Superfluid He nanodroplets resonantly excited by extreme ultraviolet (XUV) pulses can relax via interatomic coulombic decay (ICD), generally considered an ultrafast process. Here, we introduce a novel approach to probe the dynamics of ICD in He nanodroplets over timescales ranging from femtoseconds to nanoseconds. Our method relies on detecting XUV fluorescence emitted from the nanodroplets as they are driven into a nanoplasma by subsequent intense infrared pulses. Nanoplasma ignition is facilitated by tunnel ionization of XUV-excited He ^* atoms attached to the droplets; it thus serves as a sensitive probe of their relaxation dynamics. The observed nanosecond-scale decay is attributed to ICD between pairs of He ^* atoms undergoing roaming motion on the droplet surface, as supported by quantum-mechanical and classical model calculations.

The solvation process of an alkali ion (Na+, K+, Rb+, and Cs+) inside a superfluid 4He2000 nanodroplet is investigated theoretically using liquid 4He time-dependent density functional theory at zero temperature. We simulate both steps of the pump-probe experiment conducted on Na+ [Albrechtsen et al., Nature 623, 319 (2023)], where the alkali atom residing at the droplet surface is ionized by the pump pulse and its solvation is probed by ionizing a central xenon atom and detecting the expulsed Na+Hen ions. Our results confirm the Poissonian model for the binding of the first five He atoms for the lighter Na+ and K+ alkalis, with a rate in good agreement with the more recent experimental results on Na+ [Albrechtsen et al., J. Chem. Phys. 162, 174309 (2025)]. For the probe step, we show that the ion takes several picoseconds to get out of the droplet. During this rather long time, the solvation structure around it is very hot and far from equilibrium, and it can gain or lose more He atoms. Surprisingly, analyzing the Na+ solvation structure energy reveals that it is not stable by itself during the first few picoseconds of the solvation process. After that, energy relaxation follows a Newton behavior, as found experimentally, but with a longer time delay, 5.0 ≤ t0 ≤ 6.5 ps vs 0.23 ± 0.06 ps, and characteristic time, 7.3 ≤ τ ≤ 16.5 ps vs 2.6 ± 0.4 ps. We conclude that the first instants of the solvation process are highly turbulent and that the solvation structure is stabilized only by the surrounding helium "solvent."

We study superfluid helium droplets multiply charged with Na+ or Ca+ ions. When stable, the charges are found to reside in equilibrium close to the droplet surface, thus representing a physical realization of Thomson's model. We find the minimum radius of the helium droplet that can host a given number of ions using a model whose physical ingredients are the solvation energy of the cations, calculated within the helium density functional theory approach, and their mutual Coulomb repulsion energy. Our model goes beyond the often used liquid drop model, where charges are smeared out either within the droplet or on its surface, and which neglects the solid-like helium shell around the ions. We find that below a threshold droplet radius R0, the total energy of the system becomes higher than that of the separated system of the pristine helium droplet and the charges embedded in their solvation microcluster ("snowball"). However, the ions are still kept within the droplet by the presence of energy barriers, which hinder Coulomb explosion. A further reduction of the droplet radius below a value Rexpl eventually results in the disappearance of such barrier, leading to Coulomb explosion. Surprisingly, our results are rather insensitive to the ion atomic species. This makes room to discuss them in the context of intrinsic multicharged helium droplets, where the charges are triatomic He3+ ions. Our calculated values for Rexpl display the correct scaling with the number of cations compared to the available experimental results, at variance with other estimates for the critical radii.

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.

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.

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)nNa+/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.

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.

The vibrational predissociation of van der Waals complexes has been the object of study using a wide range of theoretical and experimental methods, producing a large number of results. We focus here on the ArBr _2 ( v=16,… ,25 ) system. For its study, we employ two important theoretical methods: the trajectory surface hopping (TSH) and the quasiclassical trajectory method (QCTM). In the first case, the dynamics of the system are reproduced on a potential energy surface (PES) corresponding to quantum molecular vibrational states. The possibility of hopping to other vibrational surfaces is also included, which can then lead to van der Waals bond dissociation. On the other hand, the second case consists of propagating the dynamics over a single potential energy surface. We incorporate the kinetic mechanism into the TSH method for better comparison of the evolution of the complex. Both methods allow us to study the dynamical behavior of the ArBr _2 as well as several observables. We compute the lifetime, exit channel, rotational energy, and maximum angular momentum ( j_max ) of Br _2 . We compare our results with previous experimental and theoretical work and also report new results for cases that have not previously been considered. Graphical abstract

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.

The vibrational predissociation of van der Waals complexes has been the object of study using a wide range of theoretical and experimental methods, producing a large number of results. We focus here on the ArBr $$_2$$ ( $$v=16,\ldots ,25$$ ) system. For its study, we employ two important theoretical methods: the trajectory surface hopping (TSH) and the quasiclassical trajectory method (QCTM). In the first case, the dynamics of the system are reproduced on a potential energy surface (PES) corresponding to quantum molecular vibrational states. The possibility of hopping to other vibrational surfaces is also included, which can then lead to van der Waals bond dissociation. On the other hand, the second case consists of propagating the dynamics over a single potential energy surface. We incorporate the kinetic mechanism into the TSH method for better comparison of the evolution of the complex. Both methods allow us to study the dynamical behavior of the ArBr $$_2$$ as well as several observables. We compute the lifetime, exit channel, rotational energy, and maximum angular momentum ( $$j_{max}$$ ) of Br $$_2$$ . We compare our results with previous experimental and theoretical work and also report new results for cases that have not previously been considered.

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].

The vibrational predissociation of NeBr2 has been studied using a variety of theoretical and experimental methods, producing a large number of results. It is therefore a useful system for comparing different theoretical methods. Here, we apply the trajectory surface hopping (TSH) method that consists of propagating the dynamics of the system on a potential energy surface (PES) corresponding to quantum molecular vibrational states with possibility of hopping towards other surfaces until the van der Waals bond dissociates. This allows quantum vibrational effects to be added to a classical dynamics approach. We have also incorporated the kinetic mechanism for a better compression of the evolution of the complex. The novelty of this work is that it allows us to incorporate all the surfaces for (v=16,17,…,29) into the dynamics of the system. The calculated lifetimes are similar to those previously reported experimentally and theoretically. The rotational distribution, the rotational energy and jmax are in agreement with other works, providing new information for this complex.

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.

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.

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.

We have studied the dynamic evolution of a Cs atom photo-excited from 6s to 6p and 7s states on a helium droplet using time-dependent 4He-DFT simulations. Depending on the excited electronic state, the Cs impurity remains on the droplet surface or it is ejected. Upon subsequent photo-ionization of the excited Cs atom the resulting Cs+ cation may either be ejected or come back to the droplet, depending on the time delay between photo-excitation and photo-ionization. We have calculated the critical time delay separating these two different behaviors, as well as final ion velocities. These observables will be used for future comparison with planned pump-probe experiments.

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.

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.

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.