Explorer Optical activity of the super-atom molecular orbital (SAMO) states in Li@ C60+ conformers

: Super Atom Molecular Orbitals (SAMOs) are electronic excited states found in fullerenes in which an electron is excited to one or, more generally, several virtual orbitals with hydrogen-like character. The photoexcitation mechanism of the SAMO states strongly depends on the symmetry of the fullerene. For instance the SAMOs of the spherical C 60 fullerene are not optically active while breaking the symmetry by adding a dopant can make the SAMO states optically active. In this proceeding we investigate the optical activity of the SAMO states in several conformers of the Li@C 60+ fullerene and we show that the position of the lithium atom inside the fullerene cage strongly affects the computed oscillator strengths and transition dipole moments of the SAMO states.


INTRODUCTION
Fullerenes are nanostructures with a dense manifold of electronic excited states mostly composed of excitations from the HOMO or HOMO-1, to one or more often several virtual orbitals. Depending on the nature of the virtual orbital in which the electron has been promoted, the excited states are called (i) valence excited states if the virtual orbital is localized around the carbon atoms and contains numerous nodal surfaces, (ii) Rydberg states if the orbital is a diffuse hydrogenic orbital localized several tens of angstrom away from the fullerene cage or (iii) Super Atom Molecular Orbital (SAMO) states if the orbital has an hydrogenic character such as in Rydberg states but where the electronic density is localized inside or in the close vicinity of the fullerene cage. Therefore the SAMO states have binding energies that are a few eV higher than Rydberg states.
The SAMO states have been observed in STM experiments of fullerenes adsorbed on surfaces 1-2 and in photoelectron spectroscopy experiments of fullerenes such as C60 3-5 , C70, C82 6 or the endohedral fullerene Sc3N@C80. 6 Despite the dense manifold of excited states and the small number of SAMO states, in visible or near infrared femtosecond photoelectron spectroscopy experiments, the SAMO states dominate the photoelectron spectra because they ionize several orders of magnitude faster than the isoenergetic valence states. Due to the diffuse character and simple hydrogenic shape of the SAMOs, they ionize on a few femtosecond timescale while the valence states ionize on a longer picosecond timescale. 7 Therefore in experiments using femtosecond laser pulses only the SAMO states can ionize significantly during the pulse. The assignment of the SAMO states in the photoelectron spectra is confirmed by determining the angular distribution of the ionized electron 3, 7 that directly depends on the patterns of the corresponding Dyson orbitals. [8][9][10] The Dyson orbital represents the orbital from which the electron is ionized and for the SAMO states, it corresponds to hydrogenic orbitals.
Before being ionized, the SAMO states need to be populated during the pulse and the photoexcitation mechanism strongly depends on the symmetry of the fullerenes. For C60 that has an icosahedral symmetry and belongs to the Ih point group, the SAMO states are not optically active and can only be accessed by vibronic coupling 11 between optically active valence states and the SAMO states, which can take several tens of femtosecond. However the high symmetry of the C60 fullerene can be broken by elongating the cage in one direction and doping the fullerene such as in the Ho3N@C80 fullerene. 12 In endohedral fullerenes the degeneracy of the p and d SAMO is lifted and the SAMOs become optically active, which results in a higher ion yield for Ho3N@C80 compared to C60 when ionized by a 800nm 30fs pulse at intensities lower than 10 14 W/cm 2 . 12 In this article we show that the optical activity and binding energy of the SAMO states of the endohedral Li@C60 + fullerene strongly depends on the position of the lithium atom inside the C60 cage. This dependence should be reflected in the photoelectron spectrum and in the ion yield dependence with the laser intensity.

RESULTS
The optical properties and fragmentation of the neutral Li@C60 fullerene have been reported by the Campbell group. [13][14] In this proceeding, we focus on the optical activity of the SAMO states of the cationic close shell endohedral fullerene Li@C60 + . [15][16] We first determined the equilibrium geometry of several Li@C60 + conformers with the aim to determine the lowest energy one. The electronic structure computations are carried out at the DFT level with the B3LYP functional and a 6-31G(d) basis set for the carbon atoms and a 6-311++G(2df,3dp) basis set for the Li atom. The equilibrium geometries of the low energy conformers are shown in Fig. 1. The conformer with the Li + atom centered in the cage (conformer 3 in Fig. 1) is the least stable. 17 There are three conformers within 0.5kcal/mol in which the Li + atom is slightly off-center. to the most stable conformer are also reported. In the isomer 1, 2 and 4, the lithium is off-center and localized respectively along a 6:5 bond (between a hexagon and pentagon), at the center of a pentagon and at the center of a hexagon for the projection of the fullerene shown here. The shortest Li-C bond for these three isomers is around 2.23 Å, which is shorter than the Li-C bond of the spherical isomer (3.53 Å).
We investigated the electronic structure of the SAMO states and Dyson orbitals for two of the four conformers (Fig. 2), the conformer 3 that retains the spherical symmetry of the bare C60 (the Li ion is at the center of the cage) and the lowest energy conformer in which the Li atom is off-center (conformer 1). The calculated ionization energies of the two conformers are respectively, 11.11eV and 11.02eV. For the conformer 3 with the Li at the center of the cage, we computed the electronic structure of the 400 lowest excited states in CAM-B3LYP with the 6-31G(d) basis set for the C and a 6-31G(d)+6 s,p,d diffuse functions for the Li atom. In order to readily compute the electronic structure, we limited the excitations to build the excited states from the HOMO-4 to the LUMO+100. 18  is not five fold degenerate because of the endohedral Li ion. The energies of the SAMO and Rydberg states computed in the band of the 400 lowest excited states are reported in Table 1 and some of the Dyson orbitals are reported in Fig. 2. Amongst the excited states in which an electron has been excite to a hydrogen like orbital, we differentiate the excited states of the Li ion with respect the SAMO states. The s and p excited states of the Li ion have a binding energy of respectively 7.22eV and 5.11eV and their Dyson orbitals are fully localized inside the fullerene cage. The SAMO states have smaller binding energies (Table 1) and their Dyson orbitals are localized both inside and in the close vicinity of the C60 cage. The first band of s and p SAMO (Fig. 2) are similar to one observed in the bare C60 except that the binding energies are larger, which can be understood from the positive charge of the endohedral fullerene. For the lowest energy conformer, in which the Li ion is not localized at the center of the cage (conformer 1), we computed the electronic structure of the 400 lowest excited states using the same functional and basis set as for the centered Li@C60 + except that we added a ghost atom localized at the center of cage with a 6-31G(d)+6 s,p,d basis set in order to describe accurately SAMO and Rydberg states of the C60 cage. The change of position of the Li ion strongly affects the binding energies and Dyson orbitals of lithium excited states as well as of the p SAMO states ( Table 1). The Dyson orbitals of the excited states in which an electron has been excited to s or p orbital of the Li ion exhibit a strong distortion compared to the Dyson orbitals of the spherical isomer (Fig. 2).  (Table 1). It is not the case of the p SAMO states that are strongly distorted with an accumulation of electronic density on the p lobe close to the lithium ion, which impacts the binding energies. The f and g states have a broader range of binding energies due to the lifting of the degeneracy induced by the off-center Li ion. The bands of SAMO states are no longer well separated as is the case for s and p states in C60. An interesting effect of the symmetry breaking induced by the offcenter Li ion is the non-zero value of transition dipole moments between the ground state and the SAMO states. The magnitude of the transition dipole moments is significantly smaller than for the endohedral fullerene Ho3N@C80 in which the large Ho3N complex induces a stronger effect on the SAMO states than the Li ion. Unlike in the spherical C60 or Li@C60 + with the Li centered in the cage, the SAMO states of Li@C60 + with the lithium off-center can be optically accessed. The absorption spectrum should therefore strongly depend on the position of the Li atom in the cage.

CONCLUSIONS
By using a time-saving way to compute the electronic structure of a large band of excited states in fullerenes in TDDFT, we were able to investigate the effect of the position of the lithium ion in Li@C60 + conformers on the binding energies and transition dipole moments of SAMO states. When the lithium is localized at the center of the cage, the SAMO states are degenerate and they are not optically active, similar to the situation for C60. Once the lithium is moved off-center, it breaks the spherical symmetry, which lifts the degeneracy of the SAMO states and makes them optically active.