Computational Modeling: Up-to-Date Approaches and Cutting-Edge Applications from Clusters, Nanostructures to Bulk Systems.

The contributions in this special theme collection, in honor to Prof. P. Villarreal, cover a broad variety of computational methodologies and experimental techniques, containing studies on gas phase, clusters and condensed phase systems.

Trihydrogen Cation Helium Clusters: A New Potential Energy Surface.

We present a new analytical potential energy surface (PES) for the interaction between the trihydrogen cation and a He atom, H 3 + - H e ${{H}_{3}^{+}-He}$ , in its electronic ground state. The proposed PES has been built as a sum of two contributions: a polarization energy term due to the electric field generated by the molecular cation at the position of the polarizable He atom, and an exchange-repulsion and dispersion interactions represented by a sum of "atom-bond" potentials between the three bonds of H 3 + ${{H}_{3}^{+}}$ and the He atom. All parameters of this new PES have been chosen and fitted from data obtained from high-level ab-initio calculations. Using this new PES plus the Aziz-Slaman potential for the interaction between Helium atoms and assuming pair-wise interactions, we carry out classical Basin-Hopping (BH) global optimization, semiclassical BH with Zero Point Energy corrections, and quantum Diffusion Monte Carlo simulations. We have found the minimum energy configurations of small He clusters doped with H 3 + ${{H}_{3}^{+}}$ , H 3 + H e N ${{H}_{3}^{+}{\left(He\right)}_{N}}$ , with N=1-16. The study of the energies of these clusters allows us to find a pronounced anomaly for N=12, in perfect agreement with previous experimental findings, which we relate to a greater relative stability of this aggregate.

Ar+ ArH+ Reactive Collisions of Astrophysical Interest: The Case of 36 Ar.

The reactive collision between 36 Ar and the 36 ArH+ species has been investigated by means of quantum mechanical (QM), quasiclassical trajectories (QCT) and statistical quantum mechanical (SQM) approaches. Reaction probabilities, cross sections as a function of the energy and rate constants in terms of the temperature have been obtained. Cumulative distributions as a function of the collision time and the inspection of selected QCT corresponding to specific dynamical mechanisms have been analysed. Predictions by means of the SQM method are in good agreement with the QM results, thus supporting the complex-forming nature of the process.

Correction: Helium nanodroplets as an efficient tool to investigate hydrogen attachment to alkali cations.

Correction for 'Helium nanodroplets as an efficient tool to investigate hydrogen attachment to alkali cations' by Siegfried Kollotzek et al., Phys. Chem. Chem. Phys., 2023, 25, 462-470, https://doi.org/10.1039/D2CP03841B.

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.

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.

A statistical investigation of the rate constants for the H+ + HD reaction at temperatures of astrophysical interest.

The H+ + HD(v, j) reaction has been investigated in detail by means of a statistical quantum method. State-to-state cross sections and rate constants for transitions between reactants and rovibrational states HD(v', j') of the product arrangement with energies below 0.9 eV collision energy [that is, HD(v = 0, j = 0-11) and HD(v = 1, j = 0-6)] have been calculated. For the other product channel, D+ + H2(v', j'), rovibrational states up to (v' = 0, j' = 9) have been considered for the calculation of the corresponding thermal rate. Present predictions are compared with previously reported theoretical and experimental rates. Finally, cooling functions for HD due to proton and atomic hydrogen collisions are computed in the low-density regime. We find that the much larger HD-H+ cooling function, as compared with that of HD-H, does not compensate for the low H+/H abundance ratio in astrophysical media so that HD cooling is dominated by HD-H (or HD-H2) collisions.

Helium structures around SF5+ and SF6+: novel intermolecular potential and mass spectrometry experiments.

Helium clusters around the recently experimentally observed sulphur hexafluoride SF6+ and sulphur pentafluoride SF5+ ions are investigated using a combined experimental and theoretical effort. Mass spectrometry ion yields are obtained and the energetics and structure of the corresponding HeN-SF6+ and HeN-SF5+ clusters are analyzed using path integral molecular dynamics calculations as a function of N, the number of He atoms, employing a new intermolecular potential describing the interaction between the dopant and the surrounding helium. The new force field is optimized on benchmark potential energy ab initio calculations and represented by improved Lennard-Jonnes analytical expressions. This procedure improves the previous potentials employed in similar simulations for neutral SF6 attached to helium nanodroplets. The theoretical analysis explains the characteristic features observed in the experimental ion yields which suggest the existence of stable configurations at specific sizes.

Atom-Diatom Reactive Scattering Collisions in Protonated Rare Gas Systems.

The study of the dynamics of atom-diatom reactions involving two rare gas (Rg) atoms and protons is of crucial importance given the astrophysical relevance of these processes. In a series of previous studies, we have been investigating a number of such Rg(1)+ Rg(2)H+→ Rg(2)+ Rg(1)H+ reactions by means of different numerical approaches. These investigations comprised the construction of accurate potential energy surfaces by means of ab initio calculations. In this work, we review the state-of-art of the study of these protonated Rg systems making special emphasis on the most relevant features regarding the dynamical mechanisms which govern these reactive collisions. The aim of this work therefore is to provide an as complete as possible description of the existing information regarding these processes.

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.

Rate constants for the H+ + H2 reaction from 5 K to 3000 K with a statistical quantum method.

An exhaustive investigation of state-to-state H+ + H2(v, j) → H+ + H2(v', j') transitions for rovibrational levels of molecular hydrogen below 1.3 eV from the bottom of the H2 well is carried out by means of a statistical quantum method, which assumes the complex-forming nature of the process. Integral cross sections for transitions involving states H2(v = 0, j = 0-12), H2(v = 1, j = 0-8), and H2(v = 2, j = 0-3) are obtained for collision energies within a range of Emin = 10-5 eV and Emax = 2 eV. Rate constants are then calculated between T = 5 K and 3000 K, and they are compared, when possible, with previous values reported in the literature. As a first application, the cooling rate coefficient of H2 excited by protons is determined and compared with a recent estimate.

Experimental and theoretical studies of the N(2D) + H2 and D2 reactions.

This study reports the results of an experimental and theoretical investigation of the N(2D) + H2 and N(2D) + D2 reactions at room temperature and below. On the experimental side, a supersonic flow (Laval nozzle) reactor was employed to measure rate constants for these processes at temperatures as low as 127 K. N(2D) was produced indirectly by pulsed laser photolysis and these atoms were detected directly by pulsed laser induced fluorescence in the vacuum ultraviolet wavelength region. On the theoretical side, two different approaches were used to calculate rate constants for these reactions; a statistical quantum mechanical (SQM) method and a quasi-classical trajectory capture model including a semi-classical correction for tunneling (SC-Capture). This work is described in the context of previous studies, while the discrepancies between both experiment and theory, as well as between the theoretical results themselves are discussed.

Dynamics of H + HeH+(v = 0, j = 0) → H2+ + He: Insight on the Possible Complex-Forming Behavior of the Reaction.

The H + HeH+→ He + H2+ reaction has been studied by means of a combination of theoretical approaches: a statistical quantum method (SQM), ring polymer molecular dynamics (RPMD), and the quasiclassical trajectory (QCT) method. Cross sections and rate constants have been calculated in an attempt to investigate the dynamics of the process. The comparison with previous calculations and experimental results reveals that despite the fact that statistical predictions seem to reproduce some of the overall observed features, the analysis at a more detailed state-to-state level shows noticeable deviations from a complex-forming dynamics. We find some differences in cross sections and rate constants obtained in the QCT calculation with a Gaussian binning procedure with respect to previous works in which the standard histogram binning was employed.

Complexes of Alkali Metal Cations and Molecular Hydrogen: Potential Energy Surfaces and Bound States.

Complexes between metal cations and molecular hydrogen are systems quite amenable for precise spectroscopic and theoretical studies, and at the same time, they are relevant for applications in hydrogen storage and astrochemistry. In this work, we report new intermolecular potential energy surfaces and rovibrational states calculations for complexes involving molecular hydrogen and alkaline metal cations, M+-H2 (M+ = Na+, K+, Rb+, Cs+). The intermolecular potentials, formulated in an internally consistent way to emphasize differences in the properties of the systems, are represented by simple analytical expressions whose parameters have been optimized from comparison with accurate ab initio calculations. Properties of the low-lying bound states-binding energies, frequencies, and rotational constants-are compared with previous measurements or computations and an overall good agreement is achieved, supporting the reliability of the present formulation. Variations of these properties as a function of the cation size and isotopic substitution, with a proper sequence of ortho and para rotational levels, are also discussed.

Experimental and Theoretical Study of the O(1D) + HD Reaction.

This work addresses the kinetics and dynamics of the gas-phase reaction between O(1D) and HD molecules down to low temperature. Here, measurements were performed by using a supersonic flow (Laval nozzle) reactor coupled with pulsed laser photolysis for O(1D) production and pulsed-laser-induced fluorescence for O(1D) detection to obtain rate constants over the 50-300 K range. Additionally, temperature-dependent branching ratios (OD + H/OH + D) were obtained experimentally by comparison of the H/D atom atom yields with those of a reference reaction. In parallel, theoretical rate constants and branching ratios were calculated by using three different techniques; mean potential phase space theory (MPPST), the statistical quantum mechanical method (SQM), and ring polymer molecular dynamics (RPMD). Although the agreement between experimental and theoretical rate constants is reasonably good, with differences not exceeding 30% over the entire temperature range, the theoretical branching ratios derived by the MPPST and SQM methods are as much as 50% larger than the experimental ones. These results are presented in the context of earlier work, while the possible origins of the discrepancies between experiment and theory are discussed.

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.

The dynamics of the C(1D)+H2/D2/HD reactions at low temperature.

We present results of a theoretical investigation on the dynamics of the C(1D)+H2 reaction and the corresponding isotopic variants in which the carbon atom collides either with D2 or HD. Statistical techniques have been tested in comparison with the recent experimental information at low temperature (T < 300 K) and exact quantum mechanical calculations reported on the title reactions in an attempt to establish their possible complex-forming character. Our study includes the calculation of probabilities, rotational distributions, integral cross sections, differential cross sections, and rate constants. Previous quantum mechanical results have been extended here to complete the analysis of the underlying mechanisms which govern the collision process.

A combined theoretical and experimental investigation of the kinetics and dynamics of the O(1D) + D2 reaction at low temperature.

The O(1D) + H2 reaction is a prototype for simple atom-diatom insertion type mechanisms considered to involve deep potential wells. While exact quantum mechanical methods can be applied to describe the dynamics, such calculations are challenging given the numerous bound quantum states involved. Consequently, efforts have been made to develop alternative theoretical strategies to portray accurately the reactive process. Here we report an experimental and theoretical investigation of the O(1D) + D2 reaction over the 50-296 K range. The calculations employ three conceptually different approaches - mean potential phase space theory, the statistical quantum mechanical method and ring polymer molecular dynamics. The calculated rate constants are in excellent agreement over the entire temperature range, exhibiting only weak temperature dependence. The agreement between experiment and theory is also very good, with discrepancies smaller than 26%. Taken together, the present and previous theoretical results validate the hypothesis that long-lived complex formation dominates the reaction dynamics at low temperature.