Rotational Superfluidity in Small Helium Droplets

Onset of Rotational Decoupling for a Molecular Ion Solvated in Helium: From Tags to Rings and Shells

Little is known about how rotating molecular ions interact with multiple ^{4}He atoms and how this relates to microscopic superfluidity. Here, we use infrared spectroscopy to investigate ^{4}He_{N}⋯H_{3}O^{+} complexes and find that H_{3}O^{+} undergoes dramatic changes in rotational behavior as ^{4}He atoms are added. We present evidence of clear rotational decoupling of the ion core from the surrounding helium for N>3, with sudden changes in rotational constants at N=6 and 12. In sharp contrast to studies on small neutral molecules microsolvated in helium, accompanying path integral simulations show that an incipient superfluid effect is not needed to account for these findings.

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.

Quantum dynamics of the Br2 (B-excited state) photodissociation in superfluid helium nanodroplets: importance of the recombination process

We have studied the Br₂ photodissociation dynamics (B ← X electronic transition) of Br₂(v = 0, X)@(⁴He)_N doped nanodroplets (T = 0.37 K) at zero angular momentum, with N in the 100-1000 interval. To do this, we have used a quantum mechanical hybrid strategy proposed by us and, as far as we know, this is the second quantum dynamics study available on the photodissociation of molecules in superfluid helium nanodroplets. While the results obtained for some properties are qualitatively similar to those reported previously by us for the Cl₂(B ← X) related case (in particular, the oscillating Br final velocity distribution which also arises from quantum interferences), large differences are evident in three key properties: the photodissociation mechanism and probability and the time scale of the process. This can be interpreted on the basis of the significantly lower excitation energy achieved by the Br₂(B ← X) transition and the higher reduced mass of Br-Br in comparison to the chlorine case. The Br₂(B) photodissociation dynamics is significantly more complex than that of Cl₂(B) and leads to the fragmentation of the initial wave packet. Thus, the probability of non-dissociation is equal to 17, 18, 51, 85 and 100% for N = 100, 200, 300, 500 and 1000, respectively, while for chlorine this probability is equal to zero. In spite of the very large experimental difficulties that exist for obtaining nanodroplets with a well defined size, we hope that these results will encourage experimentalists to investigate these interesting systems.

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.

Laser spectroscopy of helium solvated molecules: probing the inertial response

Helium is the only solvent within which molecules can "freely" rotate, albeit with an increased moment of inertia relative to the gas phase. Evidence for this can be obtained by performing infrared laser spectroscopy on molecules embedded large helium clusters (nanodroplets), which often reveals rotationally resolved lines that are more closely spaced than in vacuo. The additional rotational inertia results from coupling of the helium to the molecule (rotor), and decreases in going from heavy (e.g., SF₆) to light (e.g., CH₄) rotors due to a partial breakdown in the adiabatic (following) approximation; faster (lighter) rotors cannot couple as well to helium since their effective interaction with helium is less anisotropic. In addition to this "mass" dependence to the coupling, there is also a time dependence to it, which shows up in the IR spectra as an asymmetry in the rovibrational lineshapes; this results from a delay in the response of helium to the change in rotational speed of the solvated molecule (when ΔJ = ±1). In this perspective we discuss the coupling between various probe molecules and helium that have been investigated by infrared laser spectroscopy in the frequency domain.

Quantum-classical approach to the reaction dynamics in a superfluid helium nanodroplet. The Ne2 dimer and Ne-Ne adduct formation reaction Ne + Ne-doped nanodroplet

The dynamics of the Ne₂ dimer and Ne-Ne adduct formation in a superfluid helium nanodroplet [(⁴He)_N; T = 0.37 K], Ne + Ne@(⁴He)_N→ Ne₂@(⁴He)_N'/Ne-Ne@(⁴He)_N' + (N-N')⁴He with N = 500, has been investigated using a hybrid approach (quantum and classical mechanics (QM-CM) descriptions for helium and the Ne atoms, respectively) and taking into account the angular momentum of the attacking Ne atom, Ne₍₁₎. Comparison with zero angular momentum QM results of our own shows that the present results are similar to the quantum ones for the initial Ne₍₁₎ velocities (v₀) of 500 and 800 m s^-1 (the former one being the most probable velocity of Ne at 300 K), in all cases leading to the Ne₂ dimer (r_e = 3.09 Å). However, significant differences appear below v₀ = 500 m s^-1, because in the QM-CM dynamics, instead of the dimer, a Ne-Ne adduct is formed (r₀ = 5.45 Å). The formation of this adduct will probably dominate as the contribution to reactivity of angular momenta larger than zero is the leading one and angular momentum strongly acts against the Ne₂ production. Angular momentum adds further difficulties in producing the dimer, since it makes it more difficult to remove the helium density between both Ne atoms to lead, subsequently, to the Ne₂ molecule. Hence, the formation of the neon-neon adduct, Ne-Ne@(⁴He)_N', clearly dominates the reactivity of the system, which results in the formation of a "quantum gel"/"quantum foam", because the two Ne atoms essentially maintain their identity inside the nanodroplet. Large enough Ne₍₁₎ initial angular momentum values can induce the formation of vortex lines by the collapse of superficial excitations (ripplons), but they occur with greater difficulty than in the case of the capture of the Ne atom by a non doped helium nanodroplet, due to the wave interferences induced by the Ne induced by the solvation layers of the Ne atom originally placed inside the nanodroplet. We hope that this work will encourage other researchers to investigate the reaction dynamics in helium nanodroplets, an interesting topic on which there are few studies available.

Rotational energy relaxation quantum dynamics of a diatomic molecule in a superfluid helium nanodroplet and study of the hydrogen isotopes case

The rotational energy relaxation (RER) of a molecule X2(j,mj) in a 4He superfluid nanodroplet [HeND or (4He)N; T = 0.37 K] has been investigated using a hybrid quantum dynamics approach recently proposed by us. As far as we know, this is the first theoretical study about rotational relaxation inside HeNDs, and here several (real and hypothetical) isotopes of H2 have been examined, in order to analyze the influence of the rotational constant Be of these fast rotors on the dynamics. The structure of the nanodroplet practically does not change during the RER process, which approximately takes place according to a cascade mechanism j → j - 2; j - 2 → j - 4; …; 2 → 0, and mj is conserved. The results are consistent with the very scarce estimated experimental data available. The lifetime of an excited rotational state (≈1.0-7.6 ns) increases when: (a) Be increases; (b) j increases; and (c) N decreases (above N = 100 there is a small influence of N on the lifetime). This also applies to the global relaxation time and transition time. The analysis of the influence of the coupling between the j and j - 2 rotational states (due to the X2-helium interaction) and the X2 angular velocity on the lifetime and related properties has been helpful to better understand the dynamics. In contrast to the RER results, for the vibrational energy relaxation (VER) in HeNDs, when the quantum number v increases a decrease is observed in the lifetime of the excited vibrational state. This difference can be interpreted taking into account that RER and VER are associated with very different types of motion. Besides, in VER the intermediate excited states show metastability, differing from the RER case. We hope that the present study will encourage more studies to be developed on the RER dynamics in HeNDs, a basic, interesting and difficult to study physical phenomenon about which we still know very little.

Quantum-classical dynamics of the capture of neon atoms by superfluid helium nanodroplets

The capture dynamics of Ne by a HeND was studied theoretically in a detailed manner (energy and angular momentum transfer and vortex formation).

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].

Atomically resolved phase transition of fullerene cations solvated in helium droplets

Helium has a unique phase diagram and below 25 bar it does not form a solid even at the lowest temperatures. Electrostriction leads to the formation of a solid layer of helium around charged impurities at much lower pressures in liquid and superfluid helium. These so-called ‘Atkins snowballs' have been investigated for several simple ions. Here we form He_nC₆₀⁺ complexes with n exceeding 100 via electron ionization of helium nanodroplets doped with C₆₀. Photofragmentation of these complexes is measured by merging a tunable narrow-bandwidth laser beam with the ions. A switch from red- to blueshift of the absorption frequency of He_nC₆₀⁺ on addition of He atoms at n=32 is associated with a phase transition in the attached helium layer from solid to partly liquid (melting of the Atkins snowball). Elaborate molecular dynamics simulations using a realistic force field and including quantum effects support this interpretation.

'Atkins snowballs', solid layers of helium around an ion core in bulk superfluid He, have been investigated for simple ions but many properties remain unknown. Here, the authors show via photofragmentation experiments that a phase transition occurs in C₆₀-doped He droplets depending on the number of He atoms.

Lieb-Liniger-like model of quantum solvation in CO-(4)HeN clusters

Small (4)He clusters doped with various molecules allow for the study of "quantum solvation" as a function of cluster size. A peculiarity of quantum solvation is that, as the number of (4)He atoms is increased from N = 1, the solvent appears to decouple from the molecule which, in turn, appears to undergo free rotation. This is generally taken to signify the onset of "microscopic superfluidity." Currently, little is known about the quantum mechanics of the decoupling mechanism, mainly because the system is a quantum (N + 1)-body problem in three dimensions which makes computations difficult. Here, a one-dimensional model is studied in which the (4)He atoms are confined to revolve on a ring and encircle a rotating CO molecule. The Lanczos algorithm is used to investigate the eigenvalue spectrum as the number of (4)He atoms is varied. Substantial solvent decoupling is observed for as few as N = 5 (4)He atoms. Examination of the Hamiltonian matrix, which has an almost block diagonal structure, reveals increasingly weak inter-block (solvent-molecule) coupling as the number of (4)He atoms is increased. In the absence of a dopant molecule the system is similar to a Lieb-Liniger (LL) gas and we find a relatively rapid transition to the LL limit as N is increased. In essence, the molecule initially-for very small N-provides a central, if relatively weak, attraction to organize the cluster; as more (4)He atoms are added, the repulsive interactions between the identical bosons start to dominate as the solvation ring (shell) becomes more crowded which causes the molecule to start to decouple. For low N, the molecule pins the atoms in place relative to itself; as N increases the atom-atom repulsion starts to dominate the Hamiltonian and the molecule decouples. We conclude that, while the notion of superfluidity is a useful and correct description of the decoupling process, a molecular viewpoint provides complementary insights into the quantum mechanism of the transition from a molecular cluster to a quantum solvated molecule.

Mass effects in the photodissociation of homonuclear diatomic molecules in helium nanodroplets: inelastic collision and viscous flow energy exchange regimes

The photodissociation of a diatomic molecule X₂ in a superfluid helium nanodroplet presents two sequential dynamic regimes: the starting perfectly inelastic collision followed by the viscous flow. This mechanism has probably general character.

Reaction dynamics inside superfluid helium nanodroplets: the formation of the Ne2 molecule from Ne + Ne@(4He)N

A hybrid TDDFT approach was proposed to consider bimolecular reactive processes in superfluid helium nanodroplets. The Ne + Ne@(⁴He)_N reaction was considered as the first application example. The formation of Ne₂ is a complex process related to the nature of the helium density waves and their reflection from the nanodroplet surface.

Relaxation dynamics of helium nanodroplets after photodissociation of a dopant homonuclear diatomic molecule. The case of Cl2@(4He)N

The quantum (TDDFT) dynamics of the relaxation process (Δt ∼ 500 ps) of excited helium nanodroplets was studied for the first time.

Quantum dynamics of the pick up process of atoms by superfluid helium nanodroplets: the Ne + (4He)1000 system

The quantum dynamics of neon atom capture by a superfluid helium-4 nanodroplet has been theoretically investigated using a hybrid method.

Quantum interferences in the photodissociation of Cl2(B) in superfluid helium nanodroplets (4He)N

The origin of quantum interferences theoretically found in the photodissociation of chlorine in superfluid ⁴He nanodroplets was investigated in detail.