Virtual indentation of the empty capsid of the minute virus of mice using a minimal coarse-grained model.

A minimal coarse-grained model for T=1 viral capsids assembled from 20 protein rigid trimers has been designed by extending a previously proposed form of the interaction energy written as a sum of anisotropic pairwise interactions between the trimeric capsomers. The extension of the model has been performed to properly account for the coupling between two internal coordinates: the one that measures the intercapsomer distance and the other that gives the intercapsomer dihedral angle. The model has been able to fit with less than a 10% error the atomic force microscopy (AFM) indentation experimental data for the empty capsid of the minute virus of mice (MVM), providing in this way an admissible picture of the main mechanisms behind the capsid deformations. In this scenario, the bending of the intercapsomer dihedral angle is the angular internal coordinate that can support larger deformations away from its equilibrium values, determining important features of the AFM indentation experiments as the elastic constants along the three symmetry axes of the capsid and the critical indentations. From the value of one of the parameters of our model, we conclude that trimers in the MVM must be quite oblate tops, in excellent agreement with their known structure. The transition from the linear to the nonlinear regimes sampled in the indentation process appears to be an interesting topic for future research in physical virology.

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.

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.

Many-Body Contributions in Water Nanoclusters.

Many-body interactions in water are known to be important but difficult to treat in atomistic models and often are included only as a correction. Polarizable models treat them explicitly, with long-range many-body potentials, within their classical approximation. However, their calculation is computationally expensive. Here, we evaluate how relevant the contributions to the many-body interaction associated with different coordination shells are. We calculate the global energy minimum, and the corresponding configuration, for nanoclusters of up to 20 water molecules. We find that including the first coordination shell, i.e., the five-body term of the central molecule, is enough to approximate within 5% the global energy minimum and its structure. We show that this result is valid for three different polarizable models, the Dang-Chang, the MB-pol, and the Kozack-Jordan potentials. This result suggests a strategy to develop many-body potentials for water that are reliable and, at the same time, computationally efficient.

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.

Minimal Design Principles for Icosahedral Virus Capsids.

The geometrical structures of single- and multiple-shell icosahedral virus capsids are reproduced as the targets that minimize the cost corresponding to relatively simple design functions. Capsid subunits are first identified as building blocks at a given coarse-grained scale and then represented in these functions as point particles located on an appropriate number of concentric spherical surfaces. Minimal design cost is assigned to optimal spherical packings of the particles. The cost functions are inspired by the packings favored for the Thomson problem, which minimize the electrostatic potential energy between identical charged particles. In some cases, icosahedral symmetry constraints are incorporated as external fields acting on the particles. The simplest cost functions can be obtained by separating particles in disjoint nonequivalent sets with distinct interactions, or by introducing interacting holes (the absence of particles). These functions can be adapted to reproduce any capsid structure found in real viruses. Structures absent in Nature require significantly more complex designs. Measures of information content and complexity are assigned to both the cost functions and the capsid geometries. In terms of these measures, icosahedral structures and the corresponding cost functions are the simplest solutions.

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.

The Structure of Adamantane Clusters: Atomistic vs. Coarse-Grained Predictions From Global Optimization.

Candidate structures for the global minima of adamantane clusters, (C10H16) N , are presented. Based on a rigid model for individual molecules with atom-atom pairwise interactions that include Lennard-Jones and Coulomb contributions, low-energy structures were obtained up to N = 42 using the basin-hopping method. The results indicate that adamantane clusters initially grow accordingly with an icosahedral packing scheme, followed above N = 14 by a structural transition toward face-centered cubic structures. The special stabilities obtained at N = 13, 19, and 38 are consistent with these two structural families, and agree with recent mass spectrometry measurements on cationic adamantane clusters. Coarse-graining the intermolecular potential by averaging over all possible orientations only partially confirm the all-atom results, the magic numbers at 13 and 38 being preserved. However, the details near the structural transition are not captured well, because despite their high symmetry the adamantane molecules are still rather anisotropic.

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.

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.

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.

Applicability of Quantum Thermal Baths to Complex Many-Body Systems with Various Degrees of Anharmonicity.

The semiclassical method of quantum thermal baths by colored noise thermostats has been used to simulate various atomic systems in the molecular and bulk limits, at finite temperature and in moderately to strongly anharmonic regimes. In all cases, the method performs relatively well against alternative approaches in predicting correct energetic properties, including in the presence of phase changes, provided that vibrational delocalization is not too strong-neon appearing already as an upper limiting case. In contrast, the dynamical behavior inferred from global indicators such as the root-mean-square bond length fluctuation index or the vibrational spectrum reveals more marked differences caused by zero-point energy leakage, except in the case of isolated molecules with well separated vibrational modes. To correct for such deficiencies and reduce the undesired transfer among modes, empirical modifications of the noise power spectral density were attempted to better describe thermal equilibrium but still failed when used as semiclassical preparation for microcanonical trajectories.

Energy landscapes for shells assembled from pentagonal and hexagonal pyramids.

We present new rigid body potentials that should favour efficient self-assembly of pentagonal and hexagonal pyramids into icosahedral shells over a wide range of temperature. By adding an extra repulsive site opposite the existing apex sites of the pyramids considered in a previously published model, frustrated energy landscapes are transformed into systems identified with self-assembling properties. The extra interaction may be considered analogous to a hydrophobic-hydrophilic repulsion, as in micelle formation.

Energy landscapes for water clusters in a uniform electric field.

The behavior of small water clusters, (H2O)n, n=2-5 and n=8, in a uniform electric field is investigated for three related rigid-body models. Changes in the properties of the low-lying potential energy minima and the rearrangement pathways between them are examined. Results for certain structural transitions are compared with recent ab initio calculations. The models are found to give qualitatively similar trends, and there is some evidence that as the applied field strength is increased the quantitative differences between the models are also reduced.

Thermodynamics of water octamer in a uniform electric field.

We study the water octamer in a uniform electric field using the all-exchanges parallel tempering Monte Carlo method in the canonical ensemble. The heat capacity, quenched energy configurations, and the order parameter Q(4) are employed to understand the phase changes observed as a function of temperature and the strength of the applied electric field. At a low field strength of 0.1 V A(-1) a solidlike to liquidlike "melting" transition is detected. The corresponding heat capacity peak appears around 206 K, where Q(4) shows a significant change of slope. For E> or =0.5 V A(-1) such features are absent. However, at E=0.5 V A(-1) we find a solidlike to solidlike transition between cubic and extended structures around T approximately 25 K.