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 HeNCa2+ 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.

Zwitter Ionization of Glycine at Outer Space Conditions due to Microhydration by Six Water Molecules.

We investigate glycine microsolvation with water molecules, mimicking astrophysical conditions, in our laboratory by embedding these clusters in helium nanodroplets at 0.37 K. We recorded mass selective infrared spectra in the frequency range 1500-1800 cm^{-1} where two bands centered at 1630 and 1724 cm^{-1} were observed. By comparison with the extensive accompanying calculations, the band at 1630 cm^{-1} was assigned to the COO^{-} asymmetric stretching mode of the zwitter ion and the band at 1724 cm^{-1} was assigned to redshifted C=O stretch within neutral clusters. We show that zwitter ion formation of amino acids readily occurs with only few water molecules available even under extreme conditions.

Ca+ Ions Solvated in Helium Clusters.

We present a combined experimental and theoretical investigation on Ca+ ions in helium droplets, HeNCa+. The clusters have been formed in the laboratory by means of electron-impact ionization of Ca-doped helium nanodroplets. Energies and structures of such complexes have been computed using various approaches such as path integral Monte Carlo, diffusion Monte Carlo and basin-hopping methods. The potential energy functions employed in these calculations consist of analytical expressions following an improved Lennard-Jones formula whose parameters are fine-tuned by exploiting ab initio estimations. Ion yields of HeNCa+ -obtained via high-resolution mass spectrometry- generally decrease with N with a more pronounced drop between N=17 and N=25, the computed quantum HeNCa+ evaporation energies resembling this behavior. The analysis of the energies and structures reveals that covering Ca+ with 17 He atoms leads to a cluster with one of the smallest energies per atom. As new atoms are added, they continue to fill the first shell at the expense of reducing its stability, until N=25, which corresponds to the maximum number of atoms in that shell. Behavior of the evaporation energies and radial densities suggests liquid-like cluster structures.

Unveiling Zwitterionization of Glycine in the Microhydration Limit.

Charge separation under solvation stress conditions is a fundamental process that comes in many forms in doped water clusters. Yet, the mechanism of intramolecular charge separation, where constraints due to the molecular structure might be intricately tied to restricted solvation structures, remains largely unexplored. Microhydrated amino acids are such paradigmatic molecules. Ab initio simulations are carried out at 300 K in the frameworks of metadynamics sampling and thermodynamic integration to map the thermal mechanisms of zwitterionization using Gly(H2O) n with n = 4 and 10. In both cases, a similar water-mediated proton transfer chain mechanism is observed; yet, detailed analyses of thermodynamics and kinetics demonstrate that the charge-separated zwitterion is the preferred species only for n = 10 mainly due to kinetic stabilization. Structural analyses disclose that bifurcated H-bonded water bridges, connecting the cationic and anionic sites in the fluctuating microhydration network at room temperature, are enhanced in the transition-state ensemble exclusively for n = 10 and become overwhelmingly abundant in the stable zwitterion. The findings offer potential insights into charge separation under solvation stress conditions beyond the present example.

Generating Excess Protons in Microsolvated Acid Clusters under Ambient Conditions: An Issue of Configurational Entropy versus Internal Energy.

Acid dissociation, and thus liberation of excess protons in small water droplets, impacts on diverse fields such as interstellar, atmospheric or environmental chemistry. At cryogenic temperatures below 1 K, it is now well established that as few as four water molecules suffice to dissociate the generic strong acid HCl, yet temperature-driven recombination sets in simply upon heating that cluster. Here, the fundamental question is posed of how many more water molecules are required to stabilize a hydrated excess proton at room temperature. Ab initio path integral simulations disclose that not five, but six water molecules are needed at 300 K to allow for HCl dissociation independently from nuclear quantum effects. In order to provide the molecular underpinnings of these observations, the classical and quantum free energy profiles were decomposed along the dissociation coordinate in terms of the corresponding internal energy and entropy profiles. What decides in the end about acid dissociation, and thus ion pair formation, in a specific microsolvated water cluster at room temperature is found to be a fierce competition between classical configurational entropy and internal energy, where the former stabilizes the undissociated state whereas the latter favors dissociation. It is expected that these are generic findings with broad implications on acid-base chemistry depending on temperature in small water assemblies.

Snowball formation for Cs+ solvation in molecular hydrogen and deuterium.

Interactions of atomic cations with molecular hydrogen are of interest for a wide range of applications in hydrogen technologies. These interactions are fairly strong despite being non-covalent, hence one can ask whether hydrogen molecules would form dense, solid-like, solvation shells around the ion (snowballs) or rather a more weakly bound compound. In this work, the interactions between Cs+ and H2 are studied both experimentally and computationally. Isotopic substitution of H2 by D2 is also investigated. On the one hand, helium nanodroplets doped with cesium and hydrogen or deuterium are ionized by electron impact and the (H2/D2)nCs+ (up to n = 30) clusters formed are identified via mass spectrometry. On the other hand, a new analytical potential energy surface, based on ab initio calculations, is developed and used to study cluster energies and structures by means of classical and quantum-mechanical Monte Carlo methods. The most salient features of the measured ion abundances are remarkably mimicked by the computed evaporation energies, particularly for the clusters composed of deuterium. This result supports the reliability of the present potential energy surface and allows us to recommend its use in related systems. Clusters with either twelve H2 or D2 molecules stand out for their stability and quasi-rigid icosahedral structures. However, the first solvation shell involves thirteen or fourteen molecules for hydrogenated or deuterated clusters, respectively. This shell retains its internal structure when extra molecules are added to the second shell and is nearly solid-like, especially for the deuterated clusters. The role played by three-body induction interactions as well as the rotational degrees of freedom is analyzed and they are found to be significant (up to 15% and 18%, respectively) for the molecules belonging to the first solvation shell.

A combined experimental and theoretical investigation of Cs+ ions solvated in HeN clusters.

Solvation of Cs+ ions inside helium droplets has been investigated both experimentally and theoretically. On the one hand, mass spectra of doped helium clusters ionized with a crossed electron beam, HeNCs+, have been recorded for sizes up to N = 60. The analysis of the ratio between the observed peaks for each size N reveals evidences of the closure of the first solvation shell when 17 He atoms surround the alkali ion. On the other hand, we have obtained energies and geometrical structures of the title clusters by means of basin-hopping, diffusion Monte Carlo (DMC), and path integral Monte Carlo (PIMC) methods. The analytical He-Cs+ interaction potential employed in our calculations is represented by the improved Lennard-Jones expression optimized on high level ab initio energies. The weakness of the existing interaction between helium and Cs+ in comparison with some other alkali ions such as Li+ is found to play a crucial role. Our theoretical findings confirm that the first solvation layer is completed at N = 17 and both evaporation and second difference energies obtained with the PIMC calculation seem to reproduce a feature observed at N = 12 for the experimental ion abundance. The analysis of the DMC probability distributions reveals the important contribution from the icosahedral structure to the overall configuration for He12Cs+.

Lithium ions solvated in helium.

We report on a combined experimental and theoretical study of Li+ ions solvated by up to 50 He atoms. The experiments show clear enhanced abundances associated with HenLi+ clusters where n = 2, 6, 8, and 14. We find that classical methods, e.g. basin-hopping (BH), give results that qualitatively agree with quantum mechanical methods such as path integral Monte Carlo, diffusion Monte Carlo and quantum free energy, regarding both energies and the solvation structures that are formed. The theory identifies particularly stable structures for n = 4, 6 and 8 which line up with some of the most abundant features in the experiments.

Acid Dissociation in HCl-Water Clusters is Temperature Dependent and Cannot be Detected Based on Dipole Moments.

The dissociation of acids in aqueous environments at low temperatures in the presence of a limited amount of water is underlying a wealth of processes from atmospheric to interstellar science. For the paradigmatic case of HCl(H_{2}O)_{n} clusters, our extensive ab initio path integral simulations quantify in terms of free energy differences and barriers that n=4 water molecules are indeed required to dissociate HCl at low temperatures. Increasing the temperature, however, reverses the process and thus counteracts dissociation by fluctuation-driven recombination. The size of the electric dipole moment is shown to not correlate with the acid being in its dissociated or molecular state, thus rendering its measurement as a function of n unable to detect the dissociation transition.

Adsorption of molecular hydrogen on coronene with a new potential energy surface.

Benchmark interaction energies between coronene, C24H12, and molecular hydrogen, H2, have been computed by means of high level electronic structure calculations. Binding energies, equilibrium distances and strengths of the long range attraction, evaluated for the basic configurations of the H2-C24H12 complex, indicate that the system is not too affected by the relative orientations of the diatom, suggesting that its behavior can be approximated to that of a pseudoatom. The obtained energy profiles have confirmed the noncovalent nature of the bonding and serve to tune-up the parameters of a new force field based on the atom-bond approach which correctly describes the main features of the H2-coronene interaction. The structure and binding energies of (para-H2)N-coronene clusters have been investigated with an additive model for the above mentioned interactions and exploiting basin-hopping and path integral Monte Carlo calculations for N = 1-16 at T = 2 K. Differences with respect to the prototypical (rare gas)N-coronene aggregates have been discussed.

Comparative investigation of pure and mixed rare gas atoms on coronene molecules.

Clusters formed by the combination of rare gas (RG) atoms of He, Ne, Ar, and Kr on coronene have been investigated by means of a basin-hopping algorithm and path integral Monte Carlo calculations at T = 2 K. Energies and geometries have been obtained and the role played by the specific RG-RG and RG-coronene interactions on the final results is analysed in detail. Signatures of diffuse behavior of the He atoms on the surface of the coronene are in contrast with the localization of the heavier species, Ar and Kr. The observed coexistence of various geometries for Ne suggests the motion of the RG atoms on the multi-well potential energy surface landscape offered by the coronene. Therefore, the investigation of different clusters enables a comparative analysis of localized versus non-localized features. Mixed Ar-He-coronene clusters have also been considered and the competition of the RG atoms to occupy the docking sites on the molecule is discussed. All the obtained information is crucial to assess the behavior of coronene, a prototypical polycyclic aromatic hydrocarbon clustering with RG atoms at a temperature close to that of interstellar medium, which arises from the critical balance of the interactions involved.

Publisher's Note: Acid Dissociation in HCl-Water Clusters is Temperature Dependent and Cannot be Detected Based on Dipole Moments [Phys. Rev. Lett. 119, 223001 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.119.223001.

Water-Induced Zwitterionization of Glycine: Stabilization Mechanism and Spectral Signatures.

Not only the question of how many water molecules are required to stabilize the physiologically relevant charge-separated zwitterionic form of amino acids upon solvation but also the stabilization mechanism is still under debate. It is well known that a water bridge connecting the carboxyl with the amino group must be established. Here, we show that this is not yet a sufficient condition to stabilize the zwitterion. Instead, the formation of a bifurcated H-bonded water wire that connects the two charged groups turns out to be the key, which explains why an unexpectedly large number of water molecules of about nine is required to enable zwitterionization of microsolvated glycine. Moreover, this bifurcated wire allows one to pinpoint a frequency window that enables the detection of zwitterionization by spectroscopy. These findings will be relevant to probe and rationalize microsolvation-induced zwitterionization of not only amino acids but of other acid/base reactions that involve somewhat distant such functional groups within the same molecule.

Examination of the Feynman-Hibbs Approach in the Study of NeN-Coronene Clusters at Low Temperatures.

Feynman-Hibbs (FH) effective potentials constitute an appealing approach for investigations of many-body systems at thermal equilibrium since they allow us to easily include quantum corrections within standard classical simulations. In this work we apply the FH formulation to the study of NeN-coronene clusters (N = 1-4, 14) in the 2-14 K temperature range. Quadratic (FH2) and quartic (FH4) contributions to the effective potentials are built upon Ne-Ne and Ne-coronene analytical potentials. In particular, a new corrected expression for the FH4 effective potential is reported. FH2 and FH4 cluster energies and structures-obtained from energy optimization through a basin-hopping algorithm as well as classical Monte Carlo simulations-are reported and compared with reference path integral Monte Carlo calculations. For temperatures T > 4 K, both FH2 and FH4 potentials are able to correct the purely classical calculations in a consistent way. However, the FH approach fails at lower temperatures, especially the quartic correction. It is thus crucial to assess the range of applicability of this formulation and, in particular, to apply the FH4 potentials with great caution. A simple model of N isotropic harmonic oscillators allows us to propose a means of estimating the cutoff temperature for the validity of the method, which is found to increase with the number of atoms adsorbed on the coronene molecule.

Coronene molecules in helium clusters: Quantum and classical studies of energies and configurations.

Coronene-doped helium clusters have been studied by means of classical and quantum mechanical (QM) methods using a recently developed He-C24H12 global potential based on the use of optimized atom-bond improved Lennard-Jones functions. Equilibrium energies and geometries at global and local minima for systems with up to 69 He atoms were calculated by means of an evolutive algorithm and a basin-hopping approach and compared with results from path integral Monte Carlo (PIMC) calculations at 2 K. A detailed analysis performed for the smallest sizes shows that the precise localization of the He atoms forming the first solvation layer over the molecular substrate is affected by differences between relative potential minima. The comparison of the PIMC results with the predictions from the classical approaches and with diffusion Monte Carlo results allows to examine the importance of both the QM and thermal effects.

Energetics and solvation structure of a dihalogen dopant (I2) in (4)He clusters.

The energetics and structure of small HeNI2 clusters are analyzed as the size of the system changes, with N up to 38. The full interaction between the I2 molecule and the He atoms is based on analytical ab initio He-I2 potentials plus the He-He interaction, obtained from first-principle calculations. The most stable structures, as a function of the number of solvent He atoms, are obtained by employing an evolutionary algorithm and compared with CCSD(T) and MP2 ab initio computations. Further, the classical description is completed by explicitly including thermal corrections and quantum features, such as zero-point-energy values and spatial delocalization. From quantum PIMC calculations, the binding energies and radial/angular probability density distributions of the thermal equilibrium state for selected-size clusters are computed at a low temperature. The sequential formation of regular shell structures is analyzed and discussed for both classical and quantum treatments.

Stress Test for Quantum Dynamics Approximations: Deep Tunneling in the Muonium Exchange Reaction D + HMu → DMu + H.

Quantum effects play a crucial role in chemical reactions involving light atoms at low temperatures, especially when a light particle is exchanged between two heavier partners. Different theoretical methodologies have been developed in the last decades attempting to describe zero-point energy and tunneling effects without abandoning a classical or semiclassical framework. In this work, we have chosen the D + HMu → DMu + H reaction as a stress test system for three well-established methods: two representative versions of transition state theory (TST), canonical variational theory and semiclassical instanton, and ring polymer molecular dynamics (RPMD). These calculations will be compared with accurate quantum mechanical results. Despite its apparent simplicity, the exchange of the extremely light muonium atom (0.114 u) becomes a most challenging reaction for conventional methods. The main result of this work is that RPMD provides an overall better performance than TST-based methods for such a demanding reaction. RPMD might well turn out to be a useful tool beyond TST applicability.

Full-dimensional quantum calculations of the dissociation energy, zero-point, and 10 K properties of H7+/D7+ clusters using an ab initio potential energy surface.

Diffusion Monte Carlo (DMC) and path-integral Monte Carlo computations of the vibrational ground state and 10 K equilibrium state properties of the H7 (+)/D7 (+) cations are presented, using an ab initio full-dimensional potential energy surface. The DMC zero-point energies of dissociated fragments H5 (+)(D5 (+))+H2(D2) are also calculated and from these results and the electronic dissociation energy, dissociation energies, D0, of 752 ± 15 and 980 ± 14 cm(-1) are reported for H7 (+) and D7 (+), respectively. Due to the known error in the electronic dissociation energy of the potential surface, these quantities are underestimated by roughly 65 cm(-1). These values are rigorously determined for first time, and compared with previous theoretical estimates from electronic structure calculations using standard harmonic analysis, and available experimental measurements. Probability density distributions are also computed for the ground vibrational and 10 K state of H7 (+) and D7 (+). These are qualitatively described as a central H3 (+)/D3 (+) core surrounded by "solvent" H2/D2 molecules that nearly freely rotate.

Chemical Reaction Rates from Ring Polymer Molecular Dynamics: Zero Point Energy Conservation in Mu + H2 → MuH + H.

A fundamental issue in the field of reaction dynamics is the inclusion of the quantum mechanical (QM) effects such as zero point energy (ZPE) and tunneling in molecular dynamics simulations, and in particular in the calculation of chemical reaction rates. In this work we study the chemical reaction between a muonium atom and a hydrogen molecule. The recently developed ring polymer molecular dynamics (RPMD) technique is used, and the results are compared with those of other methods. For this reaction, the thermal rate coefficients calculated with RPMD are found to be in excellent agreement with the results of an accurate QM calculation. The very minor discrepancies are within the convergence error even at very low temperatures. This exceptionally good agreement can be attributed to the dominant role of ZPE in the reaction, which is accounted for extremely well by RPMD. Tunneling only plays a minor role in the reaction.

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.