Rovibrational Characterization and Interstellar Implications of the

Article http://pubs.acs.org/journal/aesccq

Rovibrational Characterization and Interstellar Implications of the Proton-Bound, Noble Gas Complexes: ArHAr+, NeHNe+, and ArHNe+ Ryan C. Fortenberry* Department of Chemistry and Biochemistry, Georgia Southern University, Post Office Box 8064, Statesboro, Georgia 30460, United States ABSTRACT: The detection of the noble gas molecule ArH+ initially in the Crab nebula and elsewhere since has reinvigorated the search for naturally occurring, noble gas compounds. Additionally, proton-bound complexes are known to possess exceptionally bright vibrational modes corresponding to the shifting of the proton between the two, more massive moieties. As such, smaller column densities are required for unique detection of molecules with such intense transitions. In light of this, vibrational, rotational, and rovibrational spectroscopic data are provided here for ArHAr+, NeHNe+, and ArHNe+ to assist in laboratory characterization or even astronomical detection of these noble gas molecular cations. NeHNe+ is shown to be a surprisingly well-bound system, while the neon atom is not nearly as tightly bound to ArHNe+ in comparison. Furthermore, the reaction of the astronomically detected argonium cation with the strongly supported, potential interstellar ArH3+ cation will produce ArHAr+ with favorable energetics. This coupled with the fact that the proton shuttle fundamental has the largest intensity and lowest frequency in ArHAr+ of the three cations examined supports the idea that ArHAr+ is likely observable through either its vibrational mode or the rotations of this vibrationally excited state. KEYWORDS: noble gas molecules, proton-bound complexes, molecular cations, rovibrational spectroscopy, quartic force fields, quantum chemistry

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for n = 2, 4, and 6,21 and various van der Waals complexes.22−27 However, quantum chemical computation has long been one of the most accessible means of exploring the chemistry of these systems.10,14,17,28−31 Quantum chemical work has shown that the hypothesized formation of argonium proceeding from cosmic ray-ionized argon atomic cations and ubiquitous hydrogen gas proceeds through a ArH2+ global minimum before creating ArH+ and a hydrogen atom.32−34 Additionally, ionization of H2 is nearly isoenergetic to atomic Ar, making H2+ and argon atoms another viable set of starting materials in the interstellar synthesis of argonium. Meanwhile, the ionization of neon is much greater than the hydrogen molecule. The most favored product on the [Ne, H, H]+ potential energy surface (PES) is actually the ionized hydrogen molecule and a neutral neon atom. Both factors cast doubt on the presence of NeH+ in the ISM.11,34 Even so, ArOH+, NeOH+, ArNH+, ArCCH+, NeCCH+, and ArCN+ have all been shown to be minima on the respective PESs.14,35−39 Additionally, all are shown to form in the gas phase, with the exception of NeCCH+, and all have bond strengths, again with the exception of NeCCH+, typical of

INTRODUCTION The full valence of a noble gas atom does not always inhibit its chemistry, even beyond the controlled confines of the chemistry laboratory. Argonium, ArH+, has been detected in the interstellar medium (ISM) toward various astronomical objects1,2 and may even have an abundance in the range of carbon monoxide in some regions where the observable matter is almost exclusively atomic gas.2−4 Argon is one of the most abundant atoms in the universe5,6 and is known to be polarizable with the proper ligands.7−10 Consequently, it is not entirely surprising that the first noble gas molecule observed in nature is the simple argonium cation. However, neon is the fifth most abundant atom in the universe, even more so than nitrogen, but natural compounds containing it, even neonium (NeH+),11 have yet to be observed beyond the laboratory.12,13 While helium is actually the second most abundant element in the ISM, with He+ also being fairly abundant, the small electron cloud present in the helium atom9,14−17 makes naturally occurring bonds to helium in any form doubtful besides the almost guaranteed interstellar presence of the HeH+ molecule.18 The presence of argonium in the Crab nebula and dark molecular clouds has raised questions about the possibility of other noble gas molecules lurking in the depths of the ISM.19 The terrestrial and experimental exploration of noble gas chemistry has produced interesting species, like HArF+,20 XeFn © 2017 American Chemical Society

Received: Revised: Accepted: Published: 60

January 20, 2017 February 8, 2017 February 10, 2017 February 10, 2017 DOI: 10.1021/acsearthspacechem.7b00003 ACS Earth Space Chem. 2017, 1, 60−69

Article

ACS Earth and Space Chemistry

argonium cation with the addition of the more common neon atom together in a single molecule. Granted, 40Ar is the most common isotope found on Earth, making the isolation of ArHNe+ (and its more common mass-61 isotopologue) in the laboratory not as much of an issue as was the case with OCHCO+, NNHNN+, NN−HCO+, and CO−HNN+. However, 36Ar is the most abundant isotope of argon in the greater universe, followed by 38Ar, with only trace amounts of 40Ar. Hence, laboratory or quantum chemical analysis of 36ArH20Ne+ is essential if it is to be observed in the ISM. While 36Ar is difficult and expensive to obtain terrestrially, quantum chemical computation is uniquely suited to analyze the structure and spectroscopic data for this proton-bound complex and its isotopologues. ArHNe+ and its homoatomic cousins ArHAr+ and NeHNe+ are known to form surprisingly strong bonds,31,68−74 making them excellent choices for further searches within the ISM or in upper planetary atmospheres. Their IR spectra will likely be dominated by the exceptionally bright proton-shuttle motions, but thus far, only some of the harmonic vibrational frequencies have been computed for these proton-bound complexes. Consequently, the present work will build upon previous experience with QFFs, noble gas molecules, and proton-bound complexes to provide accurate spectroscopic constants and vibrational frequencies for ArHNe+, ArHAr+, NeHNe+, and their isotopologoues to aid in the astronomical or laboratory detection75 of these noble gas compounds.

carbon or oxygen bonded with third-row atoms: between 120 and 60 kcal/mol.36,38,40,41 It should be noted that NeCCH+ could form in the adsorbed phase on polycyclic aromatic hydrocarbon (PAH) surfaces as a first examination, and the formation for most of the others suggested can be further enhanced by similar reactions.38 Because these noble gas molecules are predicted to be stable and can form in environments akin to the ISM, it is likely that they may exist in space or the upper atmospheres of planetary bodies if they can be detected. Consequently, the utilization of quantum chemistry for astrochemistry has extended to providing highly accurate ab initio rovibrational spectroscopic constants and vibrational frequencies for these systems.36,37,39,42 The coupled cluster singles, doubles, and perturbative triples [CCSD(T)] method43,44 combined with quartic force fields (QFFs), fourthorder Taylor series expansions of the Watson internuclear Hamiltonian,45 have been shown to provide such data to within a few tens of megahertz for observed rotation constants and 1.0 cm−1 for experimental fundamental vibrational frequencies in many cases.40,46−58 Consequently, accurate foreknowledge of the spectra for such systems can be provided to assist greatly in laboratory characterization or even direct, telescopic observation of such noble gas species from the ISM. One class of molecules whose rovibrational spectral data have been recently characterized through quantum chemical computation is the mass-57 proton-bound complexes: OCHCO+, NNHNN+, NN−HCO+, CO−HNN+, their isotopologues, and some of their third-row analogues.59−66 These molecules are particularly fascinating for astrochemical observation because the “proton rattle” or “proton shuttle” motions are exceptionally bright vibrational modes.67 The total molecular charge is almost exclusively centered on the proton, yet it contains less than 2% of the total molecular mass. The center of charge is moving tremendously, while the center of mass barely budges. As a result, a huge change in dipole moment and a very active and strongly observable vibrational transition arises. Consequently, such proton-bound complexes are likely detectable in the ISM even if their concentrations and column densities are relatively low. While QFF data are shown to provide narrow ranges for the position of most fundamental vibrational frequencies, some modes in a selection of these proton-bound complexes are not as reliable. Those modes where the PES is flat or has a double well as present in NNHNN+ and OCHCO+, respectively, are troublesome, but nearly all of the other modes are welldescribed with the QFFs compared to vibrational structure computations with larger PESs.62,63 Furthermore, the molecules where a clearly defined miniumum is present, such as NN− HCO+ and CO−HNN+, appear to provide the same, trustworthy QFF behavior and accuracies as the known benchmarks for less exotic systems.65,66 Because the mass-57 complexes obviously have the same mass, their resolution in the laboratory is exceptionally difficult to determine without highly precise mass selection equipment or some theoretical insights. Quantum chemistry has shown that OCHCO+ and NNHNN+ have their bright mode present in the far-infrared (far-IR), while NN−HCO+ and CO−HNN+ have theirs in the mid-IR. Additionally, CO−HNN+ has a second bright mode red-shifted from the primary bright mode, creating a secondary peak for observation. There actually exists another mass-57 proton-bound complex, 36ArH20Ne+, which may yet be significant in the ISM. This molecule combines the simplicity of the known

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COMPUTATIONAL DETAILS The geometries for each of ArHAr+, NeHNe+, and ArHNe+ are all initially optimized with restricted Hartree−Fock reference wave functions,76 CCSD(T), and the aug-cc-pV5Z basis set.77−79 The basis set nomenclature should be understood to contain the (X + d) functions for the third-row argon atom in each case. Further optimized geometries of these linear cations are carried out with and without the core electrons frozen using the Martin−Taylor (MT) core correlating basis set.80 The differences in the two cases of CCSD(T)/MT bond lengths are added to the corresponding values from the CCSD(T)/aug-ccpV5Z computations. From these reference geometries, displacements of 0.005 Å and 0.005 radians, respective of bond lengths and bond angles, are taken with the following symmetry-internal coordinate system: S1(Σg) =

1 [(X1−H) + (X 2−H)] 2

(1)

S2(Σ u) =

1 [(X1−H) − (X 2−H)] 2

(2)

S3(Πxz) = ∠X1−H−X 2−y

(3)

S4(Πyz) = ∠X1−H−X 2−x +

(4) +

for the ArHAr and NeHNe cations with X 1 and X 2 corresponding to the two noble gas atoms in each molecule. The ArHNe+ simple-internal coordinate system uses the same scheme as that employed for several other triatomic, C∞v structures, including some noble gas compounds.34,39,40,81,82

61

S1(Σ+) = Ne−H

(5)

S2(Σ+) = Ar−H

(6) DOI: 10.1021/acsearthspacechem.7b00003 ACS Earth Space Chem. 2017, 1, 60−69

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ACS Earth and Space Chemistry S3(Πxz) = ∠Ne−H−Ar−y

(7)

S3(Πyz) = ∠Ne−H−Ar−x

(8)

inference can be made about the individual bond strengths. As a result, the Ar−H individual force constant is actually 1.735 mdyne/Å2 after manipulating eq 1. This puts the individual, present noble gas hydride bond strength at roughly half that of ArH+ and in line with the corresponding force constant in ArH2+.34 A discussion of the actual bond energies is reserved for later in the document. The sharing of the proton elongates the Ar−H bonds from 1.292 Å in ArH+ and 1.441 Å in ArH2+ to 1.518 Å here in ArHAr+. The bond lengthening is also likely a product of the bond weakening from the reduced effect of the shared proton on the polarized electron clouds of individual argon atoms. In the argon mono- and dihydride cations, a single argon atom is polarized by the proton, producing the shorter bond lengths and larger harmonic, diagonal force constants. A similar behavior is observed in NNHNN+, where the proton is further away from each nitrogen molecule than it is in a single diazenylium cation.63 While rotational spectroscopy has been the workhouse of astrochemical detection for the past 50+ years, the lack of a permanent dipole moment will require detection of ArHAr+ to take place via either vibrational transitions in the IR or rotations of vibrationally active modes. However, the newest generation of air- and space-based observatories, the Stratospheric Observatory for Infrared Astronomy (SOFIA) and the upcoming James Webb Space Telescope (JWST), work within IR wavelengths for which vibrational transitions are optimal for observation. Furthermore, the detection limits of the Atacama Large Millimeter Array (ALMA) in Chile are capable of deciphering rotational transitions of vibrationally excited states if the transitions are strong enough or the density of material is great enough. The vibrational intensities for ArHAr+ in Table 2 clearly indicate that the ω1 proton shuttle mode will be exceptionally bright, as it has been for other proton-bound complexes. The 5321 km/mol intensity is powerfully strong and of similar magnitude as that predicted for the highly intense proton shuttle fundamental in OCHCO+.62 Strangely, there exists a positive anharmonicity for this mode in ArHAr+, indicating that the actual, physical fundamental frequency will lie very close to 1100 cm−1 at 1094.0 cm−1 (9.135 μm), approaching the midIR. Such a positive anharmonicity is not without precedent for similar proton stretching modes,66,95 indicating that the frequency likely shifts as predicted here. The harmonic frequencies are in line with those computed previously.68 The ν1 = 1 rotations could likely also be observed by ALMA using the B1 rotation constant from Table 2 in rotational models for comparison to astronomical observations. This is the smallest of the rotation constants for all νx = 1 modes because the mass is shifting away from the center to the greatest extent. The isotopologue data also give a clear indication of the molecular structure, with the proton shuttle basically unaffected by an increase in argon mass, while a greater than 30% shift is present upon deuteration. However, the shift in B1 between 40 Ar and 36Ar is quite significant from 2584.4 to 2871.5 MHz, respectively. Consequently, any rotational observations of the ν1 = 1 vibrational state will require careful consideration of the isotope. While this was key in observing ArH+ in the first place,1,2 the shift in ArHAr+ is much greater because the argon atoms are now on the outside of the molecule and not the significant central mass, like in ArH+. Additionally, the anharmonic zero-point vibrational energies (ZPEs) are provided in Table 2, allowing for reaction scheme modeling including these species.

Subsequently, 57 and 69 total PES points, respective of the D∞h and C∞v connectivities, construct the QFF. At each point, CCSD(T)/aug-cc-pVTZ, QZ, and 5Z computations are extrapolated to the complete basis set (CBS) limit via a three-point formula.83 Again, energy differences for the MT computations with and without the core electrons included are added to the CBS energy. This is further appended by differences in the Douglas−Kroll scalar relativistic84 basis sets85 with the relativity included and excluded. The use of the CBS, core correlation, and relativistic energies defines the CcCR QFF50 employed in previous work. The CcCR energies are then tightly fit with a sum of squared residuals on the order of 10−17 au2 via a least squares formula to obtain the equilibrium geometry. The QFFs are well-defined with an absence of the flat potentials or double wells in each of the three molecules examined here. Hence, the issues encountered in some cases previously62,63 should, therefore, not be an issue. A refitting produces the necessary zero gradients as well as the quadratic, cubic, and quartic force constants that define the QFF. After the force constants are redefined into the more generic Cartesian coordinates with the INTDER program,86 rotational87 and vibrational88,89 secondorder perturbation theory (VPT2) available within the SPECTRO program90 produces the rovibrational observables. No resonances are required for these VPT2 computations. All electronic structure computations use the MOLPRO2010.1 program,91 except for the double-harmonic intensities and some of the relative energy computations, which use MP2/631+G* from Gaussian 09.92−94

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RESULTS AND DISCUSSION ArHAr+. The CcCR equilibrium geometry for ArHAr+ is given in Figure 1; the force constants are provided in Table 1;

Figure 1. CcCR equilibrium geometry for ArHAr+.

Table 1. ArHAr+ CcCR Symmetry-Internal Force Constants (in mdyn Å−n rad−m)a F11 F22 F33 F44 F111 F221

2.453244 0.280216 0.148020 0.148020 −10.1851 −4.3711

F331 F441 F1111 F2211 F3311 F4411

−0.4223 −0.4223 36.90 17.55 1.37 1.37

F2222 F3322 F3333 F4422 F4433 F4444

24.50 −0.43 0.70 −0.43 0.43 0.70

1 mdyn = 10−8 N. n and m are exponents corresponding to the number of units from the type of modes present in the specific force constant.

a

and the structural/spectroscopic data are in Table 2. The D∞h structure is obvious in Figure 1. Badger’s law is often employed to compare harmonic, diagonal force constants to bond strengths, but the D∞h F11 symmetry-internal force constant has to be broken down into its constituent parts before any 62

DOI: 10.1021/acsearthspacechem.7b00003 ACS Earth Space Chem. 2017, 1, 60−69

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Table 2. CcCR Zero-Point (Rα Vibrationally Averaged) and Equilibrium Structures, Rotation Constants, Vibrationally ExcitedRotation Constants, Distortion Constants, and Vibrational Frequencies and Intensitiesa of ArHAr+ and Its Various Isotopologues 36

r0(Ar−H) (Å) re(Ar−H) (Å) Be (MHz) B0 (MHz) B1 (MHz) B2 (MHz) B3 (MHz) De (kHz) He (μHz) ω1(σu) proton shuttle (cm−1) ω2(π) bend (cm−1) ω3(σg) symm. Ar−H (cm−1) ν1(σu) proton shuttle (cm−1) ν2(π) bend (cm−1) ν3(σg) symm. Ar−H (cm−1) ZPE (cm−1)

ArH36Ar

36

1.518842 1.504590 3103.5 3047.5 2871.5 3084.9 3036.4 1.149 24.141 978.2 668.3 340.2 1094.0 648.3 285.8 1400.0

ArD36Ar

38

ArH38Ar

38

ArD38Ar

40

ArH40Ar

40

ArD40Ar

1.515323

1.518784

1.515263

1.518730

1.515207

3103.5 3062.0 2939.6 3087.2 3050.9 1.149 24.141 696.8 476.0 340.2 749.7 465.2 299.7 1027.5

2940.4 2887.5 2720.6 2923.1 2877.3 1.032 20.531 977.9 668.1 331.2 1094.4 648.2 278.3 1395.5

2940.4 2901.2 2785.1 2925.2 2891.1 1.032 20.531 696.3 475.7 331.2 749.6 464.9 291.9 1022.7

2793.2 2743.1 2584.4 2777.0 2733.6 0.931 17.601 977.6 (5321) 667.8 (89) 322.8 1094.7 648.0 271.4 1391.3

2793.2 2751.7 2629.3 2776.9 2740.7 0.931 17.601 695.8 475.3 322.8 749.6 464.7 284.7 1018.2

a MP2/6-31+G* double-harmonic vibrational intensities in km/mol are in parentheses. The modes where the intensities are zero by symmetry have no values.

NeHNe+. The most striking item for NeHNe+ is its F11 force constant given in Table 3 as 3.052 mdyne/Å2. Deconvoluting

Even though the noble gas hydride bond is strengthened in NeHNe+ but weakened in ArHAr+, the qualitative patterns between the two noble gas species are similar. The proton shuttle is also exceptionally bright, with an intensity in ω1 of 2648 km/mol. This intensity is less compared to ArHAr+ because the mass ratio of the shifting proton compared to the other two atoms is less in NeHNe+ than in the argon analogue. A comparison of the harmonic frequencies to the previous theory is not as good70 because ω1 and ω2 vary by less than a few wavenumbers but the ω3 509.0 cm−1 frequency is over 300 cm−1 less than that predicted in the earlier study at 851.3 cm−1. However, the present CcCR VPT2 approach employs a higher level of theory, indicating that the presently reported results are likely an improvement over the literature. Even so, the anharmonic fundamental vibrational frequencies computed herein trump any harmonic predictions. The degenerate, ω2 bending mode is a brighter absorber than its ArHAr+ counterpart, with an intensity of 310 km/mol. The bending mode is also positively anharmonic but only to a small degree, with ν2 predicted to lie at 735.7 cm−1, 3.5 cm−1 above the harmonic. The strongly intense ν1 proton shuttle fundamental at 1436.6 cm−1 lies directly in the mid-IR at 6.961 μm, making it an excellent candidate for observation with SOFIA from a spectroscopic perspective. The 1436.6 cm−1 ν1 fundamental frequency is higher in NeHNe+ than in ArHAr+ at 1094.7 cm−1, as one would expect for second- and third-row analogues. However, this has traditionally not been the case for neon compounds because neon bonds are so weak in a manner similar to the shorter Ne−H bond lengths mentioned above. For instance, the anharmonic Ar−C stretch in ArCCH+ is 675.8 cm−1, while the Ne−C stretch in NeCCH+ is a mere 278.5 cm−1.39 Again, this implies that NeHNe+ is a well-bound system, especially compared to its neon-containing molecular cation counterparts. NeHNe+ exhibits the most covalent behavior of any neon-containing noble gas molecule explored thus far through similar means, again besides neonium itself. The isotopic comparisons are performing as expected for inclusion of D and 22Ne with more notable shifts in the ZPEs for the heavier neon isotopes than observed in ArHAr+.

Table 3. NeHNe+ CcCR Symmetry-Internal Force Constants (in mdyn Å−n rad−m) F11 F22 F33 F44 F111 F221

3.052307 0.682311 0.101588 0.101588 −17.1078 −7.9807

F331 F441 F1111 F2211 F3311 F4411

−0.4124 −0.4124 82.26 39.86 1.80 1.80

F2222 F3322 F3333 F4422 F4433 F4444

49.91 −0.40 0.58 −0.40 0.37 0.58

this down from the symmetry-internal coordinate to the simpleinternal coordinate realizes an individual 2.158 mdyne/Å2 Ne atom stretch. This is the greatest produced thus far for any neon-containing molecular cation besides neonium, even greater than NeOH+.34,37,39,42 The Ne−H bond is actually strengthened when the two neon atoms are placed opposite of the proton in this complex visually depicted in Figure 2. The

Figure 2. CcCR equilibrium geometry for NeHNe+.

stronger force constant is indicative of a stronger Ne−H bond and a shorter bond length of 1.156 Å given in Table 4. This is shorter than the 1.234 Å N−H bond in NeH2+ but longer than the computationally determined (but never experimentally observed) 0.9911 Å bond length in neonium.96 Additionally, the Ne−H bond length is much shorter in NeHNe+ than the corresponding Ar−H bond length in ArHAr+. This is different from other noble gas cation analogue pairs, where the argon bond lengths are shorter than the neon bond lengths as a result of the typical weakness of neon bonding. 63


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Table 4. NeHNe+ and Isotopologue CcCR Zero-Point (Rα Vibrationally Averaged) and Equilibrium Structures, Rotation Constants, Vibrationally Excited-Rotation Constants, Distortion Constants, and Vibrational Frequencies and Intensitiesa 20

r0(Ne−H) (Å) re(Ne−H) (Å) Be (MHz) B0 (MHz) B1 (MHz) B2 (MHz) B3 (MHz) De (kHz) He (mHz) ω1(σu) proton shuttle (cm−1) ω2(π) bend (cm−1) ω3(σg) symm. Ne−H (cm−1) ν1(σu) proton shuttle (cm−1) ν2(π) bend (cm−1) ν3(σg) symm. Ne−H (cm−1) ZPE (cm−1)

NeH20Ne

20

1.156383 1.143997 9657.5 9465.9 8785.4 9663.3 9391.8 15.475 −0.526 1534.9 (2648) 732.2 (310) 509.0 1436.6 735.7 429.5 1791.3

NeD20Ne

22

NeH22Ne

22

NeD22Ne

1.153798

1.156220

1.153631

9657.5 9509.3 9033.5 9636.0 9435.1 15.475 −0.526 1099.0 524.2 509.0 1041.9 524.7 447.9 1342.1

8779.7 8607.3 7988.0 8776.8 8543.0 12.789 −0.395 1533.2 731.4 485.4 1436.7 735.2 410.1 1778.9

8779.7 8646.8 8213.4 8762.8 8582.5 12.789 −0.395 1096.6 523.1 485.4 1040.8 523.7 427.9 1328.6

a

MP2/6-31+G* double-harmonic vibrational intensities in km/mol are in parentheses. The modes where the intensities are zero by symmetry have no values.

similar to previous theoretical results.70 The rotational constants for ArHNe+ fall expectedly in between that for ArHAr+ and NeHNe+ but closer to the ArHAr+ values. B1 is actually the largest rotational constant of the vibrationally excited values, in direct opposition to the trends shown for both of the homoatomic cations. All of the ArHNe+ vibrational modes are reduced upon inclusion of anharmonicity, and the harmonic values reported here are in good agreement with previous CCSD(T)/aug-ccpVTZ results.70 The intensity of the ω1 proton shuttle motion is, again, quite large at 1255 km/mol, but this is less than the other two. The bend is also vibrationally active and so is the other fundamental frequency. While ω1 can be viewed as the proton shuttling back and forth between the heavy atoms, ω3 is truly the stretching of the neon atom. The Ar−H bond is perturbed very little in this fundamental. Additionally, the Ne− H stretch is weak and low in frequency, with ν3 coming in at 167.1 cm−1 for 36ArH20Ne+. These items further support the claim that the neon atom is more of a spectator than a participant in ArHNe+, but it does have some influence. For instance, the fundamental frequency of 36ArH+ is 2595.7 cm−1,97 but the ν1 Ar−H stretch in 36ArHNe+ is 2145.3 cm−1, 450.4 cm−1 less. Hence, the presence of the neon atom is enough to hinder the motion of the proton in the Ar−H stretch/shuttle mode to a marked degree, and the neon atom allows for a nontrivial 260.2 cm−1 ν2 bend. Interstellar and Atmospheric Implications. Absolute energetics for various creation and destruction reactions of these three noble gas cations are given in Table 8. These do not include the ZPEs, but those will only affect the predicted energies by less than half of a kcal/mol, within the expected error for the computations.38 Negative values in Table 8 favor products, while positive values favor reactants. These have been computed with MP2/6-31+G* as well as CCSD(T)/aug-ccpV5Z in a fashion similar to that performed in ref 38. The differences in the two methods are fairly small, giving qualitatively the same results in each case with a few exceptions discussed below. While kcal/mol is used throughout this discussion, the reader should note that 1 kcal/mol is equivalent

ArHNe+. The neon bond weakens substantially in the heteroatomic ArHNe+ complex. The F11, Ne−H force constant given in Table 5 plummets to 0.241 mdyne/Å2, while the Ar−H Table 5. ArHNe+ CcCR Reduced Simple-Internal Force Constants (in mdyn Å−n rad−m) F11 F21 F22 F33 F44 F111 F211 F221

0.240897 0.358677 3.791296 0.044455 0.044455 −1.5573 −1.3502 −0.3944

F222 F331 F332 F441 F442 F1111 F2111 F2211

−23.0325 −0.1651 −0.0690 −0.1651 −0.0690 7.21 5.63 1.92

F2221 F2222 F3311 F3321 F3322 F4411 F4421 F4422

0.46 120.61 1.03 2.04 0.18 1.03 2.04 0.18

force constant strengthens significantly to 3.791 mdyne/Å2, nearly the same value as that in pure ArH+.34 Hence, ArHNe+ can be viewed as a complex between ArH+ and a neon atom. Figure 3 supports this view, and the 1.605 Å Ne−H bond

Figure 3. CcCR equilibrium geometry for ArHNe+.

length in Table 6 compared to the 1.292 Å Ar−H bond length offers further support. This is in line with the previous work referenced above with argon bond lengths being shorter than counterpart neon bond lengths, even though neon is a smaller atom. Argon shares its electron density with the proton here in ArHNe+, while neon retains its electrons for itself, adding support to the classification of ArHNe+ as a complex of argonium with a neon atom. ArHNe+ will be rotationally active, and a CCSD(T)/aug-ccpV5Z dipole moment computed with the center of mass located at the origin reports a 1.43 D dipole moment in Table 7 64


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Table 6. CcCR 36ArHNe+ and 38ArHNe+ Family Zero-Point (Rα Vibrationally Averaged) and Equilibrium Structures, Rotation Constants, Vibrationally Excited-Rotation Constants, Distortion Constants, and Vibrational Frequencies 36

ArH20Ne

r0(Ne−H) (Å) r0(Ar−H) (Å) re(Ne−H) (Å) re(Ar−H) (Å) Be (MHz) B0 (MHz) B1 (MHz) B2 (MHz) B3 (MHz) De (kHz) He (Hz) ω1(σ) shuttle (cm−1) ω2(π) bend (cm−1) ω3(σ) Ne−H (cm−1) ν1(σ) shuttle (cm−1) ν2(π) bend (cm−1) ν3(σ) Ne−H (cm−1) ZPE (cm−1)

1.605534 1.292494 1.584605 1.304660 4708.2 4691.3 4851.6 4661.7 4556.3 14.764 −0.160 2398.1 386.0 175.8 2145.3 260.2 167.1 1568.9

36

ArD20Ne

36

ArH22Ne

36

ArD22Ne

38

ArH20Ne

38

ArD20Ne

38

ArH22Ne

38

ArD22Ne

1.606431 1.295588

1.604797 1.292482

1.605701 1.295851

1.605314 1.292518

1.606223 1.295909

1.604569 1.292507

1.605486 1.295882

4704.9 4673.8 4789.1 4652.4 4539.3 14.644 −0.159 1721.1 275.5 174.7 1595.2 211.2 164.5 1170.7

4434.5 4420.5 4571.9 4392.5 4297.1 13.123 −0.134 2398.1 385.8 170.5 2144.9 260.3 162.5 1566.2

4432.7 4405.3 4514.4 4384.9 4282.3 13.049 −0.133 1721.1 275.3 169.5 1594.9 211.2 160.0 1167.9

4618.9 4602.9 4759.8 4574.0 4471.7 14.199 −0.150 2396.3 385.9 174.2 2143.6 260.2 165.7 1567.2

4615.0 4585.0 4697.6 4564.1 4454.3 14.068 −0.150 1718.5 275.4 173.3 1592.8 211.1 163.2 1168.5

4345.5 4332.3 4480.3 4305.0 4212.6 12.592 −0.126 2396.3 385.7 168.9 2143.2 260.2 161.0 1564.4

4343.4 4317.1 4423.5 4297.2 4197.7 12.508 −0.125 1718.5 275.1 167.9 1592.4 211.1 158.6 1165.7

Table 7. CcCR 40ArHNe+ Family Zero-Point (Rα Vibrationally Averaged) and Equilibrium Structures, Rotation Constants, Vibrationally Excited-Rotation Constants, Distortion Constants, and Vibrational Frequencies and Intensities.a 40

r0(Ne−H) (Å) r0(Ar−H) (Å) re(Ne−H) (Å) re(Ar−H) (Å) Be (MHz) B0 (MHz) B1 (MHz) B2 (MHz) B3 (MHz) De (kHz) He (Hz) μzb (D) ω1(σ) shuttle (cm−1) ω2(π) bend (cm−1) ω3(σ) Ne−H (cm−1) ν1(σ) shuttle (cm−1) ν2(π) bend (cm−1) ν3(σ) Ne−H (cm−1) ZPE (cm−1)

ArH20Ne

40

1.605112 1.292541 1.584605 1.304660 4538.3 4523.0 4676.9 4494.7 4395.2 13.699 −0.143 1.43 2394.6 (1255) 385.8 (146) 172.8 (27) 2142.0 260.2 164.4 1565.6

ArD20Ne

40

ArH22Ne

40

ArD22Ne

1.606033 1.295964

1.604361 1.292530

1.605290 1.295909

4533.8 4504.8 4614.9 4484.4 4377.5 13.558 −0.142

4265.1 4252.7 4397.6 4226.0 4136.3 12.122 −0.119

4262.4 4237.1 4341.1 4217.7 4121.0 12.030 −0.118

1716.2 275.3 171.9 1590.5 211.0 162.1 1166.6

2394.6 385.6 167.4 2141.6 260.2 159.7 1562.8

1716.2 275.0 166.5 1590.2 211.0 157.4 1163.8

a

MP2/6-31+G* double-harmonic vibrational intensities in km/mol in are parentheses. bThe center of mass is chosen for the origin with atomic Cartesian coordinates corresponding to Ne, −1.920 175, 0.000 000, and 0.000 000; H, −0.335 569, 0.000 000, and 0.000 000; and Ar, 0.969 091, 0.000 000, and 0.000 000.

though the difference is only 13.9 kcal/mol, less than other differences in the table, the sign changes, giving doubt as to whether or not ArHNe+ is actually stable with respect to neon loss. ArHNe + is a minimum according to the QFF computations; the gradients are all zero with no negative quadratic force constants in Table 5. Furthermore, a CCSD(T)/aug-cc-pV5Z unrelaxed scan of the Ne−H bond length produces a nice Morse potential with asymptotic convergence to 1285 cm−1 beyond 3.5 Å. Consequently, relaxation of the Ar−H bond length after removal of the neon atom may be thermodynamically favored, but ArHNe+ is a local minimum and could be a kinetic formation product. Furthermore, breaking both noble gas atomic bonds is strongly disfavored in line with the symmetric stretching force

to 4.184 kJ/mol and 503.2 K for conversion of the given energies into units more common in the astronomical sciences. The most notable thing from Table 8 is that removing one atom from these triatomic cations will have an energy cost. In other words, each of the three noble gas, proton-bound complexes are stable minima on their respective PESs and will not spontaneously dissociate in any environment in which they may be found. The strengths of the bonds described earlier in this document through force constants, relative bond lengths, and comparable vibrational frequencies are carried through in the dissociation energies. The one exception is the CCSD(T)/ aug-cc-pV5Z result for removing the neon atom from ArHNe+ with a relative energy of 12.3 kcal/mol. MP2/6-31+G* disagrees in this case, with a −1.6 kcal/mol energy. Even 65


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ACS Earth and Space Chemistry Table 8. Relative Formation/Destruction Energetics (kcal/mol) reaction

DF-MP2/6-31+G*

CCSD(T)/aug-cc-pV5Z

Ar + ArH+ → ArHAr+ 2Ar + H+ → ArHAr+ 2ArH+ → ArHAr+ + H+ ArH+ + ArH3+ → ArHAr+ + H3+ naphthalene−Ar + ArH+ → ArHAr+ + naphthalene ovalene−Ar + ArH+ → ArHAr+ + ovalene Ne + NeH+ → NeHNe+ 2Ne + H+ → NeHNe+ 2NeH+ → NeHNe+ + H+ NeH+ + NeH3+ → NeHNe+ + H3+ naphthalene−Ne + NeH+ → NeHNe+ + naphthalene ovalene−Ne + NeH+ → NeHNe+ + ovalene ArH+ + Ne → ArHNe+ Ar + NeH+ → ArHNe+ Ar + Ne + H+ → ArHNe+ ArH+ + NeH+ → ArHNe+ ArH+ + NeH3+ → ArHNe+ + H3+ NeH+ + ArH3+ → ArHNe+ + H3+ naphthalene−Ne + ArH+ → ArHNe+ + naphthalene ovalene−Ne + ArH+ → ArHNe+ + ovalene naphthalene−Ar + NeH+ → ArHNe+ + naphthalene ovalene−Ar + NeH+ → ArHNe+ + ovalene

−2.6 −79.9 74.7 −4.4 0.5 7.5 −13.4 −56.8 29.9 −12.6 −11.8 −6.6 −1.6 −35.5 −78.9 41.8 −0.7 −37.3 0.1 5.2 −32.4 −25.4

−16.6 −110.7 77.4 −7.6

−20.0 −77.1 37.1 −13.5

12.3 −24.6 −81.7 69.4 18.8 −15.6

creation of ArHNe+ is neither favored nor disfavored (if not slightly disfavored) if neon is adsorbed onto the PAH surface with ArH+ acting as the incoming reactant. The converse is true with argon atoms adsorbed onto the PAH surfaces and neonium as the other agent. In all cases, however, that involve the truly favorable creation of NeHNe+ or ArHNe+, NeH+ is a necessary reactant. It is doubtful that NeH+ will form in the ISM in the same manner as ArH+ for reasons discussed in the Introduction.34 However, the energies of some dense regions of the ISM and even planetary atmospheres ranging from relatively thin boundaries, like that of Earth, to thicker boundaries, like gas giants, are likely to have enough energy to overcome the barriers to produce NeH+ or allow for the reactions to bypass such a preceding synthesis. Additionally, the bright proton shuttle motions of these noble gas molecular cations may make their vibrational transitions strong enough to be observed even if their concentrations in such media are still fairly small, especially with modern telescopes, like ALMA and JWST.

constants in the D∞h molecules. However, simple gas-phase reactions for dimers of argonium or neonium colliding with each other or ArH+ impacting with NeH+ in the case of ArHNe+ are not likely to produce ArHAr+, NeHNe+, or ArHNe+. Each requires tens of kcal/mol with NeH+, surprisingly coming in the lowest with 37.1 kcal/mol. These values are much too high for interstellar gas-phase synthesis. However, collisions with the closed-shell noble gas− trihydrogen cation complexes are much more favorable. ArH3+ has not yet been observed in the ISM, but it has been observed in the laboratory98,99 and characterized with the same CcCR QFF approach.42 Furthermore, it has been hypothesized as an astronomical sink of H3+,8,10 a molecule of significant note in gas-phase astrochemical synthesis.6,100 The Ar−H bond in ArH3+ is fairly weak and weaker still in NeH3+, while the H3+ cation is σ-aromatic and quite stable. Consequently, the reaction of the noble gas monohydride and trihydride cations are energetically favorable for the creation of ArHAr+, NeHNe+, and ArHNe+, especially the creation of ArHNe+ from neonium and ArH3+. As was shown previously,38 gas-phase reaction product yields can be catalyzed to produce higher densities of noble gas compounds by adsorption of the noble gas atoms onto a PAH surface in a one-adsorbate, Eley−Rideal fashion. While the double adsorption, Langmuir−Hinshelwood mechanism is also likely possible, such has not been investigated here but could be possible based on recent computations.101 At any rate, as the size of the PAH grows, the adsorption energy of the single noble gas atom onto the PAH also increases.38 In this work, the two ends of the explored PAH size spectrum, naphthalene (C10H8) and ovalene (C32H14), are included and only with MP2/6-31+G* because comparison between this less expensive level of theory and CCSD(T)/aug-cc-pV5Z is qualitatively if not semi-quantitatively consistent. As a result, NeHNe+ is more likely to form via such a PAH adsorption mechanism than ArHAr+. The energies are just barely positive for the argon reactions but negative for neon, even with larger ovalene. The

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CONCLUSION

The noble gas proton-bound complexes of ArHAr+, NeHNe+, and ArHNe+ are characterized here at a high level for the first time. Significant transition intensities are computed for the proton shuttle motion of each cation, with ArHAr+ having the brightest but lowest frequency fundamental proton shuttle. ArHNe+ has the least intense (but still bright) and highest frequency such mode. NeHNe+ lies in between both molecules with regard to both. Consequently, if the formation processes in the ISM, planetary atmospheres, or even the laboratory are slow, a small concentration of material in the sightline will likely still be observable as a result of these notable transition intensities. Only ArHNe+ is purely rotationally observable, but the ν1 = 1 rotations of the other two cations cannot be ruled out for ALMA observation. Furthermore, each of these molecules are stable minima on their PESs, with NeHNe+ the most stable with respect to single 66


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noble gas atom abstraction. This is surprising with respect to previous computations, where neon does not willingly bond. The Ne−H bonds here are stronger than even NeOH+, the previous neon molecule with the strongest Ne bonds, but still not as strong as those in neonium. ArHAr+ is also a stable compound, with ArHNe+ acting more like a van der Waals or hydrogen-bonded complex between argonium and a lone neon atom. The formation of NeHNe+ via either NeH3+ or PAH surface catalysis requires the presence of neonium, whose interstellar abundance is likely significantly lower than argonium. However, ArH3+ has been strongly supported to be present in the ISM, and reactions with it and the known argonium are shown here favorably to produce ArHAr+ in the gas phase. Planetary atmospheres or regions with higher densities or temperatures, like the Crab nebula, where argonium was first detected, may be able to enhance further the formation rates for ArHAr+. Additionally, this argon molecular cation has the most intense and lowest frequency proton shuttle fundamental, making astronomical signals originating from ArHAr+ the most likely of the three triatomic, noble gas, proton-bound cations examined here to be observed in the ISM with ALMA, SOFIA, or JWST.

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AUTHOR INFORMATION

Corresponding Author

*Telephone: 912-478-7694. E-mail: rfortenberry@ georgiasouthern.edu. ORCID

Ryan C. Fortenberry: 0000-0003-4716-8225 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

Startup funds provided by Georgia Southern University were necessary to complete this work. Additionally, the author acknowledges Prof. T. Daniel Crawford of Virginia Tech for the use of computer hardware necessary to complete much of this work, Riley A. Theis formerly of Georgia Southern University for computing some of the necessary CCSD(T)/aug-cc-pV5Z geometries, Gerald T. Filipek, II, of Georgia Southern University for some help in formatting the tables, and Dr. Timothy J. Lee of the NASA Ames Research Center for helping to flesh out the initial stages of this research idea. The figures were created with the CheMVP program developed at the Center for Computational Quantum Chemistry at the University of Georgia.

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