Time-resolved solvation of alkali ions in superfluid helium nanodroplets.

The sinking of alkali cations in superfluid 4He nanodroplets is investigated theoretically using liquid 4He time-dependent density functional theory at zero temperature. The simulations illustrate the dynamics of the buildup of the first solvation shell around the ions. The number of helium atoms in this shell is found to linearly increase with time during the first stages of the dynamics. This points to a Poissonian capture process, as concluded in the work of Albrechtsen et al. on the primary steps of Na+ solvation in helium droplets [Albrechtsen et al., Nature 623, 319 (2023)]. The energy dissipation rate by helium atom ejection is found to be quite similar between all alkalis, the main difference being a larger energy dissipated per atom for the lighter alkalis at the beginning of the dynamics. In addition, the number of helium atoms in the first solvation shell is found to be lower at the end of the dynamics than at equilibrium for both Li+ and Na+, pointing to a kinetic rather than thermodynamical control of the snowball size for small and strongly attractive ions.

Electron diffraction of foam-like clusters between xenon and helium in superfluid helium droplets.

We report electron diffraction results of xenon clusters formed in superfluid helium droplets, with droplet sizes in the range of 105-106 atoms/droplet and xenon clusters from a few to a few hundred atoms. Under four different experimental conditions, the diffraction profiles can be fitted using four atom pairs of Xe. For the two experiments performed with higher helium contributions, the fittings with one pair of Xe-He and three pairs of Xe-Xe distances are statistically preferred compared with four pairs of Xe-Xe distances, while the other two experiments exhibit the opposite preference. In addition to the shortest pair distances corresponding to the van der Waals distances of Xe-He and Xe-Xe, the longer distances are in the range of the different arrangements of Xe-He-Xe and Xe-He-He-Xe. The number of independent atom pairs is too many for the small xenon clusters and too few for the large clusters. We consider these results evidence of xenon foam structures, with helium atoms stuck between Xe atoms. This possibility is confirmed by helium time-dependent density functional calculations. When the impact parameter of the second xenon atom is a few Angstroms or longer, the second xenon atom fails to penetrate the solvation shell of the first atom, resulting in a dimer with a few He atoms in between the two Xe atoms. In addition, our results for larger droplets point toward a multi-center growth process of dopant atoms or molecules, which is in agreement with previous proposals from theoretical calculations and experimental results.

Attachment of Hydrogen Molecules to Atomic Ions (Na+ , Cl- ): Examination of an Adiabatic Separation of the H2 Rotational Motion.

Interactions between molecular hydrogen and ions are of interest in cluster science, astrochemistry and hydrogen storage. In dynamical simulations, H2 molecules are usually modelled as point particles, an approximation that can fail for anisotropic interactions. Here, we apply an adiabatic separation of the H2 rotational motion to build effective pseudoatom-ion potentials and in turn study the properties of (H2 )n Na+ /Cl- clusters. These interaction potentials are based on high-level ab initio calculations and Improved Lennard-Jones parametrizations, while the subsequent dynamics has been performed by quantum Monte Carlo calculations. By comparisons with simulations explicitly describing the molecular rotations, it is concluded that the present adiabatic model is very adequate. Interestingly, we find differences in the cluster stabilities and coordination shells depending on the spin isomer considered (para- or ortho-H2 ), especially for the anionic clusters.

Quantized vortex nucleation in collisions of superfluid nanoscopic helium droplets at zero temperature.

We address the collision of two superfluid 4He droplets at non-zero initial relative velocities and impact parameters within the framework of liquid 4He time-dependent density functional theory at zero temperature. Despite the small size of these droplets (1000 He atoms in the merged droplet) imposed by computational limitations, we have found that quantized vortices may be readily nucleated for reasonable collision parameters. At variance with head-on collisions, where only vortex rings are produced, collisions with a non-zero impact parameter produce linear vortices that are nucleated at indentations appearing on the surface of the deformed merged droplet. Whereas for equal-size droplets, vortices are produced in pairs, an odd number of vortices can appear when the colliding droplet sizes are different. In all cases, vortices coexist with surface capillary waves. The possibility for collisions to be at the origin of vortex nucleation in experiments involving very large droplets is discussed. An additional surprising result is the observation of the drops coalescence even for grazing and distal collisions at relative velocities as high as 80 and 40 m/s, respectively, induced by the long-range van der Waals attraction between the droplets.

Clustering, collision, and relaxation dynamics in pure and doped helium nanoclusters: Density- vs particle-based approaches.

The clustering, collision, and relaxation dynamics of pristine and doped helium nanodroplets is theoretically investigated in cases of pickup and clustering of heliophilic argon, collision of heliophobic cesium atoms, and coalescence of two droplets brought into contact by their mutual long-range van der Waals interaction. Three approaches are used and compared with each other. The He time-dependent density functional theory method considers the droplet as a continuous medium and accounts for its superfluid character. The ring-polymer molecular dynamics method uses a path-integral description of nuclear motion and incorporates zero-point delocalization while bosonic exchange effects are ignored. Finally, the zero-point averaged dynamics approach is a mixed quantum-classical method in which quantum delocalization is described by attaching a frozen wavefunction to each He atom, equivalent to classical dynamics with effective interaction potentials. All three methods predict that the growth of argon clusters is significantly hindered by the helium host droplet due to the impeding shell structure around the dopants and kinematic effects freezing the growing cluster in metastable configurations. The effects of superfluidity are qualitatively manifested by different collision dynamics of the heliophilic atom at high velocities, as well as quadrupole oscillations that are not seen with particle-based methods, for droplets experiencing a collision with cesium atoms or merging with each other.

Dynamics of Photoexcited Cs Atoms Attached to Helium Nanodroplets.

We present an experimental study of the dynamics following the photoexcitation and subsequent photoionization of single Cs atoms on the surface of helium nanodroplets. The dynamics of excited Cs atom desorption and readsorption as well as CsHe exciplex formation are measured by using femtosecond pump-probe velocity map imaging spectroscopy and ion time-of-flight spectrometry. The time scales for the desorption of excited Cs atoms off helium nanodroplets as well as the time scales for CsHe exciplex formation are experimentally determined for the 6p states of Cs. For the 6p 2Π1/2 state, our results confirm that the excited Cs atoms only desorb from the nanodroplet when the excitation wavenumber is blue-shifted from the 6p 2Π1/2 ← 6s 2Σ1/2 resonance. Our results suggest that the dynamics following excitation to the 6p 2Π3/2 state can be described by an evaporation-like desorption mechanism, whereas the dynamics arising from excitation to the 6p 2Σ1/2 state is indicative for a more impulsive desorption process. Furthermore, our results suggest a helium-induced spin-orbit relaxation from the 6p 2Σ1/2 state to the 6p 2Π1/2 state. Our findings largely agree with the results of time-dependent 4He density functional theory (DFT) simulations published earlier [Eur. Phys. J. D 2019, 73, 94].

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 +Heq and Ar3 +Heq (q ≤ 1000), with a strong contribution of the bare Ar2 + ion, and neither Ar+ nor Ar+Heq 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 +Heq or Ar4 +Heq (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.

Alkali atoms attached to vortex-hosting helium nanodroplets.

Light absorption or fluorescence excitation spectroscopy of alkali atoms attached to 4He droplets is investigated as a possible way for detecting the presence of vortices. To this end, we have calculated the equilibrium configuration and energetics of alkali atoms attached to a 4He1000 droplet hosting a vortex line using 4He density functional theory. We use them to study how the dipole absorption spectrum of the alkali atom is modified when the impurity is attached to a vortex line. Spectra are found to be blue-shifted (higher frequencies) and broadened compared to vortex-free droplets because the dimple in which the alkali atom sits at the intersection of the vortex line and the droplet surface is deeper. This effect is smaller for lighter alkali atoms and all the more so when using a quantum description since, in this case, they sit further away from the droplet surface on average due to their zero-point motion. Spectral modifications due to the presence of a vortex line are minor for np ← ns excitation and therefore insufficient for vortex detection. In the case of higher n'p ← ns or n's ← ns (n' > n) excitations, the shifts are larger as the excited state orbital is more extended and therefore more sensitive to changes in the surrounding helium density.

4s to 5s and 4p photoexcitation dynamics of K atoms from the surface of helium nanodroplets: a theoretical study.

We study the photodissociation of the potassium atom from a superfluid helium nanodroplet upon 5s 2S or 4p 2P excitation using the time-dependent helium density functional method (He-TDDFT). The importance of quantum effects is assessed by comparing the absorption spectrum obtained for a classical or a quantum description of the K atom. In the case of the 5s 2S ← 4s 2S excitation the difference is rather large, and we use a quantum description for the ensuing direct dissociation dynamics. In the case of the 4p 2P ← 4s 2S absorption spectrum, the difference is much smaller, hence a classical description of K is used to describe 4p 2P excitation dynamics. Excitation to the 4p 2Σ1/2 state leads to the direct dissociation of the K atom, while the 4p 2Π3/2 state initially leads to the formation of an exciplex and the 4p 2Π1/2 state to a bouncing atom above the droplet surface. Remarkably, electronic relaxation can be observed for the latter two states, leading to spin-orbit relaxation and the binding of the initially departing one-atom excimer as a ring excimer for the 2P3/2 state and to the formation of a bound, ring excimer for the 2Π1/2 state.

Dynamics of impurity clustering in superfluid 4He nanodroplets.

The capture of multiple impurities by 4He droplets is investigated using real time dynamics within the density functional approach applied to liquid helium. We study the case of two or six Ar atoms colliding with a 4He5000 droplet either in its ground state or hosting a six-vortex array. Depending on initial kinematic conditions, two different Ar structures are found: either a compact, gas-phase like cluster, or a loosely bound metastable cluster with helium density caged inside. In the presence of the vortex array, the argon atoms are deflected by the superfluid flow, tending to orbit around the vortex cores. The Ar atoms end up being trapped together in a loosely bound structure attached to the central vortex core.

Desorption dynamics of RbHe exciplexes off He nanodroplets induced by spin-relaxation.

Doped He nanodroplets are ideal model systems to study the dynamics of elementary photophysical processes in heterogeneous nanosystems. Here we present a combined experimental and theoretical investigation of the formation of free RbHe exciplex molecules from laser-excited Rb-doped He nanodroplets. Upon excitation of a droplet-bound Rb atom to the 5p3/22Π3/2-state, a stable RbHe exciplex forms within about 20 ps. Only due to 2Π3/2 → 2Π1/2 spin-relaxation does the RbHe exciplex detach from the He droplet surface with a half life of about 700 ps, given by the spin-relaxation time and the coupling of spin and translational degrees of freedom.

Helium-induced electronic transitions in photo-excited Ba+-Hen exciplexes.

The possibility for helium-induced electronic transitions in a photo-excited atom is investigated using Ba+ excited to the 6p 2P state as a prototypical example. A diabatization scheme has been designed to obtain the necessary potential energy surfaces and couplings for complexes of Ba+ with an arbitrary number of helium atoms. It involves computing new He-Ba+ electronic wave functions and expanding them in determinants of the non-interacting complex. The 6p 2P ← 6s 2S photodissociation spectrum of He⋯Ba+ calculated with this model shows very weak coupling for a single He atom. However, several electronic relaxation mechanisms are identified, which could potentially explain the expulsion of barium ions from helium nanodroplets observed experimentally upon Ba+ photoexcitation. For instance, an avoided crossing in the ring-shaped He7Ba+ structure is shown to provide an efficient pathway for fine structure relaxation. Symmetry breaking by either helium density fluctuations or vibrations can also induce efficient relaxation in these systems, e.g., bending vibrations in the linear He2Ba+ excimer. The identified relaxation mechanisms can provide insight into helium-induced non-adiabatic transitions observed in other systems.

Impulsive alignment of 4He-CH3I: A theoretical study.

We simulate the non-adiabatic laser alignment of the weakly bound 4He-CH3I complex based on a quantum mechanical wave packet calculation for a model He-CH3I interaction potential. Two different regimes are found depending on the laser intensity. At intensities typical of non-adiabatic alignment experiments, the rotational dynamics resembles that of the isolated molecule. This is attributed to the fact that after the initial prompt alignment peak the complex rapidly dissociates. The subsequent revival pattern is due to the free rotation of the molecule detached from the helium atom. It is superimposed to a flat background corresponding to ∼20% of the wave packet which remains bound, containing lower rotational excitation. At lower intensities, dissociation is avoided but the rotational excitation is not high enough to provide an efficient alignment and a broad non-regular structure is observed. Besides, the interaction of the He atom with the molecule quenches any possible alignment. These interpretations are based on the calculation of different observables related to the rotational motion. We compare our findings with recent experimental and theoretical results of non-adiabatic alignment of linear molecules solvated in helium nanodroplets or weakly interacting with one helium atom.

Capture of Xe and Ar atoms by quantized vortices in 4He nanodroplets.

We present a computational study, based on time-dependent Density Functional theory, of the real-time interaction and trapping of Ar and Xe atoms in superfluid 4He nanodroplets either pure or hosting quantized vortex lines. We investigate the phase-space trajectories of the impurities for different initial conditions and describe in detail the complex dynamics of the droplets during the capture of the impurities. We show that the interaction of the incoming atom with the vortex core induces large bending and twisting excitations of the vortex core lines, including the generation of helical Kelvin waves propagating along the vortex core. We have also calculated the stationary configurations of a 4He droplet hosting a 6-vortex array whose cores are filled with Ar atoms. As observed in recent experiments, we find that doping adds substantial rigidity to the system, such that the doped vortex array remains stable, even at low values of the angular velocities where the undoped vortices would otherwise be pushed towards the droplet surface and be expelled.

A theoretical simulation of the resonant Raman spectroscopy of the H2O⋯Cl2 and H2O⋯Br2 halogen-bonded complexes.

The resonant Raman spectra of the H2O⋯Cl2 and H2O⋯Br2 halogen-bonded complexes have been studied in the framework of a 2-dimensional model previously used in the simulation of their UV-visible absorption spectra using time-dependent techniques. In addition to the vibrational progression along the dihalogen mode, a progression is observed along the intermolecular mode and its combination with the intramolecular one. The relative intensity of the inter to intramolecular vibrational progressions is about 15% for H2O⋯Cl2 and 33% for H2O⋯Br2. These results make resonant Raman spectra a potential tool for detecting the presence of halogen bonded complexes in condensed phase media such as clathrates and ice.

Dissociative Photoionization of He···Li2: A Theoretical Study.

Dissociative photoionization of the He···Li2 van der Waals complex to the ground electronic state of the He···Li2+ ion is investigated theoretically. The photoionization cross section is computed using existing interaction potentials. Resonances are found on top of a structured continuum. They are assigned to vibrational predissociation of the ion by comparison with Fermi Golden Rule calculations. Because of the differences in potential energy surfaces between the neutral and ionic complexes, only the resonances corresponding to quasibound states with the highest excitation in the van der Waals modes are visible. The other quasi bound states obtained in the Fermi Golden Rule calculations can give information on vibrational energy relaxation rates in other collisional processes involving the lithium dimer ion and a helium atom.

Excitation of Sodium Atoms Attached to Helium Nanodroplets: The 3p ← 3s Transition Revisited.

The dynamics of Na atoms on the surface of helium nanodroplets following excitation via the 3p ← 3s transition has been investigated using state-specific ion-based detection of the products. Excitation of the system to the 3p (2)Π states is found to lead to the desorption of both bare Na and NaHe exciplexes. The associated speed distributions point to an impulsive desorption process for Na products and a thermally driven process for the NaHe exciplexes. In contrast, excitation of the 3p (2)Σ state leads exclusively to the impulsive desorption of Na atoms. In this case, the desorption is accompanied by a helium-induced relaxation process, as evidenced by the large fraction of detected Na (2)P1/2 atoms. The relaxation process is thought to be related to a crossing between the (2)Π1/2 and (2)Σ potential energy curves at large distance.

Communication: angular momentum alignment and fluorescence polarization of alkali atoms photodetached from helium nanodroplets.

The theory of photofragments angular momentum polarization is applied to the photodetachment of an electronically excited alkali atom from a helium nanocluster (N = 200). The alignment of the electronic angular momentum of the bare excited alkali atoms produced is calculated quantum mechanically by solving the excited states coupled equations with potentials determined by density functional theory (DFT). Pronounced oscillations as a function of excitation energy are predicted for the case of Na@(He)200, in marked contrast with the absorption cross-section and angular distribution of the ejected atoms which are smooth functions of the energy. These oscillations are due to quantum interference between different coherently excited photodetachment pathways. Experimentally, these oscillations should be reflected in the fluorescence polarization and polarization-resolved photoelectron yield of the ejected atoms, which are proportional to the electronic angular momentum alignment. In addition, this result is much more general than the test case of NaHe200 studied here. It should be observable for larger droplets, for higher excited electronic states, and for other alkali as well as for alkali-earth atoms. Detection of these oscillations would show that the widely used pseudo-diatomic model can be valid beyond the prediction of absorption spectra and could help in interpreting parts of the dynamics, as already hinted by some experimental results on angular anisotropy of bare alkali fragments.

Exploring the importance of quantum effects in nucleation: the archetypical Ne(n) case.

The effect of quantum mechanics (QM) on the details of the nucleation process is explored employing Ne clusters as test cases due to their semi-quantal nature. In particular, we investigate the impact of quantum mechanics on both condensation and dissociation rates in the framework of the microcanonical ensemble. Using both classical trajectories and two semi-quantal approaches (zero point averaged dynamics, ZPAD, and Gaussian-based time dependent Hartree, G-TDH) to model cluster and collision dynamics, we simulate the dissociation and monomer capture for Ne(8) as a function of the cluster internal energy, impact parameter and collision speed. The results for the capture probability P(s)(b) as a function of the impact parameter suggest that classical trajectories always underestimate capture probabilities with respect to ZPAD, albeit at most by 15%-20% in the cases we studied. They also do so in some important situations when using G-TDH. More interestingly, dissociation rates k(diss) are grossly overestimated by classical mechanics, at least by one order of magnitude. We interpret both behaviours as mainly due to the reduced amount of kinetic energy available to a quantum cluster for a chosen total internal energy. We also find that the decrease in monomer dissociation energy due to zero point energy effects plays a key role in defining dissociation rates. In fact, semi-quantal and classical results for k(diss) seem to follow a common "corresponding states" behaviour when the proper definition of internal and dissociation energies are used in a transition state model estimation of the evaporation rate constants.

Large shift and small broadening of Br2 valence band upon dimer formation with H2O: an ab initio study.

Valence electronic excitation spectra are calculated for the H(2)O···Br(2) complex using highly correlated ab initio potentials for both the ground and the valence electronic excited states and a 2-D approximation for vibrational motion. Due to the strong interaction between the O-Br and the Br-Br stretching motions, inclusion of these vibrations is the minimum necessary for the spectrum calculation. A basis set calculation is performed to determine the vibrational wave functions for the ground electronic state and a wave packet simulation is conducted for the nuclear dynamics on the excited state surfaces. The effects of both the spin-orbit interaction and temperature on the spectra are explored. The interaction of Br(2) with a single water molecule induces nearly as large a shift in the spectrum as is observed for an aqueous solution. In contrast, complex formation has a remarkably small effect on the T = 0 K width of the valence bands due to the fast dissociation of the dihalogen bond upon excitation. We therefore conclude that the widths of the spectra in aqueous solution are mostly due to inhomogeneous broadening.