Spectroscopy of K[sup +]⋅Rg and transport coefficients of K[sup +] in Rg (Rg=He–Rn)

Structures and stability of K+ cation solvated in Arn clusters

The solvation of K+ cation plays an important role in various phenomena such as biological procedures, geological time, and archaeological properties. Monte Carlo (MC) simulation and DFT method are employed to study the structural and energetic characteristics of the K + Arn (n = 1-14) clusters. The potential model (PM) and the Basin-Hopping (BH) method are the foundation of the MC simulation. The pairwise PM (PW-PM) is improved by introducing the N-body interactions via the polarizable potential model (PPM). On the other side, the DFT functional M05-2X, combined with the 6-311++G(3d2f,2p) basis set, and the Grimme dispersion correction GD3 was used to deeply investigate the geometrical properties and the relative stability of the K + Arn clusters. Starting from n = 12, a structural transition from square antiprism (SA) to icosahedron (ICOS) form is detected. Additionally, the PPM allows us to examine the largest sizes (n = 15-54). Herein, the first ICOS layers are found for n = 12 and 54 cluster sizes, respectively. The binding energy and the second energy difference as a function of cluster size are used to evaluate the relative stability of K + Arn clusters. The obtained data are in concordance with the available results in the literature.

Structure, energetics, and spectroscopy of the K2+(X2Σ+g) interacting with the noble gas atoms Ar, Kr and Xe

The structure, energetic, and spectroscopy properties of the ionic system K₂⁺(X²Σ⁺_g) interacting with the noble gas atoms Argon, Krypton and Xenon are studied. The computations are done by an accurate ab initio approach based on the pseudo-potential technique, Gaussian basis sets, parameterized l-dependent polarization potentials and an analytic potential form for the K⁺Ar, K⁺Kr and K⁺Xe interactions. These interactions are added via the CCSD(T) potential taken from literature and fitted applying the analytical expression of Tang and Toennies. The application of the pseudo-potential approach reduces the number of active electrons of each complex to only one electron. The potential energy surfaces are analyzed on a large range of the Jacobi coordinates, R and θ. By the general interpolation outline based on the RKHS (Reproducing Kernel Hilbert Space) procedure, we have reproduced for each complex from our ab initio results the two-dimensional contour plots of an analytical potential. To evaluate the stability of each complex, we have determined from the potential energy surfaces the equilibrium distance (R_e), the well depth (D_e), the quantum energy (D₀), the zero-point-energy (ZPE) and the ZPE%. The results showed that the linear configurations, where the noble gas atom connected to the K₂⁺(X²Σ⁺_g) system, are the more stable.

Solvation of Isoelectronic Halide and Alkali Metal Ions by Argon Atoms

This work systematically examines the interactions of alkali metal cations and their isoelectronic halide counterparts with up to six solvating Ar atoms (M⁺Ar_n and X^-Ar_n, where M = Li, Na, K, and Rb; X = H, F, Cl, and Br; and n = 1-6) via full geometry optimizations with the MP2 method and robust, correlation-consistent quadruple-ζ (QZ) basis sets. 116 unique M⁺Ar_n and X^-Ar_n stationary points have been characterized on the MP2/QZ potential energy surface. To the best of our knowledge, approximately two dozen of these stationary points have been reported here for the first time. Some of these new structures are either the lowest-energy stationary point for a particular cluster or energetically competitive with it. The CCSD(T) method was employed to perform additional single-point energy computations upon all MP2/QZ-optimized structures using the same basis set. CCSD(T)/QZ results indicate that internally solvated structures with the ion at/near the geometric center of the cluster have appreciably higher energies than those placing the ion on the periphery. While this study extends the prior investigations of M⁺Ar_n clusters found within the literature, it notably provides one of the first thorough characterizations of and comparisons to the corresponding negatively charged X^-Ar_n clusters.

Data Needs for Modeling Low-Temperature Non-Equilibrium Plasmas: The LXCat Project, History, Perspectives and a Tutorial

Technologies based on non-equilibrium, low-temperature plasmas are ubiquitous in today’s society. Plasma modeling plays an essential role in their understanding, development and optimization. An accurate description of electron and ion collisions with neutrals and their transport is required to correctly describe plasma properties as a function of external parameters. LXCat is an open-access, web-based platform for storing, exchanging and manipulating data needed for modeling the electron and ion components of non-equilibrium, low-temperature plasmas. The data types supported by LXCat are electron- and ion-scattering cross-sections with neutrals (total and differential), interaction potentials, oscillator strengths, and electron- and ion-swarm/transport parameters. Online tools allow users to identify and compare the data through plotting routines, and use the data to generate swarm parameters and reaction rates with the integrated electron Boltzmann solver. In this review, the historical evolution of the project and some perspectives on its future are discussed together with a tutorial review for using data from LXCat.

Spin-orbit coupling in the dissociative excitation of alkali atoms at the surface of rare gas clusters: A theoretical study

We analyze the role of the spin-orbit (SO) coupling in the dissociative dynamics of excited alkali atoms at the surface of small rare gas clusters. The electronic structure of the whole system is deduced from a one-electron model based on core polarization pseudo-potentials. It allows us to obtain in the same footing the energy, forces, and non-adiabatic couplings used to simulate the dynamics by means of a surface hopping method. The fine structure state population is analyzed by considering the relative magnitude of the SO coupling ξ, with respect to the spin-free potential energy. We identify three regimes of ξ-values leading to different evolution of adiabatic state population after excitation of the system in the uppermost state of the lowest np (2)P shell. For sufficiently small ξ, the final population of the J=12 atomic states, P12, grows up linearly from P12=13 at ξ = 0 after a diabatic dynamics. For large values of ξ, we observe a rather adiabatic dynamics with P12 decreasing as ξ increases. For intermediate values of ξ, the coupling is extremely efficient and a complete transfer of population is observed for the set of parameters associated to NaAr3 and NaAr4 clusters.

A Surprisingly Simple Electrostatic Model Explains Bent Versus Linear Structures in M(+)-RG2 Species (M = Group 1 Metal, Li-Fr; RG = Rare Gas, He-Rn)

It is found that a simple electrostatic model involving competition between the attractive dispersive interaction and induced-dipole repulsion between the two RG atoms performs extremely well in rationalizing the M(+)-RG2 geometries, where M = group 1 metal and RG = rare gas. The Li(+)-RG2 and Na(+)-RG2 complexes have previously been found to exhibit quasilinear or linear minimum-energy geometries, with the Na(+)-RG2 complexes having an additional bent local minimum [A. Andrejeva, A. M. Gardner, J. B. Graneek, R. J. Plowright, W. H. Breckenridge, T. G. Wright, J. Phys. Chem. A, 2013, 117, 13578]. In the present work, the geometries for M = K-Fr are found to be bent. A simple electrostatic model explains these conclusions and is able to account almost quantitatively for the binding energy of the second RG atom, as well as the form of the angular potential, for all 36 titular species. Additionally, results of population analyses are presented together with orbital contour plots; combined with the success of the electrostatic model, the expectation that these complexes are all physically bound is confirmed.

Absorption Spectroscopy, a Tool for Probing Local Structures and the Onset of Large-Amplitude Motions in Small KAr(n) Clusters at Increasing Temperatures

Photoabsorption spectra of KArn (n = 1-10) are simulated at temperatures ranging between 5 and 25 K. The calculations associate a Monte Carlo (MC) method to sample cluster geometries at temperature T, with a one-electron ab initio model to calculate the ground-state and excited-state energies of the cluster. The latter model replaces the K(+) core electrons and all the electrons of the Ar atoms by appropriate pseudopotentials, complemented by core polarization potentials. It also provides the necessary oscillator strengths to simulate the spectra. Global optimization by basin-hopping is used in combination with MC simulation at low temperature (5 K) to identify the most stable isomer and remarkable isomers of ground-state KArn clusters, which are stable with respect to deformations of the order of those expected with Zero Point Energy motions. The absorption spectra calculated for each of these isomers at 5 K suggest that absorption spectroscopy can probe sensitively the local environment of K atom: surface location of K with respect to a close-packed Ar moiety, number of Ar atom in close vicinity, and local symmetry about K. Simulation at increasing temperatures, up to the evaporation limit of K out of the cluster, shows the onset of large amplitude motions above 20 K, when the K atom experiences a variety of local environments.

Differential ion mobility separations in up to 100% helium using microchips

The performance of differential IMS (FAIMS) analyzers is much enhanced by gases comprising He, especially He/N2 mixtures. However, electrical breakdown has limited the He fraction to ~50%-75%, depending on the field strength. By the Paschen law, the threshold field for breakdown increases at shorter distances. This allows FAIMS using chips with microscopic channels to utilize much stronger field intensities (E) than "full-size" analyzers with wider gaps. Here we show that those chips can employ higher He fractions up to 100%. Use of He-rich gases improves the resolution and resolution/sensitivity balance substantially, although less than for full-size analyzers. The optimum He fraction is ~80%, in line with first-principles theory. Hence, one can now measure the dependences of ion mobility on E in pure He, where ion-molecule cross section calculations are much more tractable than in other gases that form deeper and more complex interaction potentials. This capability may facilitate quantitative modeling of high-field ion mobility behavior and, thus, FAIMS separation properties, which would enable a priori extraction of structural information about the ions.

Potential energy curves and spin-orbit coupling of light alkali-heavy rare gas molecules

The potential energy curves of the X, A, and B states of alkali-rare gas diatomic molecules, MKr and MXe, are investigated for M = Li, Na, K. The molecular spin-orbit coefficients a(R)=<(2)Π(½)|Ĥ(SO)|(2)Π(½)> and b(R)=<(2)Π(-½)|Ĥ(SO)|(2)Σ(½)> are calculated as a function the interatomic distance R. We show that a(R) increases and b(R) decreases as R decreases. This effect becomes less and less important as the mass of the alkali increases. A comparison of the rovibrational properties deduced from our calculations with experimental measurements recorded for NaKr and NaXe shows the quality of the calculations.

Review: gas-phase ion chemistry of the noble gases: recent advances and future perspectives

This review article surveys recent experimental and theoretical advances in the gas-phase ion chemistry of the noble gases. Covered issues include the interaction of the noble gases with metal and non-metal cations, the conceivable existence of covalent noble-gas anions, the occurrence of ion-molecule reactions involving singly-charged xenon cations, and the occurrence of bond-forming reactions involving doubly-charged cations. Research themes are also highlighted, that are expected to attract further interest in the future.

Radii of atomic ions determined from diatomic ion-He bond lengths

We propose a new definition of the effective radius of an atomic ion: the bond distance (R(e)) of the ion/He diatomic complex minus the van der Waals radius of the helium atom. Our rationale is that He is the most chemically inert and least polarizable atom, so that its interaction with the outer portions of the electron cloud causes the smallest perturbation of it. We show that such radii, which we denote R(XHe), make good qualitative sense. We also compare our R(XHe) values to more traditional ionic radii from solid crystal X-ray measurements, as well as estimates of such radii from "ionic" gas-phase MF, MOM, MF(+), and MO molecules, where M is a metal atom. Such comparisons lead to interesting conclusions about bonding in ionic crystals and in simple gas-phase oxide and fluoride molecules. The definition is shown to be reasonable for -1, +1, and even for many of the larger +2 atomic ions. Another advantage of the R(XHe) definition is that it is also consistently valid for ground states and excited states of both neutral atoms and atomic ions, even for open-shell np and nd cases where the electron clouds of the ions are not spherically symmetric and R(XHe) thus depends on the "approach" direction of the He atom. Finally, we note that when there is a contribution from covalent bonding with the He atom, and/or in cases where the ion is small and has a very high charge, so that there is distortion even of the He 1s electrons, R(XHe) is not expected to be representative of the size of the ion. We then suggest that in these cases small, and sometimes unphysical, values of R(XHe) are diagnostic of the fact that simple "physical" interactions have been supplemented by a "chemical" component.

Beyond the Lennard-Jones model: a simple and accurate potential function probed by high resolution scattering data useful for molecular dynamics simulations

Scattering data, measured for rare gas-rare gas systems under high angular and energy resolution conditions, have been used to probe the reliability of a recently proposed interaction potential function, which involves only one additional parameter with respect to the venerable Lennard-Jones (LJ) model and is hence called Improved Lennard-Jones (ILJ). The ILJ potential eliminates most of the inadequacies at short- and long-range of the LJ model. Further reliability tests have been performed by comparing calculated vibrational spacings with experimental values and calculated interaction energies at short-range with those obtained from the inversion of gaseous transport properties. The analysis, extended also to systems involving ions, suggests that the ILJ potential model can be used to estimate the behavior of unknown systems and can help to assess the different role of the leading interaction components. Moreover, due to its simple formulation, the physically reliable ILJ model appears to be particularly useful for molecular dynamics simulations of both neutral and ionic systems.

Bosonic helium droplets with cationic impurities: onset of electrostriction and snowball effects from quantum calculations

Variational Monte Carlo and diffusion Monte Carlo calculations have been carried out for cations such as Li(+), Na(+), and K(+) as dopants of small helium clusters over a range of cluster sizes up to about 12 solvent atoms. The interaction has been modeled through a sum-of-potential picture that disregards higher order effects beyond atom-atom and atom-ion contributions. The latter were obtained from highly correlated ab initio calculations over a broad range of interatomic distances. This study focuses on two of the most striking features of the microsolvation in a quantum solvent of a cationic dopant: electrostriction and snowball effects. They are discussed here in detail and in relation with the nanoscopic properties of the interaction forces at play within a fully quantum picture of the cluster features.

Interaction potentials and spectroscopy of Hg+.Rg and Cd+.Rg and transport coefficients for Hg+ and Cd+ in Rg (Rg=He-Rn)

High-level ab initio calculations have been performed on the Hg(+).Rg and Cd(+).Rg species, where Rg-He-Rn. Potential-energy curves have been calculated over a wide range of internuclear separation, sampling the repulsive, equilibrium, and long-range regions. From these curves, rovibrational and spectroscopic constants were derived and compared to those available from previous studies. In addition, transport coefficients were calculated and compared to the available experimental data for the cases of Hg(+) in He, Ne, and Ar. There are two interesting features relating to the mobility results. One is the development of a "mobility minimum" for Hg(+) in the heavier rare gases--with weaker minima being found for Cd(+); a "rule of thumb" is presented for determining when mobility minima might appear. The second is that excellent agreement is found for the direct calculation of mobilities for Hg(+) in (22)Ne, and those obtained by scaling the (20)Ne mobilities. The latter result allows us to conclude that the mobilities of the various combinations of isotopes can be calculated from the results herein via a mass scaling.

Testing ion-neutral interaction potentials using calculated ion transport coefficients

Several commonly measured ion transport coefficients were investigated in order to determine their sensitivity for testing and comparing proposed ion-neutral interaction potentials. A variety of positive ions, negative ions, neutrals, and temperatures were included in order to draw as general a conclusion as possible. All transport coefficients considered were found to be sufficiently sensitive to be used to clearly distinguish between less and more accurate interaction potentials. It was also found that the longitudinal diffusion coefficient is the most sensitive test, followed by both the transverse diffusion coefficient and the ratio of the longitudinal diffusion coefficient to mobility, followed by the ratio of the transverse diffusion coefficient to mobility and that the mobility is the least sensitive test. When presently achievable levels of experimental error were also taken into account, however, there was no significant difference in the sensitivities.

Accurate potential energy curves for F−–Rg (Rg = He–Rn): Spectroscopy and transport coefficients

High-quality ab initio potential energy curves are presented for the F(-)-Rg series (Rg = He-Rn). Calculations are performed at the CCSD(T) level of theory, employing d-aug-cc-pV5Z quality basis sets, with "small core" relativistic effective core potentials being used for Kr-Rn. The quality of the curves is judged by agreement with recent high-level calculations in the case of F(-)-He and F(-)-Ne and by excellent agreement with mobility data for the systems F(-)-Rg (Rg = He-Xe). Except for these recent high-level calculations on the two lightest systems, we are able to deduce that all other previous potentials for the whole set of these systems are inadequate. We also present spectroscopic information for the titular species, derived from our potential energy curves.

Accurate potential energy curves for HeO−, NeO−, and ArO−: Spectroscopy and transport coefficients

We calculate accurate potential energy curves for HeO(-), NeO(-), and ArO(-), including the full counterpoise correction and allowing for spin-orbit effects. Comparison with previous curves is presented, where these are available. The three curves, (2)Sigma(12) (+), (2)Pi(12), and (2)Pi(32), are used to derive spectroscopic constants and to calculate the transport coefficients for O(-) moving in a bath of the respective rare gas. Conclusions are made based on a comparison with the available data.