Photoinduced nonadiabatic dynamics in quartet Na[sub 3] and K[sub 3] formed using helium nanodroplet isolation

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.

Vibrational energy relaxation of a diatomic molecule in a superfluid helium nanodroplet: influence of the nanodroplet size, interaction energy and energy gap

The influence of the nanodroplet size, molecule-helium interaction potential energy and ν = 1 - ν = 0 vibrational energy gap on the vibrational energy relaxation (VER) of a diatomic molecule (X₂) in a superfluid helium nanodroplet [HeND or (⁴He)_N; finite quantum solvent at T = 0.37 K] has been studied using a hybrid quantum approach recently proposed by us and taking as a reference the VER results on the I₂@(⁴He)₁₀₀ doped nanodroplet (Vilà et al., Phys. Chem. Chem. Phys., 2018, 20, 118, which corresponds to the first theoretical study on the VER of molecules embedded in a HeND). This has allowed us to obtain a deeper insight into the vibrational relaxation dynamics. The nanodroplet size has a very small effect on the VER, as this process mainly depends on the interaction between the molecule and the nanodroplet first solvation shell. Regarding the interaction potential energy and the energy gap, both factors play an important and comparable role in the VER time properties (global relaxation time, lifetime and transition time). As the former becomes stronger the relaxation time properties decrease in a significant way (their inverse follows a linear dependence with respect to the ν = 1 - ν = 0 coupling term) and they also decrease in a significant manner when the energy gap diminishes (linear dependence on the ν = 1 - ν = 0 energy difference). We expect that this study will motivate further work on the vibrational relaxation process in HeNDs.

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.

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.

Vibrational energy relaxation dynamics of diatomic molecules inside superfluid helium nanodroplets. The case of the I2 molecule

The vibrational relaxation (VER) of a X₂ molecule in a ⁴He superfluid nanodroplet (HeND; 0.37 K) was studied adapting a quantum approach recently proposed by us. In the first theoretical study on the VER of molecules inside HeND the I₂ molecule was examined [cascade mechanism (ν → ν − 1; ν − 1 → ν − 2; …) and time scale of ns].

Communication: Dopant-induced solvation of alkalis in liquid helium nanodroplets

Alkali metal atoms and small alkali clusters are classic heliophobes and when in contact with liquid helium they reside in a dimple on the surface. Here we show that alkalis can be induced to submerge into liquid helium when a highly polarizable co-solute, C₆₀, is added to a helium nanodroplet. Evidence is presented that shows that all sodium clusters, and probably single Na atoms, enter the helium droplet in the presence of C₆₀. Even clusters of cesium, an extreme heliophobe, dissolve in liquid helium when C₆₀ is added. The sole exception is atomic Cs, which remains at the surface.

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.

Bonding with parallel spins: high-spin clusters of monovalent metal atoms

Bonding is a glue of chemical matter and is also a useful concept for designing new molecules. Despite the fact that electron pairing remains the bonding mechanism in the great majority of molecules, in the past few decades scientists have had a growing interest in discovering novel bonding motifs. As this Account shows, monovalent metallic atoms having exclusively parallel spins, such as (11)Li10, (11)Au10, and (11)Cu10, can nevertheless form strongly bound clusters, without having even one traditional bond due to electron pairing. These clusters, which also can be made chiral, have high magnetic moments. We refer to this type as no-pair ferromagnetic (NPFM) bonding, which characterizes the (n+1)Mn clusters, which were all predicted by theoretical computations. The small NPFM alkali clusters that have been "synthesized" to date, using cold-atom techniques, support the computational predictions. In this Account, we describe the origins of NPFM bonding using a valence bond (VB) analysis, which shows that this bonding motif arises from bound triplet electron pairs that spread over all the close neighbors of a given atom in the cluster. The bound triplet pair owes its stabilization to the resonance energy provided by the mixing of the local ionic configurations, [(3)M(↑↑)(-)]M(+) and M(+)[(3)M(↑↑)(-)], and the various excited covalent configurations (involving pz and dz(2) atomic orbitals) into the repulsive covalent structure (3)(M↑↑M) with the s(1)s(1) electronic configuration. The NPFM bond of the bound triplet is described by a resonating wave function with "in-out" and "out-in" pointing hybrids. The VB model accounts for the tendency of NPFM clusters to assume polyhedral shapes with rather high symmetry. In addition, this model explains the very steep rise of the bonding energy per atom (De/n), which starts out small in the (3)M2 dimer (<1 kcal/mol) and reaches 12-19 kcal/mol for clusters with 10 atoms. The model further predicts that usage of heteroatomic clusters should increase the bonding energy of an NPFM cluster. These NPFM clusters are excited state species. We suggest here stabilizing these states and making them accessible, for example, by using magnetic fields, or a combination of magnetic and electric fields. The advent of NPFM clusters offers new horizons in chemistry and enriches the scope of chemical bonding. These prospects form a strong incentive to investigate the origins of the bound triplet pairs and further chart the territory of NPFM clusters, for example, in clusters of Be, Mg, or Zn, possibly in clusters of their monosubstituted species, and the group III metalloids, such as B, Al, as well as in transition metals such as Sc.

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.

The submersion of sodium clusters in helium nanodroplets: identification of the surface → interior transition

The submersion of sodium clusters beyond a critical size in helium nanodroplets, which has recently been predicted on theoretical grounds, is demonstrated for the first time. Confirmation of a clear transition from a surface location, which occurs for alkali atoms and small clusters, to full immersion for larger clusters, is provided by identifying the threshold electron energy required to initiate Na(n) cluster ionization. On the basis of these measurements, a lower limit for the cluster size required for submersion, n ≥ 21, has been determined. This finding is consistent with the recent theoretical prediction.

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.

Vibrational relaxation and dephasing of Rb2 attached to helium nanodroplets

The vibrational wave-packet dynamics of diatomic rubidium molecules (Rb(2)) in triplet states formed on the surface of superfluid helium nanodroplets is investigated both experimentally and theoretically. Detailed comparison of experimental femtosecond pump-probe spectra with dissipative quantum dynamics simulations reveals that vibrational relaxation is the main source of dephasing. The rate constant for vibrational relaxation in the first excited triplet state 1(3)Σ(g)+ is found to be constant γ ≈ 0.5 ns(-1) for the lowest vibrational levels v ≲ 15 and to increase sharply when exciting to higher energies.

Relativistic Jahn-Teller effects in the quartet states of K3 and Rb3: a vibronic analysis of the 2 (4)E' <-- 1 (4)A2' electronic transitions based on ab initio calculations

We apply second-order multireference Rayleigh-Schrodinger perturbation theory to obtain the adiabatic potential energy surface of the 1 (4)A(2)(') lowest quartet state and the 2 (4)E(') excited state of K(3) and Rb(3). Both trimers show a typical Emultiply sign in circlee Jahn-Teller distortion in their 2 (4)E(') state, which is analyzed in terms of relativistic Jahn-Teller effect theory. Linear, quadratic, and spin-orbit coupling terms are extracted from the ab initio results and used to generate simulated spectra for a direct comparison with laser-induced fluorescence and magnetic circular dichroism spectra of alkali-doped helium nanodroplets [Aubock et al., J. Chem. Phys. 129, 114501 (2008)].

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.

Heteronuclear and homonuclear high-spin alkali trimers on helium nanodroplets

The electronic excitation spectra of all possible homo- and heteronuclear high-spin (quartet) trimers of K and Rb (KxRb(3-x), x=0...3) assembled on the surface of superfluid helium droplets, are measured in the spectral range from 10,600 to 17,400 cm(-1). A regular series of corresponding bands is observed, reflecting the similar electronic structure of all these trimers. For the assignment and separation of overlapping bands, we determine x directly, with mass-selected beam depletion, and indirectly with a V-type double-resonance scheme. The assignment is confirmed by high-level ab initio calculations of the electronic structure of the bare trimers. The level structure is rationalized in terms of harmonic-oscillator states of the three valence electrons in a quantum-dot-like confining potential. We predict that three should be a magic number for high-spin alkali clusters.

Triplet State Excitation of Alkali Molecules on Helium Droplets: Experiments and Theory

In this paper, we discuss the electronic structure of alkali dimer molecules in 3Pig states on the surface of a helium droplet. The perturbation due to the droplet will in general not satisfy rotational symmetry around the internuclear axis of the diatom and thus, in addition to a broadening and blue shift, will cause a splitting of electronic levels that are degenerate in the free molecules. We propose a model based on general symmetry arguments and on a small number of physically reasonable parameters. We demonstrate that such a model accounts for the essential features of laser-induced fluorescence (LIF) and magnetic circular dichroism (MCD) spectra of the (1)3Pig-a3Sigma+ transition of Rb2 and K2. Furthermore the MCD spectra, analyzed according to the approach of Langford and Williamson [J. Phys. Chem. A 1998, 102, 2415], allow a determination of the populations of Zeeman sublevels in the ground state and thus a measurement of the surface temperature of the droplet. The latter agrees with the accepted temperature, 0.37 K, measured in the interior of a droplet.

Formation and properties of metal clusters isolated in helium droplets

The unique conditions forming atomic and molecular complexes and clusters using superfluid helium nanodroplets have opened up an innovative route for studying the physical and chemical properties of matter on the nanoscale. This review summarizes the specific characteristics of the formation of atomic clusters partly generated far from equilibrium in the helium environment. Special emphasis is on the optical response, electronic properties as well as dynamical processes which are mostly affected by the surrounding quantum matrix. Experiments include the optical induced response of isolated cluster systems in helium under quite different excitation conditions ranging from the linear regime up to the violent interaction with a strong laser field leading to Coulomb explosion and the generation of highly charged atomic fragments. The variety of results on the outstanding properties in the quantum size regime highlights the peculiar capabilities of helium nanodroplet isolation spectroscopy.

Ferromagnetic Bonding: High Spin Copper Clusters (n+1Cun; n = 2−14) Devoid of Electron Pairs but Possessing Strong Bonding

Density functional theoretic studies are performed for the high-spin copper clusters (n)(+1)Cu(n) (n = 2-14), which are devoid of electron pairs shared between atoms, hence no-pair clusters (J. Phys. Chem. 1988, 92, 1352; Isr. J. Chem. 1993, 33, 455; J. Am. Chem. Soc. 1999, 121, 3165). Despite the lack of electron pairing, it is found that the bond dissociation energy per atom (BDE/n) is significant and converges (to within 1 kcal mol(-1)), around a cluster size (11)Cu(10), to a value of BDE/n = 19 kcal mol(-1). This is a very large bonding energy, much larger than has previously been obtained for no-pair clusters of lithium, BDE/n = 12 kcal mol(-1), or sodium clusters, BDE/n = 3 kcal mol(-1). This bonding, so-called ferromagnetic bonding (FM-bonding) is analyzed using a valence bond (VB) model (J. Phys. Chem. A 2002, 106, 4961; Phys. Chem. Chem. Phys. 2003, 5, 158). As such, FM-bonding in no-pair clusters is described as an ionic fluctuation, of the triplet pair, that spreads over all the close neighbors of a given atom in the clusters. Thus, if we refer to each triplet pair and its ionic fluctuations as a local FM-bond, we can regard the electronic structure of a given (n)(+1)M(n) cluster as a resonance hybrid of all the local FM-bonds between close neighbors. The model shows how a weak interaction in the diatomic triplet molecule can become a remarkably strong binding force that binds together mono-valent atoms without even a single electron pair. This is achieved because the growing number of VB structures exerts a cumulative effect of stabilization that is maximized when the cluster has a compact structure with an optimal coordination number for the atoms.

Spectroscopy of Cs attached to helium nanodroplets

Cesium oligomers are formed on helium nanodroplets which are doped with one or a few Cs atoms. The monomer absorption of the first electronic p<--s transition upon laser excitation is probed. Spectra employing laser-induced fluorescence, beam depletion, and resonant photoionization are compared. In particular, mass-resolved photoionization allows us to specifically probe excitation induced processes such as, e.g., the formation of cesium-helium exciplexes. Absorption spectra of Cs dimers and trimers are recorded in the spectral region accessible by a Ti:sapphire laser. Assignment of dimer spectra is achieved by comparison with model calculations based on ab initio potentials. Electronic absorption lines of Cs trimers are attributed to transitions in the quartet manifold.

Formation of atomic tritium clusters and bose-einstein condensates

We present an extensive study of the static and dynamic properties of systems of spin-polarized tritium atoms. In particular, we calculate the two-body |F,m(F)>=|0,0> s-wave scattering length and show that it can be manipulated via a Feshbach resonance at a field strength of about 870 G. Such a resonance might be exploited to make and control a Bose-Einstein condensate of tritium in the |0,0> state. It is further shown that the quartet tritium trimer is the only bound hydrogen isotope and that its single vibrational bound state is a Borromean state. The ground state properties of larger spin-polarized tritium clusters are also presented and compared with those of helium clusters.