Path integral Monte Carlo investigations on doped helium clusters

Path Integral Monte Carlo Simulation on Molecular Systems with Multiple Electronic Degrees of Freedom

We present an imaginary time path-integral formalism for molecular systems including nuclear and electronic degrees of freedom based on the previous work of [Schmidt, J. R.; Tully, J. C. J. Chem. Phys. 2007, 127, 094103]. To sample the resulting path integral expression efficiently, a path integral Monte Carlo scheme is proposed, allowing the computation of finite temperature equilibrium properties of molecular systems including multiple low-lying electronic states directly from ab initio potential energy surfaces. Finally, we show how this generalized approach in combination with the Monte Carlo scheme can reproduce exact results for a simple model system including nonadiabatic couplings as well as thermodynamic equilibrium properties of H2 and C2. Our implementation of the algorithm is available as an open-source code.

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.

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 He_NCa²⁺ 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 Path Integral Molecular Dynamics Simulation of a Harpoon-Type Redox Reaction in a Helium Nanodroplet

We present path integral molecular dynamics (PIMD) calculations of an electron transfer from a heliophobic Cs2 dimer in its (3Σu) state, located on the surface of a He droplet, to a heliophilic, fully immersed C60 molecule. Supported by electron ionization mass spectroscopy measurements (Renzler et al., J. Chem. Phys.2016, 145, 181101), this spatially quenched reaction was characterized as a harpoon-type or long-range electron transfer in a previous high-level ab initio study (de Lara-Castells et al., J. Phys. Chem. Lett.2017, 8, 4284). To go beyond the static approach, classical and quantum PIMD simulations are performed at 2 K, slightly below the critical temperature for helium superfluidity (2.172 K). Calculations are executed in the NVT ensemble as well as the NVE ensemble to provide insights into real-time dynamics. A droplet size of 2090 atoms is assumed to study the impact of spatial hindrance on reactivity. By changing the number of beads in the PIMD simulations, the impact of quantization can be studied in greater detail and without an implicit assumption of superfluidity. We find that the reaction probability increases with higher levels of quantization. Our findings confirm earlier, static predictions of a rotational motion of the Cs2 dimer upon reacting with the fullerene, involving a substantial displacement of helium. However, it also raises the new question of whether the interacting species are driven out-of-equilibrium after impurity uptake, since reactivity is strongly quenched if a full thermal equilibration is assumed. More generally, our work points towards a novel mechanism for long-range electron transfer through an interplay between nuclear quantum delocalization within the confining medium and delocalized electronic dispersion forces acting on the two reactants.

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.

Modelling interactions of cationic dimers in He droplets: microsolvation trends in HenK2+ clusters

We report the results of a detailed theoretical investigation of small K₂⁺-doped He clusters. The structural characteristics and stabilities of such cations are determined from ab initio electronic structure calculations at the MRCI+Q level of theory. The underlying interactions show a multireference character and such effects are analyzed. The interaction potentials are constructed employing an interpolation technique within the inverse problem theory method, while the nuclear quantum effects are computed for the trimers, their spatial arrangements are discussed, and information was extracted on the orientational anisotropy of the forces. We found that energetically the most stable conformer corresponds to linear arrangements that are taking place under large amplitude vibrations, with high zero-point energy. We have further looked into the behavior of higher-order species with various He atoms surrounding the cationic dopant. By using a sum of potentials approach and an evolutionary programming method, we analyzed the structural stability of clusters with up to six He atoms in comparison with interactions energies obtained from MRCI+Q quantum chemistry computations. Structures containing He_n motifs that characterize pure rare gas clusters, appear for the larger K₂⁺-doped He clusters, showing selective growth during the microsolvation process of the alkali-dimer cation surrounded by He atoms. Such results indicate the existence of local solvation microstructures in these aggregates, where the cationic impurity could get trapped for a short time, contributing to the slow ionic mobility observed experimentally in ultra-cold He-droplets.

Quantum effects on the stability of the He5 I2 van der Waals conformers

We present 15-dimensional quantum multiconfiguration time-dependent Hartree calculations of the vibrational levels of the He₅ I₂ van der Waals (vdW) complex employing an ab initio-based potential energy surface (PES). The energies and spatial features of such bound structures are analyzed, providing predictions on the structures and relative stabilities of its three lowest isomers. We found that the most stable isomer corresponds to all five He atoms encircling the I₂ molecule, indicating that in this case the anharmonic quantum effects do not stabilize the isomers involving a He atom in a linear configuration as reported previously for the smaller He_N I₂ systems. Such finding provides information on the overall structuring of the finite-size-solvent systems, highlighting the intriguing interplay between weak intermolecular interactions and quantum effects. © 2019 Wiley Periodicals, Inc.

Theoretical Study of Cationic Alkali Dimers Interacting with He: Li2+-He and Na2+-He van der Waals Complexes

We present a theoretical study on the potential energy surface and bound states of He-A₂⁺ complexes, where A is one of the alkali Li or Na atoms. The intermolecular interactions were systematically investigated by high-level ab initio electronic structure computations, and the corresponding raw data were then employed to reproduce accurate analytical expressions of the potential surfaces. In turn, we used these potentials to evaluate bound configurations of the trimers from nuclear quantum calculations and to extract information on the effect of orientational anisotropy of the forces and the interplay between repulsive and attractive interaction within the potential surfaces. The spatial features of the bound states are analyzed and discussed in detail. We found that both systems are going under large amplitude stretching and bending motions with high zero-point energies. Despite the large differences in the potential well-depths, the correct treatment of nuclear quantum effects provides insights on the effect of different strength of the ionic interaction on the spectral structure of such cationic alkali van der Waals complexes, related to the mobility of ions and the formation of cold-molecules in He-controlled environments.

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, He_NCs⁺, 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⁺.

Diagrammatic Monte Carlo Approach to Angular Momentum in Quantum Many-Particle Systems

We introduce a diagrammatic Monte Carlo approach to angular momentum properties of quantum many-particle systems possessing a macroscopic number of degrees of freedom. The treatment is based on a diagrammatic expansion that merges the usual Feynman diagrams with the angular momentum diagrams known from atomic and nuclear structure theory, thereby incorporating the non-Abelian algebra inherent to quantum rotations. Our approach is applicable at arbitrary coupling, is free of systematic errors and of finite-size effects, and naturally provides access to the impurity Green function. We exemplify the technique by obtaining an all-coupling solution of the angulon model; however, the method is quite general and can be applied to a broad variety of systems in which particles exchange quantum angular momentum with their many-body environment.

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.

Quasiparticle Approach to Molecules Interacting with Quantum Solvents

Understanding the behavior of molecules interacting with superfluid helium represents a formidable challenge and, in general, requires approaches relying on large-scale numerical simulations. Here, we demonstrate that experimental data collected over the last 20 years provide evidence that molecules immersed in superfluid helium form recently predicted angulon quasiparticles [Phys. Rev. Lett. 114, 203001 (2015)PRLTAO0031-900710.1103/PhysRevLett.114.203001]. Most important, casting the many-body problem in terms of angulons amounts to a drastic simplification and yields effective molecular moments of inertia as straightforward analytic solutions of a simple microscopic Hamiltonian. The outcome of the angulon theory is in good agreement with experiment for a broad range of molecular impurities, from heavy to medium-mass to light species. These results pave the way to understanding molecular rotation in liquid and crystalline phases in terms of the angulon quasiparticle.