. (a) Ratio of the s- and p-peak intensities. (b) Ratio of the s- and d-peak intensities. Theoretical values shown by dashed lines (ratio of average values calculated for each band). The numbers in each panel indicate the number of photons needed to access the s and the p- or d-SAMO states, respectively. Adapted from [3]. (Online version in colour.)

Figure 10.

Comparison of experimental anisotropy parameters, β, with calculations using the simple phenomenological model potential shown in the inset. Note that the β value for the s-SAMO is independent of the potential, which can be seen from equation (5.1). (Online version in colour.)