Modelling of Krn+ clusters (n=2–20). I. Structures and energetics

Two-Center Interference in the Photoionization Delays of Kr_{2}

We present the experimental observation of two-center interference in the ionization time delays of Kr_{2}. Using attosecond electron-ion-coincidence spectroscopy, we simultaneously measure the photoionization delays of krypton monomer and dimer. The relative time delay is found to oscillate as a function of the electron kinetic energy, an effect that is traced back to constructive and destructive interference of the photoelectron wave packets that are emitted or scattered from the two atomic centers. Our interpretation of the experimental results is supported by solving the time-independent Schrödinger equation of a 1D double-well potential, as well as coupled-channel multiconfigurational quantum-scattering calculations of Kr_{2}. This work opens the door to the study of a broad class of quantum-interference effects in photoionization delays and demonstrates the potential of attosecond coincidence spectroscopy for studying weakly bound systems.

Fragmentation of KrN+ clusters after electron impact ionization II. Long-time dynamics simulations of Kr7+ evolution and the role of initial electronic excitation

Long time simulations, up to 100 ns, have been performed for the fragmentation of Kr₇⁺ clusters after electron impact ionization. They rely on DIM approaches and hybrid non-adiabatic dynamics combining mean field and decoherence driven either by Tully fewest switches (TFS) algorithm or through electronic amplitude (AMP) calculations. With both methods, for the first time, when the initial electronic excited state belongs to group II correlating to P_1/2 atomic ions, the fragmentation ratio in mainly monomer and dimer ions agrees very well with known experimental results. A complex non-adiabatic dynamics is found where initial neutral monomer evaporations due to gradual deexcitation over electronic states of group II are followed by a non-adiabatic transition across a wide energy gap of the spin-orbit origin to electronic states of group I. The resulting excess of kinetic energy causes the final fragmentation of charged intermediate fragments to stable ionic monomers or dimers. Characteristic times of these processes have been estimated. The kinetic energy distribution of the neutral and ionic monomers (the dominating final fragments) has been analyzed in detail. Interestingly they exhibit some signature of the initial excited electronic state which could allow for an experimental identification.

A guided-ion beam study of the collisions and reactions of I(+) and I2 (+) with I2

Growing interest in developing and testing iodine Hall effect thrusters requires measurements of the cross sections of reactions that generate low energy plasma following discharge. Limited experimental and theoretical work necessitates a decisive experiment to elucidate the charge exchange and collision-induced dissociation channels. To this end, we have used guided-ion beam techniques to measure cross sections for both I(+) + I2 and I2 (+)+I2 collisions. We present total collision cross sections as well as collision-induced dissociation cross sections for center-of-mass collision energies ranging from 0.5 to 200 eV for molecular iodine cations. Similarly, we present total collision cross section and charge-exchange cross sections for atomic iodine cations for center-of-mass collision energies ranging from 0.67 to 167 eV. Time-of-flight measurements of the collision products allow determination of velocity distributions, which show evidence of complex formation of I3 (+) from the I(+) + I2 reaction at collision energies below 6 eV.

On the size and structure of helium snowballs formed around charged atoms and clusters of noble gases

Helium nanodroplets doped with argon, krypton, or xenon are ionized by electrons and analyzed in a mass spectrometer. HenNgx(+) ions containing up to seven noble gas (Ng) atoms and dozens of helium atoms are identified; the high resolution of the mass spectrometer combined with advanced data analysis make it possible to unscramble contributions from isotopologues that have the same nominal mass but different numbers of helium or Ng atoms, such as the magic He20(84)Kr2(+) and the isobaric, nonmagic He41(84)Kr(+). Anomalies in these ion abundances reveal particularly stable ions; several intriguing patterns emerge. Perhaps most astounding are the results for HenAr(+), which show evidence for three distinct, solid-like solvation shells containing 12, 20, and 12 helium atoms. This observation runs counter to the common notion that only the first solvation shell is solid-like but agrees with calculations by Galli et al. for HenNa(+) [J. Phys. Chem. A 2011, 115, 7300] that reveal three shells of icosahedral symmetry. HenArx(+) (2 ≤ x ≤ 7) ions appear to be especially stable if they contain a total of n + x = 19 atoms. A sequence of anomalies in the abundance distribution of HenKrx(+) suggests that rings of six helium atoms are inserted into the solvation shell each time a krypton atom is added to the ionic core, from Kr(+) to Kr3(+). Previously reported strong anomalies at He12Kr2(+) and He12Kr3(+) [Kim , J. H.; et al. J. Chem. Phys. 2006, 124, 214301] are attributed to a contamination. Only minor local anomalies appear in the distributions of HenXex(+) (x ≤ 3). The distributions of HenKr(+) and HenXe(+) show strikingly similar, broad features that are absent from the distribution of HenAr(+); differences are tentatively ascribed to the very different fragmentation dynamics of these ions.

Theoretical study on low-lying electronic states of Kr2(+), Xe2(+), and Rn2(+)

In this work, the equation-of-motion coupled-cluster approach with spin-orbit coupling (SOC) for ionization potentials (IP) at the singles and doubles level (EOMIP-CCSD) is employed to calculate spectroscopic constants of low-lying states of rare gas dimer ions Kr2(+), Xe2(+), and Rn2(+). Two approaches are proposed to include contributions of triples: (1) energies of these states are calculated by adding the IPs from EOMIP-CCSD and the CCSD(T) energy of the rare gas dimers and (2) CCSD(T) energies without SOC for Rg2(+) are first calculated and energies of these states with SOC are determined subsequently using the SOC matrix between these states. The first approach can provide accurate results for the three most stable states, while overestimates bond lengths for the other states. The second approach has been adopted previously and the SOC matrix element between (2)Σ1∕2 (+) and (2)Π1∕2 states was set to be 1/2 times that of the SOC constant. In our work, the SOC matrix elements are determined from the calculated IPs and reasonable results for these states can be achieved with this approach, which could be useful for experimental works.

Structures and energetics of helium cluster cations: equilibrium geometries revisited through the genetic algorithm approach

Equilibrium geometries and dissociation energies of He(N)(+) clusters have been calculated for N=3-35 using an extended genetic algorithm approach and a semiempirical model of intracluster interactions [P. J. Knowles, J. N. Murrell, and E. J. Hodge, Mol. Phys. 85, 243 (1995)]. A general aufbau principle is formulated for both ionic cores and neutral solvation shells, and the results are thoroughly compared with other theoretical data available for helium cluster cations in literature.

On the R-dependence of the spin-orbit coupling constant: Potential energy functions of Xe(2) (+) by high-resolution photoelectron spectroscopy and ab initio quantum chemistry

The pulsed-field-ionization zero-kinetic-energy photoelectron spectrum of Xe(2) has been measured between 97 350 and 108 200 cm(-1), following resonant two-photon excitation via selected vibrational levels of the C 0(u) (+) Rydberg state of Xe(2). Transitions to three of the six low-lying electronic states of Xe(2) (+) could be observed. Whereas extensive vibrational progressions were observed for the transitions to the I(32g) and I(32u) states, only the lowest vibrational levels of the II(12u) state could be detected. Assignments of the vibrational quantum numbers were derived from the analysis of the isotopic shifts and from the modeling of the potential energy curves. Adiabatic ionization energies, dissociation energies, and vibrational constants are reported for the I(32g) and the I(32u) states. Multireference configurational interaction and complete active space self-consistent field calculations have been performed to investigate the dependence of the spin-orbit coupling constant on the internuclear distance. The energies of vibrational levels, measured presently and in a previous investigation (Rupper et al., J. Chem. Phys. 121, 8279 (2004)), were used to determine the potential energy functions of the six low-lying electronic states of Xe(2) (+) using a global model that includes the long-range interaction and treats, for the first time, the spin-orbit interaction as dependent on the internuclear separation.

Electron-ion-coincidence spectra of K-shell excited Ne, Ar, and Kr clusters

Electron-ion-coincidence spectra were recorded for K-shell excited krypton, argon, and neon clusters covering the size range from 1 atom to about 3000 atoms by utilizing hard x-ray undulator beamlines. Multiply charged ions Rz+(z>or=2) and singly charged ions Rn+(n>or=1) are observed as cluster fragments, and their relative abundance exhibits a characteristic dependence on the average cluster size N. It is expected from these results that the charges generated on the cluster surface are strongly localized while those in the cluster core are more delocalized. The estimated charge separation distance increases with N, and it is longer for lighter elements.

Isomerization dynamics and thermodynamics of ionic argon clusters

The dynamics and thermodynamics of small Ar(n) (+) clusters, n=3, 6, and 9, are investigated using molecular dynamics (MD) and exchange Monte Carlo (MC) simulations. A diatomic-in-molecule Hamiltonian provides an accurate model for the electronic ground state potential energy surface. The microcanonical caloric curves calculated from MD and MC methods are shown to agree with each other, provided that the rigorous conservation of angular momentum is accounted for in the phase space density of the MC simulations. The previously proposed projective partition of the kinetic energy is used to assist MD simulations in interpreting the cluster dynamics in terms of inertial, internal, and external modes. The thermal behavior is correlated with the nature of the charged core in the cluster by computing a dedicated charge localization order parameter. We also perform systematic quenches to establish a connection with the various isomers. We find that the Ar(3) (+) cluster is very stable in its linear ground state geometry up to about 300 K, and then isomerizes to a T-shaped isomer in which a quasineutral atom lies around a charged dimer. In Ar(6) (+) and Ar(9) (+), the covalent trimer core is solvated by neutral atoms, and the weakly bound solvent shell melts at much lower energies, occasionally leading to a tetramer or pentamer core with weakly charged extremities. At high energies the core itself becomes metastable and the cluster transforms into Ar(2) (+) solvated by a fluid of neutral argon atoms.

Theoretical modeling of postionization fragmentation of rare-gas trimer cations

The dynamics of ionic rare-gas trimers (Ar(3) (+), Kr(3) (+), and Xe(3) (+)) produced by a sudden ionization of neutral precursors is investigated theoretically with a hybrid classical-quantum method for solving the equations of motion governed by a Hamiltonian obtained from a previously tested diatomics-in-molecules model. Initial conditions are selected with Monte Carlo sampling. Two possibilities for generating the initial electronic state are considered: diabatic (local) and adiabatic (delocalized). The dynamics generally leads to fragmentation, producing either monomer ions or dimer ions in a relatively short time; however, a large number of long-lived metastable trimer ions are also seen in some cases. We have analyzed the dynamics with respect to the fraction of monomer ions produced, the distribution of the kinetic energy of the products, and the distribution of fragmentation times of the trimers. Initial diabatic ionization is associated with much faster fragmentation than adiabatic ionization. Spin-orbit coupling plays an important role in the fragmentation dynamics.

High resolution measurements of kinetic energy release distributions of neon, argon, and krypton cluster ions using a three sector field mass spectrometer

Using a newly constructed three sector field mass spectrometer (resulting in a BE1E2 field configuration) we have measured the kinetic energy release distributions of neon, argon, and krypton cluster ions. In the present study we used the first two sectors, B and E1, constituting a high resolution mass spectrometer, to select the parent ions in terms of mass, charge, and energy, and studied the decay of those ions in the third field free region. Due to the improved mass resolution we were able to extend earlier studies carried out with a two sector field machine, where an upper size limit arose from the fact that several isotopomers contribute to a decaying parent ion beam when the cluster size exceeds a certain value. Furthermore we developed a new data analysis. It allows us to model also fragment ion peaks that are a superposition of different decay reactions and thus we can determine the average kinetic energy release for all decay reactions of a given cluster ion. In a further step we used these results to determine the binding energies of cluster ions Rg(n) (n> or =10) by applying finite heat bath theory. The smaller sizes have not been included in this analysis, because the validity of finite heat bath theory becomes questionable below n approximately 10. The present average kinetic energy releases and binding energies are compared with other experiments and various calculations.

Modelization of the fragmentation dynamics of krypton clusters (Krn,n=2–11) following electron impact ionization

We present the first prediction for the fragmentation dynamics following electron impact ionization of neutral krypton clusters from 2 to 11 atoms. Fragment proportions and parent ion lifetimes are deduced from a molecular dynamics with quantum transitions study in which the nuclei are treated classically and the transitions between electronic states quantum mechanically. The potential-energy surfaces are derived from a diatomics-in-molecules model to which induced dipole-induced dipole and spin-orbit interactions are added. The results show surprisingly fast and extensive fragmentation for clusters of such a heavy atom, although not as extensive as in the case of neon clusters studied previously [D. Bonhommeau et al., J. Chem. Phys. 123, 54316 (2005)]. The parent ion lifetimes range from 2.8 to 0.7 ps, and the most abundant fragment is Kr(2) (+) for all studied sizes, followed by Kr(+) for sizes smaller than 7 atoms and by Kr(3) (+) for larger sizes. Trimer and larger fragments are found to originate from the lower electronic states of parent ions. The comparison with preliminary results from experiments on size-selected neutral clusters conducted by Steinbach et al. (private communication) reveal a good agreement on the extensive character of the fragmentation. It is checked that the additional internal energy brought by the helium scattering technique used for size selection does not affect the fragment proportions. In addition, the existence of long-lived trajectories is revealed, and they are found to be more and more important for larger cluster sizes and to favor the stabilization of larger fragments. The implications of this work for microsecond-scale dynamics of ionized rare-gas clusters are discussed. In particular, given the extent of fragmentation of the parent clusters and the fast kinetics of the whole process, the small cluster ions that exhibit a monomer loss in the microsecond time window must originate from much larger neutral precursors. The decay rate of the II(12)(u) state of the ionic dimer Kr(2) (+) by spin-orbit coupling is found to be of the order of 3 ps, in contrast to the expected tens of microseconds, but only reasonably faster than the corresponding state of HeNe(+). Finally, the spin-orbit interaction strongly affects both the Kr(+)Kr(2) (+) ratio and some of the characteristic times of the dynamics, especially for smaller sizes, but not the overall dependence of the fragment proportions as a function of cluster size.