Introduction {#sec1}
============

Noble gases form covalent bonds^[@ref1]−[@ref7]^ and can be more inclined to do so through the employment of polycyclic aromatic hydrocarbons (PAHs). Because of their inherent electronic stability, it was believed to be unlikely for argon or any of the noble gases to react and form stable bonds with nearly any other atom or molecular system. However, the discovery of argonium (ArH^+^) in the Crab nebula^[@ref8]^ and other astronomical sources within the interstellar medium (ISM)^[@ref9]^ has shown that this basic tenant of chemistry is not always true. The very concept of noble gas molecules opens new possibilities and ideas for current and future astrochemistry.

^40^Ar is the most abundant isotope of argon on Earth as it is believed to decay radioactively from atomic electrolytes in seawater. However, extraterrestrial argon is primarily ^36^Ar and is the 11th most abundant element in space.^[@ref10]36^Ar forms during stellar nucleosynthesis of stars, more massive than our sun. The ionization potential of argon is relatively high at 360 kcal/mol.^[@ref4],[@ref9]^ Therefore, argon mostly exists neutrally in the diffuse ISM but can be ionized via cosmic rays.^[@ref2],[@ref3],[@ref8]^ Its proton affinity is larger than that of atomic hydrogen, indicating that ionized argon could produce ArH^+^ in clouds of atomic hydrogen without dissociating.^[@ref9],[@ref11],[@ref12]^ Additionally, the dissociation of argonium is remarkably slow allowing for it to exist longer than either of the predicted HeH^+^ or NeH^+^ molecules. Consequently, ArH^+^ has been suggested as a tracer for interstellar atomic gas.^[@ref9],[@ref13]^ The question remains as to whether or not other noble gas molecules can form and be detected in the ISM.

Studies on the possibility of forming noble gas molecules have existed for over half a century. The first noble gas molecule created in the laboratory was xenon tetraflouride (XeF~4~) by reacting xenon gas with flourine (Xe + 2F~2~ → XeF~4~).^[@ref14]^ Another significant noble gas molecule HArF is formed by dissociating HF within a solid argon matrix.^[@ref15]^ For argon hydroflouride to remain stable, it must be kept at temperatures not exceeding 17 K. The temperature of molecular clouds in the diffuse ISM remains between 10 and 20 K, which allows for the possibility of HArF to be detected therein. Additionally, McKellar has conducted extensive research around the H~2~--Ar and D~2~--Ar complexes as well as similar molecules containing other noble gas atoms.^[@ref16]−[@ref18]^ The spectral data given within his earlier research denote that these complexes are stable minima on their respective potential energy surfaces (PESs).

The issue with most of these compounds is that the larger noble gas atoms are more likely to form bonds due to the polarizability of the larger electron cloud.^[@ref19]−[@ref23]^ However, argon is the largest of the noble gases that will occur in large numbers in interstellar environments. All other atoms in this periodic table family are heavier than iron and form after stellar nucleosynthesis. Consequently, the noble gas chemistry of the ISM should focus on those compounds containing helium, neon, and argon.

One proposed pathway to the creation of the known interstellar ArH^+^ cation is believed to be ionized argon reacting with hydrogen gas. Previous quantum chemical computations in our group have shown that this reaction scheme proceeds through the ArH~2~^+^ intermediate.^[@ref11]^ ArH^+^ and the hydrogen atom exist 11.5 kcal/mol above this minimum. However, Ne^+^ + H~2~ is more likely to form bare neon atoms and H~2~^+^, with these products existing 11.5 kcal/mol above the NeH~2~^+^ minimum. Consequently, NeH^+^ will not be nearly as abundant (if at all) as ArH^+^ as current analyses appear to support.^[@ref13]^

To identify other likely noble gas molecules worthy of interstellar searches, it is necessary to understand what it takes to bond any functional group/ligand with a noble gas atom. Further quantum chemical research has since suggested a number of new noble gas molecules that may exist in the ISM. All are cations that make the noble gas atoms strong electron acceptors. These include ArOH^+^, NeOH^+^, ArNH^+^, ArH~3~^+^, and CHe^2+^.^[@ref4],[@ref7],[@ref24]^ Each exists as a minimum on its respective PES with bond strengths (measured from proportional force constants) within significant percentages of those from ArH^+^. Each of these species (except for ArH~3~^+^)^[@ref25]^ forms strong bonds due to polarization of the electron-poor valence cloud in the noble gas atomic cation. Hence, in looking for new noble gas molecules, ligands that can share electrons with noble gas cations must be considered and these ligands must be donated from known or at least strongly hypothesized interstellar molecules.

A number of potential molecules that could serve these purposes have already been detected in the ISM. The cyano radical (CN) was one of the first molecules detected in space in 1940 and is one such ligand.^[@ref26]^ It is electron-rich and also possesses a freely shared radical electron. NO was detected nearly 40 years later toward Sgr B2.^[@ref27]^ The structure of NO is similar to that of CN in that the atoms have multiple bonds to one another and a radical electron that is, again, freely shared. However, current work has highlighted the difficulty of getting the oxygen atom in NO to cooperate in bonding.^[@ref28]^ Another notable ligand is the C~2~H radical detected in 1974.^[@ref29]^ C~2~H is isoelectronic, with CN making it similarly electron-rich and open-shell. Even though these fragments are promising to bind with neon and argon, any gas-phase reaction must entail a leaving group to dissipate the additional kinetic energy.

As a result, other molecules that contain these groups must take part in the chemical reaction. The ISM is known to contain various molecules that may or may not exist on Earth, and this environment likely holds many more than we already know. Any detected or likely interstellar molecule that contains CN, NO, or C~2~H is a candidate for reactions that lead to the desired noble gas, covalently bonded molecular cation. HNC, HCNH^+^, HC~3~NH^+^, CN, HCN, and HC~3~N are all detected interstellar molecules^[@ref26],[@ref30]−[@ref35]^ whose decomposition and recombination could be used to form the ArCN^+^ molecule. For some potential reactants, the neutral or charged isomer may not yet have been detected but it is likely that they may still exist in lower abundances. ArNH^+^ is another proposed molecule whose formation could involve ligands such as HCN, HNC, HCNH^+^, NH, NH~2~, or HC~3~NH^+^.^[@ref36],[@ref37]^ The creation of ArCCH^+^ is suggested to incorporate molecules including a C~2~H group: C~2~H, C~3~H, HC~3~NH^+^, and HC~3~N.^[@ref38]^ NeCCH^+^, like ArCCH^+^, is believed to be formed using the same ligands reacting with neon.

PAHs have been suggested as receptacles for noble gases under terrestrial conditions and benzene rings have been shown to capture molecules via π-cloud interactions with a binding energy on the order of 25 kcal/mol.^[@ref39]^ The noble gas atom bound above the surface of a PAH is therefore a probable and adequate intermediate for noble gas chemical reactions. The appropriate ligand could react with the noble gas atom and form one of many speculated noble gas molecules. The PAH and remaining atoms from the incoming molecule would compose the leaving groups.

Although PAHs have not yet been absolutely confirmed to exist in the ISM, the conditions for their likely existence are present.^[@ref40],[@ref41]^ Many of the hydrocarbons necessary for the formation of PAHs have been detected inside carbon-rich stars^[@ref40],[@ref42]^ and indirect detection of PAHs has been suggested for many years.^[@ref43],[@ref44]^ The main issue with direct detection of PAHs comes from the fact that they are nearly impossible to distinguish uniquely but general trends can be shown through databases of features fed through models of different astrochemical environments.^[@ref44]^

The purpose of this research is to predict the optimized geometries, relative energies, and possible reaction schema of several noble gas molecules. These include ArCN^+^, ArNH^+^, ArCCH^+^, and NeCCH^+^ with ArNH^+^ having been explored recently for its rovibrational properties.^[@ref24]^ Earlier theoretical work actually exists on these species.^[@ref1]^ However, much of it is only at the Hartree--Fock level and only analyzes the noble gas bond dissociations and not the possible formation reactions. Although it may be possible for some reactions to create noble gas molecular cations in the gas phase, the adsorbed phase cannot be neglected. PAHs could adsorb the noble gas atom within their electron cloud above the larger molecule's surface whereby a passing ligand could bind. All of these reactions would require favorable energetics to indicate whether a final molecular product could be observed. These possibilities pave the way for further experimental and theoretical work to inform subsequent interstellar observation.

Results and Discussion {#sec2}
======================

The CCSD(T)/aug-cc-pVTZ structures of the ultimate products explored herein are shown in [Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"}. The structure and spectroscopic data regarding ArNH^+^ have already been determined at high level,^[@ref24]^ and the present results are closely in line with those from the previous work and from much earlier contributions.^[@ref1]^ The vibrational frequencies of the four target noble gas molecules are shown in [Table [1](#tbl1){ref-type="other"}](#tbl1){ref-type="other"} showcasing that these molecules are minima. The Ar--C bonds in ArCCH^+^ and ArCN^+^ are similar to typical third-row atom bonds with second-row atoms,^[@ref45]^ and both molecules are perfectly linear. NeCCH^+^ is surprisingly nonlinear confirming earlier reports.^[@ref1]^ NeCCH^+^ is isoelectronic to FCCH^+^, fluoroacetylene, a known linear molecule. The 1.715 Å Ne--C bond is similar to the Ne--O bond in NeOH^+^, which is also nonlinear.^[@ref4]^ However, the bending in NeCCH^+^ is likely the result of weakening of one of the C--C π bonds for the terminal carbon in CCH^+^ to share electrons with the neon atom. In any case, this is somewhat an unexpected result from the first observation.

![CCSD(T)/aug-cc-pVTZ Optimized Structures (in angstrom and degrees) of (a) ArCCH^+^, (b) ArCN^+^, (c) ArNH^+^, and (d) NeCCH^+^.](ao-2016-002492_0001){#fig1}

###### CCSD(T)/aug-cc-pVTZ Harmonic Vibrational Frequencies for the Target Noble Gas Molecules (in cm^--1^)

  mode   ArCCH^+^   ArCN^+^   ArNH^+^   NeCCH^+^
  ------ ---------- --------- --------- ----------
  ω~1~   98.4       223.7     525.2     252.5
  ω~2~   665.8      567.6     1224.6    302.1
  ω~3~   718.5      2201.1    3215.0    575.0
  ω~4~   2164.4                         678.5
  ω~5~   3396.9                         1654.0
  ω~6~                                  3218.8

Gas-Phase Reactions {#sec2.1}
-------------------

In finding what types of ligands can form noble gas molecules in the gas phase, NO is a good place to start because of its relative simplicity. Unfortunately, NO is not a stable ligand in the formation of ArNO^+^, ArON^+^, NeNO^+^, or NeON^+^ because no CCSD(T) geometries could be optimized with noble gas--NO bond lengths of less than 3.0 Å. Hence, NO does not produce covalently bonded minima with these noble gas atoms. The reason is due to the recoupled pair bonding present in oxygen that does not allow for strong bonds to be made with half of its distended lone pair.^[@ref28]^ As disappointing as creating a molecule that is an anagram of itself in NeON^+^ is, the possible existence of other noble gas molecules is still exciting.

Next, ArNH^+^ is a stable minimum on its PES as has been previously shown through rovibrational analysis.^[@ref24]^ Here, the energetics supports its candidacy as a viable interstellar molecule. Of the potential, interstellar noble gas molecules studied thus far, ArNH^+^ is actually the most stable with respect to breaking the noble gas bond. ArNH^+^ lies 113.5 kcal/mol below the separated argon atom and NH^+^ molecular cation reactants. This is even greater than the dissociation energy of ArH^+^ at 94.0 kcal/mol and also ArOH^+^ at 73.7 kcal/mol.^[@ref4]^ Therefore, ArNH^+^ has the potential to form in the ISM without spontaneous dissociation. Indeed, the dissociation of ArNH^+^ into Ar^+^ and neutral NH is more favorable from a stability perspective but this is less likely to take place due to the already high ionization potential of argon. In terms of creation, the best pathway for the actual formation of ArNH^+^ comes from neutral argon reacting with NH~2~^+^. This process has a total reaction energy of −68.2 kcal/mol and the leaving group is a sole hydrogen atom. The creation of ArNH^+^ from ionized argon and the NH~2~ radical is also possible at −30.2 kcal/mol. However, other reactants shown in [Table [2](#tbl2){ref-type="other"}](#tbl2){ref-type="other"} for the creation of ArNH^+^ that require breaking a C--N bond are not favorable and will not allow for the stable creation of ArNH^+^ in the gas phase.

###### Gas-Phase CCSD(T)/aug-cc-pVTZ Reaction Energies (kcal/mol) for Argon

  reaction                                  energy
  ----------------------------------------- ---------
  ^•^NH^+^ + Ar → ^•^ArNH^+^                --113.5
  NH~2~^+^ + Ar → ^•^ArNH^+^ + ^•^H         --68.2
  ^•^HNC^+^ + Ar → ^•^ArNH^+^ + C           232.9
  HCNH^+^ + Ar → ^•^ArNH^+^ + ^•^CH         270.2
  NH + ^•^Ar^+^ → ^•^ArNH^+^                --139.2
  ^•^NH~2~ + ^•^Ar^+^ → ^•^ArNH^+^ + ^•^H   --30.2
  HNC + ^•^Ar^+^ → ^•^ArNH^+^ + C           144.8
  C~3~NH + ^•^Ar^+^ → ^•^ArNH^+^ + C~3~     64.5
  CN^+^ + Ar → ArCN^+^                      --52.8
  ^•^HCN^+^ + Ar → ArCN^+^ + ^•^H           83.1
  ^•^HNC^+^ + Ar → ArCN^+^ + ^•^H           104.7
  ^•^CN + ^•^Ar^+^ → ArCN^+^                --99.5
  HCN + ^•^Ar^+^ → ArCN^+^ + ^•^H           --32.2
  HNC + ^•^Ar^+^ → ArCN^+^ + ^•^H           16.5
  HC~3~N + ^•^Ar^+^ → ArCN^+^ + ^•^C~2~H    62.7
  C~2~H^+^ + Ar → ArCCH^+^                  --67.0
  ^•^HC~2~H^+^ + Ar → ArCCH^+^ + ^•^H       107.0
  ^•^HC~4~H^+^ + Ar → ArCCH^+^ + ^•^C~2~H   169.1
  C~3~H^+^ + Ar → ArCCH^+^ + C              187.3
  ^•^C~2~H + ^•^Ar^+^ → ArCCH^+^            --142.7
  HC~2~H + ^•^Ar^+^ → ArCCH^+^ + ^•^H       4.5
  HC~4~H + ^•^Ar^+^ → ArCCH^+^ + ^•^C~2~H   39.1
  HC~3~N + ^•^Ar^+^ → ArCCH^+^ + ^•^CN      19.6
  HC~2~NC + ^•^Ar^+^ → ArCCH^+^ + ^•^CN     --7.6

Next, ArCN^+^ also exists as a minimum on the \[Ar, C, N\] PES with a dissociation energy of −52.8 kcal/mol into neutral Ar and CN^+^ as shown in [Table [2](#tbl2){ref-type="other"}](#tbl2){ref-type="other"}. Its most likely mode of gas-phase formation is through ionized argon reacting with HCN producing ArCN^+^, a hydrogen atom, and −32.2 kcal/mol of energy. It is somewhat surprising that the dissociation of HNC or HNC^+^ is actually less favorable, even promoting the reactants over the products. As shown in [Table [2](#tbl2){ref-type="other"}](#tbl2){ref-type="other"}, ArCN^+^ is not exoergically favored through any other tested reaction. Those reactions containing Ar^+^ as a product have the lowest energy but are still likely kinetically disfavored.

ArCCH^+^ is the second-most stable with respect to breaking the noble gas bond of the systems analyzed in this work. It lies 67.0 kcal/mol below argon and ionized C~2~H^+^. In the gas-phase creation of ArCCH^+^, however, the pathway with the best energetics is the reaction of Ar^+^ with HC~2~NC, yielding ArCCH^+^ and CN as a leaving group as well as only −7.6 kcal/mol of excess energy. The only other reactants that could potentially produce the desired molecule are those containing a C~2~ group reacting with a charged argon atom, HC~2~H and HC~3~N, but both reactions are endoergic.

NeCCH^+^ is the only neon system analyzed here that is a stable molecule as shown in [Table [3](#tbl3){ref-type="other"}](#tbl3){ref-type="other"}. It is computationally predicted to be a minimum on its PES, requiring 21.8 kcal/mol of energy to break the Ne--C bond. Despite this, there exist no favorable exoergic pathways for the tested set of reactants for their formation in the gas phase. The closest possibility, at 152.4 kcal/mol, is with neon reacting with acetylene cation producing NeCCH^+^ and a sole hydrogen atom. Even so, such an energy barrier could almost never be overcome in natural environments where other bonds would not be broken as well.

###### Gas-Phase CCSD(T)/aug-cc-pVTZ Reaction Energies (kcal/mol) for Neon

  reaction                                        energy
  ----------------------------------------------- --------
  C~2~H^+^ + Ne → NeCCH^+^                        --21.8
  ^•^HC~2~H^+^ + Ne → NeCCH^+^ +^•^H              152.4
  ^•^HC~4~H^+^ + Ne → NeCCH^+^ + ^•^C~2~H         214.4
  C~3~H^+^ + Ne → NeCCH^+^ + C                    232.6
  ^•^C~2~H + ^•^Ne^+^ → NeCCH^+^                  266.2
  HC~2~H + ^•^Ne^+^ → NeCCH^+^ + ^•^H             413.5
  HC~4~H + ^•^Ne^+^ → NeCCH^+^ + ^•^C~2~H         448.0
  HC~3~N + ^•^Ne^+^ → NeCCH^+^ + ^•^CN            428.5
  HC~2~NC + ^•^Ne^+^ → NeCCH^+^ + ^•^CN           401.4
  ^•^HC~4~H^+^ + ^•^Ne^+^ → NeCCH^+^ + C~2~H^+^   502.4

Previous work has found that NeOH^+^ is a stable system with a reaction energy of −12.3 kcal/mol favoring NeOH^+[@ref4]^ but NeNH^+^ is not a stable system.^[@ref24]^ Despite the promise of NeOH^+^, no pathways could be produced from the set of tested molecules that could form NeOH^+^ in the gas phase. As a fascinating side result of this work, the present set of computations indicate that HOCO + Ar^+^ will produce ArOH^+^ and the astronomically ubiquitous carbon monoxide with a relative energy of −211.1 kcal/mol, greater than the proposed HOOH + Ar^+^ mechanism,^[@ref4]^ which produces only −28.6 kcal/mol. Finally, the gas-phase reactions are not highly susceptible to zero-point vibrational energy (ZPVE) corrections, especially from a qualitative sense. The ZPVE for the creation of ArCN^+^ is small at 1.7 kcal/mol and increases to 6.7 kcal/mol for NeCCH^+^ as shown in [Table [4](#tbl4){ref-type="other"}](#tbl4){ref-type="other"}. Hence, the exoergicity of these reactions will not be affected by the ZPVEs, which are exceedingly difficult to compute for the large PAH complexes discussed in the below section. The ZPVEs of the adsorbed complexes will also be quite small as most of the ZPVEs is contained within the PAH itself, and this molecule is largely unchanged either as a reactant or π-complex product.

###### Noble Gas Dissociation Relative Energies (kcal/mol)

  reactions                  DF-MP2/6-31+G\*   CCSD(T)/aug-cc-pVTZ   ZPVE[a](#t4fn1){ref-type="table-fn"}
  -------------------------- ----------------- --------------------- --------------------------------------
  CN^+^ + Ar → ArCN^+^       --51.3            --52.8                --51.5
  C~2~H^+^ + Ar → ArCCH^+^   --102.8           --67.0                --64.6
  C~2~H^+^ + Ne → NeCCH^+^   --44.1            --21.8                --15.1

CCSD(T)/aug-cc-pVTZ ZPVE included in the dissociation energy.

Adsorbed PAH Reactions {#sec2.2}
----------------------

Even though the neon cation of interest (NeCCH^+^) is indeed a stable molecule, the lack of a viable gas-phase reaction channel limits the possibility of this cation occurring in nature. However, it may yet be possible for the noble gas atoms themselves to be presented to a matching ligand by adsorbing onto the surface of a PAH. Because the PAHs are so large, CCSD(T)/aug-cc-pVTZ computations are prohibitive for the analysis of such systems. As mentioned previously, the DF-MP2/6-31+G\* level of theory has given much promise in extending wave function-based quantum chemistry to such systems where previously only density functional theory could be utilized. To verify that DF-MP2/6-31+G\* is appropriate for application to those systems where adsorption may be required for molecular synthesis, the gas-phase dissociation energies computed with both methods are shown in [Table [4](#tbl4){ref-type="other"}](#tbl4){ref-type="other"}. DF-MP2/6-31+G\* overestimates the noble gas bond energy in ArCCH^+^ as well as NeCCH^+^ relative to CCSD(T)/aug-cc-pVTZ. On the whole, however, the significantly less computationally costly density-fitting (DF) approach is capable of producing at least semiquantitatively meaningful results for further analysis.

PAHs allow for a noble gas molecule to be adsorbed onto their surface relatively easily.^[@ref39]^ An incoming ligand could bond to the noble gas exoergically by subsequently severing the van der Waals bond between the noble gas atom and the PAH π cloud. To estimate such behavior for PAHs in general, a succession of larger, commonly utilized PAH examples are employed. These include naphthalene, pyrene, coronene, and ovalene with two, four, seven, and ten, respectively, six-membered rings. All have the ability to adsorb a noble gas atom into their π clouds and do so with successively stronger interactions as the number of rings increases. Neon, for instance, binds to naphthalene with a mere −1.9 kcal/mol as shown in [Table [5](#tbl5){ref-type="other"}](#tbl5){ref-type="other"}. Inclusion of the ZPVE for this, the smallest complex, reduces the binding energy further by −0.2 to −2.1 kcal/mol as the only new frequencies for the products are for the Ne motion adsorbed to the PAH. These lie at 46.2, 49.7, and 58.7 cm^--1^, whereas the naphthalene frequencies are all changed by negligible amounts upon complexation. The 77.3 cm^--1^ or 0.2 kcal/mol ZPVE reduction is an absolutely small change that will not affect the semiquantitative conclusions drawn in this work.

###### DF-MP2/6-31+G\* Reaction Energies (kcal/mol) for the Formation of Noble Gas Molecules on Naphthalene

  reactions                                                 energy
  --------------------------------------------------------- ---------
  naphthalene + Ne → naphthaleneNe                          --1.9
  naphthalene + CCH^+^ → naphthaleneCCH^+^                  --217.0
  naphthaleneCCH^+^ + Ne → naphthalene + NeCCH^+^           172.9
  naphthaleneNe + ^•^CCH^+^ → naphthalene + NeCCH^+^        --42.5
  naphthaleneNe + ^•^H~2~^+^ → naphthalene + ^•^NeH~2~^+^   43.1
  naphthaleneNe + H~3~^+^ → naphthalene + NeH~3~^+^         --0.4
  naphthaleneNe + OH^+^ → naphthalene + NeOH^+^             --14.2
  naphthaleneNe + ^•^NH^+^ → naphthalene + ^•^NeNH^+^       --1.3
  naphthalene + Ar → naphthaleneAr                          --3.1
  naphthaleneAr + CCH^+^ → naphthalene + ArCCH^+^           --99.7
  naphthaleneAr + ^•^H~2~^+^ → naphthalene + ^•^ArH~2~^+^   6.1
  naphthaleneAr + H~3~^+^ → naphthalene + ArH~3~^+^         --1.1
  naphthaleneAr + OH^+^ → naphthalene + ArOH^+^             --76.5
  naphthaleneAr + ^•^NH^+^ → naphthalene + ^•^ArNH^+^       --34.3
  naphthaleneAr + CN^+^ → naphthalene + ArCN^+^             --48.2

The binding energy increases in magnitude to −4.1 kcal/mol for pyrene, −5.6 kcal/mol for coronene, and −6.8 kcal/mol for ovalene as shown in [Tables [6](#tbl6){ref-type="other"}](#tbl6){ref-type="other"}, [7](#tbl7){ref-type="other"}, and [8](#tbl8){ref-type="other"}, respectively, indicating that it should stabilize somewhere around −8.0 kcal/mol for arbitrarily large PAHs. Argon is slightly more tightly bound with energies of −3.1, −6.5, −8.8, and −10.1 kcal/mol, respectively, of the four, ever-larger PAHs. Hence, its PAH binding energy to larger PAHs probably converges to around −11.5 kcal/mol. Such energies will likely require that any noble gas--PAH adsorption for subsequent chemistry will need to be in cold, dark molecular clouds like TMC-1, where such complexes will likely have lifetimes on the order of multiple years. In each case of Ar or Ne adsorption, the atoms are each placed in various positions around the PAH surface, but all migrate to the same favorable positions on each PAH upon optimization. For naphthalene, this is within the π cloud above a single ring, but directly above the center of mass/charge for pyrene, coronene, and ovalene. Any basis set superposition errors (BSSE) for these complexes are small and will not change the conclusions drawn. BSSEs for the neon complexes with naphthalene and pyrene computed via the counterpoise correction are both less than 0.1 kcal/mol, whereas the BSSEs for the argon complexes are 0.2 and 0.5 kcal/mol, respectively.

###### DF-MP2/6-31+G\* Reaction Energies (kcal/mol) for the Formation of Noble Gas Molecules on Pyrene

  reactions                                       energy
  ----------------------------------------------- --------
  pyrene + Ne → pyreneNe                          --4.1
  pyreneNe + CCH^+^ → pyrene + NeCCH^+^           --40.0
  pyreneNe + ^•^H~2~^+^ → pyrene + ^•^NeH~2~^+^   45.5
  pyreneNe + H~3~^+^ → pyrene + NeH~3~^+^         2.2
  pyreneNe + OH^+^ → pyrene + NeOH^+^             --11.7
  pyreneNe + ^•^NH^+^ → pyrene + ^•^NeNH^+^       1.2
  pyrene + Ar → pyreneAr                          --6.5
  pyreneAr + CCH^+^ → pyrene + ArCCH^+^           --96.3
  pyreneAr + ^•^H~2~^+^ → pyrene + ^•^ArH~2~^+^   9.5
  pyreneAr + H~3~^+^ →pyrene + ArH~3~^+^          2.2
  pyreneAr + OH^+^ → pyrene + ArOH^+^             --73.1
  pyreneAr + ^•^NH^+^ → pyrene + ^•^ArNH^+^       --30.9
  pyreneAr + CN^+^ → pyrene + ArCN^+^             --44.8

###### DF-MP2/6-31+G\* Reaction Energies (kcal/mol) for the Formation of Noble Gas Molecules on Coronene

  reactions                                           energy
  --------------------------------------------------- --------
  coronene + Ne → coroneneNe                          --5.6
  coroneneNe + CCH^+^ → coronene + NeCCH^+^           --38.4
  coroneneNe + ^•^H~2~^+^ → coronene + ^•^NeH~2~^+^   47.1
  coroneneNe + H~3~^+^ → coronene + NeH~3~^+^         3.7
  coroneneNe + OH^+^ → coronene + NeOH^+^             --10.1
  coroneneNe + ^•^NH^+^ → coronene + ^•^NeNH^+^       2.7
  coronene + Ar → coroneneAr                          --8.8
  coroneneAr + CCH^+^ → coronene + ArCCH^+^           --94.0
  coroneneAr + ^•^H~2~^+^ → coronene + ^•^ArH~2~^+^   11.9
  coroneneAr + H~3~^+^ → coronene + ArH~3~^+^         4.6
  coroeneAr + OH^+^ → coronene + ArOH^+^              --70.8
  coroneneAr + ^•^NH^+^ → coronene + ^•^ArNH^+^       --28.5
  coroneneAr + CN^+^ → coronene + ArCN^+^             --42.5

###### DF-MP2/6-31+G\* Reaction Energies (kcal/mol) for the Formation of Noble Gas Molecules on Ovalene

  reactions                                         energy
  ------------------------------------------------- --------
  ovalene + Ne → ovaleneNe                          --6.8
  ovaleneNe + CCH^+^ → ovalene + NeCCH^+^           --37.3
  ovaleneNe + ^•^H~2~^+^ → ovalene + ^•^NeH~2~^+^   48.3
  ovaleneNe + H~3~^+^ → ovalene + NeH~3~^+^         4.8
  ovaleneNe + OH^+^ → ovalene + NeOH^+^             --8.9
  ovaleneNe + ^•^NH^+^ → ovalene + ^•^NeNH^+^       3.9
  ovalene + Ar → ovaleneAr                          --10.1
  ovaleneAr + CCH^+^ → ovalene + ArCCH^+^           --92.7
  ovaleneAr + ^•^H~2~^+^ → ovalene + ^•^ArH~2~^+^   13.1
  ovaleneAr + H~3~^+^ → ovalene + ArH~3~^+^         5.9
  ovaleneAr + OH^+^ → ovalene + ArOH^+^             --69.5
  ovaleneAr + ^•^NH^+^ → ovalene + ^•^ArNH^+^       --27.3
  ovaleneAr + CN^+^ → ovalene + ArCN^+^             --41.2

The CCH^+^ ligand binds exceptionally tightly to naphthalene. Even so, the neon atom can interrupt this binding. If the reaction starts from the neon atom bound to naphthalene with CCH^+^ as the second reactant, NeCCH^+^ and the naphthalene molecule will be produced exoergically with a relative energy of −42.5 kcal/mol. Optimizations of the three chemical fragments (naphthalene, the neon atom, and CCH^+^) as one system are not stable, indicating that this must be a bimolecular reaction. Although it is unlikely for all the three items to collide at once in the diffuse regions of the ISM, if the neon atom is already adsorbed onto naphthalene, this process could lead to the creation of another naturally occurring noble gas molecule. Furthermore, if NeCCH^+^ could be detected, its formation is unlikely in the gas phase as highlighted above. Hence, some type of adsorptive catalysis would be required to form this molecular cation and would imply that NeCCH^+^ could be a probe of PAH density.

Interestingly, as the size of the PAH grows, the formation of NeCCH^+^ becomes less favorable. It is the inverse relationship of the binding energy for the noble gas atom adsorbed onto the PAH surface. Consequently, ovalene ([Table [8](#tbl8){ref-type="other"}](#tbl8){ref-type="other"}) has the least favorable reaction energy for the PAH-Ne + CCH^+^ → PAH + NeCCH^+^ processes at −37.3 kcal/mol. However, the asymptotic convergence of the noble gas PAH binding implies that such a reaction on a large PAH surface would be exoergic by around −35.0 kcal/mol, enough for NeCCH^+^ to form with aid of any arbitrarily sized PAH.

Similar trends are observed for ArCCH^+^ but conditions are over twice as favorable for its creation on naphthalene at −99.7 kcal/mol. Even when considering the use of ovalene as the adsorbing surface, the PAH-Ar + CCH^+^ → PAH + ArCCH^+^ reaction still produces −92.7 kcal/mol of favorable energy, significantly more than in the gas-phase reaction of HC~2~NC and ionized argon at −7.6 kcal/mol. Even though ArCCH^+^ is a strongly bound noble gas cation, it may require some surface chemistry to form, again, giving indication of the molecular environment in which it would be detected.

The formations of NeOH^+^, ArOH^+^, and ArNH^+^ from known interstellar reactants along with noble gas atomic cations are more favored in the gas phase from present and previous^[@ref4]^ works. However, the creation of NeCCH^+^, ArCCH^+^, and ArCN^+^ is required (in the case of the neon molecule), and enhanced (in the case of the two argon molecules) when PAH adsorption is involved in the formation pathway. It is unlikely that the noble gas dihydride and trihydride cations will benefit from PAH adsorption. Consequently, any observation of ArH~2~^+^ will likely be as the intermediate in the creation of the known ArH^+^ either from atomic argon and the hydrogen molecular cation or from the isoergic ionized atomic argons reacting with neutral ubiquitous H~2~.^[@ref11]^

Computational Details {#sec3}
=====================

Quantum chemistry provides unique insights into the relative energetics of chemical reactions. It can determine the favorability of certain schema to provide useful data for chemical modeling of the ISM. The first step is to determine potential reaction schema. Next, the geometries of each involved chemical structure must be computed. These include all reactants, desired products, and other leaving groups. The gas-phase reactions are modeled with coupled cluster theory at the single, double, and perturbative triple \[CCSD(T)\]^[@ref46]−[@ref48]^ levels, along with the aug-cc-pVTZ basis set.^[@ref49],[@ref50]^ CCSD(T)/aug-cc-pVTZ has been documented as the "gold standard" of quantum chemistry for producing exceptional accuracy for a modest computational cost.^[@ref51],[@ref52]^ The reaction energy is then determined using the standard chemical reaction equation of products minus reactants. The desired molecule as well as the leaving group is on the products side, whereas the noble gas atom or atomic cation along with the appropriate ligand-donating species is the reactant. The reported negative energies favor products, whereas positive energies favor reactants. All geometries are verified as minima on the respective energy surfaces by producing all real harmonic vibrational frequencies also at the CCSD(T)/aug-cc-pVTZ level. The requisite open-shell computations utilize the restricted open-shell Hartree--Fock reference wave function,^[@ref53]−[@ref55]^ whereas the closed-shell, even-numbered electron computations rely upon simply the restricted Hartree--Fock reference wave function.^[@ref56]^ All computations make use of the PSI4 quantum chemistry package.^[@ref57]^

DF algorithms promise to reduce the computational cost with little sacrifice in accuracy,^[@ref58]^ and Møller--Plesset perturbation theory at second-order (MP2)^[@ref59]^ with a double-zeta basis set has been shown to produce surprising accuracy for such a simple method.^[@ref60],[@ref61]^ Additionally, the DF-MP2 analytical derivative algorithms within the binary release of PSI4 are exceptionally fast, opening wave function-based methods to larger molecules.^[@ref62]^ Consequently, DF-MP2/6-31+G\* calculations^[@ref63]^ are utilized for the geometry optimizations and relative energetic computations of the reaction schema that employ PAHs. Such an approach is advantageous because of the large number of atoms in these molecules and their multiple electrons included therein. The noble gas (argon or neon in this case) is then adsorbed onto the surface of the PAH. Once the geometry of this has been optimized, its relative energy is recorded and standard chemical energetics determined.

Conclusions {#sec4}
===========

Noble gas atoms can actually undergo chemical reactions in both gas and adsorbed phases. As ArH^+^ is a known example of noble gas chemistry occurring on galactic scales across the ISM, the next step is to determine how other such species could be formed, and through what means it is possible to identify them. The second of these two considerations is left for quartic force field work in progress, but gas phase, quantum chemically computed reactions utilizing CCSD(T)/aug-cc-pVTZ show that all of the tested molecules, ArCCH^+^, ArCN^+^, ArNH^+^, and NeCCH^+^, are minima on their respective PESs. In fact, ArNH^+^ has a Ar--N bond energy greater than even the known ArH^+^ astromolecule. Furthermore, the reaction of NH~2~^+^ + Ar → ArNH^+^ + H has a relative reaction energy of −68.2 kcal/mol, making it 3.5 times more exoergic than the formation of ArH^+^ from Ar^+^ + H~2~. Consequently, the previous work describing the rovibrational spectroscopic data^[@ref24]^ for ArNH^+^ is vital in the detection of this molecule in interstellar environments where NH~2~^+^ is already known.

Other favorable gas-phase reaction schema are discovered herein for the other two argon noble gas molecules but not for NeCCH^+^. For NeCCH^+^ to form, surface adsorption catalysis is required. The noble gas atoms make weak but stable bonds with the π cloud above or below the plane of the PAH. The larger the PAH, the stronger the bonds become. The larger the PAH, the more kinetic energy will be required to dissociate the noble gas, but these energies are still fairly low. In any case, the PAH leaving group allows noble gas molecules to form, even NeCCH^+^. Although the argon counterpart, ArCCH^+^, and its isoelectronic companion, ArCN^+^, do not require a PAH to form with energetically favorable chemistry, the PAH surfaces can enhance their interstellar synthesis. Additionally, the detection of such systems in a given region would provide further evidence for the presence of PAHs. The formations of ArNH^+^ and ArCN^+^ are also more likely than ArCCH^+^, as well, because ionized argon is not required for the reactants.

Noble gas chemistry is not a laboratory curiosity any longer, but stable noble gas species are still difficult to analyze. This quantum chemical work provides a basis for future exploration of other noble gas molecules that may yet be lurking in the expanses of space.

The authors declare no competing financial interest.

The authors wish to thank Georgia Southern University for the provision of start-up funds necessary to perform this research. Additionally, the molecules in [Figure [1](#fig1){ref-type="fig"}](#fig1){ref-type="fig"} were produced using the WebMO graphical user interface.^[@ref64]^
