Transition from SAMO to Rydberg State Ionization in C60 in Femtosecond Laser Fields

Superatom Molecular Orbitals of Endohedral C82

Understanding superatom molecular orbital (SAMO) states in fullerene derivatives has been in the limelight ever since the first discovery of SAMOs owing to the fundamental interest in this topic as well as to the possible applications in molecular switches and other organic electronics. Nevertheless, very few reports have been published on SAMO states of larger fullerenes so far. Using density functional theory, we attempt to partially remedy this situation by presenting a study on SAMO states in C82 and its Ca and Sc endohedrally doped derivatives, comparing results with previous relevant findings for C60. We find that C82 possesses higher SAMO energies compared to C60, as associated with the symmetry of the molecule, and that endohedral doping leads to energetically favorable side positions of Ca and Sc inside the C82 cage. Among the two, Sc@C82 has more stable SAMO states compared to Ca@C82 as reflected by the shift in the density of states, while the charge states are found to be similar. In the case of the monolayer form, the pz- and 2s-SAMO orbitals overlap with the nearest neighbors, causing parabolic band dispersion with the formation of near free electron states and that the SAMO state energies move closer to the Fermi energy compared to the related molecules. These findings provide promising information about the distribution of SAMO states in C82 fullerene, which can be further relevant in studies of SAMO states of higher fullerenes and for coming applications of these systems.

Probing C60 Fullerenes from within Using Free Electron Lasers

Fullerenes, such as C60, are ideal systems to investigate energy redistribution following substantial excitation. Ultra-short and ultra-intense free electron lasers (FELs) have allowed molecular research in a new photon energy regime. FELs have allowed the study of the response of fullerenes to X-rays, which includes femtosecond multi-photon processes, as well as time-resolved ionization and fragmentation dynamics. This perspective: (1) provides a general introduction relevant to C60 research using photon sources, (2) reports on two specific X-ray FEL-based photoionization investigations of C60, at two different FEL fluences, one static and one time-resolved, and (3) offers a brief analysis and recommendations for future research.

Light-Induced Ultrafast Molecular Dynamics: From Photochemistry to Optochemistry

By precisely controlling the waveform of ultrashort laser fields, electronic and nuclear motions in molecules can be steered on extremely short time scales, even in the attosecond regime. This new research field, termed "optochemistry", presents the light field in the time-frequency domain and opens new avenues for tailoring molecular reactions beyond photochemistry. This Perspective summarizes the ultrafast laser techniques employed in recent years for manipulating the molecular reactions based on waveform control of intense ultrashort laser pulses, where the chemical reactions can take place in isolated molecules, clusters, and various nanosystems. The underlying mechanisms for the coherent control of molecular dynamics are explicitly explored. Challenges and opportunities coexist in the field of optochemistry. Advanced technologies and theoretical modeling are still being pursued, with great prospects for controlling chemical reactions with unprecedented spatiotemporal precision.

Superatomic Rydberg State Excitation

Superatomic molecular orbitals (SAMOs) have symmetries (angular quantum numbers) similar to those of atoms, and thus, it is possible to realize Rydberg state excitations (RSEs) in superatomic molecules. In this Letter, the feasibility of superatomic Rydberg state excitation (SRSE) is explored using gold superatoms based on first-principles calculations. The results show that the SRSE exists in the high and low excited states of the gold superatoms and their SAMOs make a major contribution to electronic transitions. The radial distribution function of electronic density shows that the main distribution of electrons in the lowest unoccupied molecular orbitals and other unoccupied superatomic molecular orbitals is extremely far from the geometric center, and thus, they can be unambiguously identified as Rydberg orbitals. We found that due to the two-dimensional ductility of the planar SAMOs, superatoms are superior in the RSE regulation. Our findings may provide a new source of superatom-based RSE and will contribute to the regulation and efficient preparation of Rydberg states.

Direct Visualization of Nearly Free Electron States Formed by Superatom Molecular Orbitals in a Li@C60 Monolayer

Using scanning tunneling microscopy (STM) and density functional theory (DFT) calculations, we directly determine the spatial and energetic distributions of superatom molecular orbitals (SAMOs) of an Li@C₆₀ monolayer adsorbed on a Cu(111) surface. Utilizing a weakly bonded [Li⁺@C₆₀] NTf₂^- (NTf₂^-: bis(trifluoromethanesulfonyl)imide) salt makes it possible to produce a Li@C₆₀ monolayer with high concentration of Li@C₆₀ molecules. Because of the very uniform adsorption geometry of Li@C₆₀ on Cu(111), the p_z-SAMO, populated above the upper hemisphere of the molecule, exhibits an isotropic and delocalized nature, with an energy that is significantly lower compared to that of C₆₀. The isotropic overlapping of p_z-SAMOs in the condensed monolayer of Li@C₆₀ results in a laterally homogeneous STM image contributing to the formation of a free-electron-like states. These findings make an important step toward further basic research and applicative utilization of Li@C₆₀ SAMOs.

Caged-Electron States in Endohedral Li Fullerenes

By employing large-scale high-level EA-EOM-CCSD calculations, we have computed and analyzed the low-lying states of neutral Li@C₆₀. Apart from one state, all states are found to be charge-separated states of the type Li⁺@C₆₀^-. The new state is the first reported non-charge-separated state in endohedral alkali fullerenes. This caged-electron state is analyzed in detail. Arguments are given that in larger highly symmetric endohedral fullerenes the caged-electron state can be the electronic ground state of the system. HF and DFT calculations on Li@C₁₈₀ indeed find that the caged-electron state is the ground state and that in its equilibrium geometry Li sits at the center of the cage. Applications are mentioned.

Charge separated states of endohedral fullerene Li@C20

We report on high-level coupled-cluster calculations of electronic states of the neutral endohedral fullerene Li@C₂₀. All computed states of neutral Li@C₂₀ are found to be the charge separated states of the Li⁺@C₂₀ ^- type. Using the state-of-the-art EA-EOM-CCSD method, we found that neutral Li@C₂₀ (D_3d) possesses several valence and superatomic charge separated states with considerable electron binding energies, the strongest bound state of Li⁺@C₂₀ ^- being the 1²E_u state (6.73 eV). The valence charge separated states correspond to two sets of states of C₂₀ ^-. The states 1²E_u, 1²A_2u, 2²E_u, and 2²A_2u correspond to the respective bound states of C₂₀ ^-, and the states 2²A_2g, 1²E_g, 1²A_1g, and 4²E_u correspond to the unbound states of C₂₀ ^-. There are eight superatomic states with electron binding energy higher than 1.0 eV, being much stronger bound than the single weakly bound superatomic state of the parent fullerene anion. The analysis of the radial density distribution of the excess electron on the carbon cage indicates the important role of the inner part of the superatomic states in forming the charge separated states.

Diffractive Imaging of C_{60} Structural Deformations Induced by Intense Femtosecond Midinfrared Laser Fields

Theoretical studies indicated that C_{60} exposed to linearly polarized intense infrared pulses undergoes periodic cage structural distortions with typical periods around 100 fs (1  fs=10^{-15}  s). Here, we use the laser-driven self-imaging electron diffraction technique, previously developed for atoms and small molecules, to measure laser-induced deformation of C_{60} in an intense 3.6  μm laser field. A prolate molecular elongation along the laser polarization axis is determined to be (6.1±1.4)% via both angular- and energy-resolved measurements of electrons that are released, driven back, and diffracted from the molecule within the same laser field. The observed deformation is confirmed by density functional theory simulations of nuclear dynamics on time-dependent adiabatic states and indicates a nonadiabatic excitation of the h_{g}(1) prolate-oblate mode. The results demonstrate the applicability of laser-driven electron diffraction methods for studying macromolecular structural dynamics in four dimensions with atomic time and spatial resolutions.

The Role of Super-Atom Molecular Orbitals in Doped Fullerenes in a Femtosecond Intense Laser Field

The interaction of gas phase endohedral fullerene Ho₃N@C₈₀ with intense (0.1–5 × 10¹⁴ W/cm²), short (30 fs), 800 nm laser pulses was investigated. The power law dependence of Ho₃N@C₈₀^q+, q = 1–2, was found to be different from that of C₆₀. Time-dependent density functional theory computations revealed different light-induced ionization mechanisms. Unlike in C_60, in doped fullerenes, the breaking of the cage spherical symmetry makes super atomic molecular orbital (SAMO) states optically active. Theoretical calculations suggest that the fast ionization of the SAMO states in Ho₃N@C₈₀ is responsible for the n = 3 power law for singly charged parent molecules at intensities lower than 1.2 × 10¹⁴ W/cm².

Low-lying, Rydberg states of polycyclic aromatic hydrocarbons (PAHs) and cyclic alkanes

TD-DFT calculations of low-lying, Rydberg states of a series of polycyclic hydrocarbons and cyclic alkanes are presented.