Density functional theory study of the proton-bound rare-gas dimers Rg2H+ and (RgHRg′)+ (Rg=Ar, Kr, Xe): Interpretation of experimental matrix isolation infrared data

A kernel-based machine learning potential and quantum vibrational state analysis of the cationic Ar hydride (Ar2H+)

One of the most fascinating discoveries in recent years, in the cold and low pressure regions of the universe, was the detection of ArH+ and HeH+ species. The identification of such noble gas-containing molecules in space is the key to understanding noble gas chemistry. In the present work, we discuss the possibility of [Ar2H]+ existence as a potentially detectable molecule in the interstellar medium, providing new data on possible astronomical pathways and energetics of this compound. As a first step, a data-driven approach is proposed to construct a full 3D machine-learning potential energy surface (ML-PES) via the reproducing kernel Hilbert space (RKHS) method. The training and testing data sets are generated from CCSD(T)/CBS[56] computations, while a validation protocol is introduced to ensure the quality of the potential. In turn, the resulting ML-PES is employed to compute vibrational levels and molecular spectroscopic constants for the cation. In this way, the most common isotopologue in ISM, [36Ar2H]+, was characterized for the first time, while simultaneously, comparisons with previously reported values available for [40Ar2H]+ are discussed. Our present data could serve as a benchmark for future studies on this system, as well as on higher-order cationic Ar-hydrides of astrophysical interest.

Spectral Signatures of Protonated Noble Gas Clusters of Ne, Ar, Kr, and Xe: From Monomers to Trimers

The structures and spectral features of protonated noble gas clusters are examined using a first principles approach. Protonated noble gas monomers (NgH⁺) and dimers (NgH⁺Ng) have a linear structure, while the protonated noble gas trimers (Ng₃H⁺) can have a T-shaped or linear structure. Successive binding energies for these complexes are calculated at the CCSD(T)/CBS level of theory. Anharmonic simulations for the dimers and trimers unveil interesting spectral features. The symmetric NgH⁺Ng are charactized by a set of progression bands, which involves one quantum of the asymmetric Ng-H⁺ stretch with multiple quanta of the symmetric Ng-H⁺ stretch. Such a spectral signature is very robust and is predicted to be observed in both T-shaped and linear isomers of Ng₃H⁺. Meanwhile, for selected asymmetric NgH⁺Ng’, a Fermi resonance interaction involving the first overtone of the proton bend with the proton stretch is predicted to occur in ArH⁺Kr and XeH⁺Kr.

Fermi resonance switching in KrH+Rg and XeH+Rg (Rg = Ne, Ar, Kr, and Xe)

Matrix isolation experiments have been successfully employed to extensively study the infrared spectrum of several proton-bound rare gas complexes. Most of these studies have focused on the spectral signature for the H⁺ stretch (ν₃) and its combination bands with the intermolecular stretch coordinate (ν₁). However, little attention has been paid to the Fermi resonance interaction between the H⁺ stretch (ν₃) and H⁺ bend overtone (2ν₂) in the asymmetric proton-bound rare gas dimers, RgH⁺Rg'. In this work, we have investigated this interaction on KrH⁺Rg and XeH⁺Rg with Rg = (Ne, Ar, Kr, and Xe). A multilevel potential energy surface (PES) was used to simulate the vibrational structure of these complexes. This PES is a dual-level comprising of second-order Møller-Plesset perturbation theory and coupled-cluster singles doubles with perturbative triples [CCSD(T)] levels of ab initio theories. We found that when both the combination bands (nν₁ + ν₃) and bend overtone 2ν₂ compete to borrow intensity from the ν₃ band, the latter wins over the former, which then results in the suppression of the nν₁ + ν₃ bands. The current simulations offer new assignments for the ArH⁺Xe and KrH⁺Xe spectra. Complete basis set (CBS) binding energies for these complexes were also calculated at the CCSD(T)/CBS level.

On the Proton-Bound Noble Gas Dimers (Ng-H-Ng)+ and (Ng-H-Ng')+ (Ng, Ng'= He-Xe): Relationships betweenStructure, Stability, and Bonding Character

The structure, stability, and bonding character of fifteen (Ng-H-Ng)⁺ and (Ng-H-Ng’)⁺ (Ng, Ng’ = He-Xe) compounds were explored by theoretical calculations performed at the coupled cluster level of theory. The nature of the stabilizing interactions was, in particular, assayed using a method recently proposed by the authors to classify the chemical bonds involving the noble-gas atoms. The bond distances and dissociation energies of the investigated ions fall in rather large intervals, and follow regular periodic trends, clearly referable to the difference between the proton affinity (PA) of the various Ng and Ng’. These variations are nicely correlated with the bonding situation of the (Ng-H-Ng)⁺ and (Ng-H-Ng’)⁺. The Ng-H and Ng’-H contacts range, in fact, between strong covalent bonds to weak, non-covalent interactions, and their regular variability clearly illustrates the peculiar capability of the noble gases to undergo interactions covering the entire spectrum of the chemical bond.

Quantum and quasiclassical dynamical simulations for the Ar2H+ on a new global analytical potential energy surface

A new analytical potential energy surface (PES) has been constructed for the Ar₂H⁺ system from a dataset consisting of a large number of ab initio energies computed using the coupled-cluster singles, doubles and perturbative triples method and aug-cc-pVQZ basis set. The long-range interaction is added to the diatomic potentials using a standard long range expansion form to better describe the asymptotic regions. The vibrational states for the most stable structures of the Ar₂H⁺ system have been calculated, and few low lying states are assigned to quantum numbers. Reactive scattering studies have been performed for the Ar + Ar'H⁺ → Ar' + ArH⁺ proton exchange reaction on the newly generated PES. Reaction probability, cross sections, and rate constants are calculated for the Ar + Ar'H⁺(v = 0, j = 0) collisions within 0.01 eV-0.6 eV of relative translational energy using exact quantum dynamical simulations as well as quasiclassical trajectory (QCT) calculations. The effect of vibrational excitation of the reactants is also explored for the reaction. State averaged rate constants are calculated for the proton exchange reaction at different temperatures using the QCT method. The mechanistic pathways for the reaction are understood by analyzing the quasiclassical trajectories.

Structure and Vibrational Spectra of ArnH+ (n = 2-3)

The structure and vibrational spectra of protonated Ar clusters Ar_nH⁺ (n = 2-3) are studied using potential energy surfaces at the CCSD(T)/aug-cc-pVTZ level and basis set. Ar binding energies, as well as position isomerism in Ar₃H⁺, were investigated. In our previous work, the spectra of Ar₂H⁺ reveal a strong progression of combination bands, which involves the asymmetric Ar-H⁺ stretch with multiple quanta of the symmetric Ar-H⁺ stretch. In this work, insights on the origin of such progression were examined using an adiabatic model. In addition, contributions from mechanical and electrical anharmonicity on the progressions' intensities were also examined. Comparison of the calculated spectrum for the bare and Ar-tagged ions reveals that the reduction of the symmetry group, from D_∞h to either C_∞v or C_2v, results in a richer vibrational structure in the 500-1700 cm^-1 region. When compared with previously reported action spectra (D. C. McDonald III, D. T. Mauney, D. Leicht, J. H. Marks, J. A. Tan, J.-L. Kuo, and M. A. Duncan, J. Chem. Phys., 2016, 145, 231,101), it appears that the position isomers, because of the binding of the weakly bound Ar messenger, are needed to account for the additional bands in the infrared photodissociation spectrum for Ar₃H⁺. These findings demonstrate the active role of the messenger atom in relaxing some of the selection rules for the bare ion's vibrational transitions - resulting in an augmentation of the bands in the action spectrum.

Cationic Noble-Gas Hydrides: From Ion Sources to Outer Space

Cationic species with noble gas (Ng)-hydrogen bonds play a major role in the gas-phase ion chemistry of the group 18 elements. These species first emerged more than 90 years ago, when the simplest HeH+ and HeH2 + were detected from ionized He/H2 mixtures. Over the years, the family has considerably expanded and currently includes various bonding motifs that are investigated with intense experimental and theoretical interest. Quite recently, the results of these studies acquired new and fascinating implications. The diatomic ArH+ and HeH+ were, in fact, detected in various galactic and extragalactic regions, and this stimulates intriguing questions concerning the actual role in the outer space of the Ng-H cations observed in the laboratory. The aim of this review is to briefly summarize the most relevant information currently available on the structure, stability, and routes of formation of these fascinating systems.

A theoretical study on the infrared signatures of proton-bound rare gas dimers (Rg-H+-Rg), Rg = {Ne, Ar, Kr, and Xe}

The infrared spectrum of proton-bound rare gas dimers has been extensively studied via matrix isolation spectroscopy. However, little attention has been paid on their spectrum in the gas phase. Most of the Rg₂H⁺ has not been detected outside the matrix environment. Recently, Ar_nH⁺ (n = 3-7) has been first detected in the gas-phase [D. C. McDonald et al., J. Chem. Phys. 145, 231101 (2016)]. In that work, anharmonic theory can reproduce the observed vibrational structure. In this paper, we extend the existing theory to examine the vibrational signatures of Rg₂H⁺, Rg = {Ne, Ar, Kr, and Xe}. The successive binding of Rg to H⁺ was investigated through the calculation of stepwise formation energies. It was found that this binding is anti-cooperative. High-level full-dimensional potential energy surfaces at the CCSD(T)/aug-cc-pVQZ//MP2/aug-cc-pVQZ were constructed and used in the anharmonic calculation via discrete variable representation. We found that the potential coupling between the symmetric and asymmetric Rg-H⁺ stretch (ν₁ and ν₃ respectively) causes a series of bright n₁ν₁ + ν₃ progressions. From Ne₂H⁺ to Xe₂H⁺, an enhancement of intensities for these bands was observed.

ArCH2 + : A Detectable Noble Gas Molecule

The noble gas molecular cation, ArCH₂ ⁺ , has been observed in mass spectrometry experiments, and the present work is providing high-level quantum chemical predictions for the vibrational and rotational spectroscopic data necessary to observe this molecule in situ in other laboratory conditions. The Ar-C stretch in this cation is a bright fundamental vibrational frequency that should be observable in the early regions of the far-infrared at 421.2 cm^-1 for the universally most common ³⁶ Ar isotope. The near-prolate nature of this molecule and its 2.91 D dipole moment should also make it distinguishable for submillimeter detection, as well. Furthermore, the Ar-C bond strength in ArCH₂ ⁺ is greater than the global minimum for the dissociation of the experimentally known ArOH⁺ cation. As a result, the infrared spectrum of this simple organo-noble gas molecule is likely waiting to be observed and may already exist in the spectra of hydrocarbon cations in argon-matrix condensed phase experiments.

Scattering study of the Ne + NeH(+)(v0 = 0, j0 = 0) → NeH(+) + Ne reaction on an ab initio based analytical potential energy surface

Initial state selected dynamics of the Ne + NeH(+)(v0 = 0, j0 = 0) → NeH(+) + Ne reaction is investigated by quantum and statistical quantum mechanical (SQM) methods on the ground electronic state. The three-body ab initio energies on a set of suitably chosen grid points have been computed at CCSD(T)/aug-cc-PVQZ level and analytically fitted. The fitting of the diatomic potentials, computed at the same level of theory, is performed by spline interpolation. A collinear [NeHNe](+) structure lying 0.72 eV below the Ne + NeH(+) asymptote is found to be the most stable geometry for this system. Energies of low lying vibrational states have been computed for this stable complex. Reaction probabilities obtained from quantum calculations exhibit dense oscillatory structures, particularly in the low energy region and these get partially washed out in the integral cross section results. SQM predictions are devoid of oscillatory structures and remain close to 0.5 after the rise at the threshold thus giving a crude average description of the quantum probabilities. Statistical cross sections and rate constants are nevertheless in sufficiently good agreement with the quantum results to suggest an important role of a complex-forming dynamics for the title reaction.

Stable Lithium Argon compounds under high pressure

High pressure can fundamentally alter the bonding patterns of chemical elements. Its effects include stimulating elements thought to be “inactive” to form unexpectedly stable compounds with unusual chemical and physical properties. Here, using an unbiased structure search method based on CALYPSO methodology and density functional total energy calculations, the phase stabilities and crystal structures of Li−Ar compounds are systematically investigated at high pressure up to 300 GPa. Two unexpected Li_mAr_n compounds (LiAr and Li₃Ar) are predicted to be stable above 112 GPa and 119 GPa, respectively. A detailed analysis of the electronic structure of LiAr and Li₃Ar shows that Ar in these compounds attracts electrons and thus behaves as an oxidizing agent. This is markedly different from the hitherto established chemical reactivity of Ar. Moreover, we predict that the P4/mmm phase of Li₃Ar has a superconducting transition temperature of 17.6 K at 120 GPa.

Wave packet and statistical quantum calculations for the He + NeH⁺ → HeH⁺ + Ne reaction on the ground electronic state

A real wave packet based time-dependent method and a statistical quantum method have been used to study the He + NeH(+) (v, j) reaction with the reactant in various ro-vibrational states, on a recently calculated ab initio ground state potential energy surface. Both the wave packet and statistical quantum calculations were carried out within the centrifugal sudden approximation as well as using the exact Hamiltonian. Quantum reaction probabilities exhibit dense oscillatory pattern for smaller total angular momentum values, which is a signature of resonances in a complex forming mechanism for the title reaction. Significant differences, found between exact and approximate quantum reaction cross sections, highlight the importance of inclusion of Coriolis coupling in the calculations. Statistical results are in fairly good agreement with the exact quantum results, for ground ro-vibrational states of the reactant. Vibrational excitation greatly enhances the reaction cross sections, whereas rotational excitation has relatively small effect on the reaction. The nature of the reaction cross section curves is dependent on the initial vibrational state of the reactant and is typical of a late barrier type potential energy profile.

Infrared identification of proton-bound rare-gas dimers (XeHXe)⁺, (KrHKr)⁺, and (KrHXe)⁺ and their deuterated species in solid hydrogen

Proton-bound rare-gas dimer (RgHRg)(+), in which Rg represents a rare-gas atom, serves as a prototypical system for proton solvation by inert-gas atoms. Until now, only centrosymmetric species with Rg = Ar, Kr, or Xe have been identified with infrared spectra. We employed electron bombardment during deposition of a mixture of Xe (or Kr) in p-H2 at 3.2 K to prepare (RgHRg)(+). Lines at 847.0 and 972.1 cm(-1) are assigned as the Rg-H-Rg antisymmetric stretching (ν3) mode and its combination with the Rg-H-Rg symmetric stretching (ν1 + ν3) mode of (XeHXe)(+) in solid p-H2, respectively. Lines at 871.1 and 974.0 cm(-1) are assigned as the ν3 and ν1 + ν3 modes of (KrHKr)(+) in solid p-H2, respectively. Slightly shifted and broadened lines were observed for these species in solid n-H2. These results agree satisfactorily with reported experimental values of (XeHXe)(+) and (KrHKr)(+) in solid Xe, Kr, and Ar, and with the quantum-chemically predicted anharmonic vibrational wavenumbers of these species in the gaseous phase; the significant spectral shifts in various matrixes are rationalized with the proton affinities of the hosts. When a mixture of Xe and Kr in p-H2 was used, an additional broad feature at 1284 cm(-1) was observed and assigned as the ν3 mode of (KrHXe)(+) in solid p-H2. This line shifted to 1280 cm(-1) in solid n-H2 and the corresponding line of (KrDXe)(+) was observed at 954 cm(-1) in n-D2. The observations of these lines are new; the wavenumbers significantly blue shifted from those of the centrosymmetric (RgHRg)(+) agree with the quantum-chemically predicted anharmonic vibrational wavenumbers of 1279 cm(-1) for (KrHXe)(+) and 916 cm(-1) for (KrDXe)(+). Analysis of the computational results shows that electronic correlation effects play a much greater role for the asymmetric than for the symmetric species. An interpretation for this is provided.

Quantum dynamical study of the He + NeH+ reaction on a new analytical potential energy surface

An analytical potential energy surface (PES) for the ground state of the [HeHNe](+) system has been constructed from a set of 19,605 ab initio data points, obtained from coupled cluster singles and doubles with perturbative triples correction calculations and the aug-cc-pVQZ basis set. The PES is based on the many-body expansion form proposed by Aguado and Paniagua (J. Chem. Phys. 1992, 96, 1265), and it has a root-mean-square error of 0.03 kcal/mol. The minimum energy pathways (MEPs) for different Ne-H-He angles are calculated, and it is found that the MEP for 180° (linear) goes through the deepest potential energy well. Preliminary quantum dynamical studies are performed for the He + NeH(+) (v = 0-2, j = 0-3) → HeH(+) + Ne reaction in the 0.0-0.5 eV collision energy range. Quantum calculations are carried out using a time-dependent wave packet method within the centrifugal sudden approximation. Reaction probabilities exhibit strong oscillatory behavior arising because of the metastable [HeHNe](+). Vibrational excitation has been found to enhance the reaction cross sections.

Theoretical prediction of rare gas containing hydride cations: HRgBF+ (Rg = He, Ar, Kr, and Xe)

The existence of rare-gas-containing hydride ions of boron (HRgBF(+)) has been predicted by using ab initio quantum chemical methods. The HRgBF(+) ions are obtained by inserting a rare gas (Rg) atom in between the H and B atoms of a HBF(+) ion, and the geometries are optimized for minima as well as transition states using second-order Møller-Plesset perturbation theory (MP2), density functional theory (DFT), and coupled-cluster theory (CCSD(T)) based techniques. The predicted HRgBF(+) ions are found to be metastable, and they exhibit a linear structure at the minima and a nonlinear planar structure at the transition state, corresponding to C∞v and Cs symmetries, respectively. All of the predicted HRgBF(+) ions show negative binding energies with respect to the two-body dissociation channel, leading to global minima (HBF(+) + Rg) on the singlet potential energy surface. In contrast, the dissociation energies corresponding to another two-body dissociation channel leading to HRg(+) + BF and two three-body dissociation channels corresponding to the dissociation into H + Rg + BF(+) and H(+) + Rg + BF show very high positive energies. Apart from positive dissociation energies, the predicted ions show finite barrier heights corresponding to the transition states involving a H-Rg-B bending mode, leading to the global minima products (HBF(+) + Rg). The finite barrier heights in turn would prevent the metastable HRgBF(+) species from transforming to global minima products. Structure, harmonic vibrational frequencies, stability, and Mulliken and natural bonding orbital (NBO) charge distribution values for all of the species are reported using the MP2 and DFT methods. Furthermore, the intrinsic reaction coordinate analysis confirms that the metastable minimum-energy structure and the global minimum products are connected through the corresponding transition state for each of the species on the respective singlet potential energy surface. Atoms-in-molecules (AIM) analysis indicates that the HRgBF(+) ions are best described as HRg(+)BF and are analogous to the isoelectronic HRgCO(+) and HRgN2(+) ions. The energetic along with charge redistribution and spectroscopic data strongly support the possible existence of HRgBF(+) ions. Hence, it might be possible to generate HRgBF(+) ions in the DC discharge plasma of a BF3/H2/Rg mixture at low temperature, and the predicted ions may be characterized using the magnetic field modulated infrared laser spectroscopic technique, which has been used earlier to characterize HBF(+) ions.

Theoretical investigation of rare gas hydride cations: HRgN2+ (Rg=He, Ar, Kr, and Xe)

Rare gas containing protonated nitrogen cations, HRgN(2)(+) (Rg=He, Ar, Kr, and Xe), have been predicted using quantum computational methods. HRgN(2)(+) ions exhibit linear structure (C(∞v) symmetry) at the minima and show planar structure (C(s) symmetry) at the transition state. The stability is determined by computing the energy differences between the predicted ions and its various unimolecular dissociation products. Analysis of energy diagram indicates that HXeN(2)(+) is thermodynamically stable with respect to dissociated products while HHeN(2)(+), HArN(2)(+), and HKrN(2)(+) ions are metastable with small barrier heights. Moreover, the computed intrinsic reaction coordinate analysis also confirms that the minima and the 2-body global dissociation products are connected through transition states for the metastable ions. The coupled-cluster theory computed dissociation energies corresponding to the 2-body dissociation (HN(2)(+) + Rg) is -288.4, -98.3, -21.5, and 41.4 kJ mol(-1) for HHeN(2)(+), HArN(2)(+), HKrN(2)(+), and HXeN(2)(+) ions, respectively. The dissociation energies are positive for all the other channels implying that the predicted ions are stable with respect to other 2- and 3-body dissociation channels. Atoms-in-molecules analysis indicates that predicted ions may be best described as HRg(+)N(2). It should be noted that the energetic of HXeN(2)(+) ion is comparable to that of the experimentally observed stable mixed cations, viz. (RgHRg')(+). Therefore, it may be possible to prepare and characterize HXeN(2)(+) ions in an electron bombardment matrix isolation technique.

Cationic Van-der-Waals Complexes: Theoretical Study of Ar2H+ Structure and Stability

The electronic and geometric structure, stability and molecular properties of the cationic van-der-Waals complex Ar2H+ in its ground electronic state are studied by means of two ab-initio quantum-chemical approaches: conventional configuration interaction (multi-reference and coupled-cluster methods) and a diatomics-in-molecules model with ab-initio input data. To ensure consistency between the two approaches, one and the same one-electron atomic basis set (aug-cc-pVTZ by Dunning) is employed in both. The topography of the ground-state potential-energy surface is examined with respect to the nature of the binding and the stability of structures corresponding to stationary points. In accordance with most earlier theoretical work, there are two local minima at linear arrangements: a strongly bound centro-symmetric moiety, (Ar–H–Ar)+, and a weakly bound van-der-Waals complex, Ar···ArH+. These are separated by a low barrier. Only the centro-symmetric molecule is significantly stable (D e = 0.68eV) against fragmentation into Ar + ArH+ and should have structural and dynamical relevance. A fairly simple diatomics-in-molecules model taking into account only the few lowest electronic fragment states yields a qualitatively correct description of the ground state but shows quantitative deviations from the more accurate configuration-interaction data in detail. Nevertheless, it should provide a good starting point for the treatment of larger complexes Ar n H+ with n > 2.

Infrared Spectra of the OH+ and H2O+ Cations Solvated in Solid Argon

Infrared spectra of various OH+ and H2O+ isotopomers solvated in solid argon are presented. The OH+ and H2O+ cations were produced by co-deposition of H2O/Ar mixture with high-frequency discharged Ar at 4 K. Detailed isotopic substitution studies confirm the assignments of absorptions at 3054.9 and 3040.0 cm(-1) to the antisymmetric and symmetric H-O-H stretching vibrations of H2O+ and 2979.6 cm(-1) to the O-H stretching vibration of OH+. The frequencies of H2O+ solvated in solid argon are red-shifted, whereas the frequency of OH+ is blue-shifted with respect to the gas-phase fundamentals. On the basis of previous gas-phase studies and quantum chemical calculations, the OH+ and H2O+ cations solvated in solid argon may be regarded as the OH+-Ar5 and H2O+-Ar4 complexes isolated in the argon matrix.

Equilibrium geometry, vibrational frequencies, and heat of formation of HOBr, HBrO2, and HBrO3 isomers

The equilibrium geometries, vibrational frequencies, heat capacity, and heat of formation for compounds of general formula HBrOx were calculated by DFT (BP and pBP methods) with DN* and DN** numerical basis sets. The comparison of our HOBr calculated results with the HOBr experimental values points out that the BP and pBP methods are as good as other ab initio and DFT methods related in the literature employing extended basis sets. The calculated HBrOx total energy and heat of formation values, at 0 and 298.15 K, present the following order: HOBr < HBrO; HOOBr < HOBrO < HBrO2; HOOOBr < HOBrO2 < HOOBrO < HBrO3. The HBrOx heat of formation was calculated using isodesmic and homodesmic reactions and the results show that, in general, the use of these reactions gives similar results.Key words: HOBr, HBrO2, HBrO3, DFT, numerical basis.