The role of small molecular cations in the chemical flow of the interstellar environments

Abstract

Molecular ions have been ubiquitous in a variety of environments in the interstellar medium, from Circumstellar Envelopes to Dark Molecular Clouds and to Diffuse Clouds. Their role in the multitude of molecular processes which have been found to occur in those environments has been the subject of many studies over the years, so that we have acquired by now a complex body of data on their chemical structures, their possible function within chemical reactions and their most likely paths to formation. In the present work we review a broad range of such molecular ions, focusing exclusively on positive ions involving the smallest and simplest cations which have been either detected or conjectured as present in the interstellar medium (ISM). We therefore consider mainly molecular cations formed with components like H, H⁺, He and He⁺, atomic species which are by far the most abundant baryons in the ISM in general. Their likely structures and their roles in a variety of chemical energy flow paths are discussed and presented within the context of their interstellar environments.

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1 Introduction

Most of the matter in the universe is localized into large gatherings of stars known as galaxies. In most of the galaxies that can be studied by direct observation, the space between stars is found to be frequently occupied by a variety of material that contains the so-called interstellar clouds, which in turn consist of gas and dust and are embedded in a more rarefied medium. Densities and temperatures of interstellar clouds vary widely, and indeed few clouds are homogeneous. The simplest clouds are known as “diffuse” since the gas and dust in such regions is not dense enough to keep out starlight, so that astronomical observations can detect diffuse material in between the bright stars and our position. Typical temperatures of such regions are in the vicinity of 50–100 K and total gas densities are perhaps of the order of 10² cm⁻³.¹ As in all interstellar clouds, the gas is mainly hydrogen, betraying the fact that the material in clouds comes from previous generation of stars, which are also mainly hydrogen in content. Some average “cosmic” elemental abundances, normalized with respect to hydrogen, and taken from the atmospheres of nearby stars, have also been reported in the literature.² The heavy elements in stars are found to be depleted in interstellar gas because they also constitute the dust particles which are mainly silicates and carbonaceous material. By mass, the dust is typically 1% of the gas, and consists of particles ranging widely in radius from ≤10 nm to more than 1 μm. A standard size often quoted by astronomers is 0.1 μm.³

Although the gas phase in diffuse clouds is mainly neutral, virtually all of the carbon is ionized by ultra-violet radiation from stars, leading to a fractional ionization of about 10⁻⁴.¹ The more abundant elements, which are H and He, cannot be ionized by stellar ultra-violet radiation because it does not extend to high enough energies, terminating at 13.6 eV, the ionization potential of atomic hydrogen. Some ionization of these abundant atoms comes from cosmic rays, which are mainly protons traveling at relativistic speeds. The hydrogen is typically divided evenly between neutral atomic and molecular forms and it is thought that the molecules are produced not in the gas but via recombination on the surfaces of dust particles. Other than molecular hydrogen, all molecules are trace constituents of the gas. Until recently, it was thought that only diatomic species (e.g. CH, CN, OH, NH, C₂) were present in diffuse clouds but the situation is now known to be more complex and includes several ionized molecules and also a fairly large variety of polyatomic molecules. The most prominent molecular ion detected is CH⁺, which can be seen via its visible spectrum. This ion possesses a fractional abundance of only 10⁻⁷, far below that of C⁺.

The chemistry that occurs in the dense interstellar gas is considered to be far more complex than that assumed to occur in the diffuse gas. Dense gas is normally associated with giant molecular clouds, which are large heterogeneous assemblies of gas and dust ranging in mass up to about 10⁵ solar masses. The dense portions, virtually black in the visible region, are known as ‘cores’ and have typical temperatures of only 10 K and densities of about 10⁴ cm⁻³, consisting by their major parts of molecular rather than atomic hydrogen.⁴ Although some cores are termed ‘quiescent’, others are actively collapsing to form stars. The detection of molecules in regions of active star formation tells us much about the physical conditions and their evolution. The earliest active stage of stellar evolution is known as a pre-stellar core; here the collapse is still isothermal but a condensation of higher density begins to form in the center as collapse occurs. In this denser region within a core, heavy molecules condense out onto the surfaces of dust particles to form mantles of ices, and the gas becomes almost completely hydrogen and helium. In the next stage, known as a protostellar core and subdivided into various categories, the collapse turns adiabatic in the center and a warm ‘protostar’ develops. Near the star's location the dust grains can become warmer so that the mantles can evaporate and return to the gas.³

The result of the above sketch on the evolutionary aspects of interstellar clouds is that a broad variety of molecular species can be present, and have been observed, in both translucent and dark molecular clouds and that many of the observed species have been molecular ions, especially cations, produced often by starlight ionization of the corresponding neutrals. It is the aim of the present perspective article to discuss a series of small molecular cations which have been observed in the Interstellar Medium (ISM) and to evaluate their efficiencies in transferring various forms of energies to other partners. The latter will be obviously the most abundant ISM components and therefore we will discuss, whenever possible, collision energy transfer probabilities with He, H and H₂ as the likely partners and under the expected features of that environment. Since under the very special conditions of what is termed as the early universe, the formations of cations are also considered the only viable molecular paths, we will discuss in detail the role of the first molecule suggested to have been existing at that redshift: the HeH⁺ cation and also the H₃⁺, the simplest polyatomic molecular cation. Additionally, the possible presence of heavier baryon species like LiH⁺ and LiHe⁺, of small C-bearing cations and of cations with higher metalicity will also be briefly discussed.

2 Cations in the interstellar medium

Even before molecular ions were detected in dense interstellar clouds, it was suggested that ions must play a prominent role in the chemistry occurring in the gas-phase since, especially in the cold regions, the dominant processes should be, in order to be effective, exothermic reactions that have no activation energy.⁵ Indeed, unlike most neutral–neutral reactions, ion–molecule reactions often do not possess activation-energy barriers, or energy barriers along the Transition State (TS) formation, and so can play a significant role within the interstellar chemical networks despite the existence, as we have discussed earlier, of the low fractional ionization in dense clouds. The primary ion in dense clouds is H₃⁺, because it is expected to be made early on in the reaction chain and can serve as a precursor for the formation of more complex species.⁶ Molecular hydrogen is formed on the surfaces of grains, and is released to the gas either during the reaction or by evaporation. Ionization is caused by encounters with cosmic rays, typically with relativistic energies of 100 MeV or more, which lead mainly to the removal of a single electron and the formation of H₂⁺.⁵ This ion reacts “immediately” (within a day) with molecular hydrogen, the dominant species, to form the H₃⁺ ion.⁷ The H₃⁺ does not react with H₂ and so is relatively abundant. Since it does not possess a permanent dipole moment, it does not exhibit a strong rotational spectrum and therefore remained undetected for a long time, until technological improvements in infra-red sensitivity led to its observation in this spectral region. The observed abundance of this special cation in dense clouds turned out to be what had been predicted, as it will be further discussed below. Another primary ion is He⁺, formed by cosmic ray bombardment of abundant helium atoms, and also often considered to be largely unreactive with H₂.⁵

Among the many molecules detected in diffuse and dense gas clouds the positive molecular ions involve simple diatomics like CH⁺, CO⁺ and SH⁺, triatomic partners like H₃⁺ and its isotopic variants, HCO⁺, HN₂⁺, and HCS⁺. Those found in diffuse clouds include the classic CH⁺, mentioned above, as well as H₃⁺ and HCO⁺. The latter two are more strongly associated with dense gas while the other ions mentioned are only found in denser material. The ion HCO⁺ is associated especially with the Photon-Dominated Regions (PDRs) and the isomer HOC⁺ has also been recently detected in such regions. The presence of deuterated ions is an important indicator of the physical conditions in star formation regions, especially pre-stellar cores. The most abundant molecular ion in dense sources is, as can be seen in the reference quoted below, the HCO⁺ cation, except for the cold pre-stellar cores where virtually all non-hydrogenic material is frozen out. An estimated fractional ionization in dense cores is considered to be around 10⁻⁷, as discussed in ref. 5.

The presence of the smaller molecular variants of diatomic or triatomic cations is particularly intriguing since their relative structural simplicity indicates that their abundances can be observed within different environments, thereby suggesting their significant participation to energy-transfer dynamics activated by collisions with the other abundant neutral partners like H, He and H₂. In the following Sections we shall therefore discuss in greater details just how much such collision events can provide significant probabilities for energy flow rate coefficients at the temperatures of interest in the interstellar environments.

The subject of molecular ions in extraterrestrial space has grown in the last several decades, with a large number of cationic and anionic species detected in the ISM regions. Since there are several reviews on the subject,^8–10 we shall not attempt a complete presentation here, but confine ourselves to a perspective that will focus on the general features of lighter species of low atomic number, and composed of only a few atoms. Such components are in fact more likely to have formed in the early universe as well as in the later interstellar media. Not surprisingly, many of them are hydrogen/helium containing species.

3 HeH⁺ and its energy exchanges with H, He and H₂ as partners

At the beginning of the chemical epoch of the early universe, there were protons (H⁺) and α particles (He⁺⁺) in the ratio 1 : 0.1 with small amounts of D⁺ and Li³⁺.^11,12 Energetics¹³ favored the formation of He, the first neutral atom to be formed in the early universe:

He⁺⁺ + e → He⁺, ΔE = − 54.418 eV (1)

He⁺ + e → He, ΔE = −24.584 eV (2)

Thus,

He⁺⁺ + 2e → He, ΔE = −79.002 eV (3)

in contrast to

H⁺ + e → H, ΔE = −13.598 eV (4)

Understandably, He atoms would have combined with the abundant H⁺ to form the first diatomic species HeH⁺ by radiative association (RA) in the early Universe:^14,15

He + H⁺ → HeH⁺ + hν, ΔE₀ = −1.84 eV (5)

It is worth pointing out at this stage that it is practically impossible to measure the rate coefficient (k) for RA under laboratory conditions because they require fairly low concentration of the relevant species ∼10² cm⁻³ in order for them to mimic early universe conditions. Therefore, we would have to rely on theoretical estimates. The values of the k_RA for reaction (5) were estimated to vary from 6.42 × 10⁻²⁰ cm³ molecule⁻¹ s⁻¹ at 2 K to 0.56 × 10⁻²⁰ cm³ molecule⁻¹ s⁻¹ at 10 000 K, with a maximum of 13.25 × 10⁻²⁰ cm³ molecule⁻¹ s⁻¹ at 18 K,¹⁶ thus confirming the generally small probabilities that such processes would have.

Although HeH⁺ was detected in a mass spectrograph¹⁷ as early as 1925, concrete spectroscopic evidence for its presence in the planetary nebula NGC 7027 came only recently.^18,19 Interestingly, the mechanism for its formation in interstellar medium (ISM) was suggested to be

He⁺ + H → HeH⁺ + hν, ΔE₀ = −12.824 eV (6)

because of the abundance of H in interstellar clouds. In addition, k_RA for reaction (6) has been estimated to be 9.93 × 10⁻¹⁵ cm³ molecule⁻¹ s⁻¹ at 1 K, decreasing monotonically to 1.01 × 10⁻¹⁵ cm³ molecule⁻¹ s⁻¹ at 4000 K;²⁰k_RA = 5.68 × 10⁻¹⁵ cm³ molecule⁻¹ s⁻¹ at 10 K, decreasing to 0.77 × 10⁻¹⁵ cm³ molecule⁻¹ s⁻¹ at 4000 K.²¹

The reaction of He⁺ with the more abundant H₂ does not seem to lead to the formation of HeH⁺ because of a large barrier arising from the potential energy surfaces of two states of the same symmetry avoiding crossing each other.²² On the other hand, the dissociative charge transfer (DCT) reaction

He⁺ + H₂ → He + H + H⁺, ΔE₀ = −6.5 eV (7)

seems to actually occur.²³ As a matter of fact, Schauer et al.²⁴ measured the k for the radiative charge transfer (RCT)

He⁺ + H₂ → He + H₂⁺, ΔE₀ = −9.16 eV (8)

and the dissociative charge transfer in He⁺ + H₂ collisions in the temperature range 15–40 K in an ion trap. While k_RCT was found to be of the order of 1 × 10⁻¹⁴ cm³ molecule⁻¹ s⁻¹ and independent of temperature, k_DCT was found to increase in the range 2.5–5 × 10⁻¹⁴ cm³ molecule⁻¹ s⁻¹ as T increased from 15 to 40 K.

In a measurement of the dissociative recombination (DR) rate coefficients for HeH⁺

HeH⁺ + e → He + H (9)

in an ion storage ring, Novotny et al.²⁵ found these coefficients to be much smaller than what was expected from earlier investigations, thereby suggesting that HeH⁺ is much more abundant in astrochemical environment than previously expected. Forrey et al.²⁶ and Courtney et al.²⁷ took stock of the factors responsible for the formation of HeH⁺ in planetary nebulae as well as in the early Universe and concluded that HeH⁺ was at least three orders of magnitude more abundant than what was predicted earlier for the larger redshifts (z) near 20.

HeH⁺ can also get destroyed by the reactions

HeH⁺ + H → He + H₂⁺, ΔE₀ = −0.80 eV (10)

and

HeH⁺ + H₂ → He + H₃⁺, ΔE = −2.63 eV (11)

Both the molecular events are exothermic and barrierless.

Karpas et al.²⁸ had determined the k for the reaction (10) to be (9.1 ± 2.5) × 10⁻¹⁰ cm³ molecule⁻¹ s⁻¹ at 300 K. Adams et al.²⁹ had estimated the k for the reaction (11) to be ≥3.5 × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹ at 200 K (∼0.017 eV). Ryan and Graham³⁰ measured it to be (1.4 ± 0.2) × 10⁻⁹ cm³ molecule⁻¹ s⁻¹ at a mean energy of 0.1 eV. Rutherford and Vroom³¹ estimated it to be 2.3 × 10⁻⁹ cm³ molecule⁻¹ s⁻¹ at E_trans = 0.3 eV. They also reported the cross section for the reaction to be 38 Ų at E_trans = 0.3 eV, decreasing to 1 Ų at E_trans = 6 eV. The rate of decay of the cross section with E_trans in the range 0.4–2 eV was as predicted by Gioumousis and Stevenson.³² Johnsen and Biondi³³ determined the k to be ≥10⁻⁹ cm³ molecule⁻¹ s⁻¹ at 300 K. Subsequently, Orient³⁴ measured it to be (1.26 ± 0.16) × 10⁻⁹ cm³ molecule⁻¹ s⁻¹ at 300 K and independent of E_trans in the range 0–0.3 eV. This is somewhat smaller than what was reported (1.8 × 10⁻⁹ cm³ molecule⁻¹ s⁻¹) earlier by Theard and Huntress.³⁵

In the case of HeH⁺ colliding with He, the potential energy surface has a well of depth of 0.578 eV as revealed by the existing ab initio calculations.³⁶ Bound state calculations have also shown that the potential well can support several bound states.

HeH⁺ + He → [He₂H⁺] → HeH⁺ + He (12)

In addition to the reactive events mentioned above, HeH⁺ can undergo rotational-vibrational inelastic state-changes due to collision with He, H and H₂. While Desrousseaux and Lique³⁷ reported the rotational inelastic cross sections for HeH⁺ due to collision with H, the present authors reported the relevant cross sections and rate coefficients for the rotational inelastic transitions due to collision with He and H₂.^38,39 It is worth adding at this point that rotational and vibrational inelastic transitions can have a reactive as well as a nonreactive component in the case of (HeH⁺, He) and (HeH⁺, H) collisions, although both the components are indistinguishable in a real detection, albeit present from quantum calculations. It was therefore found from such calculations that H₂ is more efficient than He and H in causing rotational excitations in HeH⁺ as illustrated in the example from our calculations, reported here in Fig. 1.³⁹ It is important to add that vibrational inelastic transitions in HeH⁺ have an order of magnitude lower k values when compared with the pure rotationally inelastic paths.⁴⁰

Fig. 1 Computed (Δj₁ = +1) excitation rate coefficients for a series of inelastic processes in HeH⁺ (j₁) + p-H₂ (j₂ = 0) collisions³⁹ (solid lines), compared with the corresponding results for HeH⁺ + He³⁸ (long-dashes) and HeH⁺ + H collisions³⁷ (short-dashes). Adapted from Fig. 21 of ref. 39.

It also turns out that the Dissociative Recombination (eqn (9)) has a much higher rate coefficient of ∼10⁻⁷ cm³ molecule⁻¹ s⁻¹.⁴¹ A qualitative, pictorial summary of the formation and destruction routes for HeH⁺ and its relation with other atomic and molecular species is given in Fig. 2.

Fig. 2 A pictorial view of the interconnections between He, H, H₂ and the related ionic molecular species. Formation and destruction channels for (a) HeH⁺, (b) H₂⁺ and (c) H₃⁺.

Gianturco and coworkers have shown that HeH⁺ could nucleate several helium atoms around it,⁴² although clusters larger than He₂H⁺ are unlikely to be formed under ISM conditions because of the much more diluted presence of the involved partners.

4 H₂⁺ and its isotopomers: dynamics with He as a collision partner

In the early universe, H₂⁺ was presumably formed by radiative association

H + H⁺ → H₂⁺ + hν, ΔE₀ = −2.65 eV (13)

In addition, it was likely to be formed by proton transfer reaction (10). In interstellar clouds, however, H₂⁺ seems more likely to be formed by ionization of H₂ by cosmic radiation.⁹ H₂⁺ could also be formed by the radiative charge transfer (RCT) process:

He⁺ + H₂ → He + H₂⁺ + hν (14)

Mrugala and Kraemer⁴³ estimated the k_RCT for the above process to be between 2.5 and 3.5 times larger than the experimental results (1–1.1) × 10⁻¹⁴ cm³ molecule⁻¹ s⁻¹ at 15–35 K and ∼7.5 × 10⁻¹⁵ cm³ molecule⁻¹ s⁻¹ at 40 K.²⁴

In the early Universe, H₂⁺ was, presumably, also responsible for H₂ formation:

H₂⁺ + H → H₂ + H⁺ (15)

Karpas et al.²⁸ determined the k to be (6.4 ± 1.2) × 10⁻¹⁰ cm³ molecule⁻¹ s⁻¹ at 300 K.

H₂⁺ could also be destroyed by reaction with H₂:

H₂⁺ + H₂ → H₃⁺ + H, ΔE₀ = −1.7 eV (16)

The k value for the latter reaction was found to be 2.11 × 10⁻⁹ cm³ molecule⁻¹ s⁻¹ at 300 K.²⁸ The inelastic collisions between H₂⁺ and He have been investigated by Gianturco and collaborators⁴⁴ and we shall be discussing it below.

The reaction of H₂⁺ with He is highly endothermic:

H₂⁺ + He → [HeH₂⁺] → HeH⁺ + H, ΔE₀ = 0.80 eV (17)

It is also worth mentioning that this was the first ion–molecule reaction for which vibrational enhancement was demonstrated experimentally.^45,46 The reaction as well as the inelastic collisions between H₂⁺ and He are influenced by the presence of a potential well (see below). The literature on the system has been reviewed recently.²²

We briefly mention again at this point that Vera et al.⁴⁴ computed the rotationally inelastic integral cross sections for p- and o-H₂ (v = 0) colliding with He for E_trans in the range 1–1000 cm⁻¹ and rate coefficients for T in the range 1–100 K. While the 0 → 2 (6B_e) rotational excitation cross section for p-H₂⁺ rose from the threshold to a maximum of ∼20–25 Ų, and showed several narrow peaks, the 1 → 3 (10B_e) excitation cross section for o-H₂⁺ rose to a maximum of 15 Ų. On the other hand, all other excitation cross sections turned out to be considerably smaller. These differences were readily attributed to the difference in the anisotropic coupling terms of their inelasic PES and also to the existence of an exponential decrease in the cross sections with an increase in the energy gaps between the involved states in the relevant transition.^47,48 The corresponding rate coefficients determined by the recent calculations⁴⁴ were found to be at the most of ∼10⁻¹⁰ cm³ molecule⁻¹ s⁻¹ at 100 K while they were orders of magnitude smaller at lower T. The vibrational excitation cross section values obtained by Iskandarov et al.⁴⁹ using the same PES⁵⁰ were an order of magnitude smaller for p-H₂⁺–He collisions, thus confirming the differences which exist between the two energy-transfer processes in term of their nanoscopic coupling mechanisms and as discussed in the above references.

Since optical excitation/de-excitation of H₂⁺ and D₂⁺ to different ro-vibrational states is not possible, Schiller et al.⁵¹ showed, by using quantum scattering calculations, that rotationally cooled H₂⁺ (20 K) and D₂⁺ (40 K) could, in principle, be produced in the laboratory using cold He as the buffer gas. In another simulation carried out by the same authors, and also using quantum scattering calculations, Vera et al.⁵² showed from computational simulations that differential reaction cross sections for the reaction (17), in case were to be experimentally obtained in future experiments, could be measured by using velocity mapping tools and the results would be sensitive to the initial ro-vibrational state selection for H₂⁺. Thus, one can in principle surmise that reactivity for state-selected initial partners could also become amenable to experimental observations.

Although deuterium is an isotope of hydrogen, astrophysical models treat the former as a separate element. Isotopically substituted H₂⁺, i.e. HD⁺ has a special role to play in the cooling of stellar gases because of its asymmetry and the resultant dipole moment, a feature making both radiative and collisionl interactions more likely to occur. Therefore, for that same reason, HD⁺ is formed more readily than H₂⁺ by radiative association, a property confirmed by calculations.

Furthermore, one sees that there is a difference in reactivity between the H-end and the D-end in the reaction of HD⁺ with He and other atomic and molecular species, as discussed, for example, in ref. 53. We are not going to discuss the isotopic variants here because the abundance of HD⁺ is found to be several orders of magnitude lower than that of H₂⁺. Such marked changes in column densities, therefore, are preventing the isotopic variants to work as effectively as their lighter counterparts in participating in the chemical networks where such molecular cations are deemed to be present. Hence, although they are often discussed in the current literature for completeness, we will not analyse them any further in the present perspective.

5 HeH₂⁺: structure and chemical energy flows

As mentioned earlier, Mrugala et al.⁵⁴ estimated the k_RA to have a maximum value of 2.1 × 10⁻²⁰ cm³ molecule⁻¹ s⁻¹ at about 20 K for the formation of HeH₂⁺ from He and H₂⁺:

He + H₂⁺ → HeH₂⁺ + hν (18)

These authors (e.g. see: Mrugala and Kraemer⁴³) further estimated the k_RA to have a maximum value of 3.3 × 10⁻¹⁵ cm³ molecule⁻¹ s⁻¹ around 2 K for the complementary route of formation of HeH₂⁺:

He⁺ + H₂ → HeH₂⁺ + hν (19)

As it was mentioned earlier, HeH₂⁺ was detected in a mass spectrograph in 1925, but its microwave spectrum near its dissociation limit was recorded only in 1996 by Carrington et al.^55,56 There was a sharp doublet around 21.8 GHz (0.73 cm⁻¹), which was attributed to [p-H₂–He]⁺ with the possibility of He being at either end of H₂⁺. There was a sextet around 15.2 GHz (0.51 cm⁻¹), which was attributed to [o-H₂–He]⁺, the higher multiplicity arising from the nuclear magnetic moment (I = 1) of o-H₂⁺.^57,58

Ab initio calculations²² had suggested that HeH₂⁺ could be stable by 0.34 eV, relative to the well separated He and H₂⁺. Kraemer et al.²¹ had shown that there could be a shallower potential well of −0.145 eV in the first excited state. Hopper⁵⁹ had suggested that the (He⁺, H₂) collision could result in radiative association and form HeH₂⁺, with concomitant emission at 153 nm.

Meuwly and Hutson⁵⁷ had suggested associative ionization

He* + H₂ → [HeH₂⁺] + e (20)

as a possible means of formation of HeH₂⁺. Some of us have suggested recently that it could be formed due to non-adiabatic coupling terms acting like friction.⁶⁰

The vibrational spectrum of HeH₂⁺ and HeD₂⁺ in an ion trap at 4 K was reported recently by Asvany et al.⁶¹ Based on the results of their variational calculations for the ro-vibrational bound states on the 3D PES reported by Koner et al.,⁶² Asvany et al. assigned the peak at 1840 cm⁻¹ to the H–H fundamental stretch and the peaks at 632 and 732 cm⁻¹ to the H₂⁺–He bend and stretch, respectively; The corresponding peaks for HeD₂⁺ occur around 1309, 473 and 641 cm⁻¹, respectively.

It is hoped that HeH₂⁺ will be detected soon in ISM.

6 He₂⁺: processes with H as a collision partner

It is considered to be likely¹⁵ that He₂⁺ was formed early on by radiative association

He + He⁺ → He₂⁺ + hν (21)

although it could be readily destroyed by photodissociation

He₂⁺ + hν → He + He⁺ (22)

and by dissociative recombination

He₂⁺ + e → He + He (23)

It is important to add at this point that the estimated abundance of He₂⁺ is 20 orders of magnitude less than that of HeH⁺ for z < 1000.¹²

He₂⁺ could combine with H to give He₂H⁺ and in turn to yield HeH⁺:

He₂⁺ + H → [He₂H⁺] → He + HeH⁺ (24)

The spectral characteristics of He₂H⁺ are discussed later in this article.

7 LiH⁺ in early universe chemistry

Lithium was the first metallic atom/nucleus to be formed in the early Universe, and it was 10 orders of magnitude less in abundance than hydrogen. The protonated diatomic species LiH⁺ was thought that could be formed through radiative association

Li⁺ + H → LiH⁺ + hν (25)

and with a minor contribution through

Li + H⁺ → LiH⁺ + hν (26)

while it could also be destroyed by dissociative recombination

LiH⁺ + e → Li + H (27)

and by

LiH⁺ + H → Li⁺ + H₂ (28)

and

LiH⁺ + H → Li + H₂⁺ (29)

The proton transfer, eqn (29), is less likely to occur as it is highly endothermic. Lepp et al.¹⁵ concluded that LiH⁺ was more abundant than LiH for smaller redshifts (z < 30).

Lithium hydride and its ionic counterpart, LiH⁺, have attracted for many years the interest of theorists and experimentalists. Below 3000 K the collisional excitation of rotational levels of the most abundant species, the hydrogen molecule, is negligible and therefore lithium hydride partners with their low-excitation temperatures and fast radiative decay become the most likely ones to be able to accomplish the role of coolants. Furthermore, these species have usually been taken to live longer than H₂. The possible presence of LiH⁺ was first postulated by Dalgarno and Lepp⁶³ who suggested it to be formed by efficient ion-atom radiative association, eqn (26).

However, it was further noted that the abundance of LiH⁺ could also be effectively reduced by an important destruction mechanism,

LiH⁺ + H → Li⁺ + H₂ (30)

a barrierless, exothermic gas-phase reaction, already indicated in eqn (28)^64,65 that forms hydrogen molecules from the abundant atomic H known to be present in that environment. Another important destruction mechanism was also suggested by Stancil et al.⁶⁶ and includes the charge-exchange depletion reaction,

LiH⁺ + H → Li + H₂⁺ (31)

and the charge-transfer reaction that contributes to the abundance of the neutral molecule

LiH⁺ + H → LiH + H⁺ (32)

However, these two reactions are unlikely to occur as they are both endoergic by 5.7 and 5.8 eV, respectively. The fully dissociative channel, i.e., the three-body (3B) break-up process induced by collision (collision-induced dissociation (CID)), as suggested in our earlier work⁶⁴ would also be probable at low energies although it would not be important from the point of view of altering the LiH⁺ abundances.

A careful analysis of various primordial molecules which are expected to be present in the early universe has led to the identification of LiH and LiH⁺ as the best candidates that could have left their imprints on the Cosmic Background Radiation (CBR) via Doppler shift.^67,68 Primary and secondary anisotropies, in fact, could be produced from these molecules, e.g. see: ref. 69, 70. However, such findings strongly depend on their assumed abundances relative to the primary abundance of H. In the work published by some of us (FAG) in 2009 with Bovino et al.,⁷¹ the authors were able to show from quantum calculations that LiH abundance (as suggested by Stancil et al.⁶⁶) is strongly reduced by a destruction mechanism that should then lead to no erasing of primordial CBR anisotropies and no production of secondary anisotropies in the recombination era. When one now turns to the ionic LiH⁺, however, besides its being important in the formation of the LiH molecules through the exchange reaction (LiH⁺, H), it was found that it is a molecule which could have survived at low redshifts and could have left its imprint on the CBR, thanks to its large permanent dipole moment (as suggested by Dubrovich⁶⁷).

Therefore, quantum reactive scattering calculations for the exothermic reaction of the LiH⁺ molecular cation with hydrogen atom at the temperatures corresponding to the redshift values deemed to be important for the lithium chemistry in the early universe environment (z < 400) have been trying to establish from first principles the possible efficiency of the chemical routes to the depletion rates. The calculations described in ref. 71 found that the survival process for LiH⁺ to be the most likely process at low-T, indicating that, because of specific features of their reactive PES⁷¹ the two partners undergo essentially repulsive interaction at short range in the product region due to the marked increase of the products relative kinetic energy, while the more stable bound complex (LiH₂⁺) is formed within a range of distances that correspond to the reactants region of interaction.

Furthermore, the depletion reaction mentioned before remains, however, an important reactive process that leads to the disappearance of LiH⁺ cations initially formed during the recombination era. In other words, it was found from the quantum calculations of ref. 65 that the exothermic process is indeed the dominant reactive process that leads to density reduction for the cationic hydride. The LiH⁺ partner is therefore expected, from the balancing role of the above two pathways, to remain present in the low-z period, thereby becoming able to contribute to molecular cooling processes during the post-recombination era. As the temperature increases, the 3B break-up process has been shown to become more important, as surmised by the calculations of ref. 72 thereby leading to the disappearance of the LiH⁺ that survived the exothermic depletion reaction discussed before, hence leading to a reduction of its role as a coolant.

8 LiHe⁺ formation in the ISM

Because of its large dipole moment and its low ionization potential, LiH has been considered for a long time a potential candidate for inducing spatial and/or spectral distortions of the Cosmic Background Radiation, as originally suggested a while ago by Dubrovich⁶⁷ and observationally tested by Maoli et al.⁶⁹ It is, in fact, its possible role as a molecular coolant of the primordial gas, because of its efficient radiative decay down its manifold of rotovibrational levels, that made its likely presence a very important issue in several earlier studies.⁷³ By the same token, other molecular species formed as cations after atomic ionization during gravitational collapse, e.g. LiH⁺, HeH⁺, HD⁺ and LiHe⁺, could also play a similar role as additional molecular coolants and their non-equilibrium level populations may also have left a possible signature in protogalactic clouds, imprinting spatial or spectral distortions in the CBR spectrum.⁷⁴

A few years back some of us, e.g. see ref. 75, had carried out an extensive analysis via a series of quantum calculations to determine the relative role of several pathways to its formation and destruction within the chemical network acting at low redshift. As a matter of fact, in previous papers by Bovino et al.,^76,77 the photonic paths to the formation and destruction of LiHe⁺ were examined in some detail, while in ref. 75 that work was further extended by adding the chemical paths presiding over its evolution, i.e., the chemical reaction with hydrogen,

LiHe⁺ + H → LiH⁺ + He (33)

leading to its destruction, and the formation reaction from the lithium hydride cation:

LiH⁺ + He → LiHe⁺ + H (34)

The physical characteristics of the above reaction were discussed extensively in ref. 78. An additional path that was also considered in the above study is that driven by the presence of a residual electron fraction in the early universe (Stancil et al.⁶⁶), i.e., the fragmentation of the polar cation by the dissociative recombination process:

LiHe⁺ + e⁻ → LiHe* → Li + He + hν (35)

a reaction that, from those extensive calculations, also turned out to be fairly efficient.

In the work reported in ref. 75 the authors analyzed in greater detail the variety of molecular processes, partly summarized above, which involve a usually poorly studied molecular cation, LiHe⁺ (¹Σ⁺), and which deal with its possible formation and destruction in the pregalactic gas through an extensive network of photon-induced and chemically driven processes. In the range of redshifts of interest, they carried out quantum calculations of chemical formation/destruction reactions which have never been considered before from realistic computational models and which have been reported above in eqn (33), (34) and (35).

The results of that study clearly showed the existence of the close competition between production and destruction pathways which however also turned out to have very similar efficiencies. Hence, the estimated abundances for LiHe⁺, within z values from about 30 and 10, do not increase as highly as those found in the same study for LiH⁺ and for HeH⁺. Such findings therefore indicated from accurate calculations that the expected abundances, and hence the chemical role, of the above cation would not be as significant as that involving other, albeit just as simple, molecular cations.

9 The role of H₃⁺ in Interstellar chemistry

Detected first in 1911 by J. J. Thompson,⁷⁹ H₃⁺ was also detected along with HeH⁺ and HeH₂⁺ in a mass spectrograph by Hogness and Lunn¹⁷ in 1925. It is the simplest two-electron-three-nuclei system one could think of and is a prototype for a 3-centre two-electron bond. Since it has an equilateral triangular geometry in its ground electronic state, it does not have a permanent dipole moment and its rotational spectrum is not active in infrared or microwave. However, its bending motion is infrared active. This was predicted by ab initio calculations by Carney and Porter⁸⁰ in 1976 and verified in the laboratory by Oka⁸¹ in 1980. That formed the basis for the detection of the species in ISM conditions in 1996.⁷ Subsequent astronomical observations have shown that it is perhaps the most abundant molecular ionic species in dense molecular clouds (responsible for star formation) as well as in diffuse clouds.⁸²

While an electron impact causes ionization of H₂ in a mass spectrometer, cosmic radiation is believed to be responsible for the ionization in molecular clouds.⁹ H₂⁺ reacts readily with the abundant H₂ and forms H₃⁺ as mentioned earlier.

In the early universe, the H₃⁺ formation was perhaps through the reaction of HeH⁺ with H₂. It is considered the major coolant for the gravitationally condensing gas. Zicler et al.⁸³ estimated the k_RA for

HeH⁺ + H₂ → HeH₃⁺ + hν, ΔE = −2.68 eV (36)

to rise from 3.1 × 10⁻¹⁹ cm³ molecule⁻¹ s⁻¹ at 10 K to 2.01 × 10⁻¹⁸ cm³ molecule⁻¹ s⁻¹ at 100 K and to decline to 7.1 × 10⁻¹⁹ cm³ molecule⁻¹ s⁻¹ at 500 K.

Once formed, H₃⁺ facilitates proton transfer to atoms like He, C, N and O and molecules like CO, CN and N₂:

H₃⁺ + He → HeH⁺ + H₂ (37)

H₃⁺ + C → CH⁺ + H₂ (38)

H₃⁺ + N → NH⁺ + H₂ (39)

H₃⁺ + O → OH⁺ + H₂ (40)

H₃⁺ + CO → HCO⁺ + H₂ (41)

H₃⁺ + CN → HCN⁺ + H₂ (42)

H₃⁺ + N₂ → N₂H⁺ + H₂ (43)

in dense molecular clouds.

H₃⁺ seems to be quenched by the electrons arising from the photoionization of C in diffuse clouds:

H₃⁺ + e → H₂ + H (44)

The interconnection between He, H, H₂ and related ionic species is depicted in Fig. 2.

We must also point out here that the singly deuterated H₃⁺, i.e. H₂D⁺ has the virtue, akin to that of HD⁺, that H₂D⁺ is now provided by a permanent dipole moment. As a consequence of this structural change it can participate much more effectively as a molecular coolant than H₃⁺, but its occurrence would be several orders of magnitude lower than that of H₃⁺. Furthermore, one needs to distinguish between o- and p-H₂D⁺ as well, thereby unduly complicating the establishment of realistic percentage densities involved in the chemical kinetics models of linked reaction processes.

10 The HeHHe⁺ cation: a possible ionic entry in ISM networks

From the chemical viewpoint it is reasonable to assume that HeH⁺ cation was the very first diatomic molecule formed in the early universe.⁸⁴ Larger helium containing cationic species (HHe_n⁺ with n = 2–6) have been predicted, although not observed. Among them, the first term, HeHHe⁺, has been discussed as a possible efficient emitter for observations at high-z⁸⁵ because of it large dipole transition moment under vibrational excitations, as we shall further discuss below.

This symmetric linear molecule has been studied both theoretically^36,86–88 and experimentally.⁸⁹ Using the CCSD(T)-F12/aug-cc-pVTZ level of theory, Fortenberry and Wiesenfeld⁸⁵ have investigated the possibility of HeHHe⁺ formation through the insertion mechanism:

He₂⁺ + H → HeHHe⁺(singlet/triplet) (45)

In addition to the formation of a symmetric linear [HeHHe]⁺ in its ground electronic singlet state, there could be the formation of the first excited triplet state with a well defined isosceles triangular geometry and a dipole moment of 0.83 D. While the antisymmetric stretch and bending modes of the singlet [HeHHe]⁺ would be infrared active, the rotational motion of the triplet state could be microwave active. There could be another route to the formation of [HeHHe]⁺:

He₂⁺ + H₂ → HeHHe⁺(singlet) + H (46)

Recent quantum inelastic scattering studies^90,91 of this molecule with He atoms show fairly large rate coefficients, compared to HeH⁺ colliding with He and H,^37,92 under similar conditions, suggesting a possible energy dissipation process after the recombination era. With these results, modeling of the kinetic evolution of the early universe should realistically include HeHHe⁺.⁹³

11 Small C-bearing cations

The number of few-carbon atoms-containing cations which have come under observation in the interstellar environments, and which have been finally detected with an acceptable level of reliability, has certainly increased in the last few years. It is therefore useful for the present perspective article to report a few cases which have been spotted and analysed under different points of view to elucidate both their occurrence and their possible roles within the chemical networks which are being modelled within circunstellar envelopes (CSE) environments.

11.1 The CH⁺: the smallest C-bearing cation

Due to their low dissociation energies, the molecules CN, CH⁺ and CH are most frequently found in molecular clouds where dust provides shielding from the ambient radiation field. The current data are generally towards low-reddening objects, in contrast to many previous studies, which until recently had the aim of determining the conditions within normal and high-latitude molecular clouds or star-forming regions. The methylidyne ion CH⁺ was among the first molecules detected in the interstellar medium (ISM).⁹⁴ For decades, CH⁺ remained accessible only in absorption at 423.2 nm, restricting its investigation to the lines-of-sight (LOS) toward bright nearby stars. The CH⁺ abundances observed in the local diffuse ISM are several orders of magnitude above the predictions of UV-driven steady-state models (see references in ref. 95), raising one of the most intractable puzzles in our understanding of the ISM. Unfortunately, the detection of the CH⁺ ground-state rotational transitions has been prevented for a long time since CH⁺ is a light molecule; its lowest rotational transition lies in the submillimetre range. Additionally, its high reactivity makes it difficult to isolate in laboratory experiments.⁹⁶ Only recently did successful experiments provide accurate frequency determinations.⁹⁷ Moreover, ground-based astronomical detection of ¹²CH⁺ (1-0 emission) is prevented by its proximity to a strong atmospheric line of water vapor. The first detection of the CH⁺ rotational lines (above j = 2-1) was achieved by ISO-LWS in the planetary nebula NGC7027 as in ref. 98. The CH⁺ (1-0) line has been detected in emission and absorption with the Herschel/HIFI instrument in DR21 (see ref. 99) and, as spectrally unresolved lines with the Herschel/SPIRE FTS (see ref. 100), in emission in the Orion Bar and in absorption in two SFRs (see ref. 101). The ground-state transition of the isotopologue ¹³CH⁺, at a frequency lower by ∼5 GHz, can be observed under exceptional atmospheric conditions and was detected in absorption toward SgrB2(M) and several massive SFRs of the inner Galaxy with the Atacama Pathfinder EXperiment (APEX) telescope and the Caltech Submillimeter Observatory (CSO) telescope (see ref. 102). The large observed abundances of CH⁺ have always been a major puzzle of the diffuse interstellar chemistry, since the only reaction efficient enough to form this molecular ion would be:

C⁺ + H₂ → [CH⁺] + H (47)

turns out to be highly endothermic (E/k = 4640 K). This suggests that large amounts of suprathermal energy need to be deposited in the cold neutral medium. In the past, several scenarios have been investigated, including C-shocks (e.g. see ref. 103), turbulent interfaces between the warm and cold neutral medium¹⁰⁴ and regions of intermittent turbulent dissipation (TDR models, see ref. 95). While the reaction between C⁺ and vibrationally excited H₂ could account for the large abundances of this cation in dense and highly illuminated photodissociation regions (PDR), this mechanism is found inefficient for the physical conditions of the diffuse ISM (Agundez et al.¹⁰⁵). This riddle could be related to the observed excess of HCO⁺ in the diffuse ISM (see references in ref. 106) because CH⁺-rich environments with H₂ molecular fractions as low as 25% enhance the production of HCO⁺ through the ion-neutral reaction chain

CH⁺ + H₂ → CH₂⁺ + H (48)

CH₂⁺ + H₂ → CH₃⁺ + H (49)

CH₃⁺ + O → HCO⁺ + H₂ (50)

The TDR code is a 1-dimensional model in which the chemical and thermal evolution of a turbulent dissipative burst – namely a magnetized vortex – is computed. The lifetime of the burst is controlled by the turbulent rate-of-strain a of the large scales. At any time, a large number of these tiny regions (∼100 AU), altogether filling a small fraction of the entire LOS, are developing a transient warm chemistry triggered by both the viscous dissipation and the ion-neutral friction, where local CH⁺ and HCO⁺ abundances reach 10⁻⁶ and 3 × 10⁻⁷, respectively.⁹⁵ A random LOS therefore samples three kinds of diffuse gas: (1) mainly the ambient medium in which the chemistry is driven by the UV radiation field, (2) the active vortices with a filling factor set by the energy transfer rate in the turbulent cascade and identified with a significant turbulent dissipation rate, and (3) the long-lasting relaxation stages where the gas previously heated cools down to its original state. Hence, the use of this model has suggested that the high abundances of CH⁺ observed in various ISM environments could be explained within the framework of models where the chemistry chains include routes which are locally open to turbulent dissipation bursts (i.e. within TDR models as in ref. 106).

11.2 C₃H⁺: a longer carbonaceous cation

Small hydrocarbon molecules play an important role in the as-trochemistry of the interstellar and circumstellar medium since they are expected to be leading to the formation of large organic molecules and ultimately to polycyclic aromatic hydrocarbons (PAHs) and carbonaceous dust (e.g. see ref. 107 and 108). In UV-rich environments, like diffuse clouds and photodissociation regions (PDRs), they can also be considered as exceptional tracers of the interplay between PAH formation and their photo-destruction.¹⁰⁹ On the other hand, although small neutral hydrocarbons like C₃H₂ and C₂H are commonly used as probes for physical and chemical conditions in the interstellar medium (for references see ref. 110), observations of reactive carbocations, which are important intermediates in carbon astrochemistry (Wakelam et al. in ref. 111) have so far been limited to C⁺ and CH⁺ (e.g.: Nagy et al.¹¹²), mostly due to a lack of accurate laboratory spectroscopic work on the larger cationic species. More recent observational work¹¹³ attributed a series of rotational emission lines observed at millimeter-wavelengths toward the Horsehead PDR to the carbocation C₃H⁺. The identification was based on spectroscopic constants resulting from a fit of six (plus two tentatively) detected harmonically related rotational lines to a closed-shell linear-rotor Hamiltonian. The derived rotational constant B = 11.245 GHz agreed well with the value obtained from previous theoretical calculations of the closed-shell (¹Σ⁺) isomeric ground state of the ion with this chemical composition. More recent laboratory experiments in a 4 K cryogenic ion trap (see ref. 114) were able to detect the line positions of four rotational transitions with a relative precision of 3 × 10⁻⁷. These experimentally derived transition frequencies and related spectroscopic constants turned out to agree with those from the previous astronomical onservations, thereby unambiguously confirming the detection of this important carbonaceous cation and excluding its anionic variant suggested earlier on. More recent computational work has also been directed to the study of the interaction of this cation with He atoms (see ref. 115) whereby the corresponding collisional rate coefficients for its rotational transitions were reported for temperatures up to about 100 K. Not yet specific chemical routes have been discussed or verified to explain the formation of this cations, thus leaving fairly open the general suggestions on the preparation of more complex carbon-bearing positive ions in interstellar environments.

12 Cations with higher metallicity

While the elements formed in the early Universe were only He, H, D and Li, subsequent events in the evolution of the Universe led to the formation of stars and galaxies and in the process higher elements up to iron (atomic number = 26) in the periodic table.^116,117 Elements with atomic number >26 seem to have been formed only as a result of supernovae. Understandably all those elements could also form cations either by themselves or also when in associaton with other elements in the periodic table.

Without going into the details of stellar nucleosynthesis, it is important to point out that in general there seems to be enough C, N and O in the Sun, playing an important role in the helium formation as the hydrogen “burns”. Atoms/ions of many other elements are spewed out from a variety of stars during their stellar dynamics and the ISM appears to contain several cations, anions and neutral molecular species. For a recent review on the subject, the reader is referred to ref. 10.

We mention here the discovery of NO⁺ through its j = 2-1 line¹¹⁸ and HCNH⁺ through its j = 3-2 line.¹¹⁹ The former is special in that it contains N as well as O. The latter is special because it is the protonated form of HCN (vital for the formation of life giving molecules) and could be formed through

HCN + HCO⁺ → HCNH⁺ + CO (51)

under “warm” (T = 27 K) conditions. The characteristics and the significance of HCO⁺ are discussed further below. Under cold (T = 10 K) conditions, it appears that HCNH⁺ is formed through the pathway

HCN⁺(HNC⁺) + H₂ → HCNH⁺ + H (52)

and destroyed by the dissociative recombination:

HCNH⁺ + e → HCN + H;HNC + H (53)

HCNH⁺ + e → CN + H + H (54)

HCN⁺ (HNC⁺) itself is formed presumably from the reaction

CN + H₃⁺ → HCN⁺(HNC⁺) + H₂ (55)

12.1 A small polyatomic partner: H₃O⁺

Predicted to be present in dense molecular clouds by Herbst and Klemperer⁶ in 1973, H₃O⁺ was first observed astronomically in 1986 by Wootten et al.¹²⁰ and Hollis et al.¹²¹ A review of subsequent observations and the characteristics of the species is given in the work of Demes et al.¹²² It is believed that the observation of H₃O⁺ in ISM is adequate proof for the existence of H₂O in the same environment. Dissociative recombination of the former leads to the latter:

H₃O⁺ + e → H₂O + H (56)

The mechanism of formation of H₃O⁺ in molecular clouds was discussed by Demes et al.¹²³ The understanding is that in diffuse clouds, H₃O⁺ is formed through the route,

OH⁺ + H₂ → H₂O⁺ + H (57)

H₂O⁺ + H₂ → H₃O⁺ + H (58)

The OH⁺ itself could be formed through the reaction¹²⁴

O⁺ + H₂ → OH⁺ + H (59)

Deep within dense molecular clouds, H₃O⁺ plays a central role in producing OH⁺ through the reaction

H₃O⁺ + O → H₂ + OH⁺ (60)

Demes et al.^122,123 reported the results of quantum mechanical close coupling calculations using a 5D ab initio PES¹²⁵ in the form of rotational de-excitation cross sections for o-/p-H₃O⁺ in collision with o-/p-H₂

for a range of E_trans. They reported many Feshbach and shape resonances, particularly at lower energies. Interestingly, the reported rate coefficients were comparable in magnitude for o-H₃O⁺ and p-H₃O⁺ for T in the range 10–300 K. They were slightly less than 10⁻⁹ cm³ molecule⁻¹ s⁻¹ for Δj₁ = −1 transitions and decreased to 10⁻¹⁰ cm³ molecule⁻¹ s⁻¹ for larger Δj₁ transitions and changed very little in going from p-H₂ to o-H₂ as the collision partner. The k values decreased slightly (in the logarithmic scale) in going from T = 10 to 100 K and remained nearly flat for higher T.

12.2 The HCO⁺ cation

One of the fundamental questions concerning the chemistry in circumstellar envelopes of evolved stars is the role of ion–molecule reactions. Such reactions are thought to be significant contributors to molecule formation in the outer part of the envelope, where they are initiated by either cosmic rays or UV photoionization.

One molecular ion that has been searched for decades in circumstellar material has been HCO⁺. This species is thought to be critical in the ion–molecule schemes because it is expected to be formed directly from H₃⁺ and CO:

H₃⁺ + CO → HCO⁺ + H₂ (62)

HCO⁺ in fact is observed in virtually all phases of the dense interstellar medium, including molecular clouds, planetary nebulae, and diffuse clouds, as well as in comets.¹²⁶ However, the presence of HCO⁺ in IRC + 10216, the best-studied circumstellar shell, has been debated for years. More recently, Millimeter-wave observations of HCO⁺ have been conducted toward oxygen-rich circumstellar envelopes, as well as IRC + 10216, using the facilities of the Arizona Radio Observatory (ARO).¹²⁷ Hence, the j = 1 → 0 and the 2 → 1 transitions of this cation were measured with the ARO 12m. antenna, while the j = 3 → 2 and 4 → 3 lines were observed using the ARO Sub-Millimeter Telescope.¹²⁷ Additionally, the HCO⁺ cation was detected toward the supergiant NML Cyg and the asymptotic giant branch (AGB) stars IK Tau, TX Cam, and W Hya in at least two transitions. The j = 2 → 1 and 3 → 2 lines of this ion were also detected toward IRC + 10216, confirming the identification of HCO⁺ in this object.¹²⁷

Chemical models suggest that HCO⁺ is formed in the outer envelopes of stars via two primary synthetic routes.¹²⁸ One pathway is from the simple protonation reaction of CO, as is thought to occur in molecular clouds; and we mentioned earlier in this Subsection. Another pathway is via H₂O:

C⁺ + H₂O → HCO⁺ + H (63)

The destruction of HCO⁺ is thought to occur via electron dissociative recombination, or proton transfer to water to create H₃O⁺.¹²⁸ Based on these pathways, fractional abundances for HCO⁺ have been computed by several models as extensively discussed in ref. 127, where it was concluded that HCO⁺ appears to be a common species in oxygen-rich circumstellar shells, both of supergiants and AGB stars. It is also present in the carbon-rich envelope of IRC + 10216, but in much lower concentration. The abundance of HCO⁺ appears to be best correlated with that of water in stellar envelopes; however, its production from CO must also play a significant role. The abundance of HCO⁺ also appears from that study to be inversely proportional to the mass-loss rate, although they concluded that additional sources warrant investigation to further examine such trends. These observations also suggest that ion–molecule reactions must be occurring in circumstellar gas at some level. It follows, in fact, that other ions such as H₃O⁺ may be detectable in O-rich shells.

It is also interesting to note at this point that a recent computational study¹²⁹ has investigated the possibility that, in cold galactic molecular clouds, dust grains coated by icy mantles are prevalently charged negatively because of the capture of the electrons in the gas. It would therefore follow that the interaction of the charged grains with gaseous cations could efficiently neutralize them thereby taking them off the chemical chain of likely reactions.¹²⁹ More specifically, by means of electronic structure calculations, the energy and the structure of all possible product species once the HCO⁺ ion adsorbs on water clusters holding an extra electron were searched and characterized. Among the possible situations considered, those results indicated that spontaneous formation of the HCO radical by electron transfer is energetically the most favorable path, although no actual rates were obtained. Accordingly, they suggested that interstellar grain particles could act as a reservoir of electrons, triggering electron transfer processes with the molecular cations, like HCO⁺, adsorbed on such grain particles, thereby modifying the overall abundance of this specific molecular ion in molecule-rich Circumstellar Envelopes.

12.3 Mg-Bearing cations

Radiative association seems to play an important role in bringing cations together with neutrals with the rates governed by Langevin capture. See for example, the recent report of Cernicharo et al.¹³⁰ on the discovery of MgC₄H⁺, MgC₃N⁺, MgC₆H⁺ and MgC₅N⁺. These findings are particularly relevant since polytomic, metal-containig molecules have been detected only toward the Circumstellar Envelopes (CSEs) of fully evolved stars, while simpler diatomic species containing Al, Na or K attached to a halogen atom have been detected in the earlier Carbon star envelope IRC + 10216¹³¹ where these species are formed in the hot inner parts of the envelope, closer to the stellar core. More recently, the only metal that was found to lead to molecular formations with more than three atoms in the IRC + 10216 has been magnesium (see ref. 132–134). It is only in very recent publications, like ref. 130, that the presence of Mg-containing cations has been put forward and its formation routes explored with quantum calculations. In particular, the various cations listed above have been suggested to be formed by radiative association between Mg⁺ and the corresponding neutral radicals like C₄H, C₃N, C₆H and C₅N, while also being destroyed via dissociative recombination with electrons and by reaction with atomic hydrogen.

Comparison of the corresponding association rate coefficients within a larger chemical model for the formation of the initial radical species and the Mg cation indeed suggested that the radiative asociation paths involving the atomic cation of the metal species with the molecular radicals is a realistic process for explaining the appearance of molecular cations with heavier metal atoms. Such findings therefore constitute a very recent confirmation that molecular cations in different ISM environments can indeed be formed with heavier atoms than previously expected.¹³⁰

13 Conclusions

In the present perspective article, we have focussed on a specific subset of a variety of molecular cations, involving combinations of the most abundant light atoms present in ISM environments, i.e. H and He. Because of the all-present effects from starlight, it turns out that these small cations can be efficiently formed but also easily destroyed by recombination processes involving the free electrons in that same environments or in other regions of the Dark and of the Diffuse Molecular Clouds. Besides cations involving H and He, we have also looked at the formation of cations involving lithium partners, one of the important atomic species which is considered to be relevant in the high-z regions of the early universe conditions. Additionally, we discuss very recently detected Mg-bearing molecular cations which constitute current examples of molecular ions that involve heavier metal species.

The examples in this work clearly point at a surprisingly varied presence of molecular cations in the same interstellar environments where also neutral molecules and molecular anions are detected, thus suggesting that chemical routes involving positive ions as possible partners, are indeed a significant aspect of the ISM chemistry.

Before closing, we would like to re-iterate that many of the ion–molecule reactions mentioned in this perspective article are exothermic and face no potential energy barrier. In addition, there is a long-range attraction that goes as R⁻⁴ that is particularly important at low temperatures. Langevin cross sections lead to rate coefficients of the order of 10⁻⁹ cm³ molecule⁻¹ s⁻¹. In comparison, dissociative (electron) recombination has k values of the order of 10⁻⁷ cm³ molecule⁻¹ s⁻¹.

In spite of the fact that k values which deal with several exothermic reactions are only weakly T-dependent, Herbst¹³⁵ has pointed out that they can have a U-shaped T-dependence at very low temperatures. Rotationally inelastic rate coefficients for Δj = ±1, ±2 (depending upon the molecule being heteronuclear or homonuclear) transitions are also of the order of 10⁻⁹ cm³ molecule⁻¹ s⁻¹. For larger Δj transitions, the k values decrease exponentially with an increase in the energy gap between the initial and the final rotational states. The k values for the vibrationally inelastic transitions (Δv = ±1) are at least an order of magnitude lower than those for the rotationally inelastic (Δj = ±1, ±2) transitions for a given molecular (ionic) species.

Although the k values for the formation of di-/tri-/polyatomic molecular cations by radiative association are often estimated to be ≤10⁻¹⁵ cm³ molecule⁻¹ s⁻¹, way below the k-values mentioned above, they are still expected to play a significant role at extremely low densities (in the absence of any third body), as it is the case in the early universe conditions.

In conclusion, the small cations examined in this perspective indicate that their formation in the ISM conditions are linked to a broad range of kinetic mechanisms that take advantage of the presence of efficient long-range interaction forces and of the efficient coupling which they generate for both reactive and state-changing processes.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

F. A. G. acknowledge the support from the Computer Center of the University of Innsbruck. L. G.-S. further acknowledges the financial support by Ministerio de Ciencia e Innovación (Spain) MCIN/AEI/10.13039/501100011033 (Refs. PID2020-113147GA-I00 and PID2021-122839NB-I00).

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