Heteronuclear and homonuclear high-spin alkali trimers on helium nanodroplets

Precision engineering of nano-assemblies in superfluid helium by the use of van der Waals forces

The ability to precisely engineer nanostructures underpins a wide range of applications in areas such as electronics, optics, and biomedical sciences. Here we present a novel approach for the growth of nanoparticle assemblies that leverages the unique properties of superfluid helium. Unlike viscous solvents at or near room temperature, superfluid helium provides an unperturbed and cold environment in which weak van der Waals interactions between molecular templates and metal atoms become significant and can define the spatial arrangement of nanoparticles. To demonstrate this concept, diol and porphyrin-based molecules are employed as templates to grow gold nanoparticle assemblies in superfluid helium droplets. After soft-landing on a solid surface to remove the helium, transmission electron microscopy (TEM) imaging shows the growth of gold nanoparticles at specific binding sites within the molecular templates where the interaction between gold atoms and the molecular template is at its strongest.

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 ± 0.15 Å, Req(K3) = 5.03 ± 0.18 Å, and Req(Rb3) = 5.45 ± 0.22 Å. For K3 and Rb3, these values agree well with existing theoretical calculations, while for Na3, the value is 0.2-0.3 Å 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.

Bonding in the high spin lithium clusters: Non-nuclear attractors play a crucial role

The bonding in lithium high-spin clusters contradicts the usual chemical bonding concept since there are no electron pairs between the atoms, and they are bound with parallel spin electrons. Quantum theory of atoms in molecules and interacting quantum atom analysis (IQA) were used to investigate the nature of bonding in the high-spin Li n n + 1 n = 2 - 5 clusters. Our findings demonstrate that the non-nuclear attractors (NNAs) are an essential component of the high-spin lithium clusters and play a key role in keeping them stable. Based on IQA energy terms, an electrostatic destabilizing interaction between the lithium atoms works against the cluster formation. On the other hand, the interactions between lithium atoms and NNA basins are stabilizing and outweigh the lithium-lithium destabilizing effects. In fact, NNAs tend to draw lithium atoms together and stabilize the resulting cluster. The high-spin clusters of lithium can be regarded as electrostatically driven compounds since the electrostatic components are primarily responsible for the stabilizing interactions between NNAs and Li atoms. The only exception is ³ Li₂ , which lacks NNA and has a non-repellent lithium-lithium interaction. Indeed, in the ³ Li₂ , the interatomic electrostatic component is negligibly small, and the exchange-correlation term leads to a weak bonding interaction.

Diamondoid ether clusters in helium nanodroplets

Diamondoid ethers were introduced into superfluid helium nanodroplets and the resulting clusters were analyzed by time-of-flight mass spectrometry. Clusters of higher abundances (magic number clusters) were identified and the corresponding potential cluster geometries were obtained from GFN2-xTB and DFT computations. We found that the studied diamondoid ethers readily self-assemble in helium nanodroplets and that London dispersion attraction between hydrocarbon subunits acts as a driving force for cluster formation. On the other hand, hydrogen bonding between ether oxygens and trace water molecules fosters the eventual breakdown of the initial supramolecular aggregate.

Quantum-State-Sensitive Detection of Alkali Dimers on Helium Nanodroplets by Laser-Induced Coulomb Explosion

Rubidium dimers residing on the surface of He nanodroplets are doubly ionized by an intense femtosecond laser pulse leading to fragmentation into a pair of Rb^{+} ions. We show that the kinetic energy of the Rb^{+} fragment ions can be used to identify dimers formed in either the X ^{1}Σ_{g}^{+} ground state or in the lowest-lying triplet state, a ^{3}Σ_{u}^{+}. From the experiment, we estimate the abundance ratio of dimers in the a and X states as a function of the mean droplet size and find values between 4∶1 and 5∶1. Our technique applies generally to dimers and trimers of alkali atoms, here also demonstrated for Li_{2}, Na_{2}, and K_{2}, and will enable femtosecond time-resolved measurements of their rotational and vibrational dynamics, possibly with atomic structural resolution.

London dispersion dominating diamantane packing in helium nanodroplets

Diamantane clusters formed inside superfluid helium nanodroplets were analyzed by time-of-flight mass spectrometry. Distinct cluster sizes were identified as "magic numbers" and the corresponding feasible structures for clusters consisting of up to 19 diamantane molecules were derived from meta-dynamics simulations and subsequent DFT computations. The obtained interaction energies were attributed to London dispersion attraction. Our findings demonstrate that diamantane units readily form assemblies even at low pressures and near-zero Kelvin temperatures, confirming the importance of the intermolecular dispersion effect for condensation of matter.

Metal clusters synthesized in helium droplets: structure and dynamics from experiment and theory

Metal clusters have drawn continuous interest because of their high potential for the assembly of matter with special properties that may significantly differ from the corresponding bulk. Controlled combination of particular elements in one nanoparticle can increase the options for the creation of new materials for photonic, catalytic, or electronic applications. Superfluid helium droplets provide confinement and ultralow temperature, i.e. an ideal environment for the atom-by-atom aggregation of a new nanoparticle. This perspective presents a review of the current research progress on the synthesis of tailored metal and metal oxide clusters including core-shell designs, their characterization within the helium droplet beam, deposition on various solid substrates, and analysis via surface diagnostics. Special attention is given to the thermal properties of mixed metal clusters and questions about alloy formation on the nanoscale. Experimental results are accompanied by theoretical approaches employing computational chemistry, molecular dynamics simulations and He density functional theory.

Ultrafast photoinduced dynamics of single atoms solvated inside helium nanodroplets

Helium nanodroplets can serve as reaction containers for photoinduced time-resolved studies of cold, isolated molecular systems that are otherwise inaccessible. Recently, three different dynamical processes, triggered by photoexcitation of a single atom inside a droplet, were observed in their natural time scale: Expansion of the He solvation shell (He bubble) within 600 fs initiates a collective bubble oscillation with a ∼30 ps oscillation period, followed by dopant ejection after ∼60 ps. Here, we present a systematic investigation of these processes by combining time-resolved photoelectron and photoion spectroscopy with time-dependent He density functional theory simulations. By variation of the photoexcitation energy, we find that the full excess excitation energy, represented by the blue-shifted in-droplet excitation band, is completely transferred to the He environment during the bubble expansion. Surprisingly, we find that variation of the droplet size has only a minor influence on the ejection time, providing insight into the spatial distribution of the ground-state atoms before photoexcitation. Simulated particle trajectories after photoexcitation are in agreement with experimental observations and suggest that the majority of ground-state atoms are located at around 16 Å below the droplet surface. Bubble expansion and oscillation are purely local effects, depending only on the ultimate dopant environment. These solvation-induced dynamics will be superimposed on intramolecular dynamics of molecular systems, and a mechanistic description is fundamental for the interpretation of future experiments.

Stability of "No-Pair Ferromagnetic" Lithium Clusters

High-spin lithium clusters, ⁿ⁺¹Li_n (n = 2-21), have been systematically studied by using density functional theory. Although these high-spin clusters have no bonding electron pairs, they are stable with respect to isolated atoms. A set of 42 density functional theory functionals were benchmarked against CCSD(T)/cc-pVQZ results for clusters from the dimer to the hexamer. For these clusters, the strong non-additivity on the binding energy is analyzed employing a many-body energy decomposition scheme, concluding that most of the binding energy is due to a balance between the three- and four-body contributions. After a quality parameter had been defined, the LC-BP86 functional was identified as the most promising one for the description of high-spin lithium clusters. We employ the dependence of the second energy difference on cluster size to predict the formation of a higher-stability cluster.

Coherent multidimensional spectroscopy of dilute gas-phase nanosystems

Two-dimensional electronic spectroscopy (2DES) is one of the most powerful spectroscopic techniques with unique sensitivity to couplings, coherence properties and real-time dynamics of a quantum system. While successfully applied to a variety of condensed phase samples, high precision experiments on isolated systems in the gas phase have been so far precluded by insufficient sensitivity. However, such experiments are essential for a precise understanding of fundamental mechanisms and to avoid misinterpretations. Here, we solve this issue by extending 2DES to isolated nanosystems in the gas phase prepared by helium nanodroplet isolation in a molecular beam-type experiment. This approach uniquely provides high flexibility in synthesizing tailored, quantum state-selected model systems of single and many-body character. In a model study of weakly-bound Rb₂ and Rb₃ molecules we demonstrate the method's unique capacity to elucidate interactions and dynamics in tailored quantum systems, thereby also bridging the gap to experiments in ultracold quantum science.

Spectroscopy of gold atoms and gold oligomers in helium nanodroplets

The 6p ²P_1/2 ← 6s ²S_1/2 and 6p ²P_3/2 ← 6s ²S_1/2 transitions (D lines) of gold atoms embedded in superfluid helium nanodroplets have been investigated using resonant two-photon ionization spectroscopy. Both transitions are strongly blue-shifted and broadened due to the repulsive interaction between the Au valence electron and the surrounding helium. The in-droplet D lines are superimposed by the spectral signature of Au atoms relaxed into the metastable ²D states. These features are narrower than the in-droplet D lines and exhibit sharp rising edges that coincide with bare atom transitions. It is concluded that they originate from metastable ²D state AuHe_n exciplexes that have been ejected from the helium droplets during a relaxation process. Interestingly, the mechanism that leads to the formation of these complexes is suppressed for very large helium droplets consisting of about 2 × 10⁶ He atoms, corresponding to a droplet diameter on the order of 50 nm. The assignment of the observed spectral features is supported by ab initio calculations employing a multiconfigurational self-consistent field method and a multi-reference configuration interaction calculation. For large helium droplets doped with Au oligomers, excitation spectra for mass channels corresponding to Au_n with n = 2, 3, 4, 5, 7, and 9 are presented. The mass spectrum reveals even-odd oscillations in the number of Au atoms that constitute the oligomer, which is characteristic for coinage metal clusters. Resonances are observed close by the in-droplet D1 and D2 transitions, and the corresponding peak forms are very similar for different oligomer sizes.

Photoinduced Molecule Formation of Spatially Separated Atoms on Helium Nanodroplets

Besides the use as cold matrix for spectroscopic studies, superfluid helium droplets have served as a cold environment for the synthesis of molecules and clusters. Since vibrational frequencies of molecules in helium droplets exhibit almost no shift compared to the free molecule values, one could assume the solvated particles move frictionless and undergo a reaction as soon as their paths cross. There have been a few unexplained observations that seemed to indicate cases of two species on one droplet not forming bonds but remaining isolated. In this work, we performed a systematic study of helium droplets doped with one rubidium and one strontium atom showing that besides a reaction to RbSr, there is a probability of finding separated Rb and Sr atoms on one droplet that only react after electronic excitation. Our results further indicate that ground-state Sr atoms can reside at the surface as well as inside the droplet.

Lithium atoms on helium nanodroplets: Rydberg series and ionization dynamics

The electronic excitation spectrum of lithium atoms residing on the surface of helium nanodroplets is presented and analyzed employing a Rydberg-Ritz approach. Utilizing resonant two-photon ionization spectroscopy, two different Rydberg series have been identified: one assigned to the nS(Σ) series and the other with predominantly nP(Π) character. For high Rydberg states, which have been resolved up to n = 13, the surrounding helium effectively screens the valence electron from the Li ion core, as indicated by the apparent red-shift of Li transitions and lowered quantum defects on the droplet with respect to their free atom counterparts. For low n states, the screening effect is weakened and the prevailing repulsive interaction gives rise to strongly broadened and blue-shifted transitions. The red-shifts originate from the polarization of nearby He atoms by the positive Li ion core. As a consequence of this effect, the ionization threshold is lowered by 116 ± 10 cm^-1 for Li on helium droplets with a radius of about 40 Å. Upon single-photon ionization, heavy complexes corresponding to Li ions attached to intact helium droplets are detected. We conclude that ionization close to the on-droplet ionization threshold triggers a dynamic process in which the Li ion core undergoes a transition from a surface site into the droplet.

Rydberg states of alkali atoms on superfluid helium nanodroplets: inside or outside?

Electronic excitations of an electron bound to an alkali metal ion inside a droplet of superfluid 4He are computed via a combination of helium density functional theory and the numerical integration of the Schrödinger equation for a single electron in a modified, He density dependent atomic pseudopotential. The application of a spectral method to the radial part of the valence electron wavefunction allows the computation of highly excited Rydberg states. For low principal quantum numbers, the energy required to push the electron outward is larger than the solvation energy of the ion. However, for higher principal quantum numbers the situation is reversed, which suggests the stability of a system where the ion sits inside the droplet while the valence electron orbits the nanodroplet.

Spatial quenching of a molecular charge-transfer process in a quantum fluid: the Csx-C60 reaction in superfluid helium nanodroplets

A recent experimental study [Renzler et al., J. Chem. Phys., 2016, 145, 181101] on superfluid helium nanodroplets reported different reactivities for Cs atoms and Cs₂ dimers with C₆₀ fullerenes inside helium droplets. Alkali metal atoms and clusters are heliophobic, therefore typically residing on the droplet surface, while fullerenes are fully immersed into the droplet. In this theoretical study, which combines standard methods of computational chemistry with orbital-free helium density functional theory, we show that the experimental findings can be interpreted in the light of a quenched electron-transfer reaction between the fullerene and the alkali dopant, which is additionally hindered by a reaction barrier stemming from the necessary extrusion of helium upon approach of the two reactants.

On the Nature of Bonding in Parallel Spins in Monovalent Metal Clusters

As we approach the Lewis model centennial, it may be timely to discuss novel bonding motifs. Accordingly, this review discusses no-pair ferromagnetic (NPFM) bonds that hold together monovalent metallic atoms using exclusively parallel spins. Thus, without any traditional electron-pair bonds, the bonding energy per atom in these clusters can reach 20 kcal mol(-1). This review describes the origins of NPFM bonding using a valence bond (VB) analysis, which shows that this bonding motif arises from bound triplet electron pairs that are delocalized over all the close neighbors of a given atom in the cluster. The VB model accounts for the tendency of NPFM clusters to assume polyhedral shapes with rather high symmetry and for the very steep rise of the bonding energy per atom. The advent of NPFM clusters offers new horizons in chemistry of highly magnetic species sensitive to magnetic and electric fields.

Investigation of the RbCa molecule: Experiment and theory

We present a thorough theoretical and experimental study of the electronic structure of RbCa. The mixed alkali-alkaline earth molecule RbCa was formed on superfluid helium nanodroplets. Excited states of the molecule in the range of 13 000-23 000 cm^-1 were recorded by resonance enhanced multi-photon ionization time-of-flight spectroscopy. The experiment is accompanied by high level ab initio calculations of ground and excited state properties, utilizing a multireference configuration interaction method based on multiconfigurational self consistent field calculations. With this approach the potential energy curves and permanent electric dipole moments of 24 electronic states were calculated. In addition we computed the transition dipole moments for transitions from the ground into excited states. The combination of experiment and theory allowed the assignment of features in the recorded spectrum to the excited [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] states, where the experiment allowed to benchmark the calculation. This is the first experimental work giving insight into the previously unknown RbCa molecule, which offers great prospects in ultracold molecular physics due to its magnetic and electronic dipole moment in the [Formula: see text] ground state.

Helium-droplet-assisted preparation of cold RbSr molecules

We present a combined experimental and theoretical study of the RbSr molecule. The experimental approach is based on the formation of RbSr molecules on helium nanodroplets. Utilizing two-photon ionization spectroscopy, an excitation spectrum ranging from 11,600 up to 23,000 cm(-1) was recorded. High level ab initio calculations of potential energy curves and transition dipole moments accompany the experiment and facilitate an assignment of transitions. We show that RbSr molecules desorb from the helium droplets upon excitation, which enables dispersed fluorescence spectroscopy of free RbSr. These spectra elucidate X(2)Σ(+) ground and excited state properties. Emission spectra originating from states corresponding to the Rb(5s(2)S) + Sr(5s5p(3)P) asymptote were recorded; spin-orbit coupling was included for the simulation. The results should provide a good basis for achieving the formation of this molecule in cold collisions, thus offering intriguing prospects for ultracold molecular physics.

One- and two-color resonant photoionization spectroscopy of chromium-doped helium nanodroplets

We investigate the photoinduced relaxation dynamics of Cr atoms embedded into superfluid helium nanodroplets. One- and two-color resonant two-photon ionization (1CR2PI and 2CR2PI, respectively) are applied to study the two strong ground state transitions z⁷P_2,3,4^° ← a⁷S₃ and y⁷P_2,3,4^° ← a⁷S₃. Upon photoexcitation, Cr* atoms are ejected from the droplet in various excited states, as well as paired with helium atoms as Cr*–He_n exciplexes. For the y⁷P_2,3,4^° intermediate state, comparison of the two methods reveals that energetically lower states than previously identified are also populated. With 1CR2PI we find that the population of ejected z⁵P₃^° states is reduced for increasing droplet size, indicating that population is transferred preferentially to lower states during longer interaction with the droplet. In the 2CR2PI spectra we find evidence for generation of bare Cr atoms in their septet ground state (a⁷S₃) and metastable quintet state (a⁵S₂), which we attribute to a photoinduced fast excitation–relaxation cycle mediated by the droplet. A fraction of Cr atoms in these ground and metastable states is attached to helium atoms, as indicated by blue wings next to bare atom spectral lines. These relaxation channels provide new insight into the interaction of excited transition metal atoms with helium nanodroplets.

Solvation and spectral line shifts of chromium atoms in helium droplets based on a density functional theory approach

The interaction of an electronically excited, single chromium (Cr) atom with superfluid helium nanodroplets of various size (10 to 2000 helium (He) atoms) is studied with helium density functional theory. Solvation energies and pseudo-diatomic potential energy surfaces are determined for Cr in its ground state as well as in the y⁷P, a⁵S, and y⁵P excited states. The necessary Cr–He pair potentials are calculated by standard methods of molecular orbital-based electronic structure theory. In its electronic ground state the Cr atom is found to be fully submerged in the droplet. A solvation shell structure is derived from fluctuations in the radial helium density. Electronic excitations of an embedded Cr atom are simulated by confronting the relaxed helium density (ρ_He), obtained for Cr in the ground state, with interaction pair potentials of excited states. The resulting energy shifts for the transitions z⁷P ← a⁷S, y⁷P ← a⁷S, z⁵P ← a⁵S, and y⁵P ← a⁵S are compared to recent fluorescence and photoionization experiments.

An ab initio study of the CrHe diatomic molecule: the effect of van der Waals distortion on a highly magnetic multi-electron system

The interaction between He and Cr is investigated by means of post-Hartree-Fock molecular orbital theory. We analyze the influence of the van der Waals forces on the complex electronic structure of the chromium atom, starting with its septet manifold and cover the first few electronically excited states up to 30 000 cm(-1). For the sake of a direct comparison with ongoing experiments on Cr-doped helium nanodroplets we extend our analysis to selected states of the quintet manifold in order to explain a non-radiating relaxation from y (7)P(o) to z (5)P(o).

Laser ionization and spectroscopy of Cu in superfluid helium nanodroplets

Mass and optical spectroscopic methods are used for the analysis of copper (Cu) atoms and clusters doped to helium nanodroplets (He_N). A two-color resonant two-photon ionization scheme is applied to study the Cu ²P[Formula: see text]S_1/2 ground state transition. The absorption is strongly broadened for Cu atoms submerged inside helium nanodroplets and a comparison with computed literature values is provided. An observed ejection of the dopant from the droplet is triggered upon excitation, populating energetically lower states. The formation of Cu _n clusters up to Cu₇ inside helium nanodroplets was observed by means of electron impact ionization mass spectroscopy.

Spectroscopy of cold LiCa molecules formed on helium nanodroplets

We report on the formation of mixed alkali-alkaline earth molecules (LiCa) on helium nanodroplets and present a comprehensive experimental and theoretical study of the ground and excited states of LiCa. Resonance enhanced multiphoton ionization time-of-flight (REMPI-TOF) spectroscopy and laser induced fluorescence (LIF) spectroscopy were used for the experimental investigation of LiCa from 15000 to 25500 cm(-1). The 4(2)Σ(+) and 3(2)Π states show a vibrational structure accompanied by distinct phonon wings, which allows us to determine molecular parameters as well as to study the interaction of the molecule with the helium droplet. Higher excited states (4(2)Π, 5(2)Σ(+), 5(2)Π, and 6(2)Σ(+)) are not vibrationally resolved and vibronic transitions start to overlap. The experimental spectrum is well reproduced by high-level ab initio calculations. By using a multireference configuration interaction (MRCI) approach, we calculated the 19 lowest lying potential energy curves (PECs) of the LiCa molecule. On the basis of these calculations, we could identify previously unobserved transitions. Our results demonstrate that the helium droplet isolation approach is a powerful method for the characterization of tailor-made alkali-alkaline earth molecules. In this way, important contributions can be made to the search for optimal pathways toward the creation of ultracold alkali-alkaline earth ground state molecules from the corresponding atomic species. Furthermore, a test for PECs calculated by ab initio methods is provided.

Growing metal nanoparticles in superfluid helium

Helium droplets provide a cold and confined environment where atomic and/or molecular dopants can aggregate into clusters and nanoparticles. In particular, the sequential addition of different materials to helium droplets can lead to the formation of a wide range of nanoparticles, including core-shell nanoparticles, which can then be deposited onto a surface. Here we briefly discuss the fundamental properties of helium droplets and then address their implications for the formation of clusters and nanoparticles. Several key experiments on atomic and molecular clusters will be highlighted and new results obtained for nanoparticles formed in this way will be presented. Finally, the versatility, the limitations and new possibilities provided by superfluid helium droplets in nanoscience and nanotechnology will be addressed.

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.

Coherent spin manipulation and ESR on superfluid helium nanodroplets

Superfluid helium nanodroplets provide a versatile substrate to cool atoms and molecules, and to assemble weakly bound complexes. Absence of spin-relaxation mechanisms makes He nanodroplets ideal to isolate open-shell atoms and create a spin-polarized system. Here, we show the first coherent manipulation of such a system by resonant excitation of a magnetic-dipole transition. Observation of approximately 50 Rabi oscillations demonstrates coherent population transfer with minimal dephasing. Ours is also the first application of ESR spectroscopy to doped He nanodroplets. This unique environment results in extremely sharp lines and hyperfine-resolved spectra: those of single 39K and 85Rb dopant atoms presented here denote an increase of the Fermi contact interaction, which we can follow as a function of droplet size, reflecting the distortion of the valence-electron wave function due to the surrounding He.

On the doublet states of the potassium trimer

The potassium trimer is investigated in its lowest electronic doublet states, employing several high-level ab initio methods (coupled cluster with single, double, and noniterative triple excitations, multiconfiguration self-consistent field, and multireference Rayleigh-Schrodinger perturbation theory of second order). One-dimensional cuts through the lowest 12 electronic states at C(2v) symmetry give insight in the complex electronic structure of the trimer, showing several (pseudo-)Jahn-Teller distortions that involve two or three excited states. Contour plots of the involved molecular orbitals are shown to prove the validity of the shell model frequently used for a qualitative description of metallic clusters.