Oscillations in the photoionization cross section of C60

Computational tools to study non-covalent interactions and confinement effects in chemical systems

Confinement is a very common phenomenon in chemistry, for example, when molecules are located inside cavities. In these conditions, the electronic structure of atoms and molecules is modified. These changes could be mapped through the interaction with other molecules since non-covalent interactions between molecules are also influenced by confinement. In this work we address both topics, non-covalent interactions, and confined systems, using quantum chemistry tools with new software, emphasizing the importance of analyzing both fields simultaneously.

Photoionization of C60: Effects of Correlation on Cross Sections and Angular Distributions of Valence Subshells

Calculations of the photoionization cross section and asymmetry parameter, β, are performed at the density functional theory (DFT) and time-dependent density functional theory (TDDFT) levels for all 32 valence levels of C₆₀. Accurate numerical results are obtained for the isolated molecule in icosahedral symmetry. A detailed analysis based on the comparison between the DFT and TDDFT results allows the identification of four types of resonances: the well-known confinement resonances of mainly geometrical origin, shape resonances native to the ionization channel, induced shape resonances, and autoionization resonances brought about by interchannel coupling, as well as their different prominence in cross section or asymmetry parameter. Generally, cross sections are enhanced at the TDDFT level, which includes contribution from the bound-state excitations from closed channels, neglected at the DFT level, and the effect persists even well above the highest ionization threshold. This effect is best seen in the total cross section, although not as dramatic as found from simpler models, probably due to the stiffer electronic structure inherent in the full molecular description. The effects of interchannel coupling on individual native resonances are rather less predictable, leading to both enhancement and decreases and often altering the details of the structure significantly. A comparison with the previous accurate total cross-sectional calculations, as well as with the available experimental data, is very good for cross sections but slightly inferior for β's. The results reported can serve as a reference to compare the effects of different environments on C₆₀, as well as chemical substitution, notably endohedral fullerenes.

Orbital Character Effects in the Photon Energy and Polarization Dependence of Pure C60 Photoemission

Recent direct experimental observation of multiple highly dispersive C₆₀ valence bands has allowed for a detailed analysis of the unusual photoemission traits of these features through photon energy- and polarization-dependent measurements. Previously obscured dispersions and strong photoemission traits are now revealed by specific light polarizations. The observed intensity effects prove the locking in place of the C₆₀ molecules at low temperatures and the existence of an orientational order imposed by the substrate chosen. Most importantly, photon energy- and polarization-dependent effects are shown to be intimately linked with the orbital character of the C₆₀ band manifolds which allow for a more precise determination of the orbital character within the third highest occupied molecular orbital (HOMO-2). Our observations and analysis provide important considerations for the connection between molecular and crystalline C₆₀ electronic structure, past and future band structure studies, and for increasingly popular C₆₀ electronic device applications, especially those making use of heterostructures.

A confinement induced spectroscopic study of noble gas atoms using equation of motion architecture: Encapsulation within fullerene's voids

A relativistic study of spectroscopic properties of the endohedral fullerenes Ng@C₆₀^q (where Ng = He, Ne and q=0,±1,±2 are the charges) associated with the C₆₀ molecule has been done using the equation of motion coupled cluster (EOM-CC) methodology. Specific properties estimated are the transition energies, dipole oscillator strengths, and transition probabilities for the low-lying excitations 1s²(¹S₀) → 1snp (¹P₁) (n = 2, 3, 4) for He@C₆₀^q and 1s²2s²2p⁶ (¹S₀) → 1s²2s²2p⁵ns∕nd (¹P₁) (n = 3, 4) for Ne@C₆₀^q, which have been compared with those for the isolated atom to depict the confinement effect of the host molecule on the encapsulated atom. This is accomplished by introducing an effective potential to the atomic Hamiltonian induced by the fullerene moiety and its charge. The EOM-CC results have been compared with those estimated with the random phase approximation (and configuration interaction singles) to understand the effect of electron correlation under such confinement. The systematic and interesting behavior of the properties is highlighted indicating the effect of fullerene cage potential on the redistribution of electron density of the guest atom.

Annular billiard dynamics in a circularly polarized strong laser field

We analyze the dynamics of a valence electron of the buckminsterfullerene molecule (C60) subjected to a circularly polarized laser field by modeling it with the motion of a classical particle in an annular billiard. We show that the phase space of the billiard model gives rise to three distinct trajectories: "whispering gallery orbits," which hit only the outer billiard wall; "daisy orbits," which hit both billiard walls (while rotating solely clockwise or counterclockwise for all time); and orbits that only visit the downfield part of the billiard, as measured relative to the laser term. These trajectories, in general, maintain their distinct features, even as the intensity is increased from 10(10) to 10(14) Wcm-2. We attribute this robust separation of phase space to the existence of twistless tori.

Photon energy dependent valence band response of metallic nanoparticles

We show that the valence band response to photon impact in metallic nanoparticles is highly energy dependent. This is seen as drastic variations of cross sections in valence photoionization of free and initially charge-neutral nanosized metal clusters. The effect is demonstrated in a combined experimental and theoretical study of Rb clusters. The experimental findings are interpreted theoretically using a jellium model and superatom description. The variations are attributed to the changing overlap with the photon energy between the wave functions of diffuse delocalized valence electrons and continuum electrons producing a series of minima in the cross section.

Confinement resonances in photoionization of Xe@C₆₀+

Experimental evidence is presented for confinement resonances associated with photoabsorption by a Xe atom in a C60 cage. The giant 4d resonance in photoionization of Xe is predicted to be redistributed into four components due to multipath interference of photoelectron waves reflected by the cage. The measurements were made in the photon energy range 60-150 eV by merging a beam of synchrotron radiation with a mass/charge selected Xe@C₆₀+ ion beam. The phenomenon was observed in the Xe@C(58)(3+) product ion channel. [corrected]

Electronic structure of C(84) film studied by photoemission measurement and first-principles calculation

We have measured the photoemission spectra of a C(84) film (isomer mixture) with synchrotron radiation. The valence band exhibits abundant spectral features from the Fermi level to ∼18 eV binding energy. The relative intensity between the lowest binding energy feature (labeled as A) and the next lowest binding energy feature (labeled as B) oscillates distinctly within the experimental photon energy region from 21.0 to 63.0 eV. The energy levels and density of states (DOS) are calculated for the D(2d)(23)- C(84) and four D(2) symmetric (D(2)(1), D(2)(5), D(2)(21) and D(2)(22)) C(84) isomers to help us to understand the electronic structure. The experimental features and the theoretical DOS peaks have one-to-one correspondence. The number of electrons occupying the states of feature A is 12 or 13.3, depending on the different kinds of isomer mixtures. The electron occupation of feature B is 18.67 e. With the spherical symmetric approximation, features A and B can be characterized with angular momenta of 6 and 5, respectively. The angular momentum difference is the reason for the photoelectron intensity oscillations.

Relative partial cross sections for single, double, and triple photoionization of C60 and C70

Partial cross sections for the photoion formation from C(60) and C(70) were determined from the yields of singly, doubly, and triply charged ions which were measured by mass spectrometry combined with tunable synchrotron radiation at hnu = 25-120 eV. The dependence of the detection efficiencies on the mass-to-charge ratio was evaluated by using the formula proposed by Twerenbold et al. Corrections of the detection efficiency were found to be critical for obtaining accurate partial cross sections for photoionization of fullerenes. Revisions were made of the partial cross-section curves for single and double photoionization of C(60) and C(70). The curve for triple photoionization of C(70) was newly proposed. The ratios between the cross sections for double and single photoionization increase with hnu and reach saturated values of 0.78 at 85 eV for C(60) and approximately 1.3 at 100 eV for C(70). In contrast, the ratios at 120 eV between the cross sections for triple and single photoionization of C(60) and C(70) amount to 0.14 and approximately 0.38, respectively. The formation mechanism of multiply charged fullerene ions was discussed in terms of valence-electron excitation to antibonding unoccupied orbitals and/or spherical standing waves inside the cavity of a fullerene. This excitation could be followed by Spectator Auger processes and transmission of the excess electronic energy among numerous vibrational degrees of freedom.

Experimental evidence for modulations in the relative double-photoionization cross section of C60 from threshold up to 280 eV

The relative double-photoionization cross section of neutral C60 clusters was investigated using monochromatized synchrotron radiation between 18 and 283 eV. Our measurement of the double-to-single photoionization ratio reveals two modulating components that are superimposed on a smooth ratio curve from threshold (19.0 eV) up to 280 eV, when inner-shell excitations become possible. The maxima in the modulation can be related to geometrical dimensions of the C60 cluster.

Strong oscillations in molecular valence photoemission intensities

Photoemission from the two outermost ionizations [highest occupied molecular orbitals (HOMO and HOMO-1)] of Mg(eta(5)-C(5)H(5))(2) has been studied with synchrotron radiation in the gas phase. Strong oscillations in the HOMO-1/HOMO ratio, qualitatively similar to those well-known for fullerenes, are found. Excellent agreement with the experimental ratio is provided by accurate cross section calculations both at the density-functional theory and time-dependent density-functional theory level, indicating that a many electron response has a minor role for this effect. A comparison with the calculated values for other metal sandwich compounds indicate that the presence of oscillations is a widespread phenomenon, and a potential source of interesting information on the structural and electronic properties of the target molecule.

Multiphoton photodetachment of C60-

A model delta-function potential is considered for simulating the interaction of the attached electron in C(60) (-) with the fullerene environment. The analytical expressions for the energy eigenstates, and the Green's function, are used to deduce the one-, two-, and three-photon photodetachment probabilities for C(60) (-). Particularly interesting is the observation that the three-photon photodetachment is greatly enhanced by the bound states with energies close to the energies for resonant absorption of one and two photons, and a resonance in the l=3 state.

Imaging delocalized electron clouds: photoionization of C(60) in Fourier reciprocal space

The dynamics of the photoionization of the two outermost orbitals of C(60) has been studied in the oscillatory regime from threshold to the carbon K edge. We show that geometrical properties of the fullerene electronic hull, such as its diameter and thickness, are contained in the partial photoionization cross sections by examining ratios of partial cross sections as a function of the photon wave number in the Fourier conjugated space. Evaluated in this unconventional manner photoemission data reveal directly the desired spatial information.

Experimental evidence of a dynamic Jahn-Teller effect in C60(+)

Detailed analysis of the highest occupied molecular orbital band shape in the photoelectron spectrum of gaseous C60 reveals a dynamic Jahn-Teller effect in the ground state of C60(+). The direct observation of three tunneling states asserts a D(3d) geometry for the isolated cation, originating from a strong vibronic coupling. These results show that the ionic motion plays an important role in the electron-phonon interaction.