Internal laser-induced dipole force at work in C60 molecule

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.

High-Stability Light-Element Magnetic Superatoms Determined by Hund's Rule

Achieving stable high-magnetism light-element structures at nanoscale is vital to the field of magnetism, which has traditionally been ruled by transition-metal elements with localized d or f electrons. By first-principles calculations, we show that superatoms made of pure earth-abundant light elements (i.e., boron and nitrogen) exhibit desired magnetic properties that rival those of rare-earth elements, and the magnetism is dictated entirely by Hund's maximum spin rule. Importantly, the chemical and structural stabilities of the superatoms are not jeopardized by its high spins and are in fact better than those of transition-metal-element-embedded clusters. Our work thus establishes the basic principles for designing novel light-element, high-stability, and high-moment magnetic superatoms.

Smallest Organic Tetracation in the Gas Phase: Stability of Multiply Charged Diiodoacetylene Produced in Intense Femtosecond Laser Fields

Coulomb explosion imaging, which is the reconstruction of a molecular structure by measuring the three-dimensional momenta of atomic ions formed by a Coulomb explosion of multiply charged molecular cations (MMCs), has been utilized widely. In contrast, intact MMCs, whose properties and reactions are interesting from both fundamental and applied scientific perspectives, themselves have been little explored to date. This study demonstrates that the four-atom molecule diiodoacetylene (DIA) can survive as a long-lived species in the gas phase after the removal of four electrons in intense femtosecond laser fields. The electron configurations of the equilibrium structures of the electronic ground states calculated by the complete active space self-consistent field (CASSCF) method reveal the stability of multiply charged DIA. The dissociation energies are estimated to be 3.01, 3.59, 2.57, 1.82, and 1.61 eV for neutral, cation radical, dication, trication radical, and tetracation, respectively. A fairly deep potential well suggests that a DIA tetracation is metastable toward dissociation, whereas the repulsive potential of a pentacation radical confirms its absence in the mass spectrum. With their sufficiently long lifetimes, minimum number of atoms, and simple dissociation paths, DIA MMCs are promising candidates for further experimental and theoretical investigations of multiply charged ion chemistry.

Coulomb blocking of sequential tunnel ionization in complex systems

When atoms and molecules are exposed to intense low frequency laser fields, the dominant response is sequential tunnel ionization of charge states with increasing ionization potential. Sequential ionization is assumed to proceed as separate one electron processes. The theoretical analysis developed here reveals that in complex systems sequential tunnel ionization can be inhibited by Coulomb blocking. When ionization potentials of subsequent charge states are close to each other, multiple tunneling events can occur during a half cycle and in close proximity, so that a tunneled electron can block the next tunneling electron. In sub-nm clusters driven by near infrared single-cycle pulses, Coulomb blocking reduces two-electron sequential tunneling by up to 2-3 orders of magnitude.

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.

Unraveling the Metastability of C n2+ ( n = 2-4) Clusters

Pure carbon clusters have received considerable attention for a long time. However, fundamental questions, such as what the smallest stable carbon cluster dication is, remain unclear. We investigated the stability and fragmentation behavior of C _n²⁺ ( n = 2-4) dications using state-of-the-art atom probe tomography. These small doubly charged carbon cluster ions were produced by laser-pulsed field evaporation from a tungsten carbide field emitter. Correlation analysis of the fragments detected in coincidence reveals that they only decay to C _n-1⁺ + C⁺. During C₂²⁺ → C⁺ + C⁺, significant kinetic energy release (∼5.75-7.8 eV) is evidenced. Through advanced experimental data processing combined with ab initio calculations and simulations, we show that the field-evaporated diatomic ¹²C₂²⁺ dications are either in weakly bound ³Π_u and ³Σ_g^- states, quickly dissociating under the intense electric field, or in a deeply bound electronic ⁵Σ_u^- state with lifetimes >180 ps.

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.

Roles of dynamical symmetry breaking in driving oblate-prolate transitions of atomic clusters

This paper explores the driving mechanisms for structural transitions of atomic clusters between oblate and prolate isomers. We employ the hyperspherical coordinates to investigate structural dynamics of a seven-atom cluster at a coarse-grained level in terms of the dynamics of three gyration radii and three principal axes, which characterize overall mass distributions of the cluster. Dynamics of gyration radii is governed by two kinds of forces. One is the potential force originating from the interactions between atoms. The other is the dynamical forces called the internal centrifugal forces, which originate from twisting and shearing motions of the system. The internal centrifugal force arising from twisting motions has an effect of breaking the symmetry between two gyration radii. As a result, in an oblate isomer, activation of the internal centrifugal force that has the effect of breaking the symmetry between the two largest gyration radii is crucial in triggering structural transitions into prolate isomers. In a prolate isomer, on the other hand, activation of the internal centrifugal force that has the effect of breaking the symmetry between the two smallest gyration radii is crucial in triggering structural transitions into oblate isomers. Activation of a twisting motion that switches the movement patterns of three principal axes is also important for the onset of structural transitions between oblate and prolate isomers. Based on these trigger mechanisms, we finally show that selective activations of specific gyration radii and twisting motions, depending on the isomer of the cluster, can effectively induce structural transitions of the cluster. The results presented here could provide further insights into the control of molecular reactions.

Communication: Two-step explosion processes of highly charged fullerene cations C60(q+) (q = 20-60)

To establish the fundamental understanding of the fragmentation dynamics of highly positive charged nano- and bio-materials, we carried out on-the-fly classical trajectory calculations on the fragmentation dynamics of C60(q+) (q = 20-60). We used the UB3LYP/3-21G level of density functional theory and the self-consistent charge density-functional based tight-binding theory. For q ≥ 20, we found that a two-step explosion mechanism governs the fragmentation dynamics: C60(q+) first ejects singly and multiply charged fast atomic cations C(z+) (z ≥ 1) via Coulomb explosions on a timescale of 10 fs to stabilize the remaining core cluster. Thermal evaporations of slow atomic and molecular fragments from the core cluster subsequently occur on a timescale of 100 fs to 1 ps. Increasing the charge q makes the fragments smaller. This two-step mechanism governs the fragmentation dynamics in the most likely case that the initial kinetic energy accumulated upon ionization to C60(q+) by ion impact or X-ray free electron laser is larger than 100 eV.

Laser induced C(60) cage opening studied by semiclassical dynamics simulation

Laser induced opening of the C(60) cage is studied by a semiclassical electron-radiation-ion dynamics technique. The simulation results indicate that the C(60) cage is abruptly opened immediately after laser excitation. The opening of the C(60) cage induces a quick increase in kinetic energy and a sharp decrease in electronic energy, suggesting that the breaking of the C(60) cage efficiently heats up the cluster and enhances the thermal fragmentation of C(60) fullerene.

High-harmonic generation in H2O

We demonstrate high-harmonic generation in H(2)O using 800 and 1300 nm laser pulses up to a maximum intensity of 5x10(14) W/cm(2). Under optimal phase-matching conditions, photon energies up to approximately 60 and approximately 87 eV are produced by using 800 and 1300 nm light, respectively. The harmonic spectra in H(2)O, when compared with Xe with a similar ionization potential, exhibit significant extension of the cutoff region, indicating suppression of ionization arising from molecular orbital symmetry.

Buckminsterfullerene cations: new dimensions in gas-phase ion chemistry

The author provides a brief overview, and shares the extraordinary excitement, of the years of unprecedented discoveries in ion chemistry that followed the first production of fullerene powder in 1990. Various charge states of the buckminsterfullerene C60n+ cation became available by conventional electron-impact ionization of the vapor of this powder and so for mass-spectrometric measurements of ion reactivity. The emphasis here will be on fullerene-ion research performed in the author's own laboratory at York University using electron ionization flow-tube mass spectrometry techniques.

Theoretical study of unimolecular decomposition of allene cations

Ab initio coupled clusters and multireference perturbation theory calculations with geometry optimization at the density functional or complete active space self-consistent-field levels have been carried out to compute ionization energies and to unravel the dissociation mechanism of allene and propyne cations, C(3)H(4)(n+) (n=1-3). The results indicate that the dominant decomposition channel of the monocation is c-C(3)H(3)(+) + H, endothermic by 37.9 kcal/mol and occurring via a barrier of 43.1 kcal/mol, with possible minor contributions from H(2)CCCH(+) + H and HCCCH(+) + H(2). For the dication, the competing reaction channels are predicted to be c-C(3)H(3)(+) + H(+), H(2)CCCH(+) + H(+), and CCCH(+) + H(3)(+), with dissociation energies of -20.5, 8.5, and 3.0 kcal/mol, respectively. The calculations reveal a H(2)-roaming mechanism for the H(3)(+) loss, where a neutral H(2) fragment is formed first, then roams around and abstracts a proton from the remaining molecular fragment before leaving the dication. According to Rice-Ramsperger-Kassel-Marcus calculations of energy-dependent rate constants for individual reaction steps, relative product yields vary with the available internal energy, with c-C(3)H(3)(+) + H(+) being the major product just above the dissociation threshold of 69.6 kcal/mol, in the energy range of 70-75 kcal/mol, and CCCH(+) + H(3)(+) taking over at higher energies. The C(3)H(4)(3+) trication is found to be not very stable, with dissociation thresholds of 18.5 and 3.7 kcal/mol for allene and propyne, respectively. Various products of Coulomb explosion of C(3)H(4)(3+), H(2)CCCH(2+) + H(+), CHCHCH(2+) + H(+), C(2)H(2)(2+) + CH(2)(+), and CCH(2)(2+) + CH(2)(+) are highly exothermic (by 98-185 kcal/mol). The tetracation of C(3)H(4) is concluded to be unstable and therefore no more than three electrons can be removed from this molecule before it falls apart. The theoretical results are compared to experimental observations of Coulomb explosions of allene and propyne.

Fragmentation and ionization dynamics of C60 in elliptically polarized femtosecond laser fields

Ionization and fragmentation of C60 fullerenes is studied in elliptically polarized, intense fs laser fields at 797 nm [I=(0.5-4.3)x10;{14} W cm;{-2}] and contrasted with Xe+, utilizing time-of-flight mass spectrometry. Very pronounced changes of parent and fragment ion yield as a function of ellipticity are observed. At lower intensities reduction of the ion yield for circular polarization establishes a coherent two-photon process connected with the key role of the LUMO+1(t_{1g}) "doorway state" and multielectron dynamics. Comparison with the behavior at 399 nm corroborates this finding. At high intensities enhanced fragmentation is observed which is tentatively attributed to returning loops of electron trajectories by the combined action of the C60+ field and the circular laser field.

Higher-order harmonic generation from fullerene by means of the plasma harmonic method

We demonstrate, for the first time, high-order harmonic generation from C60 by an intense femtosecond Ti:sapphire laser. Laser-produced plasmas from C60-rich epoxy and C60 films were used as the nonlinear media. Harmonics up to the 19th order were observed. The harmonic yield from fullerene-rich plasma is about 25 times larger compared with those produced from a bulk carbon target. Structural studies of plasma debris confirm the presence and integrity of fullerenes within the plasma plume, indicating fullerenes as the source of high-order harmonics.

Theoretical study of the stability of multiply charged C70 fullerenes

We have calculated the electronic energies and optimum geometries of C(70) (q+) and C(68) (q+) fullerenes (q=0-14) by means of density functional theory. The ionization energies for C(70) and C(68) fullerenes increase more or less linearly as functions of charge, consistent with the previously reported behavior for C(60) and C(58) [S. Diaz-Tendero et al., J. Chem. Phys. 123, 184306 (2005)]. The dissociation energies corresponding to the C(70) (q+)-->C(68) (q+)+C(2), C(70) (q+)-->C(68) ((q-1)+)+C(2) (+), C(70) (q+)-->C(68) ((q-2)+)+C(+)+C(+), C(70) (q+)-->C(68) ((q-3)+)+C(2+)+C(+), and C(70) (q+)-->C(68) ((q-4)+)+C(2+)+C(2+) decay channels show that C(70) (q+) (like C(60) (q+)) is thermodynamically unstable for q>or=6. However, the slope of the dissociation energy as a function of charge for a given decay channel is different from that of C(60) (q+) fullerenes. On the basis of these results, we predict q=17 to be the highest charge state for which a fission barrier exists for C(70) (q+).

Single-active-electron ionization of C60 in intense laser pulses to high charge states

Sequential ionization of the C(60) fullerene to high charge states in ultrashort intense laser pulses is investigated within the strong-field S-matrix approach. Ion yields are calculated and saturation intensities are determined for a broad range of laser wavelengths between 395 and 1800 nm at different pulse lengths. Comparisons of the S-matrix predictions for the saturation intensities with recent experimental data are in an overall satisfactory agreement, indicating that saturation of ionization of this complex molecule can be well described using the single-active-electron approach. The analysis of the results shows that the contributions from the h(u)-highest occupied molecular orbital to the ion yields dominate as compared to those from the inner valence shells h(g) and g(g). Finally, it is demonstrated that the suppression of ionization of C(60) and its ions, as observed in experiments, can be interpreted within the present theory as due to the finite cage size of the fullerenes and a multi-slit-like interference effect between partial waves emitted from the different nuclei of the fullerenes.

Control of giant breathing motion in c60 with temporally shaped laser pulses

Femtosecond laser pulses tailored with closed-loop, optimal control feedback were used to excite oscillations in C60 with large amplitude by coherent heating of nuclear motion. A characteristic pulse sequence results in significant enhancement of C2 evaporation, a typical energy loss channel of vibrationally hot C60. The separation between subsequent pulses in combination with complementary two-color pump-probe data and time-dependent density functional theory calculations give direct information on the multielectron excitation via the t(1g) resonance followed by efficient coupling to the radial symmetric a(g)(1) breathing mode.

C60 in intense short pulse laser fields down to 9fs: Excitation on time scales below e-e and e-phonon coupling

The interaction of C60 fullerenes with 765-797 nm laser pulses as short as 9 fs at intensities of up to 3.7 x 10(14) W cm(-2) is investigated with photoion spectroscopy. The excitation time thus addressed lies well below the characteristic time scales for electron-electron and electron-phonon couplings. Thus, energy deposition into the system is separated from energy redistribution among the various electronic and nuclear degrees of freedom. Insight into fundamental photoinduced processes such as ionization and fragmentation is obtained from the analysis of the resulting mass spectra as a function of pulse duration, laser intensity, and time delay between pump and probe pulses, the latter revealing a memory effect for storing electronic energy in the system with a relaxation time of about 50 fs. Saturation intensities and relative abundances of (multiply charged) parent and fragment ions (C60(q+), q=1-6) are fingerprints for the ionization and fragmentation mechanisms. The observations indicate that for final charge states q>1 the well known C60 giant plasmon resonance is involved in creating ions and a significant amount of large fragments even with 9 fs pulses through a nonadiabatic multielectron dynamics. In contrast, for energetic reasons singly charged ions are generated by an essentially adiabatic single active electron mechanism and negligible fragmentation is found when 9 fs pulses are used. These findings promise to unravel a long standing puzzle in understanding C60 mass spectra generated by intense femtosecond laser pulses.

Saturated ionization of fullerenes in intense laser fields

We investigate the ionization of icosahedral fullerenes (C20, C60, C80, and C180) in an intense laser pulse using the S-matrix theory. The results obtained are in excellent agreement with the recent observations of unexpectedly high saturation intensities of the Buckminster fullerene and its multiply charged ions. Our analysis strongly suggests that the related phenomenon of suppressed ionization of these complex fullerenes is due to the finite cage size and the "multislit" interference effect between partial waves emitted from the different nuclei rather than to a dynamical multielectron polarization effect.

Ionisation of fullerenes and fullerene clusters using ultrashort laser pulses

We give a brief review of the literature concerning the ultra-short pulse ionisation of fullerenes in the gas phase. Emphasis is placed on the excitation time dependence of different ionisation regimes as manifested by photoelectron spectroscopy. The ionisation rates are modelled for the intermediate situation where the excitation energy is equilibrated between electronic degrees of freedom but not yet coupled to vibrational degrees of freedom. The model is shown to describe many aspects of the experiments. New results are presented on the intra-cluster molecular fusion of fullerene molecules when van der Waals bound clusters of fullerenes are exposed to ultra-short laser pulses. Pump-probe measurements give a decay time constant for the intra-cluster fusion reaction of 520 +/- 55 fs. A comparison with monomer ionisation results suggests that the time window for the fusion reaction is influenced by the coupling of the electronic excitation energy to vibrational degrees of freedom of the molecules in the cluster.

Structure and electronic properties of highly charged C60 and C58 fullerenes

We present a theoretical study of the structure and electronic properties of positively charged C60(q+) and C58(q+) fullerenes (q = 0-14). Electronic energies and optimum geometries have been obtained using density-functional theory with the B3LYP functional for exchange and correlation. We have found that closed- and semiclosed-shell C60(q+) ions (q = 0, 5, and 10) preserve the original icosahedral symmetry of neutral C60. For other charges, significant distortions have been obtained. The C58(q+) fullerenes are, in general, less symmetric, being C58(8+) the closest to the spherical shape. Most C60(q+) fullerenes follow Hund's rule for spin multiplicity, while most C58(q+) fullerenes are more stable with the lowest spin multiplicity. The calculated ionization potentials for both kinds of fullerenes increase almost linearly with charge, except in the vicinity of C60(10+) and C58(8+). We have also explored the region of the potential-energy surface of C60(q+) that leads to asymmetric fission. Minima and transition states corresponding to the last steps of the fission process have been obtained. This has led us to conclude that, for 3 < or = q < or = 8, C2(+) emission is the preferred fragmentation channel, whereas, for higher q values, emission of two charged atomic fragments is more favorable. The corresponding fission barrier vanishes for q > 14.

Structure and reactivity of C54q+ (q = 0, 1, 2 and 4) fullerenes

Using density functional theory we have studied the structural properties of eleven C54 isomers that appear in the C60 fragmentation. We have evaluated the relative stability of the different isomers with respect the most stable one, which corresponds to the structure with the minimum number (four) of adjacent pentagons. On average, the length of a bond shared by pentagons and/or hexagons increases in the order hexagon-hexagon, hexagon-pentagon and pentagon-pentagon. However, we have found that the central bond in the confluence of four hexagons, i.e. a pyrene substructure, is anomalously large, becoming in some cases the largest one. We have also evaluated the nucleus-independent chemical shifts (NICS) at the center of every individual ring in the most stable isomers. For the chlorine derivatives, our calculations show that the favorite position for chlorine addition are the bonds shared by pentagons.

Numerical Simulation of Nonadiabatic Electron Excitation in the Strong Field Regime. 2. Linear Polyene Cations

Time-dependent Hartree-Fock theory has been used to study the electronic optical response of a series of linear polyene cations (+1 and +2) in strong laser fields. The interaction of ethylene, butadiene, and hexatriene, with pulsed and CW fields corresponding to 8.75 x 10(13) W/cm(2) and 760 nm, have been calculated using the 6-31G(d,p) basis set. Nonadiabatic processes including nonlinear response of the dipole moment to the field and non-resonant energy deposition into excited states were more pronounced for the monocations in comparison with dications. For a given charge state and geometry, the nonadiabatic effects in the charge distribution and instantaneous dipole increased with the length of the polyene. For pulsed fields, the instantaneous dipole continued to oscillate after the field returned to zero and corresponded to a non-resonant electronic excitation involving primarily the lowest electronic transition. For a given molecule and fixed charge state, the degree of nonadiabatic coupling and excitation was greater for geometries with lower excitation energies.

Effects of Polarization of 1.4 μm Femtosecond Laser Pulses on the Formation and Fragmentation of Naphthalene Molecular Ions Compared at the Same Effective Ionization Intensity

Naphthalene was ionized with 130 fs pulses of different polarizations at 1.4 microm. In contrast to the results of ionization by 0.8 microm pulses, fragmentation was dramatically suppressed and naphthalene molecular ions of up to 3+ were produced. The use of this simple model of ionization and large electron kinetic energy enabled us to study the electron-recollision-induced fragmentation and/or double ionization more precisely. The failure of the theoretical prediction of ion yield for the case of naphthalene prevented us from judging the electron recollision solely by a comparison with theoretical curves. Therefore, the effects of laser polarization on the ratios between differently charged states and between molecular and total ions were compared at the same effective (peak) intensity instead of average intensity. Comparison under the same effective intensity enabled us to identify the effects of ellipticity clearly. Evidence of the electron recollision was found in the doubly charged molecular ion formation but not in the fragmentation. The single-electron recollision event was not sufficient to induce fragmentation because of its low energy transfer efficiency. We concluded that the fragmentation originated in the unstable nature of the highly charged molecular ion itself and in the Coulomb explosion in the case of naphthalene.

Theory of tunnel ionization in complex systems

A quasianalytical theory of tunnel ionization is developed that is applicable to general complex systems, such as large molecules. Our analysis reveals strong deviations from conventional tunnel ionization theories, dependent upon the system's geometry, angular momentum, and polarizability. A comparison of our theory with recent C(60) ionization experiments yields reasonable agreement.

Coulomb stability limit of highly charged Cq+60 fullerenes

We perform density functional theory calculations of Cq+60 and Cq+58 fullerenes as well as of transition states related to dissociation of Cq+60 into Cq-s(+)58 and C(s+)2 for charges q=0-14. For q< or =8, the lowest fission barrier corresponds to C+2 emission, whereas, for higher q values, the lowest barrier corresponds to the emission of two atomic fragments [2C]s+ with s> or =2. We conclude that the Coulomb stability limit corresponds to q=14.