Helium Nanodroplets Research Articles

Collision of cesium atoms on helium nanodroplets: Unraveling mechanisms for surface capture at experimental velocities.

The collision of cesium atoms on the surface of helium nanodroplets (HNDs) containing 1000 atoms is described by the ZPAD-mPL approach, a zero-point averaged dynamics (ZPAD) method based on a He-He pseudopotential adjusted to better reproduce the total energy of He1000. Four types of collisional patterns were identified depending on the initial projectile speed v0 and impact parameter b. At the lowest speeds (v0 ≲ 250ms-1), Cs atoms are softly captured by the HND surface, while at the highest ones (v0 ≳ 500-600ms-1), Cs atoms can travel through the droplet and move away. In between these two extreme cases, Cs atoms can be temporarily submerged in the HND before being expelled to the surface if b = 0 or cross the HND before being captured on its surface. The possibility for Cs capture at experimental velocities and droplet piercings at the highest ones contrasts with time-dependent density functional theory calculations, which predict Cs capture for velocities lower than 75ms-1, and ring-polymer molecular dynamics (RPMD) or former ZPAD-like methods, which predict soft Cs capture up to 500ms-1. ZPAD-mPL results are attributed to the liquid but non-superfluid nature of the droplet, which favors energy exchanges with the helium environment, and to low He-He binding energy and HND surface tension, which can stimulate helium ejections, especially at high projectile speeds. Despite the use of a pseudopotential to model He-He interactions, the heliophobicity of Cs atoms is maintained as demonstrated by their ability to remain localized on the HND surface or to be expelled to the HND surface after transient submersion in helium.

Interatomic and intermolecular decay processes in quantum fluid clusters.

In this comprehensive review, we explore interatomic and intermolecular correlated electronic decay phenomena observed in superfluid helium nanodroplets subjected to extreme ultraviolet (XUV) radiation. Helium nanodroplets, known for their distinctive electronic and quantum fluid properties, provide an ideal environment for examining a variety of non-local electronic decay processes involving the transfer of energy, charge, or both between neighboring sites and resulting in ionization and the emission of low-kinetic energy electrons. Key processes include interatomic or intermolecular Coulombic decay (ICD) and its variants, such as electron transfer-mediated decay (ETMD). Insights gained from studying these light-matter interactions in helium nanodroplets enhance our understanding of the effects of ionizing radiation on other condensed-phase systems, including biological matter. We also emphasize the advanced experimental and computational techniques that make it possible to resolve electronic decay processes with high spectral and temporal precision. Utilizing ultrashort pulses from free-electron lasers, the temporal evolution of these processes can be
followed, significantly advancing our comprehension of the dynamics within quantum fluid clusters and non-local electronic interactions in nanoscale systems.

On the nature of hydrogen bonding in the H2S dimer

Hydrogen bonding is a central concept in chemistry and biochemistry, and so it continues to attract intense study. Here, we examine hydrogen bonding in the H2S dimer, in comparison with the well-studied water dimer, in unprecedented detail. We record a mass-selected IR spectrum of the H2S dimer in superfluid helium nanodroplets. We are able to resolve a rotational substructure in each of the three distinct bands and, based on it, assign these to vibration-rotation-tunneling transitions of a single intramolecular vibration. With the use of high-level potential and dipole-moment surfaces we compute the vibration-rotation-tunneling dynamics and far-infrared spectrum with rigorous quantum methods. Intramolecular mode Vibrational Self-Consistent-Field and Configuration-Interaction calculations provide the frequencies and intensities of the four SH-stretch modes, with a focus on the most intense, the donor bound SH mode which yields the experimentally observed bands. We show that the intermolecular modes in the H2S dimer are substantially more delocalized and more strongly mixed than in the water dimer. The less directional nature of the hydrogen bonding can be quantified in terms of weaker electrostatic and more important dispersion interactions. The present study reconciles all previous spectroscopic data, and serves as a sensitive test for the potential and dipole-moment surfaces.

Mixed H2S and H2O Clusters─New Insights into Dispersion-Dominated Hydrogen Bonding.

Here, we report the results of an IR spectroscopy study on heteroclusters of H2S and H2O and several of their isotopomers using mass-selective IR spectroscopy in superfluid helium nanodroplets in the range of 2560-2800 cm-1. Based on DFT calculations on the B3LYP-D3/6-311++G(d,p) level of theory, we were able to assign the experimentally observed O-D stretching bands to heterodimer and heterotrimer clusters. Since no bands of the S-H-bound conformer HSH···OH2 could be observed, we were able to determine the O-H-bound conformer HOH···SH2 to be the global minimum structure. A trapping of the local minima in helium nanodroplets was not observed. This is in line with the weaker hydrogen bond expected for H2S complexes. In these clusters, the interaction energy is expected to be more dominated by dispersion and less dictated by highly directional electrostatic forces.

Infrared Spectroscopy of CH5+ Cations in Helium Nanodroplets.

The methanium CH5+ is a prototypical fluxional ion whose infrared spectra remain unassigned. Here we report on the infrared spectra of CH5+ cations and its deuterated isotopomer, CH4D+, in helium droplets at a low temperature of 0.38 K. The ions were produced upon protonation of CH4 molecules, a technique that was developed in this work. The spectra of CH5+ around 3000 cm-1 show two strong and broad infrared bands and a weak shoulder, reflecting its highly fluxional nature. The spectrum of CH4D+ shows a much sharper infrared band, indicating a partial quenching of the exchange of H/D atoms. This work also reports on the infrared spectrum of the methane dimer radical cations (CH4)2+.

Geometric structures and adsorption energies of mixed methanol and C60 cationic clusters produced within helium nanodroplets

Mass spectrometry is a useful technique for studying molecular cluster sizes, their distributions, compositions, and stability. Methanol and fullerenes are among the species identified in the interstellar medium and, due to their high abundance, their interactions are an interesting investigation topic. A mass spectrometric study of mixed clusters of methanol and C60 inside helium nanodroplets is presented. Anomalies in the distribution intensities or magic numbers were observed for [CH3OH]4[C60]m+,1≤m≤7. Water molecules within clusters were also detected, arising as one of the products of intermolecular methanol dehydration. Optimized and supposedly stable geometrical structures of these molecules are presented along with corresponding HOMO–LUMO gaps and adsorption energies. A linear decrease in adsorption energy and saturation at a critical cluster size was noticed.

Intermolecular Bending States and Tunneling Splittings of Water Trimer from Rigorous 9D Quantum Calculations: I. Methodology, Energy Levels, and Low-Frequency Spectrum.

We present the computational methodology that enables the first rigorous nine-dimensional (9D) quantum calculations of the intermolecular bending states of the water trimer, as well as its low-frequency spectrum for direct comparison with experiment. The water monomers, treated as rigid, have their centers of mass (cm's) at the corners of an equilateral triangle, and the intermonomer cm-to-cm distance is set to a value slightly larger than that in the equilibrium geometry of the trimer. The remaining nine strongly coupled large-amplitude bending (angular) degrees of freedom (DOFs) enter the 9D bend Hamiltonian of the three coupled 3D rigid-water hindered rotors. Its 9D eigenstates encompass excited librational vibrations of the trimer, as well as their torsional and bifurcation tunneling splittings, which have been the subject of much interest. The calculations of these eigenstates are extremely demanding, and a sophisticated computational scheme is developed that exploits the molecular symmetry group of the water trimer, G48, in order to make them feasible in a reasonable amount of time. The spectrum of the low-frequency vibrations of the water trimer simulated using the eigenstates of the 9D bend Hamiltonian agrees remarkably well with the experimentally observed far-infrared (FIR) spectrum of the trimer in helium nanodroplets over the entire frequency range of the measurements from 70 to 620 cm-1. This shows that most peaks in the experimental FIR spectrum are associated with the intermolecular bending vibrations of the trimer. Moreover, the ground-state torsional tunneling splittings from the present 9D calculations are in excellent agreement with the spectroscopic data. These results demonstrate the high quality of the ab initio 2 + 3-body PES employed for the DOFs included in the bound-state calculations.

Concurrent processes in the time-resolved solvation and Coulomb ejection of sodium ions in helium nanodroplets

Recent pump-probe experiments [Albrechtsen et al., Nature 623, 319 (2023)] have explored the gradual solvation of sodium cations in contact with helium nanodroplets, using a fully solvated xenon atom as a probe exerting a repulsive interaction after its own ionization. In this communication, we computationally examine by means of atomistic ring-polymer molecular dynamics the mechanisms of successive ionizations, shell formation, and Coulomb ejection that all take place within tens of picoseconds and show that their interplay subtly depends on the time delay between the two ionizations but also on the droplet size. The possibility of forming solvated Na+Xe non-covalent complexes under a few tens of picoseconds in such experiments is ruled out based on fragment distributions.

Regularities and Anomalies in Neon Matrix Shifts of Hydrogen-Bonded O-H Stretching Fundamentals.

O-H bond stretching vibrations in hydrogen-bonded complexes embedded into cryogenic neon matrices are subtly downshifted from cold gas phase reference wavenumbers. To the extent that this shift is systematic, it enables neon matrices as more universally applicable spectroscopic benchmark environments for quantum chemical predictions. Outliers are indicative of either an assignment problem in one of the two cryogenic experiments or they reveal interesting dynamics or structural effects on the complexes as a function of the environment. We compile 6 literature-known pairs of experimental data in jet and neon matrix expansions and realize a 6-fold expansion of that number through targeted matrix isolation and/or slit jet expansion spectroscopy presented in this work. In many cases, the neon matrix shift is less than the uncertainty of the currently best-performing blind quantum chemical predictions for the gas phase, but in specific cases, it may exceed the currently achievable theoretical accuracy. Some evidence for a positive correlation of the matrix shift with the hydrogen bond shift is found, similar to observations for helium nanodroplets. Outliers in particular for water acting as a donor are discussed, and in a few cases they call for a future reinvestigation. Substantial improvement in the correlation of the matrix shift with the hydrogen bond shift is achieved for ketone monohydrates by removing a vibrational resonance. New insights into nitrile hydration isomerism are obtained, and the linear OH stretching spectrum of the jet-cooled ammonia-water complex is presented for the first time. Vibrational spectroscopy in weakly perturbing solid rare gas quantum matrices for the benchmarking of gas phase theory and future explicit theoretical treatments of the quantum matrix environment to better understand the outliers are both encouraged.

Collision of rare-gas atoms on helium nanodroplets: Theoretical evidence for an efficient coagulation of heavy rare-gas atoms.

The coagulation of rare-gas atoms (RG = Ne, Ar, Kr, Xe, and Rn) in helium nanodroplets (HNDs) composed of 1000 atoms is investigated by zero-point averaged dynamics where a He-He pseudopotential is used to make the droplet liquid with proper energies. This method reproduces the qualitative abundances of embedded Arn+1 structures obtained by Time-Dependent Density Functional Theory and Ring Polymer Molecular Dynamics for Ar + ArnHe1000 collisions at realistic projectile speeds and impact parameters. More generally, coagulation is found to be much more efficient for heavy rare-gases (Xe and Rn) than for light ones (Ne and Ar), a behavior mainly attributed to a slower energy dissipation of the projectile in the HND. When coagulation does not occur, the projectile maintains a speed of 10-30m s-1 within the HND, but its velocity vector is rarely oriented toward the dopant, and the projectile roams in a limited region of the droplet. The structure of embedded RGn+1 clusters does not systematically match their gas-phase global minimum structure, and more than 30% of RGn-RG unbound structures are due to one He atom located in between the projectile and a dopant atom.

Structural Characterization of Pyruvic Acid Dimers Formed inside Helium Nanodroplets by Infrared Spectroscopy and Ab Initio Study.

The structural arrangements of α-keto acid complexes hold significant interest across various fields of chemistry such as enzyme modeling, drug design, or polymer blending. Herein, we report mass-selective infrared (IR) spectra of pyruvic acid monomers and dimers in the range 1720-1820 cm-1 recorded in helium nanodroplets at 0.37 K. The monomer features IR bands at 1807.1 and 1734.5 cm-1, which are assigned to the carboxylic and ketonic C═O stretching vibrations, respectively. Furthermore, the pyruvic acid dimers generated inside the helium nanodroplets are characterized by carboxylic and ketonic C═O stretch vibrations appearing at 1799.2 and 1737.0 cm-1, respectively. This frequency shift of ±7 cm-1 for both C═O stretching bands from the monomer to the dimer demonstrates that the structural motif of the monomer is maintained upon dimer aggregation in helium nanodroplets. The structural assignments were supported by a comparison of the MP2/aug-cc-pVDZ-predicted harmonic vibrational spectra at the C═O stretching region with the experiments. The global minimum monomer structure with an intramolecular hydrogen bond and its dimer stabilized by both inter- and intramolecular hydrogen bonding interactions reproduce the experimental spectra from the monomer and dimer. This assigned dimer structure lies ca.11 kJ/mol above the corresponding global minimum and is favored in helium nanodroplets due to the long-range realignment of molecules via dipole-dipole interaction, followed by short-range stabilization upon intermolecular hydrogen bond formation. The barrier for reconfiguration of the precooled monomer conformer leading to the formation of the most stable dimer structure is around 58 kJ/mol, which is infeasible at 0.37 K.

Formation of Doubly and Triply Charged Fullerene Dimers in Superfluid Helium Nanodroplets.

Sequential ionization of fullerene cluster ions (C_{60})_{n}^{+} within multiply charged helium nanodroplets leads to the intriguing phenomenon of forming and stabilizing doubly and triply charged fullerene oligomers. While the formation of doubly charged dimers (C_{60})_{2}^{2+} has been predicted in earlier studies, the observation of even triply charged ones (C_{60})_{2}^{3+} is highly surprising. This remarkable resilience against Coulomb explosion is achieved through efficient cooling within the superfluid environment of helium nanodroplets and a sequential ionization scheme that populates covalently bound or physisorbed fullerene dimers. Calculations support the stability of four differently bonded (C_{60})_{2}^{2+} and (C_{60})_{2}^{3+} isomers and predict a low Coulomb barrier (<0.4 eV) preventing even dissociation of cold van der Waals complexes.

Infrared spectroscopy of isomers of C3H4+ in superfluid helium droplets.

Superfluid helium nanodroplets are unique nanomatrices for the isolation and study of transient molecular species, such as radicals, carbenes, and ions. In this work, isomers of C3H4+ were produced upon electron ionization of propyne and allene molecules and interrogated via infrared spectroscopy inside He nanodroplet matrices. It was found that the spectrum of C3H4+ has at least three distinct groups of bands. The relative intensities of the bands depend on the precursor employed and its pickup pressure, which indicates the presence of at least three different isomers. Two isomers were identified as allene and propyne radical cations. The third isomer, which has several new bands in the range of 3100-3200cm-1, may be the elusive vinylmethylene H2C=CH-CH+ radical cation. The observed bands for the allene and propyne cations are in good agreement with the results of density functional theory calculations. However, there is only moderate agreement between the new bands and the theoretically calculated vinylmethylene spectrum, which indicates more work is necessary to unambiguously assign it.

Cluster size distributions, electronic characteristics and geometric structures of mixed cationic clusters of cesium and sulfur hexafluoride doped in helium

Mass Spectrometry has emerged as a valuable technique for investigating molecular cluster characteristics, including size distributions, compositions, stabilities and reactivity. In this study, we present a mass spectrometric analysis of cesium Cs mixed with sulfur hexafluoride S F 6 clusters, denoted as [ Cs ] n [ S F 6 ] m + , encapsulated within helium nanodroplets HNDs. Our analysis involved precise evaluation of mass spectra and calculating ion abundances taking into account the isotope patterns of ions. Additionally, we examined geometrical structures and stabilities of these molecules along with their corresponding highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) energy gaps. This finding sheds light on the fundamental properties and behaviour of mixed molecular clusters, offering insights into their potential applications and interactions.

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.

Structure determination of alkali trimers on helium nanodroplets through laser-induced Coulomb explosion.

Alkali trimers, Ak3, located on the surface of He nanodroplets are triply ionized following multiphoton absorption from an intense femtosecond laser pulse, leading to fragmentation into three correlated Ak+ ions. Combining the information from threefold covariance analysis of the emission direction of the fragment ions and their kinetic energy distributions P(Ekin), we find that Na3, K3, and Rb3 have an equilateral triangular structure, corresponding to that of the lowest lying quartet state A2'4, and determine the equilibrium bond distance Req(Na3) = 4.65 ± 0.15Å, Req(K3) = 5.03 ± 0.18Å, and Req(Rb3) = 5.45 ± 0.22Å. For K3 and Rb3, these values agree well with existing theoretical calculations, while for Na3, the value is 0.2-0.3Å larger than the existing theoretical results. The discrepancy is ascribed to a minor internuclear motion of Na3 during the ionization process. In addition, we determine the distribution of internuclear distances P(R) under the assumption of fixed bond angles. The results are compared to the square of the internuclear wave function |Ψ(R)|2.

Femtosecond Collisional Dissipation of Vibrating D_{2}^{+} in Helium Nanodroplets.

We explored the collision-induced vibrational decoherence of singly ionized D_{2} molecules inside a helium nanodroplet. By using the pump-probe reaction microscopy with few-cycle laser pulses, we captured in real time the collision-induced ultrafast dissipation of vibrational nuclear wave packet dynamics of D_{2}^{+} ion embedded in the droplet. Because of the strong coupling of excited molecular cations with the surrounding solvent, the vibrational coherence of D_{2}^{+} in the droplet interior only lasts for a few vibrational periods and completely collapses within 140fs. The observed ultrafast coherence loss is distinct from that of isolated D_{2}^{+} in the gas phase, where the vibrational coherence persists for a long time with periodic quantum revivals. Our findings underscore the crucial role of ultrafast collisional dissipation in shaping the molecular decoherence and solvation dynamics during solution chemical reactions, particularly when the solute molecules are predominantly in ionic states.

Fragmentation of water clusters formed in helium nanodroplets by charge transfer and Penning ionization.

Helium nanodroplets ("HNDs") are widely used for forming tailor-made clusters and molecular complexes in a cold, transparent, and weakly interacting matrix. The characterization of embedded species by mass spectrometry is often complicated by the fragmentation and trapping of ions in the HNDs. Here, we systematically study fragment ion mass spectra of HND-aggregated water and oxygen clusters following their ionization by charge transfer ionization ("CTI") and Penning ionization ("PEI"). While the efficiency of PEI of embedded clusters is lower than for CTI by about factor 10, both the mean sizes of detected water clusters and the relative yields of unprotonated cluster ions are significantly larger, making PEI a "soft ionization" scheme. However, the tendency of ions to remain bound to HNDs leads to a reduced detection efficiency for large HNDs containing >104 helium atoms. These results are instrumental in determining optimal conditions for mass spectrometry and photoionization spectroscopy of molecular complexes and clusters aggregated in HNDs.

Method of kinetic energy reconstruction from time-of-flight mass spectra.

We present a method for the reconstruction of ion kinetic energy distributions from ion time-of-flight mass spectra through ion trajectory simulations. In particular, this method is applicable to complicated spectrometer geometries with largely anisotropic ion collection efficiencies. A calibration procedure using a single ion mass peak allows the accurate determination of parameters related to the spectrometer calibration, experimental alignment, and instrument response function, which improves the agreement between simulations and experiment. The calibrated simulation is used to generate a set of basis functions for the time-of-flight spectra, which are then used to transform from time-of-flight to kinetic-energy spectra. We demonstrate this reconstruction method on a recent pump-probe experiment by Asmussen etal. [Asmussen etal., Phys. Chem. Chem. Phys., 23, 15138, (2021)] on helium nanodroplets and retrieve time-resolved kinetic-energy-release spectra for the ions from ion time-of-flight spectra.

Mixed Cluster Ions of Magnesium and C60.

Magnesium clusters exhibit a pronounced nonmetal-to-metal transition, and the neutral dimer is exceptionally weakly bound. In the present study, we formed pristine Mgnz+ (n = 1-100, z = 1-3) clusters and mixed (C60)mMgnz+ clusters (m = 1-7, z = 1, 2) upon electron irradiation of neutral helium nanodroplets doped with magnesium or a combination of C60 and magnesium. The mass spectra obtained for pristine magnesium cluster ions exhibit anomalies, consistent with previous reports in the literature. The anomalies observed for C60Mgn+ strongly suggest that Mg atoms tend to wet the surface of the single fullerene positioning itself above the center of a pentagonal or hexagonal face, while, for (C60)mMgnz+, the preference for Mg to position itself within the dimples formed by fullerene cages becomes apparent. Besides doubly charged cluster ions, with the smallest member Mg22+, we also observed the formation of triply charged ions Mgn3+ with n > 24. The ion efficiency curves of singly and multiply charged ions exhibit pronounced differences compared to singly charged ions at higher electron energies. These findings indicate that sequential Penning ionization is essential in the formation of doubly and triply charged ions inside doped helium nanodroplets.