Reinvestigation of the Rb2 (2)Π3g−a Σ3u+ band on helium nanodroplets

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.

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.

Desorption Dynamics of Rb2 Molecules Off the Surface of Helium Nanodroplets

The desorption dynamics of rubidium dimers (Rb₂) off the surface of helium nanodroplets induced by laser excitation is studied by employing both nanosecond and femtosecond ion imaging spectroscopy. Similarly to alkali metal atoms, we find that the Rb₂ desorption process resembles the dissociation of a diatomic molecule. However, both angular and energy distributions of detected Rb₂⁺ ions appear to be most crucially determined by the Rb₂ intramolecular degrees of freedom rather than by those of the Rb₂He_N complex. The pump-probe dynamics of Rb₂⁺ is found to be slower than that of Rb⁺, pointing at a weaker effective guest-host repulsion for excited molecules than for single atoms.

Quantum Features of Anionic Species He*⁻ and He₂*⁻ in Small He(N) Clusters

We present variational calculations on systems containing a few boson helium atoms attached to electronically excited atomic and molecular helium anions He*⁻ and He₂*⁻ and characterize their structures and energetics. Previously reported high-level ab initio results [Huber, S. E.; Mauracher, A. Mol. Phys. 2014, 112, 794] to describe the interactions between excited (metastable) anions and a neutral He atom have been employed. For the case of the atomic species He*⁻, the corresponding interaction with He suggests large anharmonicity effects due to the presence of a deep well of ∼17,500 cm⁻¹ at short distances, together with a more external shallow secondary well of ∼4 cm⁻¹, both supporting bound levels. Moreover, when a sum of pairwise interactions is assumed to describe the full PES corresponding to the presence of several neutral He atoms, geometrical constraints already predict the complete solvation of the anionic impurity by six helium atoms, giving rise to a bipyramidal structure. In turn, for the anisotropic weak interaction He-He₂*⁻, where the anionic dimer is considered as a rigid rotor, the obtained structures show the tendency of the helium atoms to pack themselves together and largely far away from the dopant, thereby confirming the heliophobic character of He₂*⁻.

Reactive scattering calculations for (87)Rb+(87)RbHe→Rb2((3)Σ(u)(+),v)+He from ultralow to intermediate energies

We investigate atom-diatom reactive collisions, as a preliminary step,in order to assess the possibility of forming Rb(2) molecules in their lowest triplet electronic state by cold collisions of rubidium atoms on the surface of helium nanodroplets [corrected]. A simple model related to the well-known Rosen treatment of linear triatomic molecules [N. Rosen, J. Chem. Phys. 1, 319 (1933)] in relative coordinates is used, allowing to estimate reactive probabilities for different values of the total angular momentum. The best available full dimensional potential energy surface [Guillon et al., J. Chem. Phys. 136, 174307 (2012)] is employed through the calculations. Noticeable values of the probabilities in the ultracold regime, which numerically fulfill the Wigner threshold law, support the feasibility of the process. The rubidium dimer is mainly produced at high vibrational states, and the reactivity is more efficient for a bosonic helium partner than when the fermion species is considered.

Binding energies of the ground triplet state a(3) Σ(u)(+) of Rb2 and Cs2 in terms of the generalized Le Roy-Bernstein near-dissociation expansion

Formulae of Le Roy-Bernstein near-dissociation theory are derived in a general isotope-invariant form, applicable to any term in the rotational expansion of a diatomic ro-vibrational term value. It is proposed to use the generalized Le Roy-Bernstein expansion to describe the binding energies (ro-vibrational term values) of the ground triplet state a(3) Σ(u)(+) of alkali metal dimers. The parameters of this description are determined for Rb2 and Cs2 molecules. This approach gives a recipe to calculate the whole variety of the binding energies with characteristic accuracies from ∼1 × 10(-3) to 1 × 10(-2) cm(-1) using a relatively simple algebraic equation.

Spectroscopy of lithium atoms and molecules on helium nanodroplets

We report on the spectroscopic investigation of lithium atoms and lithium dimers in their triplet manifold on the surface of helium nanodroplets (He_N). We present the excitation spectrum of the 3p ← 2s and 3d ← 2s two-photon transitions for single Li atoms on He_N. The atoms are excited from the 2S(Σ) ground state into Δ, Π, and Σ pseudodiatomic molecular substates. Excitation spectra are recorded by resonance enhanced multiphoton ionization time-of-flight (REMPI-TOF) mass spectroscopy, which allows an investigation of the exciplex (Li*–He_m, m = 1–3) formation process in the Li–He_N system. Electronic states are shifted and broadened with respect to free atom states, which is explained within the pseudodiatomic model. The assignment is assisted by theoretical calculations, which are based on the Orsay–Trento density functional where the interaction between the helium droplet and the lithium atom is introduced by a pairwise additive approach. When a droplet is doped with more than one alkali atom, the fragility of the alkali–He_N systems leads preferably to the formation of high-spin molecules on the droplets. We use this property of helium nanodroplets for the preparation of Li dimers in their triplet ground state (1³Σ_u⁺). The excitation spectrum of the 2³Π_g(ν′ = 0–11) ← 1³Σ_u⁺(ν″ = 0) transition is presented. The interaction between the molecule and the droplet manifests in a broadening of the transitions with a characteristic asymmetric form. The broadening extends to the blue side of each vibronic level, which is caused by the simultaneous excitation of the molecule and vibrations of the droplet (phonons). The two isotopes of Li form ⁶Li₂ and ⁷Li₂ as well as isotope mixed ⁶Li⁷Li molecules on the droplet surface. By using REMPI-TOF mass spectroscopy, isotope-dependent effects could be studied.

Spin-polarized Rb2 interacting with bosonic He atoms: potential energy surface and quantum structures of small clusters

A new full-dimension potential energy surface of the three-body He-Rb₂(³Σ(u)(+)) complex and a quantum study of small (⁴He)(N)-Rb₂(³Σ(u)(+)) clusters, 1 ≤ N ≤ 4, are presented. We have accurately fitted the ab initio points of the interaction to an analytical form and addressed the dopant's vibration, which is found to be negligible. A Variational approach and a Diffusion Monte Carlo technique have been applied to yield energy and geometric properties of the selected species. Our quantum structure calculations show a transition in the arrangements of the helium atoms from N = 2, where they tend to be separated across the diatomic bond, to N = 4, in which a closer packing of the rare gas particles is reached, guided by the dominance of the He-He potential over the weaker interaction of the latter adatoms with the doping dimer. The deepest well of the He-Rb₂ interaction is placed at the T-shape configuration, a feature which causes the dopant to be located as parallel to the helium "minidroplet". Our results are shown to agree with previous findings on this and on similar systems.

Weakly bound finite systems: (⁴He)N-Rb₂(³Σu), clustering structures from a quantum Monte Carlo approach

We report here ((4)He)(N)-Rb(2)((3)Σ(u)) complexes, 2 ≤ N ≤ 20, analysed through a quantum diffusion Monte Carlo stochastic approach. The calculations show that the spin stretched dimer molecule is bound outside the pure He sub-complex, due to the stronger He-He potential as compared with the He-Rb(2) interaction, while the rare gas atom moiety presents, in turn, a shell-like structure with ten He adatoms completing the first shell. Our results agree with previous findings on this and similarly weakly interacting systems.

Homo- and heteronuclear alkali metal trimers formed on helium nanodroplets. Part II. Femtosecond spectroscopy and spectra assignments

Homo- and heteronuclear alkali quartet trimers of type K(3-n)Rb(n) (n = 0,1,2,3) formed on helium nanodroplets are probed by one-color femtosecond (fs) photoionization (PI) spectroscopy. The obtained frequencies are assigned to vibrations in different electronic states in comparison to high level ab initio calculations of the involved potentials including pronounced Jahn-Teller and spin-orbit couplings. Despite the fact that the resulting complex vibronic structure of the heavy alkali molecules complicates the comparison of experiment and theory we find good agreement for many of the observed lines for all species.

Quantum features of a barely bound molecular dopant: Cs2(3Σu) in bosonic helium droplets of variable size

We present in this work the study of small (4)He(N)-Cs(2)((3)Σ(u)) aggregates (2 ≤ N ≤ 30) through combined variational, diffusion Monte Carlo (DMC), and path integral Monte Carlo (PIMC) calculations. The full surface is modeled as an addition of He-Cs(2) interactions and He-He potentials. Given the negligible strength and large range of the He-Cs(2) interaction as compared with the one for He-He, a propensity of the helium atoms to pack themselves together, leaving outside the molecular dopant is to be expected. DMC calculations determine the onset of helium gathering at N = 3. To analyze energetic and structural properties as a function of N, PIMC calculations with no bosonic exchange, i.e., Boltzmann statistics, at low temperatures are carried out. At T = 0.1 K, although acceptable one-particle He-Cs(2) distributions are obtained, two-particle He-He distributions are not well described, indicating that the proper symmetry should be taken into account. PIMC distributions at T = 1 K already compare well with DMC ones and show minor exchange effects, although binding energies are still far from having converged in terms of the number of quantum beads. As N increases, the He-He PIMC pair correlation function shows a clear tendency to coincide with the experimental boson-liquid helium one at that temperature. It supports the picture of a helium droplet which carries the molecular impurity on its surface, as found earlier for other triplet dimers.

Forming Rb(+) snowballs in the center of He nanodroplets

Helium nanodroplets doped with rubidium atoms are ionized by applying a resonant two-step ionization scheme. Subsequent immersion of rubidium ions is observed in time-of-flight mass spectra. While alkali-metal atoms usually desorb from the surface of a helium nanodroplet upon electronic excitation, rubidium in its excited 5(2)P(1/2) state provides an exception from this rule (Auböck et al., Phys. Rev. Lett., 2008, 101, 35301). In our new experiment, Rb atoms are selectively excited either to the 5(2)P(1/2) or to the 5(2)P(3/2) state. From there they are ionized by a laser pulse. Time-of-flight mass spectra of the ionization products reveal that the intermediate population of the 5(2)P(1/2) state does not only make the ionization process Rb-monomer selective, but also gives rise to a very high yield of Rb(+)-He(N) complexes. Ions with masses of up to several thousand amu have been monitored, which can be explained by an immersion of the single Rb ion into the He nanodroplet, where most likely a snowball is formed in the center of the He nanodroplet. As the most stable position for an ion is in the center of a He nanodroplet, our results agree well with theory.