Lithium ions solvated in helium

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.

Trihydrogen Cation Helium Clusters: A New Potential Energy Surface

We present a new analytical potential energy surface (PES) for the interaction between the trihydrogen cation and a He atom,H 3 + - H e ${{H}_{3}^{+}-He}$ , in its electronic ground state. The proposed PES has been built as a sum of two contributions: a polarization energy term due to the electric field generated by the molecular cation at the position of the polarizable He atom, and an exchange-repulsion and dispersion interactions represented by a sum of "atom-bond" potentials between the three bonds ofH 3 + ${{H}_{3}^{+}}$ and the He atom. All parameters of this new PES have been chosen and fitted from data obtained from high-level ab-initio calculations. Using this new PES plus the Aziz-Slaman potential for the interaction between Helium atoms and assuming pair-wise interactions, we carry out classical Basin-Hopping (BH) global optimization, semiclassical BH with Zero Point Energy corrections, and quantum Diffusion Monte Carlo simulations. We have found the minimum energy configurations of small He clusters doped withH 3 + ${{H}_{3}^{+}}$ ,H 3 + H e N ${{H}_{3}^{+}{\left(He\right)}_{N}}$ , with N=1-16. The study of the energies of these clusters allows us to find a pronounced anomaly for N=12, in perfect agreement with previous experimental findings, which we relate to a greater relative stability of this aggregate.

Pairwise Model Potential and DFT Study of Li+Nen Clusters (n = 1-20): The Structural, Electronic, and Thermodynamic Properties

The structural properties, relative stabilities, electronic, and thermodynamic properties, of Li+Nen (n = 1-20) clusters have been studied based on a pairwise model and density functional theory (DFT) methods. In the pairwise method, the potential energy surface considered interactions between Li+Ne, Ne - Ne, and many-body term. For the DFT calculations, the B3LYP functional combined with the 6-311 + + G (2d,2p) basis sets has been employed. In both methods, the Li+Ne6 cluster demonstrated high stability with an octahedral structure, where the Li+ cation was surrounded by Ne atoms. Thus, the octahedral Li+Ne6 structure was considered to be the core for larger cluster sizes. Relative stabilities were assessed based on binding energies, second-order differences of energies, transition dipole moment, and HOMO-LUMO energy gaps. Furthermore, thermodynamic properties were calculated, revealing that the formation process of Li+Nen clusters is endothermic and nonspontaneous.

Observing the primary steps of ion solvation in helium droplets

Solvation is a ubiquitous phenomenon in the natural sciences. At the macroscopic level, it is well understood through thermodynamics and chemical reaction kinetics1,2. At the atomic level, the primary steps of solvation are the attraction and binding of individual molecules or atoms of a solvent to molecules or ions of a solute1. These steps have, however, never been observed in real time. Here we instantly create a single sodium ion at the surface of a liquid helium nanodroplet3,4, and measure the number of solvent atoms that successively attach to the ion as a function of time. We found that the binding dynamics of the first five helium atoms is well described by a Poissonian process with a binding rate of 2.0 atoms per picosecond. This rate is consistent with time-dependent density-functional-theory simulations of the solvation process. Furthermore, our measurements enable an estimate of the energy removed from the region around the sodium ion as a function of time, revealing that half of the total solvation energy is dissipated after four picoseconds. Our experimental method opens possibilities for benchmarking theoretical models of ion solvation and for time-resolved measurements of cation-molecule complex formation.

Observation of Multiple Ordered Solvation Shells in Doped Helium Droplets: The Case of HeNCa2

In this Letter, we report the experimental detection of likely the largest ordered structure of helium atoms surrounding a monatomic impurity observed to date using a recently developed technique. The mass spectrometry investigation of He_NCa²⁺ clusters, formed in multiply charged helium nanodroplets, reveals magic numbers at N = 12, 32, 44, and 74. Classical optimization and path integral Monte Carlo calculations suggest the existence of up to four shells surrounding the calcium dication which are closed with well-ordered Mozartkugel-like structures: He₁₂Ca²⁺ with an icosahedron, the second at He₃₂Ca²⁺ with a dodecahedron, the third at He₄₄Ca²⁺ with a larger icosahedron, and finally for He₇₄Ca²⁺, we find that the outermost He atoms form an icosidodecahedron which contains the other inner shells. We analyze the reasons for the formation of such ordered shells in order to guide the selection of possible candidates to exhibit a similar behavior.

Helium nanodroplets as an efficient tool to investigate hydrogen attachment to alkali cations

We report a novel method to reversibly attach and detach hydrogen molecules to positively charged sodium clusters formed inside a helium nanodroplet host matrix. It is based on the controlled production of multiply charged helium droplets which, after picking up sodium atoms and exposure to H2 vapor, lead to the formation of Nam+(H2)n clusters, whose population was accurately measured using a time-of-flight mass spectrometer. The mass spectra reveal particularly favorable Na+(H2)n and Na2+(H2)n clusters for specific "magic" numbers of attached hydrogen molecules. The energies and structures of these clusters have been investigated by means of quantum-mechanical calculations employing analytical interaction potentials based on ab initio electronic structure calculations. A good agreement is found between the experimental and the theoretical magic numbers.

Helium structures around SF5+ and SF6+: novel intermolecular potential and mass spectrometry experiments

Helium clusters around the recently experimentally observed sulphur hexafluoride SF₆⁺ and sulphur pentafluoride SF₅⁺ ions are investigated using a combined experimental and theoretical effort. Mass spectrometry ion yields are obtained and the energetics and structure of the corresponding He_N–SF₆⁺ and He_N–SF₅⁺ clusters are analyzed using path integral molecular dynamics calculations as a function of N, the number of He atoms, employing a new intermolecular potential describing the interaction between the dopant and the surrounding helium. The new force field is optimized on benchmark potential energy ab initio calculations and represented by improved Lennard-Jonnes analytical expressions. This procedure improves the previous potentials employed in similar simulations for neutral SF₆ attached to helium nanodroplets. The theoretical analysis explains the characteristic features observed in the experimental ion yields which suggest the existence of stable configurations at specific sizes.

The structure of the He atoms around SF₅⁺ and SF₆⁺ is investigated both experimentally and theoretically.

Solvation of Isoelectronic Halide and Alkali Metal Ions by Argon Atoms

This work systematically examines the interactions of alkali metal cations and their isoelectronic halide counterparts with up to six solvating Ar atoms (M⁺Ar_n and X^-Ar_n, where M = Li, Na, K, and Rb; X = H, F, Cl, and Br; and n = 1-6) via full geometry optimizations with the MP2 method and robust, correlation-consistent quadruple-ζ (QZ) basis sets. 116 unique M⁺Ar_n and X^-Ar_n stationary points have been characterized on the MP2/QZ potential energy surface. To the best of our knowledge, approximately two dozen of these stationary points have been reported here for the first time. Some of these new structures are either the lowest-energy stationary point for a particular cluster or energetically competitive with it. The CCSD(T) method was employed to perform additional single-point energy computations upon all MP2/QZ-optimized structures using the same basis set. CCSD(T)/QZ results indicate that internally solvated structures with the ion at/near the geometric center of the cluster have appreciably higher energies than those placing the ion on the periphery. While this study extends the prior investigations of M⁺Ar_n clusters found within the literature, it notably provides one of the first thorough characterizations of and comparisons to the corresponding negatively charged X^-Ar_n clusters.

A Path Integral Molecular Dynamics Simulation of a Harpoon-Type Redox Reaction in a Helium Nanodroplet

We present path integral molecular dynamics (PIMD) calculations of an electron transfer from a heliophobic Cs2 dimer in its (3Σu) state, located on the surface of a He droplet, to a heliophilic, fully immersed C60 molecule. Supported by electron ionization mass spectroscopy measurements (Renzler et al., J. Chem. Phys.2016, 145, 181101), this spatially quenched reaction was characterized as a harpoon-type or long-range electron transfer in a previous high-level ab initio study (de Lara-Castells et al., J. Phys. Chem. Lett.2017, 8, 4284). To go beyond the static approach, classical and quantum PIMD simulations are performed at 2 K, slightly below the critical temperature for helium superfluidity (2.172 K). Calculations are executed in the NVT ensemble as well as the NVE ensemble to provide insights into real-time dynamics. A droplet size of 2090 atoms is assumed to study the impact of spatial hindrance on reactivity. By changing the number of beads in the PIMD simulations, the impact of quantization can be studied in greater detail and without an implicit assumption of superfluidity. We find that the reaction probability increases with higher levels of quantization. Our findings confirm earlier, static predictions of a rotational motion of the Cs2 dimer upon reacting with the fullerene, involving a substantial displacement of helium. However, it also raises the new question of whether the interacting species are driven out-of-equilibrium after impurity uptake, since reactivity is strongly quenched if a full thermal equilibration is assumed. More generally, our work points towards a novel mechanism for long-range electron transfer through an interplay between nuclear quantum delocalization within the confining medium and delocalized electronic dispersion forces acting on the two reactants.

Ca+ Ions Solvated in Helium Clusters

We present a combined experimental and theoretical investigation on Ca+ ions in helium droplets, HeNCa+. The clusters have been formed in the laboratory by means of electron-impact ionization of Ca-doped helium nanodroplets. Energies and structures of such complexes have been computed using various approaches such as path integral Monte Carlo, diffusion Monte Carlo and basin-hopping methods. The potential energy functions employed in these calculations consist of analytical expressions following an improved Lennard-Jones formula whose parameters are fine-tuned by exploiting ab initio estimations. Ion yields of HeNCa+ -obtained via high-resolution mass spectrometry- generally decrease with N with a more pronounced drop between N=17 and N=25, the computed quantum HeNCa+ evaporation energies resembling this behavior. The analysis of the energies and structures reveals that covering Ca+ with 17 He atoms leads to a cluster with one of the smallest energies per atom. As new atoms are added, they continue to fill the first shell at the expense of reducing its stability, until N=25, which corresponds to the maximum number of atoms in that shell. Behavior of the evaporation energies and radial densities suggests liquid-like cluster structures.

Modelling interactions of cationic dimers in He droplets: microsolvation trends in HenK2+ clusters

We report the results of a detailed theoretical investigation of small K₂⁺-doped He clusters. The structural characteristics and stabilities of such cations are determined from ab initio electronic structure calculations at the MRCI+Q level of theory. The underlying interactions show a multireference character and such effects are analyzed. The interaction potentials are constructed employing an interpolation technique within the inverse problem theory method, while the nuclear quantum effects are computed for the trimers, their spatial arrangements are discussed, and information was extracted on the orientational anisotropy of the forces. We found that energetically the most stable conformer corresponds to linear arrangements that are taking place under large amplitude vibrations, with high zero-point energy. We have further looked into the behavior of higher-order species with various He atoms surrounding the cationic dopant. By using a sum of potentials approach and an evolutionary programming method, we analyzed the structural stability of clusters with up to six He atoms in comparison with interactions energies obtained from MRCI+Q quantum chemistry computations. Structures containing He_n motifs that characterize pure rare gas clusters, appear for the larger K₂⁺-doped He clusters, showing selective growth during the microsolvation process of the alkali-dimer cation surrounded by He atoms. Such results indicate the existence of local solvation microstructures in these aggregates, where the cationic impurity could get trapped for a short time, contributing to the slow ionic mobility observed experimentally in ultra-cold He-droplets.

Mixed cationic clusters of nitrogen and hydrogen

The addition of small impurities, such as a single proton charge carrier, in noble gas clusters has recently been shown to have considerable effects on their geometries and stabilities. Here, we report on a mass spectrometric study of cationic clusters of N2 molecules and the effects that adding hydrogen, in the form of D2, has on the systems. Protonated nitrogen clusters formed by the breakup of D2 are shown to have similar behaviors as protonated rare gas clusters. For larger systems consisting of different mixtures of intact N2 and D2, different molecular species are found to be interchangeable sometimes with regard to magic numbers. This is especially true for the (N2)n(D2)mD+ systems with n + m = 17, which is particularly abundant for all measured combinations of n and m.

de Almeida M, Marques JMC, Prudente FV. A thermodynamic view on the microsolvation of ions by rare gas: application to Li+ with argon

Parallel tempering Monte Carlo calculations on the Li⁺Ar_n microsolvation clusters have shown that the two peaks appearing in the heat capacity curve as a function of temperature correspond to the melting of the second and first solvation shells.

Considerable matrix shift in the electronic transitions of helium-solvated cesium dimer cation Cs2He

We investigate the photodissociation of helium-solvated cesium dimer cations using action spectroscopy and quantum chemical calculations. The spectrum of Cs2He+ shows three distinct absorption bands into both bound and dissociative states. Upon solvation with further helium atoms, considerable shifts of the absorption bands are observed, exceeding 0.1 eV (850 cm-1) already for Cs2He10+, along with significant broadening. The shifts are highly sensitive to the character of the excited state. Our calculations show that helium atoms adsorb on the ends of Cs2+. The shifts are particularly pronounced if the excited state orbitals extend to the area occupied by the helium atoms. In this case, Pauli repulsion leads to a deformation of the excited state orbitals, resulting in the observed blue shift of the transition. Since the position of the weakly bound helium atoms is ill defined, Pauli repulsion also explains the broadening.

Complexes of Alkali Metal Cations and Molecular Hydrogen: Potential Energy Surfaces and Bound States

Complexes between metal cations and molecular hydrogen are systems quite amenable for precise spectroscopic and theoretical studies, and at the same time, they are relevant for applications in hydrogen storage and astrochemistry. In this work, we report new intermolecular potential energy surfaces and rovibrational states calculations for complexes involving molecular hydrogen and alkaline metal cations, M⁺-H₂ (M⁺ = Na⁺, K⁺, Rb⁺, Cs⁺). The intermolecular potentials, formulated in an internally consistent way to emphasize differences in the properties of the systems, are represented by simple analytical expressions whose parameters have been optimized from comparison with accurate ab initio calculations. Properties of the low-lying bound states-binding energies, frequencies, and rotational constants-are compared with previous measurements or computations and an overall good agreement is achieved, supporting the reliability of the present formulation. Variations of these properties as a function of the cation size and isotopic substitution, with a proper sequence of ortho and para rotational levels, are also discussed.

Theoretical Study of Cationic Alkali Dimers Interacting with He: Li2+-He and Na2+-He van der Waals Complexes

We present a theoretical study on the potential energy surface and bound states of He-A₂⁺ complexes, where A is one of the alkali Li or Na atoms. The intermolecular interactions were systematically investigated by high-level ab initio electronic structure computations, and the corresponding raw data were then employed to reproduce accurate analytical expressions of the potential surfaces. In turn, we used these potentials to evaluate bound configurations of the trimers from nuclear quantum calculations and to extract information on the effect of orientational anisotropy of the forces and the interplay between repulsive and attractive interaction within the potential surfaces. The spatial features of the bound states are analyzed and discussed in detail. We found that both systems are going under large amplitude stretching and bending motions with high zero-point energies. Despite the large differences in the potential well-depths, the correct treatment of nuclear quantum effects provides insights on the effect of different strength of the ionic interaction on the spectral structure of such cationic alkali van der Waals complexes, related to the mobility of ions and the formation of cold-molecules in He-controlled environments.

A combined experimental and theoretical investigation of Cs+ ions solvated in HeN clusters

Solvation of Cs⁺ ions inside helium droplets has been investigated both experimentally and theoretically. On the one hand, mass spectra of doped helium clusters ionized with a crossed electron beam, He_NCs⁺, have been recorded for sizes up to N = 60. The analysis of the ratio between the observed peaks for each size N reveals evidences of the closure of the first solvation shell when 17 He atoms surround the alkali ion. On the other hand, we have obtained energies and geometrical structures of the title clusters by means of basin-hopping, diffusion Monte Carlo (DMC), and path integral Monte Carlo (PIMC) methods. The analytical He-Cs⁺ interaction potential employed in our calculations is represented by the improved Lennard-Jones expression optimized on high level ab initio energies. The weakness of the existing interaction between helium and Cs⁺ in comparison with some other alkali ions such as Li⁺ is found to play a crucial role. Our theoretical findings confirm that the first solvation layer is completed at N = 17 and both evaporation and second difference energies obtained with the PIMC calculation seem to reproduce a feature observed at N = 12 for the experimental ion abundance. The analysis of the DMC probability distributions reveals the important contribution from the icosahedral structure to the overall configuration for He₁₂Cs⁺.

Snowball formation for Cs+ solvation in molecular hydrogen and deuterium

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