Trihydrogen Cation with Neon and Argon: Structural, Energetic, and

Article pubs.acs.org/JPCA

Trihydrogen Cation with Neon and Argon: Structural, Energetic, and Spectroscopic Data from Quartic Force Fields Riley A. Theis and Ryan C. Fortenberry* Georgia Southern University, Department of Chemistry, Statesboro, Georgia 30460 United States S Supporting Information *

ABSTRACT: The argonium cation, ArH+, has been previously detected in nature for the first time. This cation is believed to form through the gas-phase reaction of Ar+ and H2. In this work, quantum chemical techniques show that the reaction of Ar and H3+ may be a viable alternative or contributor to the creation of ArH+ corroborating previous analysis. In order to further evaluate this claim, highly accurate quartic force field computations are used to produce spectroscopic data and anharmonic vibrational frequencies for ArH3+ in its 18 isotopologues. NeH3+ is also analyzed but has a low Ne−H3+ dissociation barrier. Therefore, it less likely to be observed. Consequently, NeH+ is also unlikely to be formed from NeH3+ as it was also not from NeH2+.

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above the minimum. The Ne+ + H2 potential energy surface is corroborated by previous computations.25 Hence, NeH+ is not likely to form in the ISM, at least not in a similar fashion as ArH+,28 also casting doubt on any detectable amounts of neon hydride cations of any kind to be present in the ISM. Since ArH+ is known to exist in the ISM and is likely a product of the dissociation of ArH2+, it is natural to extend the study of noble gas molecular cations to molecules with larger numbers of hydrogens. The trihydrogen cation (H3+) is a wellstudied interstellar molecular system of much significance for the chemistry of diffuse molecular clouds.29−34 The coupling of noble gases to this system has been analyzed computationally of late.5−8,15 It has been shown6,15 that neon prefers to function more as a lone entity loosely affiliating with the trihydrogen system while argon has more bonding character with the attached cation. This highlights a similar trend in NeH3+ versus ArH3+ as has been observed for NeH2+ versus ArH2+25,28 corroborating previous rotational spectroscopic experiments on ArH3+.9−12 However, these initial experiments utilized the most common earthly isotope of argon, 40Ar, whereas 36Ar and 38Ar are significantly more abundant in the ISM.3 Even though the larger krypton and xenon atoms increase the propensity for bonding in the noble gas atoms as a result of their larger size and higher polarizability, their expected abundances make the likelihood of any interstellar detection low. Hence, argon complexes, including ArH2+ and ArH3+, are the most likely noble gas molecules left to be observed in the ISM. This work will build on previous analysis of ArH3+ and ArH2+5−12,15,28 to produce anharmonic vibrational frequencies, vibrationally

INTRODUCTION The discovery of ArH+ in the Crab Nebula1,2 has reignited the exploration of noble gas chemistry as more than simply an academic pursuit.3,4 Naturally occurring noble gas molecules have been suspected of serving as harbors of molecular hydrogen in astronomical environments5−8 and examined in a limited scope experimentally for some time.9−12 This discovery has shown that these “inert” atoms may have more dynamism than previously believed. Complexes involving all of the noble gases have been studied computationally and experimentally over the past few decades,2,5−26 but their actual existence in nature beyond the laboratory is creating new impetus for their study. The smallest of the noble gases, helium, is a ubiquitous entity of the interstellar medium (ISM), second only to hydrogen. Neon is actually the fifth-most abundant atom observed in the ISM, greater even than nitrogen. Argon is not nearly as abundant, but its presence is certainly non-negligible, being roughly as common as sodium and calcium.27 Krypton is heavier than iron and nickel meaning that stellar nucleosynthesis is largely unable to build its necessary nuclear structure. As such, its abundance is 3 orders of magnitude less than that of argon.27 Xenon is far less abundant still. Consequently, the three smallest noble gas elements are the most likely to take part in interstellar chemistry. It has recently been shown28 that the proposed formation mechanism1 of ArH+ from ionized Ar+ and ubiquitous H2 likely proceeds through the metastable ArH2+ intermediate. The triatomic system is a minimum lying 0.493 eV below the ArH+ + H products. The creation of NeH+ from Ne+ + H2, on the other hand, also proceeds through a NeH2+ minimum, but the desired NeH+ + H products are 1.031 eV above the triatomic minimum with a competing product set, Ne + H2+, 0.560 eV © XXXX American Chemical Society

Received: March 30, 2015 Revised: April 28, 2015

A

DOI: 10.1021/acs.jpca.5b03058 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A Table 1. CcC Simple-Internal Force Constants for NeH3+ (in mdyn/Ån·radm) F11 F21 F22 F31 F32 F33 F44 F54 F55 F66 F111 F211 F221 F222 F311 F321 F322 F331 F332 F333

0.154 183 0.048 394 3.427 467 0.159 066 −1.927 658 3.603 946 2.956 206 0.003 168 0.011 278 0.023 123 −0.9623 −0.2603 −0.0525 −14.1509 −0.0012 0.0590 5.2213 0.0042 −9.7324 28.1569

F441 F442 F443 F541 F542 F543 F551 F552 F553 F661 F662 F663 F1111 F2111 F2211 F2221 F2222 F3111 F3211 F3221

−0.4186 −9.0167 −4.6272 −0.2238 0.0159 −2.6815 −0.1138 0.0040 −0.1377 0.2934 −4.8946 9.4786 7.59 1.10 4.12 −0.06 74.58 −44.25 −0.10 −38.04

COMPUTATIONAL DETAILS In order to determine accurately the structure and potential presence of both NeH3+ and ArH3+ in the ISM, a quartic force field (QFF) is constructed for each molecule. QFFs are fourthorder Taylor series expansion approximations of the anharmonic nuclear potential and are defined from the following equation:

1 + 24

∑ FijkΔiΔjΔK ijk

∑ FijklΔiΔjΔk Δl ijkl

−32.52 7.15 −0.09 3.64 13.13 −0.12 7.12 9.44 −32.60 6.03 3.63 0.14 21.45 −24.42 −32.66 104.57 −5.26 −19.59 6.01 82.23

S1(a1) = Ng−H1

■

∑ FijΔiΔj + 1 6 ij


of 0.005 radians. The internal symmetric coordinates for the NgH3+ (Ng = Ne, Ar) molecules are as follows:

averaged rotational constants, and relative energetic data for ArH3+ for all of the interesting isotopologues including 36Ar, 38 Ar, 40Ar, H, and D as well as to comment on the bonding of ArH3+ and NeH3+.

1 V= 2

−12.37 4.98 0.16 20.83 −45.72 −46.42 198.89 8.06 0.21 33.43 12.68 28.84 −54.44 65.79 10.35 −0.08 −35.57 217.45 0.06 10.37


(2)

S2(a1) =

1 [(H1−H 2) + (H1−H3)] 2

(3)

S3(a1) =

1 [∠(Ng−H1−H 2) + ∠(Ng−H1−H3)] 2

(4)

S4(b2) =

1 [(H1−H 2) − (H1−H3)] 2

(5)

S5(b2) =

1 [∠(Ng−H1−H 2) − ∠(Ng−H1−H3)] 2

(6)

S6(b1) = OPB∠(Ng−H1−H 2−H3) (1)

(7)

49

Using the INTDER program, the torsional motion is described with the out-of-plane (OPB) angle which is defined as the perpendicular angle between the Ng atom and the plane created by H1, H2, and H3. The noble gas is bonded to the Hydrogen defined as H1, while H2 and H3 are the symmetrical atoms completing the ring. Such a construction utilizes the same geometrical connectivity as that from ref 50. For each of the 413 points, CCSD(T) energies are computed using the augcc-pVTZ, aug-cc-pVQZ, and the aug-cc-pV5Z basis sets, which are then extrapolated to the 1-particle complete basis set (CBS) limit by a three-point formula.51 Corrections using the MT basis set with and without core electrons are also used for the computed energies. The CcC QFF is therefore constructed, where the “C” is for CBS and the “cC” is for core correlation building on the composite QFF nomenclature created by Fortenberry and co-workers.52 The force constants are derived by fitting the energy points using a least-squares technique. Refitting the points once more guarantees a minimum on the potential surface, and this process also produces the equilibrium geometry and zero gradients along with refined quadratic, cubic, and quartic terms. The force constants are then included in the nuclear Hamiltonian by means of the SPECTRO program53 in which

The displacements are represented by Δi, whereas the force constants are depicted as Fij.... All electronic structure computations use restricted reference wave functions for the present closed-shell cations35 and the free and open-source PSI4 quantum chemistry program.36 To begin constructing the QFFs,37−39 coupled cluster singles, doubles and perturbative triples [CCSD(T)]40 geometry optimizations are computed for both NeH3+ and ArH3+ using the aug-cc-pV5Z basis set.41,42 Argon, however, requires aug-cc-pV(5+d)Z,43 but this is abbreviated as simply aug-cc-pV5Z here. Using the Martin− Taylor (MT) core-correlating basis set,44 the geometries are further corrected to compensate for core−electron effects. The difference between the CCSD(T)/MT bond lengths and bond angles with and without core electrons are added to the corresponding geometrical parameters determined from CCSD(T)/aug-cc-pV5Z. QFFs of this type have been used to produce harmonic vibrational frequencies to as good as within 1 cm−1 of gas-phase experimental results, especially for hydride stretches.39,45−48 Once the geometries are obtained, a grid of 413 points are used to define the QFF. Displacements of the bond lengths are in increments of 0.005 Å, and the bond angle is in increments B


Article

The Journal of Physical Chemistry A Table 2. CcC Simple-Internal Force Constants for ArH3+ (in mdyn/Ån·radm) F11 F21 F22 F31 F32 F33 F44 F54 F55 F66 F111 F211 F221 F222 F311 F321 F322 F331 F332 F333

0.478 761 0.296 078 2.864 337 0.487 116 −2.441 475 5.084 349 2.289 836 −0.016 222 0.048 262 0.093 195 −2.5950 −0.9054 −0.1997 −11.2555 −1.0104 0.1371 5.2473 0.3013 −12.6252 41.6474


−0.8924 −5.0307 −6.9198 0.0241 0.0426 0.0137 −0.1420 −0.0047 −0.0134 1.1354 −7.0437 14.6062 11.56 2.78 1.20 0.10 42.93 1.29 0.21 −0.70


the vibrational frequencies54,55 and the spectroscopic constants56 are produced through the second-order perturbation theory. Second-order vibrational perturbation theory is denoted as VPT2 herein. The SPECTRO computations require input of various resonances. The Argon isotopes do not affect these inputs so they are standard across the heavy atom set. ArDDH+, where H1 and H2 are replaced with deuterium atoms, requires input of a 2ν3 = ν1 type-1 Fermi resonance as well as ν5 + ν3 = ν6 + ν3 = ν2 type-2 Fermi resonances. ArHDD+ possesses a ν5 + ν2 = ν1 type-2 Fermi resonance while ArHHD+ has a ν6 + ν3 = ν2 type-2 Fermi resonance. All of the deuterated isotopologues possess a ν6/ν5 Darling−Denison resonance. ArDHH+ and ArDDH+ also have an additional ν5/ν4 Darling−Denison resonance while ArD3+ has both of these as well as another ν 3 /ν 2 resonance of the same type. All but ArHDD + demonstrate a ν5/ν4 A-type Coriolis resonance. This exception requires input of a ν3/ν2 C−type Coriolis resonance. ArD3+ and ArH3+ possess both types of Coriolis resonance.

−11.89 0.41 0.80 19.16 −0.06 −63.85 326.43 2.68 0.40 13.56 −2.03 39.51 −95.82 59.13 0.05 −0.00 0.09 0.04 −0.24 −0.02


−0.03 1.08 0.05 −0.02 −0.09 0.09 0.31 0.27 −0.03 0.47 −1.93 0.68 15.18 3.40 −49.22 173.61 −19.79 0.20 0.92 127.18

Table 3. CCSD(T)/aug-cc-pV5Z Dissociation Pathway Energies (in eV) Relative to NeH3+ and ArH3+ NeH3+ products H3+

Ne + NeH+ + H2 Ne + H2 + H+ NeH2+ + H a b

relative energy

ArH3+ product

0.113 2.417 4.722 6.129

H3+

Ar + ArH+ + H2 Ar + H2 + H+ ArH2+ + H

relative energy 0.392 0.923 5.001 5.159

(0.313a) (0.739a) (4.644b) (5.204b)

MP2/cc-pVQZ results with zero-point energy corrections from ref 8. CCSD(T)/aug-cc-pVTZ results from ref 5.

cm−1. This is much less than any of the expected hydride stretches. Consequently, the likelihood that NeH3+ will be detected is quite low, but the abundance of neon in the ISM may create an observable population especially for the rotational features at cold temperatures. ArH3+ is much more stable (the dissociation limit is 0.392 eV or 3164.4 cm−1), in accordance with previous studies,5−8 such that most vibrational features of this cation should be observable. As a result, only the vibrational, rotational, and rovibrational spectral features are reported for ArH3+, and the low energy barrier does not allow for such with regards to NeH3+. Additionally, the minimum energy well-defined by the optimized geometry reported is fairly deep. The barrier to inplane rotations of the argon with respect to the center-of-mass for the trihydrogen cation is computed herein via CCSD(T)/ aug-cc-pVTZ to be greater than 1.5 eV (12 000 cm−1). The direct bending of ∠Ar−H1−H2/3 is much lower and is estimated from a parabolic fit to be 0.35 eV (2800 cm−1). A fit of these same points to a sine function, which gives proper limiting behavior,57 puts this barrier much lower at 0.16 eV (1300 cm−1) in line with the energy barrier previously determined.10 CCSD(T)/aug-cc-pVTZ energy points are computed spanning 0.0° (no displacement) to 30.0° from the optimized ∠Ar−H−H and extrapolated out to 60.0°. The same ∠Ne−H−H bending coordinate produces a parabolic barrier of 0.08 eV (620 cm−1) and a sine barrier of 0.037 eV (295 cm−1). These values scale with the noble gas−hydrogen bond dissociation energies discussed above and given in Table 3 indicating that the association/dissociation of these molecules may involve either or a combination of both pathways. The

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RESULTS AND DISCUSSION Structural and Energetic Considerations. The CcC force constants are provided in Tables 1 and 2 for NeH3+ and ArH3+, respectively. The fittings produced in this work report sums of residuals squared on the order of 10−17 au2. The first thing to note about the force constants themselves is the very weak Ne−H interaction given in F11, 0.154 183 mdyn/Å2. This is nearly an order of magnitude less than the Ne−H force constant for NeH2+ (1.039 234 mdyn/Å2).28 The Ar−H F11 for ArH3+ is significantly greater than that for the neon counterpart at 0.478 761 mdyn/Å2 but also less than the same force constant for ArH2+ (1.895 279 mdyn/Å2). Hence, bonding of the neon and argon atoms to the trihydrogen cation is weak, with the argon attachment being relatively stronger by a factor of about 3. In order to provide more quantitative measures as to the strengths of the interactions between the noble gas atoms and the trihydrogen cation, CCSD(T)/aug-cc-pV5Z computations of the various dissociation pathways is given in Table 3 closely mirroring previous results where applicable.5,8 It is clear that the association of neon to H3+ is very weak at 0.113 eV or 915 C


Article

The Journal of Physical Chemistry A

Table 4. CcC QFF Equilibrium and (Rα) Vibrationally-Averaged Structures, Rotational Constants, Equilibrium Quartic and Sextic Distortion Constants, and Vibrational Frequenciesa of 36ArH3+ and Deuterium Isotopologuesb r0(Ar−H1) r0(H1−H2) ∠(Ar−H1−H2) A0 B0 C0 DJ DJK DK d1 d2 HJ HJK HKJ HK h1 h2 h3 ω1(a1) H2−H3 ω2(a1) breathing ω3(a1) Ar−H1 ω4(b2) (H1−H2) − (H1−H3) ω5(b2) Ar wagging ω6(b1) OPB ν1(a1) H2−H3 ν2(a1) breathing ν4(b2) (H1‑H2) − (H1‑H3) re(Ar−H1) re(H1−H2) ∠(Ar−H1−H2) Ae Be Ce μ

units

ArH3+

Å Å Å deg deg GHz GHz GHz MHz MHz MHz kHz kHz Hz Hz MHz MHz Hz Hz Hz cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 Å Å deg GHz GHz GHz D

1.804 904 0.959 546

previousc

ArHHD+

ArDHH+

ArD3+

ArDDH+

ArHDD+

1.814 233 0.953 371

1.809 029 0.952 468

153.917

154.028

1 473.8 26.861 26.311 0.475 28.574 1278.002 −7.383 −0.333 −12.180 −170.275 −0.570 2.021 −0.235 0.019 0.003 3534.3 1873.6 398.1 2163.7 494.9 592.7 3192.7 1586.3 1878.1 − − − 1 466.2 26.873 26.386 −

738.8 16.792 16.376 0.154 8.949 318.162 −2.964 −0.182 −2.942 −29.129 −0.058 0.240 −0.076 0.006 0.001 2519.2 1548.1 346.7 1667.0 417.8 543.7 2380.9 1339.4 1494.5 − − − 733.7 16.783 16.407 −

1.811 930 0.953 021 0.952 719 153.893 154.064 1 081.4 20.500 20.066 0.253 12.022 1358.110 −0.004 −0.201 −5.358 −12.041 −0.195 −0.954 −0.103 0.010 0.002 3093.0 1624.9 363.4 1975.1 459.7 568.7 2907.4 1415.1 1710.0 − − − 1 070.2 20.512 20.124 −

1.795 337 0.959 510

3567 2194 455 2362 597 782 − 1925 2104 1.818 0.937 156.214 1 469 30.84 30.21 −

1.800 387 0.959 797 0.959 190 154.359 154.077 1 098.2 22.797 22.269 0.274 13.641 997.797 −5.126 −0.272 −6.857 −17.882 −0.136 1.371 −0.151 0.014 0.002 3134.7 1968.1 411.8 2186.1 553.4 749.3 2929.5 1664.3 1846.0 − − − 1 084.0 22.736 22.266 −

154.145 1 480.9 31.252 30.509 0.539 32.189 1274.324 −9.638 −0.550 −18.938 −226.999 −0.404 1.856 −0.451 0.032 0.006 3561.2 2187.3 472.4 2356.6 589.5 767.7 3284.7 1766.1 2010.0 1.815 032 0.935 545 153.767 1 466.2 31.202 30.547 8.14

154.302 743.0 18.218 17.729 0.161 9.407 317.698 −3.323 −0.233 −3.472 −26.134 −0.034 0.216 −0.097 0.008 0.001 2581.6 1891.4 386.7 1921.0 487.6 730.5 2431.5 1597.7 1699.5 − − − 733.7 18.131 17.692 −

a The harmonic frequencies are labeled as ωi, and the anharmonic fundamentals are labeled as νi. bThe deuterium substitutions for the hydrogens are labeled from left-to-right as H1 (the hydrogen adjacent to the noble gas atom), H2 (one of the external hydrogens), and H3 (the other external hydrogen) giving ArH1H2H3. cCCSD(T)/aug-cc-pVQZ results from ref 7.

well-known tunneling of these molecules10,12 is not included in the present approach. However, this should not be a major concern for those values computed below the barrier, especially the rotational constants, as has been done previously with noted success for other loosely bound cationic systems.58 As a final note on dissociation energies, these computations provide an alternative formation pathway for ArH+ in nature. The current mechanism of favor involves Ar+. It first must be ionized at a cost of over 15 eV beforehand which is, coincidentally similar to the ionization energy of H2. Ar+ reacting with H2 can give ArH+ and H1,4 shedding around 1.5 eV in the process.28 Likely, this scheme proceeds through the ArH2+ intermediate which is around 0.5 eV below the final products.28 If argon is not in an environment where it can be ionized, it may still associate with hydrogen to create ArH+, but such a reaction would proceed through H3+ in this case. Creation of ArH+ and H2 from ArH3+ is an uphill reaction of 0.923 eV from Table 3, more than ArH2+ to ArH+ + H at 0.493 eV, but this type of formation pathway has long-been suggested

for the destruction of H3+ in the ISM in places such as dense molecular clouds.31 Even though the ionization potential is still quite high for molecular hydrogen to form and then create H3+,31,32 H2+ (and H3+, as a result) is still certainly more abundant than Ar+. Hence, Ar + H3+→ ArH+ + H2 may be a competing reaction with Ar+ + H2 → ArH+ + H to form the argonium cation. The energetics of neon once more disfavor any creation of NeH+ casting even more doubt on its potential interstellar detection.28 Rovibrational Spectral Data for ArH3+. The equilibrium structural and spectroscopic data for the most common extraterrestrial isotope of argon, 36Ar given in Table 4, is in line with that computed previously.7 The bond lengths are within 0.003 Å, and the rotational constants are within 3 GHz. However, vibrational averaging of the rotational constants, given here, is significant. The A-type constant is actually over 10 GHz greater than the equilibrium computations indicate at 1 480.9 GHz with B0 and C0 computed to be several hundred MHz higher at 31.252 and 30.509 GHz, respectively. D


Article


Table 5. Deuterated and Standard 38ArH3+ Equilibrium and (Rα) Vibrationally-Averaged Structures, Rotational Constants, Equilibrium Quartic and Sextic Distortion Constants, and Vibrational Frequenciesa for the CcC QFF.a r0(Ar−H1) r0(H1−H2) ∠(Ar−H1−H2) A0 B0 C0 DJ DJK DK d1 d2 HJ HJK HKJ HK h1 h2 h3 ω1(a1) H2−H3 ω2(a1) breathing ω3(a1) Ar−H1 ω4(b2) (H1−H2) − (H1−H3) ω5(b2) Ar wagging ω6(b1) OPB ν1(a1) H2−H3 ν2(a1) breathing ν4(b2) (H1−H2) − (H1−H3) re(Ar−H1) re(H1−H2) ∠(Ar−H1−H2) Ae Be Ce a

units

ArH3+

ArHHD+

ArDHH+

ArD3+

ArDDH+

ArHDD+

Å Å Å deg deg GHz GHz GHz MHz MHz MHz kHz kHz Hz Hz MHz MHz Hz Hz Hz cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 Å Å deg GHz GHz GHz

1.804 816 0.959 551

1.800 286 0.959 803 0.959 196 154.360 154.077 1 098.2 22.681 22.157 0.271 13.533 997.906 −5.050 −0.266 −6.753 −18.634 −0.135 1.369 −0.148 0.014 0.002 3134.7 1968.1 410.7 2186.1 553.3 749.3 2929.4 1664.1 1845.9 − − − 1 084.0 22.618 22.153

1.814 136 0.953 373

1.808 909 0.952 474

1.795 225 0.959 518

153.918

154.029

1 473.8 26.725 26.182 0.471 28.374 1278.207 −7.278 −0.327 −11.989 −168.899 −0.565 2.016 −0.230 0.018 0.003 3534.3 1873.6 397.1 2163.7 494.9 592.6 3192.6 1586.0 1878.0 − − − 1 466.2 26.736 26.254

738.8 16.671 16.260 0.152 8.854 318.259 −2.903 −0.177 −2.879 −29.099 −0.057 0.239 −0.073 0.006 −0.001 2519.2 1548.0 345.4 1667.0 417.7 543.6 2380.9 1339.1 1494.4 − − − 733.66 16.660 16.289

1.811 821 0.953 026 0.952 722 153.893 154.065 1 081.4 20.374 19.945 0.250 11.910 1358.322 −4.314 −0.196 −5.258 −12.414 −0.193 −0.957 −0.101 0.010 0.001 3093.0 1624.8 362.3 1975.1 459.6 568.6 2907.4 1414.8 1709.8 − − − 1 070.1 20.384 20.001

154.146 1 480.9 31.130 30.393 0.535 32.005 1274.511 −9.530 −0.541 −18.715 −226.519 −0.401 1.853 −0.444 0.032 0.006 3561.2 2187.2 471.5 2356.6 589.4 767.7 3284.7 1765.9 2009.9 1.815 032 0.935 545 153.767 1 466.2 31.078 30.429

154.303 743.0 18.104 17.621 0.159 9.317 317.789 −3.263 −0.228 −3.408 −26.350 −0.033 0.215 −0.095 0.007 0.001 2581.6 1891.4 385.5 1921.0 487.5 730.5 2431.2 1597.5 1699.4 − − − 733.66 18.016 17.583

The isotopic labels follow the ArH1H2H3 nomenclature as done in Table 4, and the harmonic (ωi) and anharmonic (νi) frequencies are given.

Arguably, the most important mode present in ArH3+ is the ν4 mode representing the antisymmetric hydride stretching. The degenerate but observable ν2 antisymmetric hydride motion of H3+ splits into the ν1 and ν4 modes of ArH3+ upon inclusion of the argon atom. H3+ ν2 falls in the 2725 cm−1 range,29,30,33 but the presence of the argon atom destabilizes the upper component to increase in frequency. The ν1 symmetric hydride stretching frequency at 3284.7 cm−1 actually moves above the computed 3164.4 cm−1 dissociation limit. However, the lower-frequency ν4 mode portion of this split fundamental is down-shifted below the dissociation threshold. Additionally, ν4 retains the antisymmetric character of the parent H3+ fundamental. The CcC QFF with VPT2 places this frequency at 2010.0 cm−1, nearly 100 cm−1 below the scaled value from previous work.7 Consequently, our computations indicate that the frequency shift brought about by the symmetry breaking is greater than previously anticipated. The other totally symmetric hydride stretch is the ν2 breathing mode where all of the bond distances are increasing simultaneously. VPT2 CcC puts the frequency for this motion at 1766.1 cm−1, which is 158.9 cm−1 below the CCSD(T)/aug-cc-pVQZ scaled value.7

Additionally, equilibrium quartic and sextic distortion constants are also provided in Table 4 with the vibration−rotation interaction constants given in Table 1 of the Supporting Information. The CCSD/aug-cc-pVTZ Born−Oppenheimer equilibrium dipole moment computed from the center of mass is quite large at 8.14 D. Previous CCSD(T)/aug-cc-pVQZ harmonic vibrational frequencies7 are congruous with the VPT2 CcC harmonic frequencies in Table 4 indicating that the baseline values provided by our methodology are consistent with the established literature. However, the inclusion of anharmonic effects shows marked deviations between the singly and fully deuterated isotopologues. The previous work relies on a general scaling factor whereas the present results are computed explicitly. The loose association of the Argon to the trihydrogen structure creates problems for the QFF, especially in regards to the vibrational motions related to the heavy atom. These VPT2 frequencies produced are either largely positively anharmonic or overly corrective in nonphysical ways giving an internal metric as to their validity. Even so, the perturbations of the hydride motions do not show any of these markers and are readily computed. E


Article


Table 6. The 40ArH3+ CcC QFF Equilibrium and (Rα) Vibrationally-Averaged Structures, Rotational Constants, Equilibrium Quartic and Sextic Distortion Constants, and Vibrational Frequencies.a r0(Ar−H1) r0(H1‑H2) ∠(Ar−H1−H2) A0 B0 C0 DJ DJK DK d1 d2 HJ HJK HKJ HK h1 h2 h3 ω1(a1) H2−H3 ω2(a1) breathing ω3(a1) Ar−H1 ω4(b2) (H1−H2) − (H2−H3) ω5(b2) Ar wagging ω6(b1) OPB ν1(a1) H1−H2 ν2(a1) breathing ν4(b2) (H1−H2) − (H2−H3) re(Ar−H1) re(H1−H2) ∠(Ar−H1−H2) Ae Be Ce

units

ArH3+

Å Å Å deg deg GHz GHz GHz MHz MHz MHz kHz kHz Hz Hz MHz MHz Hz Hz Hz cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 cm−1 Å Å deg GHz GHz GHz

1.804 736 0.959 555 − 154.146 − 1 480.9 31.020 30.288 0.532 31.840 1274.680 −9.433 −0.534 −18.516 −226.071 −0.399 1.850 −0.437 0.031 0.006 3561.2 2187.2 470.6 2356.6 589.4 767.6 3284.7 1765.6 2009.8 1.815 032 0.935 545 153.767 1 466.2 30.967 30.322

ArH3+ exptc

1 477.964 2 30.941 553 8 30.159 080 2 0.541 22 35.749 8 −11.302 −1.538 −30.38

ArHHD+

ArDHH+

ArD3+

1.800 195 0.959 809 0.959 202 154.361 154.077 1 098.2 22.576 22.057 0.269 13.436 998.003 −4.982 −0.261 −6.660 −19.294 −0.134 1.368 −0.145 0.013 0.002 3134.7 1968.1 409.8 2186.1 553.1 749.3 2929.3 1663.9 1845.7 − − − 1 084.0 22.512 22.052

1.814 047 0.953 374 − 153.918 − 1 473.8 26.603 26.065 0.467 28.193 1278.392 −7.183 −0.321 −11.817 −167.653 −0.560 2.011 −0.225 0.018 0.003 3534.3 1873.5 396.2 2163.7 494.8 592.5 3192.5 1585.8 1877.9 − − − 1 466.2 26.612 26.135

1.808 800 0.952 479 − 154.029 − 738.8 16.561 16.155 0.150 8.768 318.347 −2.848 −0.173 −2.822 −29.064 −0.056 0.238 −0.071 0.005 0.001 2519.1 1547.9 344.2 1667.0 417.6 543.5 2380.9 1338.8 1494.3 − − − 733.66 16.549 16.183

ArD3+ exptb

745.360 8 16.517 556 5 16.099 304 4 0.155 289 9.417 8 −3.304 −0.361 8 −4.124 −33.3

−0.064 0.014 1

ArDDH+

ArHDD+

1.811 723 0.953 030 0.952 725 153.893 154.066 1 081.4 20.260 19.836 0.248 11.809 1358.512 −4.245 −0.191 −5.169 −12.738 −0.191 −0.959 −0.098 0.010 0.001 3093.0 1624.8 361.3 1975.1 459.5 568.6 2907.3 1414.6 1713.4 − − − 1 070.1 20.269 19.890

1.795 122 0.959 525 − 154.303 − 743.0 18.001 17.523 0.157 9.237 317.871 −3.209 0.222 −3.351 −26.533 −0.033 0.215 −0.093 0.007 0.001 2581.6 1891.3 384.4 1921.0 487.5 730.4 2431.0 1597.2 1699.3

733.66 17.913 17.485

a c

The harmonic (ωi) and anharmonic (νi) frequencies are given. bThe isotopic labels follow the ArH1H2H3 nomenclature as done in Table 4. Experimental results from ref 12.

rovibrational spectrum when comparing Table 4 to either Table 5 or Table 6. The anharmonic vibrational frequencies for the hydride stretches are little-affected since the computed frequencies do not involve the Argon atom. The harmonic frequencies involving the heavy atom show some differences between isotopologues. The ω3 Ar−H stretch, for instance, decreases from 472.4 cm−1 in the 36Ar molecule to 471.5 cm−1 for 38Ar and 470.6 cm−1 for 40Ar. The C-type rotational constants shows a steady decrease with the inclusion of more neutrons in the Argon nucleus, and this is intrinsically tied to the shrinking of the Ar−H bond length. As a final note, the rotational constants reported in Table 6 for 40ArH3+ and 40 ArD3+ are in good agreement with early experimental work by Bogey and co-workers.9 Later refinements using “rigid” and “flexible” Hamiltonians 10 bookend the computed CcC spectroscopic constants. However, the more advanced techniques and later results from Bailleux and co-workers12 produce exceptionally good agreement for all of the rotational constants. The B- and C-type constants match the experiment to 80 MHz in some cases. Even the D- and H-type constants perform well with differences compared to experiment of less

The current work also provides data for the various isotopologues of ArH3+ in order to aid further in the potential detection for any form of this cation whether in the laboratory or even in the ISM. Deuteration at one of the symmetryequivalent external Hydrogen atoms (H2 or H3 giving the socalled 36ArHHD+ structure) significantly drops the A-type rotational constant and the vibrational frequencies in an expected manner as shown in Table 4. The shifts in spectroscopic values are less severe for deuteration of the apical hydrogen (H1) in ArDHH+. The B- and C-type rotational constants decrease to 26.860 and 26.311 GHz, but this is less than with ArHHD+. The ν4 frequency is higher for ArDHH+ than ArHHD+, but they are both more than 130 cm−1 redshifted from the standard isotopologue. Triple deuteration scales all values down, while double-deuteration expectedly falls in between the two sets. Double-deuteration of the two equivalent Hydrogens giving ArHDD+ actually produces the shortest Rα vibrationally averaged Ar−H1 bond length at 1.795 337 Å. Including either of argon’s other two stable isotopes, 38Ar and 40Ar, will not produce as drastic of changes in the F


Article


(3) Schilke, P.; Neufeld, D. A.; Müller, H. S. P.; Comito, C.; Bergin, E. A.; Lis, D. C.; Gerin, M.; Black, J. H.; Wolfire, M.; Indriolo, N.; et al. Ubiquitous Argonium (ArH+) in the Diffuse Interstellar Medium: A Molecular Tracer of Almost Purely Atomic Gas. Astron. Astrophys. 2014, 566, A29. (4) Roueff, E.; Alekseyev, A. B.; Bourlot, J. L. Photodissociation of Interstellar ArH+. Astron. Astrophys. 2014, 566, A30. (5) Pauzat, F.; Ellinger, Y. H3+ as a Trap for Noble Gases: 1 - The Case of Argon. Planet. Space Sci. 2005, 53, 1389. (6) Pauzat, F.; Ellinger, Y. H3+ as a Trap for Noble Gases - 2: Structure and Energetics of XH3+ Complexes from X=Neon to Xenon. J. Chem. Phys. 2007, 127, 014308. (7) Pauzat, F.; Ellinger, Y.; Pilmè, J.; Mousis, O. H3+ as a Trap for Noble Gases - 3: Multiple Trapping of Neon, Argon, and Krypton in XnH3+ (n = 1−3). J. Chem. Phys. 2009, 130, 174313. (8) Pauzat, F.; Ellinger, Y.; Mousis, O.; Dib, M. A.; Ozgurel, O. GasPhase Sequestration of Noble Gases in the Protosolar Nebula: Possible Consequences on the Outer Solar System Composition. Astrophys. J. 2013, 777, 29. (9) Bogey, M.; Bolvin, H.; Demuynck, C.; Destombes, J. L. High Resolution Rotational Spectroscopy of Weakly Bound Ionic Clusters: ArH3+, ArD3+. Phys. Rev. Lett. 1987, 58, 988−991. (10) Bogey, M.; Bolvin, H.; Demuynck, C.; Destombes, J. L.; Eijck, B. P. V. Tunneling Motion in ArH3+ and Isotopomers from the Analysis of their Rotational Spectra. J. Chem. Phys. 1988, 88, 4120−4126. (11) Ohshima, Y.; Endo, Y. Rotational Spectroscopy of Jet-Cooled Molecular Ions and Ion Complexes. Chem. Phys. Lett. 1996, 256, 635− 640. (12) Bailleux, S.; Bogey, M.; Bolvin, H.; Civis, S.; Cordonnier, M.; Krupnov, A. F.; Tretyakov, M. Y.; Walters, A.; Coudert, L. H. SubMillimeter-Wave Spectroscopy of the Ar·H3+ and Ar·D3+ Ionic Complexes. J. Mol. Spectrosc. 1998, 190, 130−139. (13) Tosi, P.; Dmitrijev, O.; Soldo, Y.; Bassi, D.; Cappelletti, D.; Pirani, F.; Aquilanti, V. The reaction of argon ions with hydrogen and deuterium molecules by crossed beams: Low energy resonances and role of vibronic levels of the intermediate complex. J. Chem. Phys. 1993, 99, 985−1003. (14) McKellar, A. R. W. High resolution infrared spectra of H2-Ar, HD-Ar, and D2-Ar van der Waals complexes betwee 160 and 8620 cm−1. J. Chem. Phys. 1996, 105, 2628−2638. (15) Beyer, M.; Savchenko, E. V.; Niedner-Schatteburg, G.; Bondybey, V. E. Trihydrogen cation solvated by rare gas atoms: RgnH3+. J. Chem. Phys. 1999, 110, 11950−11957. (16) Kim, S. T.; Lee, J. S. Ab initio study of He2H+ and Ne2H+: Accurate structure and energetics. J. Chem. Phys. 1999, 110, 4413− 4417. (17) Linnartz, H.; Verdes, D.; Maier, J. P. Rotationally resolved infrared spectrum of the charge transfer complex [Ar-N2]+. Science 2002, 297, 1166−1167. (18) Song, J.-B.; Gisalson, E. A. Theoretical study of collision induced dissociation in state-selected collisions of H2+ + Ar and HD+ + Ar. Chem. Phys. 2003, 293, 231−237. (19) McKellar, A. R. W. High resolution infrared spectra of H2-Kr and D2-Kr van der Waals complexes. J. Chem. Phys. 2005, 122, 084320. (20) Mayneris, J.; Sierra, J. D.; González, M. Time dependent quantum dynamics study of the Ne+H2+ (ν = 0−4) →NeH+ + H proton transfer reaction. J. Chem. Phys. 2008, 128, 194307. (21) McKellar, A. R. W. High resolution infrared spectra of H2-Ne and D2-Ne van der Waals complexes. Can. J. Phys. 2009, 87, 411−416. (22) Barletta, P. Comparative study of rare gas-H2 triatomic complexes. Eur. Phys. J. D 2009, 53, 33−40. (23) Borocci, S.; Giordani, M.; Grandinetti, F. Cationic noble gas hydrides-2: A theoretical investigation on HNgHNgH+ (Ng = Ar, Kr, Xe). Comput. Theor. Chem. 2011, 964, 318−323. (24) Grandinetti, F. Review: gas-phase ion chemistry of the noble gases: Recent advances and future perspectives. Eur. J. Mass Spectrom. 2011, 17, 423−463.

than 10 kHz (2%) and 15 Hz, respectively, in line with or better than many other D- and H-type constants.59 This indicates that our computed values for the other isotopologues should be performing in a similar, meaningful fashion.

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CONCLUSIONS ArH3+ may yet be another possible intermediate in the creation of the newly discovered interstellar argonium cation, the first noble gas molecule observed in nature. Even though energetics appear to favor Ar+ + H2 as the reactants for such a synthesis, Ar + H3+ leading to ArH+ + H2 could pose some significant contribution especially where ionization of argon is not feasible but where the trihydrogen cation may have a long lifetime. It is also shown herein that not only is NeH3+ quite unstable, analogous reactions to the argon mechanisms are still less likely to form NeH+ further corroborating previous conclusions involving NeH2+. In any case, high-level quantum chemical computations using the CcC QFF have refined the literature values for the rotational constants and some of the anharmonic vibrational frequencies for 36ArH3+ in order to assist in its possible detection in the ISM or in simulated laboratory astrophysics experiments. Additionally, quartic and sextic distortion constants are provided for the first time for this molecular ensemble in addition to the vibration−rotation interaction constants. These refinements are augmented by a full set data for all of the useful isotopologues of ArH3+ including the six deuterated systems for each of the three argon isotopes: 36Ar, 38 Ar, and 40Ar. These data will not only assist in any potential detections of these molecules but give insight into the chemistry associated with the physical environments that lead to the creation of ArH+.

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ASSOCIATED CONTENT

S Supporting Information *

Tables of vibration−rotation interaction constants. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.5b03058.

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AUTHOR INFORMATION

Corresponding Author

*(R.C.F.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to acknowledge Georgia Southern University for support of this research, especially R.C.F., who is thankful to the university for the provision of the start-up funds necessary to complete this research. Mallory L. Theis of Georgia Southern University is also acknowledged for help in editing the manuscript.

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REFERENCES

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