Improved Quantum-Classical Treatment of N2-N2 Inelastic Collisions: Effect of the Potentials and Complete Rate Coefficient Data Sets.

In this study, complete (i.e., including all vibrational quantum numbers in an N2 vibrational ladder) data sets of vibration-to-vibration and vibration-to-translation rate coefficients for N2-N2 collisions are explicitly computed along with transport properties (shear and bulk viscosity, thermal conductivity, and self-diffusion) in the temperature range 100-9000 K. To reach this goal, we improved a mixed quantum-classical (MQC) dynamics approach by lifting the constraint of a Morse treatment of the vibrational wave function and intramolecular potential and permitting the use of more realistic and flexible representations. The new formulation has also allowed us to separately analyze the role of intra- and intermolecular potentials on the calculated rates and properties. Ab initio intramolecular potentials are indispensable for highly excited vibrational states, though the Morse potential still gives reasonable values up to v = 20. An accurate description of the long-range interaction and the van der Waals well is a requisite for the correct reproduction of qualitative and quantitative rate coefficients, particularly at low temperatures, making physically meaningful analytical representations still the best choice compared to currently available ab initio potential energy surfaces. These settings were used to directly compute the MQC rates corresponding to a large number of initial vibrational quantum numbers, and the missing intermediate values were predicted using a machine learning technique (i.e., the Gaussian process regression approach). The obtained values are reliable in the wide temperature range employed and are therefore valuable data for many communities dealing with nonlocal thermal equilibrium conditions in different environments.

Attachment of Hydrogen Molecules to Atomic Ions (Na+ , Cl- ): Examination of an Adiabatic Separation of the H2 Rotational Motion.

Interactions between molecular hydrogen and ions are of interest in cluster science, astrochemistry and hydrogen storage. In dynamical simulations, H2 molecules are usually modelled as point particles, an approximation that can fail for anisotropic interactions. Here, we apply an adiabatic separation of the H2 rotational motion to build effective pseudoatom-ion potentials and in turn study the properties of (H2 )n Na+ /Cl- clusters. These interaction potentials are based on high-level ab initio calculations and Improved Lennard-Jones parametrizations, while the subsequent dynamics has been performed by quantum Monte Carlo calculations. By comparisons with simulations explicitly describing the molecular rotations, it is concluded that the present adiabatic model is very adequate. Interestingly, we find differences in the cluster stabilities and coordination shells depending on the spin isomer considered (para- or ortho-H2 ), especially for the anionic clusters.

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.

Graphene as Nanocarrier for Gold(I)-Monocarbene Complexes: Strength and Nature of Physisorption.

Gold(I) metal complexes are finding increasing applications as therapeutic agents against a variety of diseases. As their potential use as effective metallodrugs is continuously confirmed, the issue of their administration, distribution and delivery to desired biological targets emerges. Graphene and its derivatives possess attractive properties in terms of high affinity and low toxicity, suggesting that they can efficaciously be used as drug nanocarriers. In the present study, we computationally address the adsorption of a gold(I) N-heterocyclic monocarbene, namely, IMeAuCl (where IMe = 1,3-dimethylimidazol-2-ylidene), on graphene. The Au(I) N-heterocyclic carbene family has indeed shown promising anticancer activity and the N-heterocyclic ring could easily interact with planar graphene nanostructures. By means of high-level electronic structure approaches, we investigated the strength and nature of the involved interaction using small graphene prototypes, which allow us to benchmark the best-performing DFT functionals as well as assess the role of the different contributions to total interaction energies. Moreover, realistic adsorption enthalpies and free energy values are obtained by exploiting the optimal DFT method to describe the drug adsorption on larger graphene models. Such values (ΔHads = -18.4 kcal/mol and ΔGads= -7.20 kcal/mol for the largest C150H30 model) indicate a very favorable adsorption, mainly arising from the dispersion component of the interaction, with the electrostatic attraction also playing a non-negligible role.

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.

Multilayer Graphtriyne Membranes for Separation and Storage of CO2: Molecular Dynamics Simulations of Post-Combustion Model Mixtures.

The ability to remove carbon dioxide from gaseous mixtures is a necessary step toward the reduction of greenhouse gas emissions. As a contribution to this field of research, we performed a molecular dynamics study assessing the separation and adsorption properties of multi-layered graphtriyne membranes on gaseous mixtures of CO2, N2, and H2O. These mixtures closely resemble post-combustion gaseous products and are, therefore, suitable prototypes with which to model possible technological applications in the field of CO2 removal methodologies. The molecular dynamics simulations rely on a fairly accurate description of involved force fields, providing reliable predictions of selectivity and adsorption coefficients. The characterization of the interplay between molecules and membrane structure also permitted us to elucidate the adsorption and crossing processes at an atomistic level of detail. The work is intended as a continuation and a strong enhancement of the modeling research and characterization of such materials as molecular sieves for CO2 storage and removal.

Molecular hydrogen isotope separation by a graphdiyne membrane: a quantum-mechanical study.

Graphdiyne (GDY) has emerged as a very promising two-dimensional (2D) membrane for gas separation technologies. One of the most challenging goals is the separation of deuterium (D2) and tritium (T2) from a mixture with the most abundant hydrogen isotope, H2, an achievement that would be of great value for a number of industrial and scientific applications. In this work we study the separation of hydrogen isotopes in their transport through a GDY membrane due to mass-dependent quantum effects that are enhanced by the confinement provided by its intrinsic sub-nanometric pores. A reliable improved Lennard-Jones force field, optimized on accurate ab initio calculations, has been built to describe the molecule-membrane interaction, where the molecule is treated as a pseudoatom. The quantum dynamics of the molecules impacting on the membrane along a complete set of incidence directions have been rigorously addressed by means of wave packet calculations in the 3D space, which have allowed us to obtain transmission probabilities and, in turn, permeances, as the thermal average of the molecular flux per unit pressure. The effect of the different incidence directions on the probabilities is analyzed in detail and it is concluded that restricting the simulations to a perpendicular incidence leads to reasonable results. Moreover, it is found that a simple 1D model-using a zero-point energy-corrected interaction potential-provides an excellent agreement with the 3D probailities for perpendicular incidence conditions. Finally, D2/H2 and T2/H2 selectivities are found to reach maximum values of about 6 and 21 at ≈50 and 45 K, respectively, a feature due to a balance between zero-point energy and tunneling effects in the transport dynamics. Permeances at these temperatures are below recommended values for practical applications, however, at slightly higher temperatures (77 K) they become acceptable while the selectivities preserve promising values, particularly for the separation of tritium.

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.

Vibrational Energy Transfer in CO+N2 Collisions: A Database for V-V and V-T/R Quantum-Classical Rate Coefficients.

Knowledge of energy exchange rate constants in inelastic collisions is critically required for accurate characterization and simulation of several processes in gaseous environments, including planetary atmospheres, plasma, combustion, etc. Determination of these rate constants requires accurate potential energy surfaces (PESs) that describe in detail the full interaction region space and the use of collision dynamics methods capable of including the most relevant quantum effects. In this work, we produce an extensive collection of vibration-to-vibration (V-V) and vibration-to-translation/rotation (V-T/R) energy transfer rate coefficients for collisions between CO and N2 molecules using a mixed quantum-classical method and a recently introduced (A. Lombardi, F. Pirani, M. Bartolomei, C. Coletti, and A. Laganà, Frontiers in chemistry, 7, 309 (2019)) analytical PES, critically revised to improve its performance against ab initio and experimental data of different sources. The present database gives a good agreement with available experimental values of V-V rate coefficients and covers an unprecedented number of transitions and a wide range of temperatures. Furthermore, this is the first database of V-T/R rate coefficients for the title collisions. These processes are shown to often be the most probable ones at high temperatures and/or for highly excited molecules, such conditions being relevant in the modeling of hypersonic flows, plasma, and aerospace applications.

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.

Reconciling experimental and theoretical vibrational deactivation in low-energy O + N2 collisions.

Molecular dynamics calculations of inelastic collisions of atomic oxygen with molecular nitrogen are known to show orders of magnitude discrepancies with experimental results in the range from room temperature to many thousands of degrees Kelvin. In this work, we have achieved an unprecedented quantitative agreement with experiments even at low temperature, by including a non-adiabatic treatment involving vibronic states on newly developed potential energy surfaces. This result paves the way for the calculation of accurate and detailed databases of vibrational energy exchange rates for this collisional system. This is bound to have an impact on air plasma simulations under a wide range of conditions and on the development of Very Low Earth Orbit (VLEO) satellites, operating in the low thermosphere, objects of great technological interest due to their potential at a competitive cost.

An unrestricted approach for the accurate calculation of the intermolecular potential of (O2)4: Implications for the solid epsilon phase.

Oxygen in its elemental form shows a variety of magnetic properties in its condensed phases; in particular, the epsilon solid phase loses its magnetism. These phenomena reflect the nature of the intermolecular forces present in the solid and the changes that arise with variations in pressure and temperature. In this study, we use intermolecular potentials obtained with unrestricted ab initio methods to model the singlet state of the oxygen tetramer [(O2)4], which is the unit cell, consistent with the non-magnetic character of this phase. To do this, we perform an analysis of the coupled-uncoupled representations of the spin operator together with a pairwise approximation and the Heisenberg Hamiltonian. We start from unrestricted potentials for the dimer calculated at a high level as well as different density functional theory (DFT) functionals and then apply a finite model to predict the properties of the epsilon phase. The results obtained in this way reproduce well the experimental data in the entire pressure range below 60 GPa. Additionally, we show the importance of calculating the singlet state of the tetramer as opposed to previous DFT periodic calculations, where the unrestricted description leads to a mixture of spin states and a poor comparison with the experiment. This point is crucial in the recent discussion about the coexistence of two epsilon phases: one where the identity of each O2 with spin S = 1 is retained within the tetramer unit vs another at higher pressures where the tetramer behaves as a single unit with a closed-shell character.

Energy exchange rate coefficients from vibrational inelastic O2(Σg-3) + O2(Σg-3) collisions on a new spin-averaged potential energy surface.

A new spin-averaged potential energy surface (PES) for non-reactive O2(Σg-3) + O2(Σg-3) collisions is presented. The potential is formulated analytically according to the nature of the principal interaction components, with the main van der Waals contribution described through the improved Lennard-Jones model. All the parameters involved in the formulation, having a physical meaning, have been modulated in restricted variation ranges, exploiting a combined analysis of experimental and ab initio reference data. The new PES is shown to be able to reproduce a wealth of different physical properties, ranging from the second virial coefficients to transport properties (shear viscosity and thermal conductivity) and rate coefficients for inelastic scattering collisions. Rate coefficients for the vibrational inelastic processes of O2, including both vibration-to-vibration (V-V) and vibration-to-translation/rotation (V-T/R) energy exchanges, were then calculated on this PES using a mixed quantum-classical method. The effective formulation of the potential and its combination with an efficient, yet accurate, nuclear dynamics treatment allowed for the determination of a large database of V-V and V-T/R energy transfer rate coefficients in a wide temperature range.

Interaction and Reactivity of Cisplatin Physisorbed on Graphene Oxide Nano-Prototypes.

The physical adsorption of cisplatin (CP) on graphene oxide (GO) and reduced graphene oxide (rGO) is investigated at the DFT level of theory by exploiting suitable molecular prototypes representing the most probable adsorbing regions of GO and rGO nano-structures. The results show that the CP binding energy is enhanced with respect to that for the interaction with pristine graphene. This is due to the preferential adsorption of the drug in correspondence of the epoxy and hydroxy groups located on GO basal plane: an energy decomposition analysis of the corresponding binding energy reveals that the most attractive contribution comes from the electrostatic attraction between the -NH 3 ends of CP and the oxygen groups on (r)GO, which can be associated with hydrogen bonding effects. Moreover, it is found that the reactivity of the physically adsorbed CP is practically unaltered being the free energy variation of the first hydrolysis reaction almost matching that of its free (unadsorbed drug) counterpart. The reported results suggest that the CP physical adsorption on GO and rGO carriers is overall feasible being an exergonic process in aqueous solution. The CP adsorption could facilitate its solubility and transport in water solutions, exploiting the high hydrophilicity of the peripheral carboxylic groups located on the edge of the GO and rGO nano-structures. Moreover, the the higher affinity of CP with respect to the oxidized sites suggests a possible dependence of drug loading and release on pH conditions, which would highly facilitate its specific delivery.

An unrestricted approach for the accurate calculation of the interaction potentials of open-shell monomers: The case of O2-O2.

The properties of molecular oxygen including its condensed phases continue to be of great relevance for the scientific community. The richness and complexity of its associated properties stem from the fact that it is a very stable diradical. Its open-shell nature leads to low-lying multiplets with total electronic spin S = 0, 1, 2 in the case of the dimer, (O2)2, and the accurate calculation of the intermolecular potentials represents a challenge to ab initio electronic structure methods. In this work, we present intermolecular potentials calculated at a very high level, thus competing with the most accurate restricted potentials obtained to date. This is accomplished by drawing on an analogy between the coupled and uncoupled representations of angular momentum and restricted vs unrestricted methodologies. The S = 2 state can be well represented by unrestricted calculations in which the spins of the unpaired electrons are aligned in parallel; however, for the state where they are aligned in antiparallel fashion, it would seem that the total spin is not well defined, i.e., the well-known spin contamination problem. We show that its energy corresponds to that of the S = 1 state and perform unrestricted coupled cluster calculations for these two states. Then, we obtain the S = 0 state through the Heisenberg Hamiltonian and show that this is very reliable in the well region of the potentials. We make extensive comparisons with the best restricted potentials [Bartolomei et al., Phys. Chem. Chem. Phys. 10(35), 5374-5380 (2008)] and with reliable experimental determinations, and a very good agreement is globally found.

Inelastic rate coefficients based on an improved potential energy surface for N2 + N2 collisions in a wide temperature range.

A modification in the potential energy surface (PES) for N2-N2 interactions, reported in the literature [D. Cappelletti et al., Phys. Chem. Chem. Phys., 2008, 10, 4281], has been presented to improve its description of, particularly, the short range behavior for specific configurations, with the aim of producing a large database of vibration to vibration (V-V) and vibration to translation/rotation (V-T/R) energy transfer rate coefficients, with an increased accuracy extended to large temperature ranges relevant to the modeling of hypersonic gas flows. The modifications were introduced in a physically meaningful fashion and they are shown to improve the performance of the PES in a wide temperature range, not only for calculating rate coefficients, but also for determining a variety of physical properties. This new PES was then used to calculate V-V and V-T/R rate coefficients for inelastic N2-N2 collisions through a mixed quantum-classical method, based on the quantum treatment of molecular vibrations, for vibrationally excited states up to v = 40. Such a large V-T/R coefficient database is quite unprecedented, and the comparison of the efficiency of the related processes with the corresponding V-V coefficients shows that vibrational relaxation plays a very relevant role in high temperature regimes.

Helium Isotopes Quantum Sieving through Graphtriyne Membranes.

We report accurate quantum calculations of the sieving of Helium atoms by two-dimensional (2D) graphtriyne layers with a new interaction potential. Thermal rate constants and permeances in an ample temperature range are computed and compared for both Helium isotopes. With a pore larger than graphdiyne, the most common member of the γ-graphyne family, it could be expected that the appearance of quantum effects were more limited. We find, however, a strong quantum behavior that can be attributed to the presence of selective adsorption resonances, with a pronounced effect in the low temperature regime. This effect leads to the appearance of some selectivity at very low temperatures and the possibility for the heavier isotope to cross the membrane more efficiently than the lighter, contrarily to what happened with graphdiyne membranes, where the sieving at low energy is predominantly ruled by quantum tunneling. The use of more approximate methods could be not advisable in these situations and prototypical transition state theory treatments might lead to large errors.

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.

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.