Structure and stability of Ne+He(n): experiment and diffusion quantum Monte Carlo theory with "on the fly" electronic structure

Fragmentation dynamics of Ar4He1000 upon electron impact ionization: Competition between ion ejection and trapping

The fragmentation upon electron impact ionization of Ar₄He₁₀₀₀ is investigated by means of mixed quantum-classical dynamics simulations. The Ar₄ ⁺ dopant dynamics is described by a surface hopping method coupled with a diatomics-in-molecules model to properly take into account the multiple Ar₄ ⁺ electronic surfaces and possible transitions between them. Helium atoms are treated individually using zero-point averaged dynamics, a method based on the building of an effective He-He potential. Fast electronic relaxation is observed from less than 2 ps to ∼30 ps, depending on initial conditions. The main fragments observed are Ar₂ ⁺He_q and Ar₃ ⁺He_q (q ≤ 1000), with a strong contribution of the bare Ar₂ ⁺ ion, and neither Ar⁺ nor Ar⁺He_q fragments are found. The smaller fragments (q ≤ 50) are found to mostly come from ion ejection, whereas larger fragments (q > 500) originate from long-term ion trapping. Although the structure of the trapped Ar₂ ⁺ ions is the same as in the gas phase, trapped Ar₃ ⁺ and Ar₄ ⁺ are rather slightly bound Ar₂ ⁺⋯Ar and Ar₂ ⁺⋯Ar⋯Ar structures (i.e., an Ar₂ ⁺ core with one or two argon atoms roaming within the droplet). These loose structures can undergo geminate recombination and release Ar₃ ⁺He_q or Ar₄ ⁺He_q (q ≤ 50) in the gas phase and/or induce strong helium droplet evaporation. Finally, the translational energy of the fragment center of mass was found to be suitable to provide a clear signature of the broad variety of processes at play in our simulations.

Snowball formation for Cs+ solvation in molecular hydrogen and deuterium

Interactions of atomic cations with molecular hydrogen are of interest for a wide range of applications in hydrogen technologies. These interactions are fairly strong despite being non-covalent, hence one can ask whether hydrogen molecules would form dense, solid-like, solvation shells around the ion (snowballs) or rather a more weakly bound compound. In this work, the interactions between Cs+ and H2 are studied both experimentally and computationally. Isotopic substitution of H2 by D2 is also investigated. On the one hand, helium nanodroplets doped with cesium and hydrogen or deuterium are ionized by electron impact and the (H2/D2)nCs+ (up to n = 30) clusters formed are identified via mass spectrometry. On the other hand, a new analytical potential energy surface, based on ab initio calculations, is developed and used to study cluster energies and structures by means of classical and quantum-mechanical Monte Carlo methods. The most salient features of the measured ion abundances are remarkably mimicked by the computed evaporation energies, particularly for the clusters composed of deuterium. This result supports the reliability of the present potential energy surface and allows us to recommend its use in related systems. Clusters with either twelve H2 or D2 molecules stand out for their stability and quasi-rigid icosahedral structures. However, the first solvation shell involves thirteen or fourteen molecules for hydrogenated or deuterated clusters, respectively. This shell retains its internal structure when extra molecules are added to the second shell and is nearly solid-like, especially for the deuterated clusters. The role played by three-body induction interactions as well as the rotational degrees of freedom is analyzed and they are found to be significant (up to 15% and 18%, respectively) for the molecules belonging to the first solvation shell.

Effect of kinetic energy on the doping efficiency of cesium cations into superfluid helium droplets

We present an experimental investigation of the effect of kinetic energy on the ion doping efficiency of superfluid helium droplets using cesium cations from a thermionic emission source. The kinetic energy of Cs(+) is controlled by the bias voltage of a collection grid collinearly arranged with the droplet beam. Efficient doping from ions with kinetic energies from 20 eV up to 480 V has been observed in different sized helium droplets. The relative ion doping efficiency is determined by both the kinetic energy of the ions and the average size of the droplet beam. At a fixed source temperature, the number of doped droplets increases with increasing grid voltage, while the relative ion doping efficiency decreases. This result implies that not all ions are captured upon encountering with a sufficiently large droplet, a deviation from the near unity doping efficiency for closed shell neutral molecules. We propose that this drop in ion doping efficiency with kinetic energy is related to the limited deceleration rate inside a helium droplet. When the source temperature changes from 14 K to 17 K, the relative ion doping efficiency decreases rapidly, perhaps due to the lack of viable sized droplets. The size distribution of the Cs(+)-doped droplet beam can be measured by deflection and by energy filtering. The observed doped droplet size is about 5 × 10(6) helium atoms when the source temperature is between 14 K and 17 K.

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.

On the stability of cationic complexes of neon with helium--solving an experimental discrepancy

Helium nanodroplets are doped with neon and ionized by electrons. The size-dependence of the ion abundance of HenNex(+), identified in high-resolution mass spectra, is deduced for complexes containing up to seven neon atoms and dozens of helium atoms. Particularly stable ions are inferred from anomalies in the abundance distributions. Two pronounced anomalies at n = 11 and 13 in the HenNe(+) series confirm drift-tube data reported by Kojima et al. [T. M. Kojima et al., Z. Phys. D, 1992, 22, 645]. The discrepancy with previously published spectra of neon-doped helium droplets, which did not reveal any abundance anomalies [T. Ruchti et al., J. Chem. Phys., 1998, 109, 10679-10687; C. A. Brindle et al., J. Chem. Phys., 2005, 123, 064312], is most likely due to limited mass resolution, which precluded unambiguous analysis of contributions from different ions with identical nominal mass. However, calculated dissociation energies of HenNe(+) reported so far do not correlate with the present data, possibly because of challenges in correctly treating the linear, asymmetric [He-Ne-He](+) ionic core in HenNe(+). Anomalies identified in the distributions of HenNex(+) for x > 1, including prominent ones at He12Ne2(+) and He14Ne2(+), may help to better understand solvation of Ne(+) and Nex(+) in helium.

Interplay between charge and vibrational delocalization in cationic helium clusters

The stable structures and low temperature thermodynamics of cationic helium clusters are investigated theoretically using a diatomics-in-molecules model for the potential energy surfaces and a computational framework in which both electronic and nuclear degrees of freedom are treated on a quantum mechanical footing. While the charge is generally carried by two atoms, vibrational delocalization significantly spreads out the charge over multiple isomers for clusters containing five or more helium atoms. Our calculations indicate that large clusters are essentially fluid with a well-defined solvation shell around the charged core.

Vibrational spectrum of Ar3(+) and relative importance of linear and perpendicular isomers in its photodissociation

The photodissociation dynamics of the argon ionized trimer Ar(3)(+) is revisited in the light of recent experimental results of Lepère et al. [J. Chem. Phys. 134, 194301 (2009)], which show that the fragment with little kinetic energy is always a neutral one, thus the available energy is shared by a neutral and ionic fragments as in Ar(2)(+). We show that these results can be interpreted as the photodissociation of the linear isomer of the system. We perform a 3D quantum computation of the vibrational spectrum of the system and study the relative populations of the linear (trimer-core) and perpendicular (dimer-core) isomers. We then show that the charge initially located on the central atom in the ground electronic state of the linear isomer migrates toward the extreme ones in the photoexcitation process such that photodissociation of the linear isomer produces a neutral central atom at rest in agreement with measured product state distributions.

Snowballs, quantum solvation and coordination: lead ions inside small helium droplets

Ab initio calculations are used to construct an analytical many-body potential for Pb(2+)He(n) and Pb(+)He(n) clusters which accounts for non pairwise additive interactions. The potential surface reproduces the global minima for cluster sizes ranging from n = 1 to n = 16 obtained from explicit ab initio calculations and found in a previous search for ultrahigh coordination numbers. Ground state energies and structures obtained by accurate diffusion quantum Monte Carlo calculations are used to investigate if quantum effects qualitatively affect the formation of coordination shells. For Pb(2+) doped clusters a first solvation shell is closed at n = 12 and gradually softened by additional helium atoms which start to form a distinct second shell only at n = 16. Spin-orbit coupling profoundly influences the structure of Pb(+)He(n) clusters and causes a gradual structural evolution without pronounced solvation shells.

On the size of ions solvated in helium clusters

Helium nanodroplets are doped with SF(6), C(4)F(8), CCl(4), C(6)H(5)Br, CH(3)I, and I(2). Upon interaction with free electrons a variety of positively and negatively charged cluster ions X(+/-)He(n) are observed where X(+/-) = F(+/-), Cl(+/-), Br(+/-), I(+), I(2) (+), or CH(3)I(+). The yield of these ions versus cluster size n drops at characteristic sizes n(s) that range from n(s) = 10.2+/-0.6 for F(+) to n(s) = 22.2+/-0.2 for Br(-). n(s) values for halide anions are about 70% larger than for the corresponding cations. The steps in the ion yield suggest closure of the first solvation shell. We propose a simple classical model to estimate ionic radii from n(s). Assuming the helium density in the first solvation shell equals the helium bulk density one finds that radii of halide anions in helium are nearly twice as large as in alkali halide crystals, indicating the formation of an anion bubble due to the repulsive forces that derive from the exchange interaction. In spite of the simplicity of our model, anion radii derived from it agree within approximately 10% with values derived from the mobility of halide anions in superfluid bulk helium, and with values computed by quantum Monte Carlo methods for X(-)He(n) cluster anions.

Experimental evidence for the existence of an electronically excited state of the proposed dihydrogen radical cation He-H-H-He+

Survival of the weakest: The existence of a new class of centrosymmetric radical cations in which H(2) bridges two identical main group elements was recently proposed in this journal by Uggerud and co-workers. By growing complexes inside helium nanodroplets at subkelvin temperatures, we obtained experimental evidence for the existence of the most weakly bound member of this class, He-H-H-He(+) (see picture), although in a metastable, electronically excited state.In a recent report, Uggerud and co-workers (A. Krapp et al., Chem. Eur. J. 2008, 14, 4028) proposed the existence of a new class of radical cations in which a dihydrogen bridges two identical main group elements. Upon electron impact ionization of helium nanodroplets doped with one or more H(2) molecules we observe various He(x)H(y) (+) cluster ions, including He(2)H(2) (+), which would belong to the proposed class of radical cations. Mass-analyzed kinetic energy scans reveal that the ion is metastable; it dissociates in the field-free region of the mass spectrometer. One reaction is into HeH(2) (+) + He with a low kinetic energy release of 15+/-4 meV. Surprisingly, another unimolecular reaction is observed, into HeH(+) + HeH (or He + H). The probability of this reaction is an order of magnitude higher, and the average kinetic energy release is four times larger. These findings suggest the presence of a metastable electronically excited state; they are consistent with the proposed linear, centrosymmetric ion structure of He-H-H-He(+).

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.

Modeling the fragmentation dynamics of ionic clusters inside helium nanodroplets: The case of He100Ne4+

We present simulation results on the effect of a helium nanodroplet environment on the fragmentation dynamics of embedded molecular systems. The helium atoms are treated explicitly, with zero-point effects taken into account through an effective helium-helium interaction potential. The ionized neon tetramer is used as a model molecular system because, like all the small rare-gas clusters, it fragments extensively upon ionization. All the nonadiabatic effects between electronic states of the ionized neon cluster are taken into account. The results reveal a predominance of Ne2+ and HepNe2+ fragments and the absence of bare Ne+ fragments, in agreement with available experimental data. The neutral monomer fragments exhibit a rather wide kinetic energy distribution that 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 experimental results. Purely classical calculations are shown to strongly overestimate the amount of cage effect (cooling), clearly indicating the need to take into account zero-point effects.

The ground state tunneling splitting and the zero point energy of malonaldehyde: A quantum Monte Carlo determination

Quantum dynamics calculations of the ground state tunneling splitting and of the zero point energy of malonaldehyde on the full dimensional potential energy surface proposed by Yagi et al. [J. Chem. Phys. 1154, 10647 (2001)] are reported. The exact diffusion Monte Carlo and the projection operator imaginary time spectral evolution methods are used to compute accurate benchmark results for this 21-dimensional ab initio potential energy surface. A tunneling splitting of 25.7+/-0.3 cm-1 is obtained, and the vibrational ground state energy is found to be 15 122+/-4 cm-1. Isotopic substitution of the tunneling hydrogen modifies the tunneling splitting down to 3.21+/-0.09 cm-1 and the vibrational ground state energy to 14 385+/-2 cm-1. The computed tunneling splittings are slightly higher than the experimental values as expected from the potential energy surface which slightly underestimates the barrier height, and they are slightly lower than the results from the instanton theory obtained using the same potential energy surface.

Photoionization of helium nanodroplets doped with rare gas atoms

Photoionization of He droplets doped with rare gas atoms (Rg=Ne, Ar, Kr, and Xe) was studied by time-of-flight mass spectrometry, utilizing synchrotron radiation from the Advanced Light Source from 10 to 30 eV. High resolution mass spectra were obtained at selected photon energies, and photoion yield curves were measured for several ion masses (or ranges of ion masses) over a wide range of photon energies. Only indirect ionization of the dopant rare gas atoms was observed, either by excitation or charge transfer from the surrounding He atoms. Significant dopant ionization from excitation transfer was seen at 21.6 eV, the maximum of He 2p 1P absorption band for He droplets, and from charge transfer above 23 eV, the threshold for ionization of pure He droplets. No Ne+ or Ar+ signal from droplet photoionization was observed, but peaks from HenNe+ and HenAr+ were seen that clearly originated from droplets. For droplets doped with Rg=Kr or Xe, both Rg+ and HenRg+ ions were observed. For all rare gases, Rg2+ and HenRgm+ (n,m> or =1) were produced by droplet photoionization. Mechanisms of dopant ionization and subsequent dynamics are discussed.

Fragmentation dynamics of ionized neon clusters (Nen,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.