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.     

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.     

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

New data are reported for the mass-spectrometry fragmentation patterns of helium clusters, either pure or containing a Ne or an Ar atom. The patterns for He(n)+ and Ar+He(n) show clear evidence of structure, while those of Ne+He(n) do not. To better understand the surprising result for the Ne+He(n) fragments, diffusion quantum Monte Carlo (DMC) calculations of the energies and structural properties of these ions were performed using a diatomics-in-molecule (DIM) parametrization of the potential energy. Using DIM for electronic energy evaluation allows us to sample 10(9) configurations even for a cluster as large as Ne+He14. The results of the DMC calculation are very surprising. For n > 7, the DMC random walkers rarely venture within 100 cm(-1) of the minimum potential energy. Analysis of the resulting particle density distributions shows that the zero-point energy does more than spread the wave function around the potential-energy minima, resulting in very diffuse wave functions. For some of the clusters the quantum effects nearly exclude the region of the potential minimum from the overall wave function. An important result of this effect is that the incremental bonding energy of the nth helium atom varies quite smoothly with n, for n > 5. This eliminates the expected shell structure and explains the lack of magic-number-type features in the data.     

Fragmentation of HCN in optically selected mass spectrometry: nonthermal ion cooling in helium nanodroplets

A technique that combines infrared laser spectroscopy and helium nanodroplet mass spectrometry, which we refer to as optically selected mass spectrometry, is used to study the efficiency of ion cooling in helium. Electron-impact ionization is used to form He(+) ions within the droplets, which go on to transfer their charge to the HCN dopant molecules. Depending upon the droplet size, the newly formed ion either fragments or is cooled by the helium before fragmentation can occur. Comparisons with gas-phase fragmentation data suggest that the cooling provided by the helium is highly nonthermal. An "explosive" model is proposed for the cooling process, given that the initially hot ion is embedded in such a cold solvent.     

Modelization of the fragmentation dynamics of krypton clusters (Kr(n),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.     

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 cross sections of protonated water clusters

We have measured fragmentation cross sections of protonated water cluster cations (H(2)O)(n=30-50)H(+) by collision with water molecules. The clusters have well-defined sizes and internal energies. The collision energy has been varied from 0.5 to 300 eV. We also performed the same measurements on deuterated water clusters (D(2)O)(n=5-45)D(+) colliding with deuterated water molecules. The main fragmentation channel is shown to be a sequential thermal evaporation of single molecules following an initial transfer of relative kinetic energy into internal energy of the cluster. Unexpectedly, that initial transfer is very low on average, of the order of 1% of collision energy. We evaluate that for direct collisions (i.e., within the hard sphere radius), the probability for observing no fragmentation at all is more than 35%, independently of cluster size and collision energy, over our range of study. Such an effect is well known at higher energies, where it is attributed to electronic effects, but has been reported only in a theoretical study of the collision of helium atoms with sodium clusters in that energy range, where only vibrational excitation occurs.     

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.     

Ionization of doped helium nanodroplets: residual helium attached to diatomic cations and their clusters

Electron impact ionization of helium nanodroplets containing a dopant, M, can lead to the detection of both M(+) and helium-solvated cations of the type M(+)·He(n) in the gas phase. The observation of helium-doped ions, He(n)M(+), has the potential to provide information on the aftermath of the charge transfer process that leads to ion production from the helium droplet. Here we report on helium attachment to the ions from four common diatomic dopants, M = N(2), O(2), CO, and NO. For experiments carried out with droplets with an average size of 7500 helium atoms, the monomer cations show little tendency to attach and retain helium atoms on their journey out of the droplet. By way of contrast, the corresponding cluster cations, M(n)(+), where n ≥ 2, all show a clear affinity for helium and form He(m)M(n)(+) cluster ions. The stark difference between the monomer and cluster ions is attributed to more effective cooling of the latter in the aftermath of the ionization event.     

Potential energy surfaces for HenNe+ ions: ab initio and diatomics-in-molecule results

The potential energy surface of He2Ne+ has been reinvestigated using a combination of ab initio and diatomics-in-molecule (DIM) calculations. In contrast to the reports of two recent studies the ion is found to have an asymmetric linear He-Ne-He structure, with no barrier to formation from the separated atoms on the ground-state surface. The He-Ne+ bond lengths at the potential minimum are 1.51 and 1.81 A, and the total bonding energy is 0.717 eV. Comparing the He2Ne+ energy to that of HeNe+, the bonding energy for the second helium atom is 0.06 eV, about 10% of that of the first He atom. The saddle point between the two equivalent minima is a symmetric structure, 0.0074 eV above the potential minimum. A symmetric geometry becomes the overall potential minimum if the 2s hole on the Ne is excluded from the reference states of a multireference configuration interaction calculation. A DIM potential was created for the HenNe+ family of ions. The DIM potential is consistent with the asymmetric He2Ne+ ion serving as a core; it predicts a slightly more asymmetric geometry than the ab initio results. Additional helium atoms form five-membered rings around the bonds of the core ion to fill the first shell and then add to the ends of the cluster. The asymmetric core ion and the highly compact structure help to account for the lack of apparent shell structure in the mass spectrometry of HenNe+ clusters. Finally, we recommend that the value De=0.63+/-0.04 eV be adopted for the ground state of HeNe+.     

Ionic dimers in He droplets: interaction potentials for Li2(+)-He,Na2(+)-He, and K2(+)-He and stability of the smaller clusters

We present post Hartree-Fock calculations of the potential energy surfaces (PESs) for the ground electronic states of the three alkali dimer ions Li(2) (+),Na(2) (+), and K(2) (+) interacting with neutral helium. The calculations were carried out for the frozen molecular equilibrium geometries and for an extensive range of the remaining two Jacobi coordinates, R and theta, for which a total of about 1000 points is generated for each surface. The corresponding raw data were then fitted numerically to produce analytic expressions for the three PESs, which were in turn employed to evaluate the bound states of the three trimers for their J=0 configurations: The final spatial features of such bound states are also discussed in detail. The possible behavior of additional systems with more helium atoms surrounding the ionic dopants is gleaned from further calculations on the structural stability of aggregates with up to six He atoms. The validity of a sum-of-potential approximation to yield realistic total energies of the smaller cluster is briefly discussed vis-a-vis the results from many-body calculations.     

Communication: the formation of helium cluster cations following the ionization of helium nanodroplets: influence of droplet size and dopant

The He(n)(+)/He(2)(+) (n ≥ 3) signal ratios in the mass spectra derived from electron impact ionization of pure helium nanodroplets are shown to increase with droplet size, reaching an asymptotic limit at an average droplet size of approximately 50,000 helium atoms. This is explained in terms of a charge hopping model, where on average the positive charge is able to penetrate more deeply into the liquid helium as the droplet size increases. The deeper the point where the charge localizes to form He(2)(+), the greater the likelihood of collisions with the surrounding helium as the ion begins to leave the droplet, thus increasing the probability that helium will be ejected in the form of He(n)(+) (n ≥ 3) cluster ions rather than He(2)(+). The addition of a dopant alters the He(n)(+)/He(2)(+) ratio for small helium droplets, an observation attributed to the potential energy gradient created by the cation-dopant interaction and its effect in drawing the positive charge towards the dopant in the interior of the droplet.     

Accurate ab initio pair potentials between helium and the heavier group 2 elements

Interactions between the heavier Group 2 metals (Ca, Sr, and Ba) and helium were studied using the well-tempered model core potential method. Accurate pair potentials, calculated at the coupled-cluster level of theory with very large basis sets, were used in bound state calculations. Three bound rovibrational states were found for each complex. The pair-potential parameters were used to predict how each of the metal atoms would be solvated by a helium nanodroplet. The Ca atom is not fully solvated by the droplet and the interaction between the helium and the metal decreases from Ca to Ba. This agrees with the experimental observation that the spectra of these atoms in a nanodroplet are intermediate between the spectra of the free atoms and the spectra in liquid helium.     

Explicitly correlated coupled cluster calculations for the benzenium ion (C6H7(+)) and its complexes with Ne and Ar

Explicitly correlated coupled cluster theory at the CCSD(T)-F12x (x = a, b) level (Adler, T. B.; Knizia, G.; Werner, H.-J. J. Chem. Phys. 2007, 127, 221106) has been employed in a study of the benzenium ion (C6H7(+)) and its complexes with a neon or an argon atom. The ground-state rotational constants of C6H7(+) are predicted to be A0 = 5445 MHz, B0 = 5313 MHz, and C0 = 2731 MHz. Anharmonic vibrational wavenumbers of this cation were obtained by combination of harmonic CCSD(T*)-F12a values with anharmonic contributions calculated by double-hybrid density functional theory at the B2PLYP-D level. For the complexes of C6H7(+) with Ne or Ar, the lowest energy minimum is of π-bonded structure. The corresponding dissociation energies D0 are estimated to be 160 and 550 cm(-1), respectively. There is no indication of H-bonds to the aromatic or aliphatic hydrogen atoms. Instead, three nonequivalent local energy minima were found for nuclear configurations where the rare-gas atom lies in the ring-plane and approximatly points to the center of one of the six CC bonds.     

How cationic gold clusters respond to a single sulfur atom

Results describing the interaction of a single sulfur atom with cationic gold clusters (Au(n) (+), n=1-8) using density functional theory are described. Stability of these clusters is studied through their binding energies, second order differences in the total energies, fragmentation behavior, and atom attachment energies. The lowest energy structures for these clusters appear to be three dimensional right from n=3. In most cases the sulfur atom in the structure of Au(n)S(+) is observed to displace the gold atom siting at the peripheral site of the Au(n) (+) cluster. The dissociation channels of Au(n)S(+) clusters follow the same trend as Au(n) (+) cluster, based on the even/odd number of gold atoms in the cluster, with the exception of Au(3)S(+). This cluster dissociates into Au and Au(2)S(+), signifying the relative stability of Au(2)S(+) cluster regardless of having an odd number of valence electrons. Clusters with an even number of gold atoms dissociate into Au and Au(n-1)(S)(+) and clusters with an odd number of gold atoms dissociate into Au(2) and Au(n-2)(S)(+) clusters. An empirical relation is found between the conduction molecular orbital and the number of atoms in the Au(n)S(+) cluster.     

Perturbation method to calculate the interaction potentials and electronic excitation spectra of atoms in He nanodroplets

A method is proposed for the calculation of potential energy curves and related electronic excitation spectra of dopant atoms captured in/on He nanodroplets and is applied to alkali metal atoms. The method requires knowledge of the droplet density distribution at equilibrium (here calculated within a bosonic-He density functional approach) and of a set of valence electron orbitals of the bare dopant atom (here calculated by numeric solution of the Schr?dinger equation in a suitably parametrized model potential). The electron-helium interaction is added as a perturbation, and potential energy curves are obtained by numeric diagonalization of the resulting Hamiltonian as a function of an effective coordinate z(A) (here the distance between the dopant atom and center of mass of the droplet, resulting in a pseudodiatomic potential). Excitation spectra are calculated for Na in the companion paper as the Franck-Condon factors between the v = 0 vibrational state in the ground electronic state and excited states of the pseudodiatomic molecule. They agree well with available experimental data, even for highly excited states where a more traditional approach fails.     

Electron interaction with nitromethane embedded in helium droplets: attachment and ionization measurements

Results of a detailed study on electron interactions with nitromethane (CH(3)NO(2)) embedded in helium nanodroplets are reported. Anionic and cationic products formed are analysed by mass spectrometry. When the doped helium droplets are irradiated with low-energy electrons of about 2 eV kinetic energy, exclusively parent cluster anions (CH(3)NO(2))(n)(-) are formed. At 8.5 eV, three anion cluster series are observed, i.e., (CH(3)NO(2))(n)(-), [(CH(3)NO(2))(n)-H](-), and (CH(3)NO(2))(n)NO(2)(-), the latter being the most abundant. The results obtained for anions are compared with previous electron attachment studies with bare nitromethane and nitromethane condensed on a surface. The cation chemistry (induced by electron ionization of the helium matrix at 70 eV and subsequent charge transfer from He(+) to the dopant cluster) is dominated by production of methylated and protonated nitromethane clusters, (CH(3)NO(2))(n)CH(3)(+) and (CH(3)NO(2))(n)H(+).     

Collision Energetics in a Tandem Time-of-Flight (TOF/TOF) Mass Spectrometer with a Curved-Field Reflectron

Collisions of fullerene ions (C(60) (+)) with helium and neon were carried out over a range of laboratory energies (3-20 keV) on a unique tandem time-of-flight (TOF/TOF) mass spectrometer equipped with a curved-field reflectron (CFR). The CFR enables focusing of product ions over a wide kinetic energy range. Thus, ions extracted from a laser desorption/ionization (LDI) source are not decelerated prior to collision, and collision energies in the laboratory frame are determined by the source extraction voltages. Comparison of product ion mass spectra obtained following collisions with inert gases show a time (and apparent mass) shift for product ions relative to those observed in spectra obtained by metastable dissociation (unimolecular decay), consistent with impulse collision models, in which interactions of helium with fullerene in the high energy range are primarily with a single carbon atom. In addition, within a narrow range of kinetic energies an additional peak corresponding to the capture of helium is observed for fragment ions C(50) (+), C(52) (+), C(54) (+), C(56) (+) and C(58) (+).