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Virus particles consist of a protein coat that protects their genetic material and delivers it to the host cell for self-replication. Understanding the interplay between virus structure and function is a requirement for understanding critical processes in the infectious cycle such as entry, uncoating, genome metabolism, capsid assembly, maturation, and propagation. Together with well-established techniques in cell and molecular biology, physical virology has emerged as a rapidly developing field, providing detailed, novel information on the basic principles of virus assembly, disassembly, and dynamics. The Spanish research community contains a good number of groups that apply their knowledge on biology, physics, or chemistry to the study of viruses. Some of these groups got together in 2010 under the umbrella of the Spanish Interdisciplinary Network on Virus Biophysics (BioFiViNet). Thirteen years later, the network remains a fertile ground for interdisciplinary collaborations geared to reveal new aspects on the physical properties of virus particles, their role in regulating the infectious cycle, and their exploitation for the development of virus-based nanotechnology tools. Here, we highlight some achievements of Spanish groups in the field of physical virology.

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 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.

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.

We present a new analytical potential energy surface (PES) for the interaction between the trihydrogen cation and a He atom, H3+-He${{H}_{3}^{+}-He}$ , 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 H3+${{H}_{3}^{+}}$ 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 H3+${{H}_{3}^{+}}$ , H3+HeN${{H}_{3}^{+}{\left(He\right)}_{N}}$ , 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.

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.

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+.

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.

We study the growth of rare gases (Rg) Ne, Ar and Kr on coronene (Cor) molecules, Cor-(Rg). The study is taken up to sizes N=60, and we show the global energy minima for those clusters. Improved Lennard-Jones and atom-bond potentials are used to represent the Rg-Rg and Rg-Cor interactions, respectively. The Basin-Hopping (BH) global optimization technique is employed to locate the putative global energy minimum structures. Results are presented for Cor-(Ne), Cor-(Ar) and Cor-(Kr) systems. Both classical Cor-(Ar) and Cor-(Kr) clusters present the same “magic numbers” for N=3, 6, 10, 14, 19 and 38. This last number marks the first layer of solvation. For Cor-(Ne) clusters, we consider quantum effects adding the zero-point energy (ZPE) into the classical potential energy minima (BH-ZPE). This semiclassical approximation is compared with quantum diffusion Monte Carlo (DMC) calculations up to N=20, obtaining a good agreement and showing that this approximation works reasonably well. In this BH-ZPE approach, high stability configurations for Cor-(Ne) clusters are obtained at N=6, 14, 42, 51 and 57. However, we have not found any evidence of a first solvation layer using either the semiclassical BH-ZPE or the classical BH one.

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 finetuned 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

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.

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. Published by AIP Publishing.

Benchmark interaction energies between coronene, CH, and molecular hydrogen, H, 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 H-CH 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 H-coronene interaction. The structure and binding energies of (para-H)-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)-coronene aggregates have been discussed.

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. © XXXX American Chemical Society