Interaction universality and scaling laws for interaction potentials between closed‐shell atoms and ions

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.

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.

Space-resolved average kinetic energy of ion swarms in a uniform electric field

A pulse of noninteracting charged particles in an unbounded gas, exposed to a low, constant, homogeneous electric field, was studied in both space and time using a Monte Carlo simulation technique. The difference in electrical potential between the leading and trailing edges of the swarm results in the space-resolved average ion kinetic energy becoming a linearly increasing function of space. This Letter analyzes whether the average ion kinetic energy at the leading edge reaches a stationary value during the spatiotemporal evolution of the swarm, as has been considered so far. When the swarm's mean kinetic energy reaches a steady-state value, indicating that an energy balance is established over time, the gains (from the field) and losses (due to collisions) are nonuniform across space. The local power balance is negative at the front of the swarm and positive at the tail. Cooling the ions at the front and heating the ions at the tail results in a decrease in the average ion kinetic energy at the front and an increase at the tail. Thus, it can be concluded that stationary values of average ion kinetic energy do not exist at the leading and trailing edges during the evolution. Instead, they tend to approach the swarm's mean kinetic energy as t→∞.

Electronic and dynamical properties of non-covalent diatomic aggregates formed by He with neutral and ionic Li and Be

CONTEXT AND RESULTS

This work aims to study the influence of the absence and presence of permanent charges on the electronic and dynamical properties of the non-covalent bound diatomic systems involving He and Li, Be as neutral and ionic partners. The charge displacement results suggest that in the formation of HeLi[Formula: see text], HeBe[Formula: see text], and HeBe[Formula: see text], the neutral He atom undergoes, in the electric field of the ion, a pronounced electronic polarization, and the natural bond order theoretical approach indicates that in the formation of the molecular orbital He acts as a weak electron donor. The energy decomposition analysis provides the dispersion and induction components as the attractive leading terms controlling the stability of all systems, confirming that the formed bond substantially maintains a non-covalent nature which is also supported by the Quantum Theory of Atoms in Molecules (QTAIM) analysis. Finally, it was found that the HeLi and HeBe neutral systems are unstable under any condition, HeLi[Formula: see text] and HeBe[Formula: see text] ionic systems are stable below 317K and 138K, respectively, while the HeBe[Formula: see text] system becomes unstable only after 3045K.

COMPUTATIONAL AND THEORETICAL TECHNIQUES

The potential energy curves and interactions in all systems were studied theoretically based on coupled-cluster singles and doubles method with perturbative inclusion of triples CCSD(T) method with an aug-cc-pV5Z basis set. More precisely, it was determined the potential energy curves describing the stability of the HeLi, HeLi[Formula: see text], HeBe, HeBe[Formula: see text], and HeBe[Formula: see text] systems, the charge displacement within the formed adducts, the decomposition of their total interaction energy, the topological analysis of their bonds, their rovibrational energies, their spectroscopic constants and lifetimes.

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.

Gaseous transport properties of the ground and excited Cr, Co and Ni cations in He: Ab initio study of electronic state chromatography

The electronic state chromatography (ESC) effect allows the differentiation of ions in their ground and metastable states by their gaseous mobilities in the limit of low electrostatic fields. It is investigated here by means of accurate transport calculations with ab initio ion-atom potentials for the Cr, Co and Ni cations in He buffer gas near room temperature. The values for the open-shell ions in degenerate states are shown to be well approximated by using the single isotropic interaction potential. Minimalistic implementation of the multireference configuration interaction (MRCI) method is enough to describe the zero-field transport properties of metastable ions in the 3dm-14s configuration, such as Cr+(a6D), Co+(a5F) and Ni+(4F), due to their weak and almost isotropic interaction with He atom and the low sensitivity of the measured mobilities to the potential well region. By contrast, interactions involving the ions in the ground 3dm states, such as Cr+(a6S), Co+(a3F) and Ni+(2D), are strong and anisotropic; the MRCI potentials poorly describe their transport coefficients. Even the coupled cluster with singles, doubles and non-iterative triples [CCSD(T)] approach taking into account vectorial spin-orbit coupling may not be accurate enough, as shown here for Ni+(2D). The sensitivity of ion mobility and the ESC effect to interaction potentials, similarities in ion-He interactions of the studied ions in distinct configurations, accuracy and possible improvements of the ab initio schemes, and control of the ESC effect by macroscopic parameters are discussed. Extensive sets of improved interaction potentials and transport data are generated.

A Hard Sphere Model for Bimolecular Recombination of Heavy Ions

Abstract

We propose a hard sphere model of bimolecular recombination RM+ + X– → MX + R, where M+ is an alkali ion, X– is a halide ion, and R is a neutral rare gas or mercury atom. Calculations are carried out for M+ = Cs+, X– = Br–, R = Ar, Kr, Xe, Hg, for collision energies in the range from 1 to 10 eV, and for distributions of the RM+ complex internal energy corresponding to temperatures of 500, 1000, and 2000 K. The excitation functions and opacity functions of bimolecular recombination in the hard sphere approximation are found, and the classification of the collisions according to the sequences of pairwise encounters of the particles is considered. In more than half of all the cases, recombination occurs due to a single impact of the Br– ion with the R atom. For the recombination XeCs+ + Br–, the hard sphere model enables one to reproduce the most important characteristics of the collision energy dependence of the recombination probability obtained within the framework of quasiclassical trajectory calculations.

Dynamics of third order direct three-body recombination of heavy ions

The direct three-body recombination reactions Cs⁺ + X^- + R → CsX + R (X = F, I and R = Ar, Xe) are studied within the quasiclassical trajectory method using diabatic semiempirical potential energy surfaces, the encounters of the ions being non-central. The collision energies range between 1 and 10 eV (values typical for low temperature plasma), while the so-called delay parameter, which characterizes the delay in the arrival of the neutral atom R in relation to the time instant when the distance between the ions attains its minimum, is equal to 0 or 20%. The calculation results include the recombination excitation functions, the opacity functions, and the vibrational and rotational energy distributions of the recombination products. All the four reactions considered exhibit similar overall statistical dynamics, but each process has its own features. On the whole, for both the recombining pairs Cs⁺ + F^- and Cs⁺ + I^-, xenon is more effective than argon as an acceptor of excess energy from the ion pair. The rotational energy distributions of the salt molecules CsF and CsI are almost equilibrium, whereas the vibrational energy distributions are strongly non-equilibrium.

Heavy rare-gas atomic pairs and the "double penalty" issue: Isotropic Raman lineshapes by Kr2, Xe2, and KrXe at room temperature

We report absolutely calibrated isotropic Raman lineshapes for Kr2 and Xe2 and for KrXe at 294.5 K and compare them to quantum-mechanically generated lineshapes by using state-of-the-art second-order Møller-Plesset and DFT/B3LYP data sets for the induced mean dipole polarizability ᾱ. A very good agreement between the numerical and the experimental data was observed but the large uncertainty margins and the short Raman frequency interval probed in our experiment prevented us from rating on a more refined scale the performance of the tested ᾱ models. These drawbacks are inherent in isotropic Raman spectrum measurements and amplified for dissimilar pairs because, for such systems and spectra, the unreliable operation of subtracting optical signals of comparable magnitude occurs twice per Raman frequency shift value, thus penalizing twice the quality of the measured data. In light of our findings and of previously reported evidence about related electric properties in Kr2 and Xe2 and in KrXe, we are left with no doubt as to the consistency of the induced-polarizability and interatomic-potential data used for these three systems at the reported level of accuracy.

Path integral Monte Carlo study of 4He clusters doped with alkali and alkali-earth ions

Path integral Monte Carlo calculations of (4)He nanodroplets doped with alkali (Na(+), K(+) and Cs(+)) and alkali-earth (Be(+) and Mg(+)) ions are presented. We study the system at T = 1 K and between 14 and 128 (4)He atoms. For all studied systems, we find that the ion is well localized at the center of the droplet with the formation of a "snowball" of well-defined shells of localized (4)He atoms forming solid-like order in at least the first surrounding shell. The number of surrounding helium shells (two or three) and the number of atoms per shell and the degree of localization of the helium atoms are sensitive to the type of ion. The number of (4)He atoms in the first shell varies from 12 for Na(+) to 18 for Mg(+) and depends weakly on the size of the droplet. The study of the density profile and of the angular correlations shows that the local solid-like order is more pronounced for the alkali ions with Na(+) giving a very stable icosahedral order extending up to three shells.

Bosonic helium droplets with cationic impurities: onset of electrostriction and snowball effects from quantum calculations

Variational Monte Carlo and diffusion Monte Carlo calculations have been carried out for cations such as Li(+), Na(+), and K(+) as dopants of small helium clusters over a range of cluster sizes up to about 12 solvent atoms. The interaction has been modeled through a sum-of-potential picture that disregards higher order effects beyond atom-atom and atom-ion contributions. The latter were obtained from highly correlated ab initio calculations over a broad range of interatomic distances. This study focuses on two of the most striking features of the microsolvation in a quantum solvent of a cationic dopant: electrostriction and snowball effects. They are discussed here in detail and in relation with the nanoscopic properties of the interaction forces at play within a fully quantum picture of the cluster features.

Testing ion-neutral interaction potentials using calculated ion transport coefficients

Several commonly measured ion transport coefficients were investigated in order to determine their sensitivity for testing and comparing proposed ion-neutral interaction potentials. A variety of positive ions, negative ions, neutrals, and temperatures were included in order to draw as general a conclusion as possible. All transport coefficients considered were found to be sufficiently sensitive to be used to clearly distinguish between less and more accurate interaction potentials. It was also found that the longitudinal diffusion coefficient is the most sensitive test, followed by both the transverse diffusion coefficient and the ratio of the longitudinal diffusion coefficient to mobility, followed by the ratio of the transverse diffusion coefficient to mobility and that the mobility is the least sensitive test. When presently achievable levels of experimental error were also taken into account, however, there was no significant difference in the sensitivities.

Interaction potentials for Br−–Rg (Rg=He–Rn): Spectroscopy and transport coefficients

High-level ab initio CCSD(T) calculations are performed in order to obtain accurate interaction potentials for the Br(-) anion interacting with each rare gas (Rg) atom. For the Rg atoms from He to Ar, two approaches are taken. The first one implements a relativistic core potential and an aug-cc-pVQZ basis set for bromine, an aug-cc-pV5Z basis set for Rg, and a set of bond functions placed at the midpoint of the Rg-Br distance. The second one uses the all-electron approximation with aug-cc-pV5Z bases further augmented by an extra diffuse function in each shell. Comparison reveals close similarity between both sets of results, so for Rg atoms from Kr to Rn only the second approach is exploited. Calculated potentials are assessed against the previous empirical, semiempirical, and ab initio potentials, and against available beam scattering data, zero electron kinetic energy spectroscopic data, and various sets of the measured ion mobilities and diffusion coefficients. This multiproperty analysis leads to the conclusion that the present potentials are consistently good for the whole series of Br(-)-Rg pairs over the whole range of internuclear distances covered.

Accurate potential energy curves for F−–Rg (Rg = He–Rn): Spectroscopy and transport coefficients

High-quality ab initio potential energy curves are presented for the F(-)-Rg series (Rg = He-Rn). Calculations are performed at the CCSD(T) level of theory, employing d-aug-cc-pV5Z quality basis sets, with "small core" relativistic effective core potentials being used for Kr-Rn. The quality of the curves is judged by agreement with recent high-level calculations in the case of F(-)-He and F(-)-Ne and by excellent agreement with mobility data for the systems F(-)-Rg (Rg = He-Xe). Except for these recent high-level calculations on the two lightest systems, we are able to deduce that all other previous potentials for the whole set of these systems are inadequate. We also present spectroscopic information for the titular species, derived from our potential energy curves.

Interaction potentials of the RG–I anions, neutrals, and cations (RG=He, Ne, Ar)

Interaction potentials of the iodine atom, atomic cation, and anion with light rare-gas atoms from He to Ar are calculated within the unified ab initio approach using the unrestricted coupled-cluster with singles and doubles and perturbative treatment of triples correlation treatment, relativistic small-core pseudopotential, and an extended basis set. Ab initio points are fit to a flexible analytical function. The calculated potentials are compared with available literature data, assessed in the I(-)-and I+-ion mobility calculations and the Ar-I(-)-anion zero electron kinetic-energy spectra simulations, and analyzed using the correlation rules. The results indicate a high precision of the reported potentials.

Spectroscopy of K[sup +]⋅Rg and transport coefficients of K[sup +] in Rg (Rg=He–Rn)

Ab initio calculations employing the coupled-cluster method, with single and double substitutions and accounting for triple excitations noniteratively [CCSD(T)], are used to obtain accurate potential energy curves for the K(+)He, K(+)Ne, K(+)Ar, K(+)Kr, K(+)Xe, and K(+)Rn cationic complexes. From these potentials, rovibrational energy levels and spectroscopic parameters are calculated. In addition, mobilities and diffusion coefficients for K(+) cations moving through the six rare gases are calculated, under conditions that match previous experimental determinations. A detailed statistical comparison of the present and previous potentials is made with available experimental data, and critical conclusions are drawn as to the reliability of each set of data. It is concluded that the present ab initio potentials match the accuracy of the best model potentials and the most reliable experimental data.

Evaluation of carrier gases for use in high-field asymmetric waveform ion mobility spectrometry

Effects of carrier gas type (N2, O2, CO2, N2O, and SF6) on changes in the ratio of high- to low-field ion mobility, Kh/K, of cesium, gramicidin S, tetrahexylammonium, heptadecanoic acid, and aspartic acid in fields of up to 67 Td are presented. The theory of the mobility of ions at high E/N in different gases is discussed. Plots of Kh/K as a function of the ionic energy parameter, E/N, for the five ions in each of the gases were derived from experimental data collected using a high-field asymmetric waveform ion mobility spectrometer. The change in the ratio of high- to low-field ion mobility of cesium in carrier gases of O2 and N2 showed excellent agreement with literature values. The behavior of cesium in O2 and N2 is used to illustrate that the ratio Kh/K as a function of effective temperature is invariant with gas type as long as the well depth of the interaction potential significantly exceeds thermal energy. From these results, it appears that the well depth of the interaction potential of the heavier ions studied here, including gramicidin S, tetrahexylammonium, and heptadecanoic acid, with bath gases such as N2 and O2, is shallow relative to thermal energy.