Fragmentation dynamics of argon clusters (Ar(n), n = 2 to 11) following electron-impact ionization: modeling and comparison with experiment

The fragmentation dynamics of argon clusters ionized by electron impact is investigated for initial cluster sizes up to n = 11 atoms. The dynamics of the argon atoms is modeled using a mixed quantum-classical method 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 with the addition of the induced dipole-induced dipole and spin-orbit interactions. The results show extensive and fast fragmentation. The dimer is the most abundant ionic fragment, with a proportion increasing from 66% for n = 2 to a maximum of 95% for n = 6 and then decreasing down to 67% for n = 11. The next abundant fragment is the monomer for n < 7 and the trimer otherwise. The parent ion dissociation lifetimes are all in the range of 1 ps. Long-lived trajectories appear for initial cluster sizes of seven and higher, and favor the formation of the larger fragments (trimers and tetramers). Our results show quantitative agreement with available experimental results concerning the extensive character of the fragmentation: Ar+ and Ar2(+) are the only ionic fragments for sizes up to five atoms; their overall proportion is in quantitative agreement for all the studied sizes; Ar2(+) is the main fragment for all sizes; stable Ar3(+) fragments only appear for n > or = 5, and their proportion increases smoothly with cluster size from there. However, the individual ionic monomer and dimer fragment proportions differ. The experimental ones exhibit oscillations with initial cluster size, with a slight tendency to decrease on average for the monomer. In contrast our results show a monotonic, systematic evolution, similar to what was found in our earlier studies on neon and krypton clusters. Several hypotheses are discussed in order to find the origin of this discrepancy. Finally, the metastable II(1/2)u and II(1/2)g states of Ar2(+) are found to decay with a lifetime of 3.5 and 0.1 ps, respectively, due to spin-orbit coupling. The difference with the commonly accepted microsecond range value for rare-gas dimer ions could originate from the role of autoionizing states in the formation of the parent ions.     

Electron impact fragmentation of size-selected krypton clusters

Clusters of krypton are generated in a supersonic expansion and size selected by deflection from a helium target beam. By measuring angular distributions for different fragment masses and time-of-flight distributions for fixed deflection angles and fragment masses, the complete fragmentation patterns for electron impact ionization at 70 eV are obtained from the dimer to the heptamer. For each of the neutral Kr(n) clusters studied, the main fragment is the monomer Kr(+) ion with a probability f(n)(1) > 90%. The probability of observing dimer Kr(2)(+) ions is much smaller than expected for each initial cluster size. The trimer ion Kr(3)(+) appears first from the neutral Kr(5), and its fraction increases with increasing neutral cluster size n, but is always much smaller than that of the monomer or dimer. For neutral Kr(7), all possible ion fragments are observed, but the monomer still represents 90% of the overall probability and fragments with n > 3 contribute less than 1% of the total. Aspects of the Kr(n) cluster ionization process and the experimental measurements are discussed to provide possible reasons for the surprisingly high probability of observing fragmentation to the Kr(+) monomer ion.     

Fragmentation dynamics of ionized neon clusters (Ne(n), n=3-14) embedded in helium nanodroplets

We report a theoretical study of the nonadiabatic fragmentation dynamics of ionized neon clusters embedded in helium nanodroplets for cluster sizes up to n=14 atoms. The dynamics of the neon atoms is modeled using the molecular dynamics with quantum transitions method of Tully [J. Chem. Phys. 93, 1061 (1990)] with the nuclei treated classically and transitions between electronic states quantum mechanically. The potential-energy surfaces are derived from a diatomics-in-molecules model to which induced dipole-induced dipole interactions are added. The effect of the spin-orbit interaction is also discussed. The helium environment is modeled by a friction force acting on charged atoms whose speed exceeds the critical Landau velocity. The dependence of the fragment size distribution on the friction strength and on the initial nanodroplet size is investigated. By comparing with the available experimental data obtained for Ne3+ and Ne4+, a reasonable value for the friction coefficient, the only parameter of the model, is deduced. This value is then used to predict the effect of the helium environment on the dissociation dynamics of larger neon clusters, n=5-14. The results show stabilization of larger fragments than in the gas phase, but fragmentation is not completely caged. In addition, two types of dynamics are characterized for Ne4+: fast and explosive, therefore leaving no time for friction to cool down the process when dynamics starts on one of the highest electronic states, and slower, therefore leading to some stabilization by helium when it starts on one of the lowest electronic states.     

Dissociative ionization of neon clusters Ne(n), n=3 to 14: a realistic multisurface dynamical study

The molecular dynamics with quantum transitions (MDQT) method is applied to study the fragmentation dynamics of neon clusters following vertical ionization of neutral clusters with 3 to 14 atoms. The motion of the neon atoms is treated classically, while transitions between the adiabatic electronic states of the ionic clusters are treated quantum mechanically. The potential energy surfaces are described by the diatomics-in-molecules model in a minimal basis set consisting of the effective 2p orbitals on each neon atom for the missing electron. The fragmentation mechanism is found to be rather explosive, with a large number of events where several atoms simultaneously dissociate. This is in contrast with evaporative atom by atom fragmentation. The dynamics are highly nonadiabatic, especially at shorter times and for the larger clusters. Initial excitation of the neutral clusters does not affect the fragmentation pattern. The influence of spin-orbit coupling is also examined and found to be small, except for the smaller size systems for which the proportion of the Ne+ fragment is increased up to 43%. From the methodological point of view, most of the usual momentum adjustment methods at hopping events are shown to induce nonconservation of the total nuclear angular momentum because of the nonzero electronic to rotation coupling in these systems. A new method for separating out this coupling and enforcing the conservation of the total nuclear momentum is proposed. It is applied here to the MDQT method of Tully but it is very general and can be applied to other surface hopping methods.     

Fragmentation channels of K-shell excited rare-gas clusters studied by multiple-ion coincidence momentum imaging

Multiple-ion coincidence momentum imaging experiments were carried out for K-shell (1s) excited Ar clusters containing about 130 atoms and Kr clusters containing about 30, 90, and 160 atoms. The time-of-flight spectra reveal that the major products of the Coulomb explosion are singly charged ions. With increasing the number of charges generated in clusters, the momentum of monomer ions such as Ar(+) and Kr(+) increases, while that of cluster ions such as Ar(3) (+), Kr(2) (+), and Kr(3) (+) decreases. This observation indicates the site-specific decay process that the heavier ions appear in the central part of clusters. We have also investigated the momentum distribution in various fragmentation channels and the branching ratio of each channel at the Coulomb explosion. When the number N(coin) of coincidently detected ions is four, for example, the most frequent channel from Kr clusters containing 30 atoms is to emit simply four Kr(+) ions, but Kr(2) (+) ions participate in the fragmentation from the larger Kr clusters. The fragmentation channel in which two Ar(2) (+) ions are emitted becomes dominant with increasing N(coin), and the average momentum of Ar(2) (+) ion in this channel is larger than that in the channels where only single Ar(2) (+) is emitted.     

Density-functional study of small neutral and cationic bismuth clusters Bi(n) and Bi(n) (+)(n=2-24)

Density-functional theory with scalar-relativistic pseudopotential and a generalized gradient correction is used to calculate the neutral and cationic Bi(n) clusters (2< or =n< or =24), with the aim to elucidate their structural evolution, relative stability, and magnetic property. The structures of neutral Bi clusters are found to be similar to that of other group-V elemental clusters, with the extensively studied sizes of n=4 and 8 having a tetrahedron and wedgelike structure, respectively. Generally, larger Bi clusters consist of a combination of several stable units of Bi(4), Bi(6), and Bi(8), and they have a tendency to form an amorphous structure with the increase of cluster sizes. The curves of second order energy difference exhibit strong odd-even alternations for both neutral and cationic Bi clusters, indicating that even-atom (odd-atom) sizes are relatively stable in neutral clusters (cationic clusters). The calculated magnetic moments are 1micro (B) for odd-atom clusters and zero for even-atom clusters. We propose that the difference in magnetism between experiment and theory can be greatly improved by considering the orbital contribution. The calculated fragmentation behavior agrees well with the experiment, and for each cationic cluster the dissociation into Bi(4) or Bi(7) (+) subclusters confirms the special stability of Bi(4) and Bi(7) (+). Moreover, the bond orders and the gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital show that small Bi clusters would prefer semiconductor characters to metallicity.     

Structural and electronic properties of Si n, Si n+, and AlSi n-1 (n=2-13) clusters: theoretical investigation based on ab initio molecular orbital theory

The geometric and electronic structures of Si(n), Si(n) (+), and AlSi(n-1) clusters (2< or =n< or =13) have been investigated using the ab initio molecular orbital theory under the density functional theory formalism. The hybrid exchange-correlation energy function (B3LYP) and a standard split-valence basis set with polarization functions [6-31G(d)] were employed for this purpose. Relative stabilities of these clusters have been analyzed based on their binding energies, second difference in energy (Delta (2)E) and fragmentation behavior. The equilibrium geometry of the neutral and charged Si(n) clusters show similar structural growth. However, significant differences have been observed in the electronic structure leading to their different stability pattern. While for neutral clusters, the Si(10) is magic, the extra stability of the Si(11) (+) cluster over the Si(10) (+) and Si(12) (+) bears evidence for the magic behavior of the Si(11) (+) cluster, which is in excellent agreement with the recent experimental observations. Similarly for AlSi(n-1) clusters, which is isoelectronic with Si(n) (+) clusters show extra stability of the AlSi(10) cluster suggesting the influence of the electronic structures for different stabilities between neutral and charged clusters. The ground state geometries of the AlSi(n-1) clusters show that the impurity Al atom prefers to substitute for the Si atom, that has the highest coordination number in the host Si(n) cluster. The fragmentation behavior of all these clusters show that while small clusters prefers to evaporate monomer, the larger ones dissociate into two stable clusters of smaller size.     

Single photon ionization of van der Waals clusters with a soft x-ray laser: (CO2)n and (CO2)n(H2O)m

Pure neutral (CO2)n clusters and mixed (CO2)n(H2O)m clusters are investigated employing time of flight mass spectroscopy and single photon ionization at 26.5 eV. The distribution of pure (CO2)n clusters decreases roughly exponentially with increasing cluster size. During the ionization process, neutral clusters suffer little fragmentation because almost all excess cluster energy above the vertical ionization energy is taken away by the photoelectron and only a small part of the photon energy is deposited into the (CO2)n cluster. Metastable dissociation rate constants of (CO2)n+ are measured in the range of (0.2-1.5) x 10(4) s(-1) for cluster sizes of 5< or =n< or =16. Mixed CO2-H2O clusters are studied under different generation conditions (5% and 20% CO2 partial pressures and high and low expansion pressures). At high CO2 concentration, predominant signals in the mass spectrum are the (CO2)n+ cluster ions. The unprotonated cluster ion series (CO2)nH2O+ and (CO2)n(H2O)2+ are also observed under these conditions. At low CO2 concentration, protonated cluster ions (H2O)nH+ are the dominant signals, and the protonated CO2(H2O)nH+ and unprotonated (H2O)n+ and (CO2)(H2O)n+ cluster ion series are also observed. The mechanisms and dynamics of the formation of these neutral and ionic clusters are discussed.     

Fragmentation of ionized doped helium nanodroplets: theoretical evidence for a dopant ejection mechanism

We report a theoretical study of the effect induced by a helium nanodroplet environment on the fragmentation dynamics of a dopant. The dopant is an ionized neon cluster Ne(n) (+) (n=4-6) surrounded by a helium nanodroplet composed of 100 atoms. A newly designed mixed quantum/classical approach is used to take into account both the large helium cluster zero-point energy due to the light mass of the helium atoms and all the nonadiabatic couplings between the Ne(n) (+) potential-energy surfaces. The results reveal that the intermediate ionic dopant can be ejected from the droplet, possibly with some helium atoms still attached, thereby reducing the cooling power of the droplet. Energy relaxation by helium atom evaporation and dissociation, the other mechanism which has been used in most interpretations of doped helium cluster dynamics, also exhibits new features. The kinetic energy distribution of the neutral monomer fragments can be fitted to the sum of two Boltzmann distributions, one with a low kinetic energy and the other with a higher kinetic energy. This indicates that cooling by helium atom evaporation is more efficient than was believed so far, as suggested by recent experiments. The results also reveal the predominance of Ne(2) (+) and He(q)Ne(2) (+) fragments and the absence of bare Ne(+) fragments, in agreement with available experimental data (obtained for larger helium nanodroplets). Moreover, the abundance in fragments with a trimeric neon core is found to increase with the increase in dopant size. Most of the fragmentation is achieved within 10 ps and the only subsequent dynamical process is the relaxation of hot intermediate He(q)Ne(2) (+) species to Ne(2) (+) by helium atom evaporation. The dependence of the ionic fragment distribution on the parent ion electronic state reached by ionization is also investigated. It reveals that He(q)Ne(+) fragments are produced only from the highest electronic state, whereas He(q)Ne(2) (+) fragments originate from all the electronic states. Surprisingly, the highest electronic states also lead to fragments that still contain the original ionic dopant species. A mechanism is conjectured to explain this fragmentation inhibition.     

Electron solvation dynamics in I-(NH3)n clusters

Femtosecond photoelectron spectroscopy (FPES) is used to monitor the dynamics associated with the excitation of the charge-transfer-to-solvent (CTTS) precursor states in I-(NH3)n = 4-15 clusters. The FPE spectra imply that the weakly bound excess electron in the excited state undergoes partial solvation via solvent rearrangement on a time scale of 0.5-2 ps, and this partially solvated state decays by electron emission on a 10-50 ps time scale. Both the extent of solvation and the lifetimes increase gradually with cluster size, in contrast to the more abrupt size-dependent effects previously observed in I-(H2O)n clusters.     

Dynamics of charge-transfer-to-solvent precursor states in I- (water)n (n = 3-10) clusters studied with photoelectron imaging

The dynamics of charge-transfer-to-solvent states are studied in I- (H2O)(n=3-10) clusters and their deuterated counterparts using time-resolved photoelectron imaging. The photoelectron spectra for clusters with n > or = 5 reveal multiple time scales for dynamics after their electronic excitation. An increase in the vertical detachment energy (VDE) by several hundred millielectronvolts on a time scale of approximately 1 ps is attributed to stabilization of the excess electron, primarily through rearrangement of the solvent molecules, but a contribution to this stabilization from motion of the I atom cannot be ruled out. The VDE drops by approximately 50 meV on a time scale of tens of picoseconds; this is attributed to loss of the neutral iodine atom. Finally, the pump-probe signal decays with a time constant of 60 ps-3 ns, increasing with cluster size. This decay is commensurate with the growth of very slow electrons and is attributed to autodetachment. Smaller clusters (n = 3, 4) display simpler dynamics. Anisotropy parameters are reported for clusters n = 4-9.     

Fragmentation dynamics of size-selected pyrrole clusters prepared by electron impact ionization: forming a solvated dimer ion core

Structure and dynamics of size-selected charged pyrrole clusters have been studied by means of molecular beam scattering experiments and ab initio calculations. Small neutral Pyn clusters were produced in Py/He mixture expansions, and the scattering experiment with a secondary beam of He-atoms was exploited to select the neutral clusters of different sizes. The complete size-selected fragmentation patterns for the neutral dimer to the tetramer after an electron impact ionization at 70 eV were obtained from the measurements of the angular and velocity distributions at different fragment masses. All the investigated cluster sizes decay mainly to the monomer ions Py+1 (from 60 to 80% of the corresponding neutral size) and to the dimer ion Py+2 (20-30%). The trimer ions Py+3 are generated to less than 10% from the neutral trimer and tetramer. To explain the observed results, we have calculated the structures and energetics of pyrrole clusters up to the trimer for the neutral and the ionic state using DFT and PMP2 methods. The ab initio calculations show that ionized pyrrole clusters are formed with a dimeric core that is solvated by neutral pyrrole molecules. In addition, the ground and ionic state of Py-Ar complexes were calculated at CCSD(T) level with extended basis in relevance to the mixed clusters produced in supersonic expansions of Py seeded in Ar. The calculated dissociation energies of the Py-Ar and (Py-Ar)+ complexes indicate that Ar atoms are able to rapidly evaporate after ionization. The combined analysis of the fragmentation probabilities, and calculations allowed us to estimate the distribution of energy deposited in the clusters after the electron impact, which peaks above 1 eV and has a tail up to 5 eV.     

Analysis of dissociation times and fragmentation patterns in the decomposition of highly excited clusters

In this article, the dynamics of fragmentation of highly excited van der Waals clusters are analyzed. An approach to the characterization of complex cluster fragmentation is described, based on a combination of structural and dynamical analysis of classical trajectories. In this method, the final fragmentation pattern is analyzed by a depth-first search algorithm based on graph theory, which provides a partitioning of the system into intact fragments of various sizes: monomers, dimers, trimers, and higher multimers. With knowledge of the final products, a dynamical analysis is accomplished by tracing back the time dependence of the relevant fragment energies. A transition from oscillatory to constant behavior of these energies indicates that the fragment has become energetically isolated from the parent cluster. This allows an unambiguous definition of the dissociation time of the fragment. The method is applied to the characterization of cluster fragmentation of chemically activated I₂Ar ₁₂ ^* formed in the association reaction I+I(Ar)₁₂→I₂+12 Ar. It is found that cluster decomposition channels, leading to the formation of at least one multi-atom fragment, play an important role in the evaporative cooling of I₂, in addition to monoatomic sequential evaporation.     

Dissociative photodetachment dynamics of the iodide-aniline cluster

The photodetachment dynamics of the iodide-aniline cluster, I-(C6H5NH2), were investigated using photoelectron-photofragment coincidence spectroscopy at several photon energies between 3.60 and 4.82 eV in concert with density functional theory calculations. Direct photodetachment from the solvated I- chromophore and a wavelength-independent autodetachment process were observed. Autodetachment is attributed to a charge-transfer-to-solvent reaction in which incipient continuum electrons photodetached from I- are temporarily captured by the nascent neutral iodine-aniline cluster configured in the anion geometry. Subsequent dissociation of the neutral cluster removes the stabilization, leading to autodetachment of the excess electron. The dependence of the dissociative photodetachment (DPD) and autodetachment dynamics on the final spin-orbit electronic state of the iodine fragment is characterized. The dissociation dynamics of the neutral fragments correlated with autodetached electrons were found to be identical to the DPD dynamics of the I atom product spin-orbit state closest to threshold at a given photon energy, lending support to the proposed sequential mechanism.     

Stability and structure of singly-charged xenon-argon clusters [Xe1Arn−1]+,n=3–27

Monte-Carlo calculations have been performed for positively charged xenon-argon clusters in the temperature range between 10K and 40K for cluster sizes up ton=27. The argon-argon interaction potential stems from empirical data, the Xe⁺-Ar potential is determined by ab initio MRD-CI calculations and a semi-empirical treatment of spin-orbit effects. Special stability is found for cluster sizesn=10, 13, 19 and less pronounced forn=23 and 25 fairly independent of the temperature. The geometrical structure of the clusters are given and the construction principle is discussed in light of the interactions among neutral argon atoms and the xenon ion — argon interaction. Comparison with measured mass spectra for mixed rare-gas clusters and [Xe_n]⁺ clusters is made and shows a consistent picture for the building principle.     

Fragmentation of size-selected Xe clusters: Why does the monomer ion channel dominate the Xen and ionization?

The fragmentation of the small Xe_n n=2−5 clusters following 70 eV electron impact ionization has been investigated in a size selective experiment and simulated using non-adiabatic dynamics. The experimental results show that the clusters strongly fragment to yield monomer Xe⁺ (more than 90%) and dimer Xe₂⁺ fragments (the remaining few percent). Trimer Xe₃⁺ fragments first occur from the neutral pentamers Xe₅ in a very low yield of approximately 0.3%. The present results are compared with the previous ones for Kr and Ar clusters. It is shown that the Xe and Kr clusters exhibit a qualitatively similar behavior with a strong propensity for monomer fragments, while in the Ar case dimers prevail. The theoretical calculations also reveal a strong fragmentation to the dimer and monomer fragments. However, the dimer Rg₂⁺ is predicted to be the major product for all rare gases (Rg ≡ Ar, Kr, Xe). Possible reasons for the discrepancy between theory and experiment are discussed.     

Time-resolved intraband electronic relaxation dynamics of Hg(n) (-) clusters (n=7-13,15,18) excited at 1.0 eV

Time-resolved photoelectron imaging has been used to study the relaxation dynamics of small Hg(n) (-) clusters (n=7-13,15,18) following intraband electronic excitation at 1250 nm (1.0 eV). This study furthers our previous investigation of single electron, intraband relaxation dynamics in Hg(n) (-) clusters at 790 nm by exploring the dynamics of smaller clusters (n=7-10), as well as those of larger clusters (n=11-13,15,18) at a lower excitation energy. We measure relaxation time scales of 2-9 ps, two to three times faster than seen previously after 790 nm excitation of Hg(n) (-), n=11-18. These results, along with size-dependent trends in the absorption cross-section and photoelectron angular distribution anisotropy, suggest significant evolution of the cluster anion electronic structure in the size range studied here. Furthermore, the smallest clusters studied here exhibit 35-45 cm(-1) oscillations in pump-probe signal at earliest temporal delays that are interpreted as early coherent nuclear motion on the excited potential energy surfaces of these clusters. Evidence for evaporation of one or two Hg atoms is seen on a time scale of tens of picoseconds.     

Coherent control of the ultrafast dissociative ionization dynamics of bromochloroalkanes

We report on the coherent control of the ultrafast ionization and fragmentation dynamics of the bromochloroalkanes C(2)H(4)BrCl and C(3)H(6)BrCl using shaped femtosecond laser pulses. In closed-loop control experiments on bromochloropropane (C(3)H(6)BrCl) the fragment ion yields of CH(2)Cl(+), CH(2)Br(+), and C(3)H(3)(+) are optimized with respect to that of the parent cation C(3)H(6)BrCl(+). The fragment ion yields are recorded in additional experiments in order to reveal the energetics of cation fragmentation, where laser-produced plasma radiation is used as a tunable pulsed nanosecond vacuum ultraviolet radiation source along with photoionization mass spectrometry. The time structure of the optimized femtosecond laser pulses leads to a depletion of the parent ion and an enhancement of the fragment ions, where a characteristic sequence of pulses is required. Specifically, an intense pump pulse is followed by a less intense probe pulse where the delay is 0.5 ps. Similarly optimized pulse shapes are obtained from closed-loop control experiments on bromochloroethane (C(2)H(4)BrCl), where the fragment ion yield of CH(2)Br(+) is optimized with respect to that of C(2)H(4)BrCl(+) as well as the fragment ion ratios C(2)H(2)(+)/CH(2)Br(+) and C(2)H(3)(+)/C(2)H(4)Cl(+). The assignment of the underlying control mechanism is derived from one-color 804 nm pump-probe experiments, where the yields of the parent cation and several fragments show broad dynamic resonances with a maximum at Δt = 0.5 ps. The experimental findings are rationalized in terms of dynamic ionic resonances leading to an enhanced dissociation of the parent cation and some primary fragment ions.     

Photodissociation of noble metal-doped carbon clusters

Noble metal carbide cluster cations (MC(n)(+), M = Cu, Au) are produced by laser vaporization in a pulsed molecular beam and detected with time-of-flight mass spectrometry. Copper favors the formation of carbides with an odd number of carbon atoms, while gold shows marked drops in ion intensity after clusters with 3, 6, 9, and 12 carbons. These clusters are mass selected and photodissociated at 355 nm. Copper carbides with an odd number of carbons fragment by eliminating the metal from the cluster; for the small species it is eliminated as Cu(+) and for the larger species it is lost as neutral Cu. Copper carbides with an even number of carbons also lose the metal, but in addition to this they eliminate neutral C(3). This even-odd alternation, with the even clusters having mixed fragments, holds true for clusters as large as CuC(30)(+). No loss of C(2) is observed for even the largest clusters studied, indicating that fullerene formation does not occur. The gold carbide photodissociation data closely parallel that of copper, with even clusters losing primarily C(3) and odd ones losing gold. Comparisons to known carbon cluster ionization potentials give some insight into the structures of carbon photofragments. DFT calculations performed on CuC(3-11)(+) allow comparisons of the energetics of isomers likely present in our experiment, and metal-carbon dissociation energies help explain the even-odd alternation in the fragmentation channels. The simplest picture of these metal-doped carbides consistent with all the data is that the small species have linear chain structures with the metal attached at the end, whereas the larger species have cyclic structures with the metal attached externally to a single carbon.