Perspectives of Gas Phase Ion Chemistry: Spectroscopy and Modeling

Abstract

The study of ions in the gas phase has a long history and has involved both chemists and physicists. The interplay of their competences with the use of very sophisticated commercial and/or homemade instrumentations and theoretical models has improved the knowledge of thermodynamics and kinetics of many chemical reactions, even if still many stages of these processes need to be fully understood. The new technologies and the novel free-electron laser facilities based on plasma acceleration open new opportunities to investigate the chemical reactions in some unrevealed fundamental aspects. The synchrotron light source can be put beside the FELs, and by mass spectrometric techniques and spectroscopies coupled with versatile ion sources it is possible to really change the state of the art of the ion chemistry in different areas such as atmospheric and astro chemistry, plasma chemistry, biophysics, and interstellar medium (ISM). In this manuscript we review the works performed by a joint combination of the experimental studies of ion–molecule reactions with synchrotron radiation and theoretical models adapted and developed to the experimental evidence. The review concludes with the perspectives of ion–molecule reactions by using FEL instrumentations as well as pump probe measurements and the initial attempt in the development of more realistic theoretical models for the prospective improvement of our predictive capability.

1. Introduction

The study of gas phase ionic chemistry finds its fundamental relevance in different areas of physical chemistry such as atmospheric and astro chemistry [1], plasma chemistry [2], biophysics [3], interstellar medium (ISM) [4], and the activation and/or functionalization of simple starting materials [5].

The atmosphere is composed of a mixture of gases, the main components are N₂ and O₂ but also trace gases such as carbon dioxide, carbon monoxide, methane, water, nitrous oxide, ozone, argon, sulfur dioxide, and haloalkanes are important. These gases are present in very little amounts but cannot be undervalued; they are emitted in the atmosphere by natural or anthropogenic phenomena and could have a key role in some fundamental reactions that change the budget of some important species and consequently alter the composition of the atmosphere with a social healthy impact. Chlorofluorocarbon molecules are a classic and well-known example. They interact with sun light and produce chlorine radicals that catalytically destroy the ozone molecules. These species can also interact with high energetic cosmic rays with the production of reactive, neutral, and charged species. Chemical networks that explain the formation of species in the atmosphere involve mainly neutral species. Despite the fundamental role of neutrals in many processes, the formation of neutral species from ion–molecule reactions is also important because these reactions may represent more efficient paths to neutrals than neutral–neutral reactions, either destroying or producing neutral molecules by faster reactions. The study of ionic processes is fundamental to understand how they alter the neutral chemistry and identify the link between the ion and neutral chemistry in many processes occurring in different environments. Moreover, greenhouse gases (GHGs) such as carbon dioxide and depleting substances (ODSs) such as haloalkanes are considered responsible for climate change due to global warming [6]. One of the strategies to contrast global warming is solar geoengineering [7], which considers cooling the planet by introducing small reflective particles, such as sulfur dioxide, into the upper atmosphere to reflect some sunlight before it reaches the surface of the Earth. The idea is to mimic the effects of the natural emission of sulfur dioxide by volcanic eruptions. However, there are many criticisms. Some scientists say that the potential risks of such technologies are still far from being fully understood. Indeed, accurate models do not exist, and current models give controversial answers. Hence, the study of possible effects that an emission of SO₂ into stratosphere where stratosphere ionizing radiations are also not negligible, is strongly required.

The universe is also an environment where chemicals are synthesized and destroyed through complicated chemical networks that researchers are exploring. The radiation present in space ionizes and dissociates simple molecules [8,9], producing radicals and ions, which can start fast, barrierless, and exothermic ion–molecule reactions resulting in the intricate chemical synthesis of molecules. For instance, methanol, first observed in 1970 [10], is one of the most abundant astrochemical organic molecules. The planets’ atmospheres are also composed of different gases and in the interstellar medium have been identified several species both neutral and ionic [11].

Recently, plasma technology has received attention for the activation of stable molecules, such as CO₂. Plasma is an ionized gas where atoms, molecules, radicals, and excited species are present and react. Although several setups have been realized for the plasma-based molecules conversion, the mechanistic insights of their transformations are still not clear.

In this framework, the study of gas phase chemistry through different experimental equipment and methodologies, as well as theoretical calculations and modeling, became fundamental and can give a relevant contribution going beyond the state of art. This field of chemistry investigates the photofragmentation of ions and charged clusters and the dynamics of the formation of charged species, molecules, and radicals through chemical reactions. Laboratory studies have an important role in the characterization of the nature of the relevant processes down to the molecular level and give information that can be used to assess how these processes guide environmental phenomena such as climate change, human health, and stratospheric ozone depletion: “laboratory studies are an essential bridge between field measurements and models” [12]. Hence, deep insights in the kinetic, thermochemical, and mechanistic features of these reactions are of paramount multidisciplinary significance, both under thermal and no-thermal conditions as well as at a low, room, and high temperature.

The review is divided in five sections. Section 1 introduction. Section 2 methodology: typical experimental conditions used to study ion–molecule reactions and photo fragmentations at the synchrotron ELETTRA (Trieste, Italy), and computational methodology. Section 3 atom/ion transfer reactions: SO₂^•+ reactivity with water, methane, hydrogen, and carbon monoxide, and methanol reactivity. Section 4 photofragmentation studies of halomethanes. Section 5 perspectives: planning experiments at the FEL facilities and the improvement in modeling the ion–molecule reactions.

2. Methodology

2.1. Experiments at Elettra Synchrotron

The apparatus (Figure 1) for ion–molecule reaction studies is accessible at the circular polarization (CiPo) beamline of ELETTRA and is fully described in different papers [13,14]. The use of synchrotron radiation is mandatory because the experiments require high photon fluxes and tunability of the photon energy. The beamline has a normal incidence monochromator and it is provided with an electromagnetic elliptical undulator/wiggler. Two gratings can be used for the experiments: (i) an aluminum-coated holographic spherical grating with 1200 grooves per mm (Al-NIM) that provides radiation in the range 5–17 eV with an energy resolution of approximately 20 meV; (ii) gold holographic spherical grating with 2400 grooves mm⁻¹ (Au-NIM) used to cover the 16–35 eV energy range.

The ion source is equipped with ion optics (one planar repeller and three extractor lenses) set in front of the octupolar RF-driven ion guide. The effusive beam of the neutral precursor introduced at a constant pressure of approximately 10⁻⁶ mbar via a needle, arrives at the center of the ionization region crossed at 90° by the photon beam. In the ion–molecule reactions experiments, ions produced by photoionization are guided into the octupole by the extraction optics, set perpendicularly to the propagation axis of the photon beam. The neutral reagents are introduced in the octupole (reaction cell) via a needle valve that finely regulates the pressure in the range 10⁻⁷–10⁻⁴ mbar. All ions are then transferred in the quadrupole mass spectrometer equipped with a channeltron multiplier detector. The nominal collision energy (CE) is generally kept at 0 eV and it is obtained by measuring the reagent ion yields as a function of the retarding field. The energy spread of the ion packet is between 100 and 200 meV. In a typical experiment, the yields of ionic reagent and product were recorded scanning the photon energy from the ionization energy of the reagent molecule to approximately 14–15 eV at different fixed pressures and CE (0, 0.5, or 1.0 eV).

The photoionization efficiency curves (PIECs) to determine the appearance energy (AE) of the fragment ions in the photo fragmentation studies are obtained by reporting the yield of the fragment versus photon energy and scanning the undulator/monochromator in order to have the maximum flux at a given energy. The PIECs were normalized to the photon intensity, which is measured simultaneously by a photodiode located at the end of the beamline. The photon energy is also calibrated against the autoionization features observed in the Ar total photoionization efficiency spectra between the 3p spin orbit components. The contribution of the second order radiation is evaluated by comparing the Ar⁺ ion yield measured as a function of the photon energy to its ionization cross section [15]. A lithium fluoride (LiF) filter was used to remove the higher order radiation contribution when the energy was below 11.7 eV.

2.2. Computational Methodology

In the studies of ion–molecule reactions presented in this review, theoretical calculations have been carried out by combining the density functional theory formalism (DFT) [16] with variational transition state theory (VTST) [17]. DFT was used to explore the minimum energy path (MEP) of the reactions, while VTST, specifically suited for barrierless reactions, has been used to search for the “bottleneck” of the reaction, namely the variational transition state (VTS) configuration at which the reaction slows down, to compute the reaction-rate coefficients.

In the theoretical photofragmentation studies of halomethanes presented in Section 4, all calculations were performed at the MP2 level using 6-311++G** basis set for C and H atoms. For the iodine atom small-core (28 electrons), scalar-relativistic effective potential (ECP-28) in conjunction with the aug-cc-pVTZ-PP basis set have been chosen [18,19]. CCSD(T) [20] has been employed to obtain accurate total energies and both MP2 and CCSD(T) were used within the frozen-core approximation by using the 4s4p4d frozen-core orbitals for the I atom. Time-dependent density functional theory (TD-DFT) [21] with the Tamm–Dancoff approximation has been also used. More details can be found in the original papers.

The charge and spin population are based on the Mulliken analysis, and it has been computed to study, in a qualitative way, the electron rearrangement occurring during the reactions. The reaction region of the potential energy surface (PES) is studied by full optimizations during the scanning of the chosen coordinates, which generally are the formed and broken bonds in the reaction.

The evaluation of the rate constant is based on the calculation of the molecular partition functions of both reagents in their minimum-energy geometries and of the complex variational transition-state geometry, which is defined as the phase-space point where the molecular partition function of the complex $(Q^{\ne })$ itself has a minimum value. The canonical rate constant is Equation (1):

$$k\left(T\right)=\frac{{\sigma k}_{B}T}{h}\frac{Q{\left(T\right)}^{\ne }}{Q{\left(T\right)}_{ion}Q{\left(T\right)}_{neutral}}$$

(1)

The minimization of the molecular partition function of the complex along the relevant MEPs is carried out at each temperature. The vibrational partition function is computed by using the vibrational frequencies from normal mode analysis within the harmonic approximation. The σ term in Equation (1) is a symmetry factor that considers the different equivalent, indistinguishable ways in which the reaction can occur. However, when the VTS geometry of the complex is in the region of the products and, hence, the reaction is fast and efficient, the rate constant is obtained by using capture theory based on variational transition state theory/classical trajectory study of thermal energy ion–polar molecule collisions: Equation (2) [22]

$$k\left(T\right)=k_L\{\begin{array}{c}0.4767a\left(T\right)+0.6200; a\left(T\right)\ge 2\\ \frac{{\left(a\left(T\right)+0.5090\right)}^2}{10.526}+0.9754; a\left(T\right)\le 2 \end{array}$$

(2)

$$a\left(T\right)=\frac{{\mu }_D}{\sqrt{2{\alpha k}_{B}T}}$$

where k_L is the Langevin rate coefficient, and α and μ_D are the polarizability and the dipole moment of the neutral, respectively. The VTST approach is generally used when the reaction follows a statistic energy redistribution (local equilibrium) [23,24] but it could fail when a high-frequency vibration does not couple efficiently to others in the reaction complex and when reagents are not in thermal equilibrium with the surrounding and within the complex. In these cases, nonthermal rate coefficients must be calculated by modeling the system with the introduction of effective temperature and by correlating the temperature with the internal energy of the ion generated by synchrotron radiation, as in the case of the reaction of SO₂^•+ with H₂ molecules (see Section 3.2) and in a recent published work where the reaction of CO₂^•+ with H₂ has been studied [25].

The theoretical modeling of the competitive fragmentation of excited ions has been based on the calculation of the microcanonical rate coefficient:

$$k\left(E\right)=\frac{{\sigma N}^{\ne }\left(E-E_0\right)}{h\rho {\left(E\right)}^{ion}}\frac{Q_{rot}^{\ne }}{Q_{rot}^{ion}}$$

(3)

where, N^≠(E − E₀) is the sum of the vibrational states from 0 to E − E₀ in the TS, which is localized on the top of the barrier or by variational minimization of N^≠ along the coordinate of reaction for barrierless processes, σ is the reaction symmetry factor, ρ(E)^ion is the density of vibrational states of parent ion, Q_rot^ion and Q_rot^≠ are rotational partition functions of parent ion and transition state respectively. The microcanonical rate coefficients have been computed under the assumptions that the translational and rotational modes were not coupled with the vibrational modes, and that their energy distribution follows the Boltzmann law, so that Q_rot could be used.

3. Atom/Ion Transfer Reactions

3.1. SO₂-CH₄/H₂O

Sulfur dioxide is one of the main sulfur-containing molecules present on Earth, interstellar space, molecular clouds, and in the extraterrestrial atmospheres [26]. It is the main constituent of the atmosphere of Jupiter’s satellite, Io. As neutral (SO₂) and cationic radical species, SO₂^•+ (where ^• is sometime omitted for the sake of clarity) reacts with compounds R–H via a proton transfer (PT) reaction from R–H^0/+ to SO₂ and/or hydrogen atom transfer (HAT) from R–H to SO₂^•+, both leading to the same ionic HSO₂⁺ compound (Figure 2). Ions H₃O⁺ (m/z = 19) are also detected in the case of water due to the consecutive reaction of HSO₂⁺ with another H₂O molecule.

In the specific case of the reaction of SO₂^•+ with CH₄ and H₂O, the two stable molecules are activated by two different mechanisms: HAT in the first case and PT in the second case.

The reactivity of O–H and C–H bonds with comparable bond dissociation energy BDE 497.1 and 439.3 kJ/mol, respectively, depends on the dynamical processes occurring along the reaction paths on the potential energy surfaces of the ionic ground state explored by theoretical calculations (Figure 3, left panel).

The MEPs show that the reactions are barrierless. Moreover, by exploring the charge and spin evolution along the reaction path (Figure 3, right panel) it is possible to assert that in the case of water, a rapid proton-coupled electron transfer (PCET) mechanism is operative while a slower HAT occurs with methane. Indeed, in the reaction of SO₂^•+ with H₂O, the doublet spin and the charge belong to an intact water molecule before the H⁺ proton transfer from H₂O^•+ to SO₂ occurs (Figure 3, right panel (e) and (f)).

Moreover, the variational transition state theory allows us to obtain the canonical rate constants of the two reactions whose trend with temperature was compared with the experimental results obtained with tunable synchrotron radiation by plotting the ratio of the yields of both HSO₂⁺ and SO₂^•+ as a function of photon energy (Figure 4). This joint experimental and theoretical study provides new kinetic and mechanistic insights on the reactivity of the sulfur dioxide ions relevant for astro chemistry as well as for the chemistry of activation and the functionalization of simple model molecules.

3.2. SO₂/H₂

The radical cation SO₂^•+ that can be formed by ionizing radiation in the upper atmosphere, could produce species that should be taken into account in the models when this molecule is present [27]. Moreover, the non-thermal effects should be also considered, especially when SO₂^•+, excited in ro-vibrational levels of the ionic ground state after photon excitation with synchrotron radiation, reacts with a rigid molecule such as H₂:

SO₂^•+ + H₂ → HSO₂⁺ + H^•

(4)

In the stratosphere, atomic hydrogen is produced by the reaction of O(¹D) (formed by the sunlight photodissociation of ozone) and H_2, and H^• reacts with ozone with a rate coefficient of 2.89 × 10⁻¹¹ cm³∙molecule⁻¹∙s⁻¹, leading to molecular oxygen and a hydroxyl radical:

H^• + O₃ → O₂ + OH^•

(5)

The reaction of SO₂^•+ with molecular hydrogen leads always to H^•, also when sunlight is absent, and, hence, reaction (4) can be considered a nighttime alternative pathway to the sunlight formation of OH^• as well as the reaction of SO₂^•+ with H₂O (see Section 3.1).

The dynamics of reaction (4), explored by DFT and VTST, gives a thermal VTS rate k calculated at 300 K of 2.9 × 10⁻¹¹ cm³∙molecule⁻¹∙s⁻¹, close to that obtained experimentally by Anicich [28]. The calculation for the reaction with D₂ gives a rate coefficient of 1.20 × 10⁻¹¹ cm³∙molecule⁻¹∙s⁻¹, with an isotopic effect of 2.42 at 300 K. The thermal computed k for reaction with H₂ is shown in Figure 5 and it increases monotonically with the temperature (blue dashed line).

A similar behavior is observed for the D₂ reaction (green dashed line in Figure 5). The temperature of the excited ion (T_SO2•+) is shown on the bottom axis of abscissas, while the internal energy of the ion (E_SO2•+) is reported in the top axis of abscissas. A decrease in the experimental rate coefficients (black and red circles) is observed with the increase in T_SO2•+, a behavior not in agreement with canonical thermal rates (green and blue lines of Figure 5). Hence, a new model to compute the rate coefficients has been formulated, taking into account the conditions of the experiments. The Q (T = 300 K) of H₂ has been separated in two factors: a translational factor that depends on the room temperature Q^tr_VTS (300 K), and a ro-vibrational part Q^ro-vib_VTS (T_eff) depending on an effective temperature T_eff. This latter depends on the internal temperature of SO₂^•+ (T_SO2•+) and takes into account that during the reaction there is a transfer of the ro-vibrational energy towards the H–H coordinate. All these assumptions allow us to write the non-thermal rate coefficient k^NT as:

$$k^{NT}\left(T_{{SO}_2^{+},}300K\right)=\frac{{\sigma k}_{B}300K}{h}\left[\frac{Q_{VTS}^{ro-vib}\left(T_{eff}\right)Q_{VTS}^{tr}\left(300K\right)}{Q_{{SO}_2^{+}}^{ro-vib}\left(T_{{SO}_2^{+},}\right)Q_{{SO}_2^{+}}^{tr}\left(300K\right)Q_{H_2}\left(300K\right)}\right]$$

(6)

The plot of the non-thermal rate coefficient vs. T (black line of Figure 5) shows the very different behavior with respect to the thermal rate coefficient for H₂ (blue line). The non-thermal rate is in agreement with the experimental rates (black circles in Figure 5) where there is a decrease with T, whereas the thermal rate showed an opposite thermal trend. Similar data are obtained for the reaction with D₂. The work highlights the importance of non-thermal effects in the redistribution of the internal energy of the encounter complex generated in synchrotron experiments.

3.3. SO₂/CO

In chemistry, an important topic is the oxidation of CO into CO₂, together with the oxidation of simple species such as alcohols or methane [29,30]. The small dipole moment of CO (μ_D = 0.112 D), in which there is a partial negative charge on the carbon atom, together with its polarizability (1.953 ų) and bond length (1.13 Å) [31], characterize this molecule, which is one of the most common environmental pollutants due to human activities.

The oxidation can be seen as an oxygen transfer to the carbon monoxide molecule, hence all the species, either neutral or ionic, which favor the O-transfer, should be considered since the formation enthalpy of CO₂ (ΔH_f = −94.05 kcal mol⁻¹) is lower than of CO (ΔH_f = −26.42 kcal mol⁻¹). O₂ is the most important and used oxidant at high temperatures and with catalysts, but other species could be considered for the transformation of CO into CO₂, also at room temperature and without catalysts. Hence, the development of a green-friendly, more efficient and metal-free oxidation of carbon monoxide is required, and the study of the dynamical aspects of these processes is of great interest [32].

Besides the evident environmental aspects inherent to the study of the carbon monoxide oxidation, these types of reactions are relevant also for reaction studies in the chemistry of interstellar medium, of Earth’s atmosphere, and also of extra-terrestrial atmospheres. The reactivity in the troposphere is particularly interesting, where CO, SO₂, H₂O, NO_x, CO₂, and O₃ are present in a fraction of ppm (whose actual values depend on the geographical position and environmental conditions) [33], and which can be either neutral or ionized because of corona-discharged events [34]. In the reaction of SO₂^•+ with H₂O and CH₄, the H⁺ and H transfer from neutral to ions is observed. However, SO₂^•+ can be also a source of oxygen atoms in reactions with other molecules, especially when the oxidized form is more stable, as is in the case of the carbon monoxide (reaction 7). These processes can be discussed in terms of quite similar values of the formation enthalpy of SO₂^•+ and SO^•+: 213.0 and 239.2 kcal mol⁻¹, respectively [35].

SO₂^•+ + CO → SO^•+ + CO₂

(7)

At T = 300 K, this reaction is known to have a rate coefficient [36] of 3.00 × 10⁻¹⁰ ± 20% cm³ s⁻¹ molecule⁻¹ but no other experimental or computational studies were available at that time. This reaction is exothermic [35] by 41.4 kcal mol⁻¹ and its dynamics have been studied with the help of theoretical tools: DFT, VTST, and capture theory [37]. This allowed us to determine the minimum energy path (MEP) of the reaction and to compute the reaction coefficient vs. T. The charge and spin of the reactive complex [SO₂–CO]^•+ have been analyzed along the path of the reaction to obtain kinetic details of the oxidation process. By using k_coll the collision rate [38] and the experimental rate constant k, the reaction efficiency (ϕ = k/k_coll) has been obtained. SO₂^•+ is produced in its vibrational excited levels of the ionic ground state by using tunable VUV radiation. Theoretical calculations and experimental data have been compared by analyzing the role of the photon energy on the reaction. This study provided relevant kinetic details on this reaction, and this can be important in future possible applications of removal of anthropogenic CO from the lower atmosphere of the Earth. In environmental studies, this is an interesting research area because the CO reacts slowly with the O₂, and the reaction with OH, even if it seems the main tropospheric path to carbon monoxide removal, is not the only active mechanism [39]. In this work, the SO^•+ (at m/z = 48) cation has been observed as the only product of the reaction, and, hence, the CO₂ is the neutral other product. At different fixed pressures of CO, the ion yields of SO^•+ and SO₂^•+ vs. the photon energy have been recorded, and in Figure 6 the relative data are reported. These findings indicate that the reaction is favored when the internal energy of the SO₂^•+ is decreased, and this is in agreement with the presence of a weakly bound complex that leads to a very fast reaction. A full theoretical analysis has been conducted to explore the kinetic aspects of this apparently simple reaction: the MEP has a barrier that connects two different minima, which correspond to a first reactive complex [SO₂–CO]^•+ 1, and a second complex [OS–OCO]^•+ 2, which is more stable and resembles the products (Figure 7). The above energy barrier is below the reagents’ energy so that the reaction is overall barrierless. The labels of the O are shown in Figure 7: the O_a is the oxygen bound to the sulfur atom and it is not active, the O_b is the oxygen atom transferred to the carbon atom from the sulfur atom, the O_c is the third atom that is not active, and it is bound to the C atom.

The rate coefficient k at different temperatures has been calculated with the capture theory. The value of 2.95 × 10⁻¹⁰ cm³ s⁻¹ molecule⁻¹ is obtained at 300 K in very good agreement with the literature experimental value of 3.00 × 10⁻¹⁰ cm³ s⁻¹ molecule⁻¹ ± 20% and the reaction efficiency (ϕ = k/k_coll) results to be 1.

3.4. CH₃OH⁺-CH₃OH

The chemistry occurring in different gas-phase environments, such as interstellar medium or the atmosphere of planets has a relevant interest for what concerns reactive dynamics. In particular, the outer space can be considered as a chemical laboratory in which complex chemical networks are at play, and which involves the synthesis and degradation of several classes of molecules [40,41].

One of the organic molecules that is most abundant as astrochemical species is methanol, whose first observation dates back to 1970. Its radical cation [CH₃OH]^•+ has a high probability of formation, but up to now it has not been observed, probably because of its high reactivity. This cation can have a fundamental role in the formation of more complex organic molecules in the interstellar medium [42]. The most stable isomer of [CH₃OH]^•+ is the distonic ^•CH₂O(H)H⁺ methyleneoxonium radical cation, and it is lower in energy of approximately 29.3–46.0 kJmol⁻¹ with respect to [CH₃OH]^•+ [43]. In any case, this isomerization is forbidden because the activation barrier [44] for this process is 104.6 kJ mol⁻¹, and, hence, the [1,2] H-shift is strongly improbable even if the very low temperatures of the interstellar medium can activate the hydrogen tunneling [45]. The most abundant and low-energy fragments are CH₂OH⁺ and H, which appear at 11.649 ± 0.003 eV [46], only approximately 1 eV over the ionization energy of methanol, which has been determined at 10.84 ± 0.01 eV [31]. In hydrocarbon synthesis, the methanol cation and its fragment CH₂OH⁺ play a fundamental role in reacting with neutral CH₃OH, whose neutral products are CH₃O^•, CH₂O, ^•CH₂OH, and ionic CH₃OH₂⁺. These species can be involved in the process of molecular growth, which happens via the coupling with C-C or C-O, in particular temperature and pressure conditions, as observed in extraterrestrial ices where CH₃OH is activated and ionized by radiation [47].

The methanol can be a source of H atoms either from the O-H bond (437.6 ± 2.9 kJ mol⁻¹) or from the C-H bond (402.1 ± 0.8 kJ mol⁻¹) [48]. The isotopic species CD₃OH has been used to understand the source of hydrogen in reactions involving the methanol cation. The branching ratio (BR) and the rate coefficient of the reaction between methanol with its cation form have been the object of studies in the past years, and in Scheme 1 they are reported. These reactions have been studied with a tunable VUV synchrotron to form methanol radical cations in an energy range between the ionization energy threshold and 14.0 eV and by computational chemistry in order to analyze the (a) and (b) paths of Scheme 1. The main purpose of these studies was to assess the role of the internal energy distribution of the ions on the branching ratio of paths (a) and (b), whereas for path (c) we were interested in analyzing the kinetics in the energy range above the AE (11.739 ± 0.003 eV) [49] of the fragment CD₂OH⁺. The masses at m/z = 36 and 37, corresponding to the ions CD₃O(H)H⁺ and CD₃O(H)D⁺, have been observed, and their intensities have been recorded as a function of photon energy from 10.6 to 11.7 eV (Figure 8a).

The BR have been determined at the reaction cell pressure of 3.0 × 10⁻⁵ mbar, and relative data are shown in Figure 8b.

From experimental data, the formation of CD₃O(H)D⁺ and CD₃O(H)H⁺ ions are observed, whereas the isomerization of CD₃O^• into a ^•CD₂OD radical should also be considered when the energy gain obtained in the formation of the reactive complex is enough to overcome the barrier that leads to the formation of ^•CD₂OD. The interaction of CH₃OH (CD₃OH) with CH₃OH^•+ (CD₃OH^•+) has been also studied with computational chemistry models, so that a full comprehension of the dynamical aspects of these reactions can be obtained at hν < 11.7 eV [51]. In Figure 9, the geometries and the relative energies of the molecules active in reaction (a) and (b) of the Scheme 1 are reported.

From the experimental point of view, these ion–molecule reactions have been analyzed also at energies higher (hν > 11.7 eV) when the fragment CD₂OH⁺ (m/z = 33) can be formed, and whose appearance energy has been determined at 11.739 ± 0.003 eV [49].

The mass spectrum of CD₃OH⁺, without reaction with neutral methanol, is reported in Figure 10a at hν = 12.5 eV. The loss of the D atom from CD₃OH^•+ produces the peak at m/z = 33, which is related to the CD₂OH⁺ ion, whereas the very small peak at m/z = 34 can be related to the CD₂OD⁺ due to the scrambling of the hydrogen atom. We have excluded the formation of the CD₃O⁺ species since its appearance energy is determined to be higher than 15.0 eV [49].

The branching ratio of all the products and reagent ions of the (a–c) reactions of Scheme 1 have been reported in Figure 10b at p = 5.1 × 10⁻⁵ mbar, and for hv in the range of 11.9–14.0 eV.

It has to be noted that the relative intensity of CD₃O(H)H⁺ (m/z = 36), with respect to the intensity of CD₃O(H)D⁺ (m/z = 37), has a positive increase with the increase in hv. This is due to the fact that here, the production of CD₂OH⁺ is increased, and it protonates by H⁺ transfer from the O-H bond as seen in path (c) of Scheme 1. Both protonated methanol and CD₂O (CH₂O) are formed, which are also possible precursors of prebiotic compounds.

4. Photofragmentations of Halomethanes

Many halomethanes have relevant roles in atmospheric chemistry, for instance, CH₂Cl₂, which is used as a solvent and a propellant in industry, has an air emission that can modify the budget of ozone due to the production of the Cl radical [52]. On the other hand, CH₂F₂ (HFC-32, Freon 32) is a greenhouse gas, playing a fundamental role in the terrestrial atmosphere with no depletion potential. It is used as etching gas replacing also chlorofluorcarbons in the refrigerant industry. As regards the presence of iodine and bromine organic compounds, they are predominantly natural, and mostly of oceanic source by macroalgae and phytoplankton [53]. In particular, CH₂I₂, which is one of the most photolabile iodocarbons emitted in the atmosphere from marine algae [54], is a source of reactive iodine atoms by the photoreaction with VUV light, playing an important role in ozone depletion and in affecting the oxidative ability of the atmosphere. Furthermore, iodine participates to the ultrafine marine aerosol particles affecting the Earth’s radiation budget and, thus, drives climate change [55]. In addition, bromine-containing compounds, coming primarily from oceans and called “very short-lived substances” (VSLSs), bromocarbons, such as CH₂Br₂ and CHBr₃, have been largely studied in the past few years [56]. These compounds are very interesting because together with mainly anthropogenic, long-lived gases such as chlorofluorocarbons (CFC), bromofluorocarbons and methyl bromide are thought to contribute significantly to the production of reactive inorganic bromine (Br, BrO, HOBr, and HBr) after their degradation. Actually, they are rapidly destroyed in the troposphere (atmospheric lifetime shorter than six months) via a reaction with hydroxyl radicals and photolysis. Eventually, these reactive species can enter the stratosphere and participate in the catalytic destruction of molecules.

Up to now, much effort has been devoted to the understanding of the chemical physics of halomethanes in order to manipulate and control their use and to explain their behavior in different processes. In particular, many studies have been devoted to investigating the halomethanes fragmentation leading to different radicals and/or cations, which can play a role in several fields, from atmospheric chemistry to etching- and plasma-assisted industrial processes as well as organic synthesis. Several works have been dedicated to the study of the photodissociation of CH₂I₂ and CH₂Cl₂ molecules by proton impact or VUV absorption [57,58,59]. Several studies have been carried out to obtain thermochemical data with different radiation sources [60]. Quite exhaustive is the paper where there is a discussion of the VUV photofragmentation of the series of halomethane compounds where either the halogen atom (dihalomethane, CH₂X₂ with X = F, Cl, Br, I) or the number of halogen atoms (chloromethane, CH_nCCl_4-n with n = 0–3) are changed [61].

This work has three main goals: (a) the study in the VUV range of the two competitive channels, X-loss (X = F, Cl, Br, I) and H-loss, observed in the fragmentation of the dihalomethanes even though other channels have also been considered; (b) the study of the effect of the particular halogen atom in the photofragmentation, comparing CH₂X₂ molecules; and (c) the investigation of the effect of the number of halogen atoms in the photofragmentation, going from chloromethanes containing one (CH₃Cl) to four (CCl₄) chlorine atoms. The results show that the CH₂F₂ compound is the only dihalomethane that opens the H-loss channel yielding a CHF₂⁺ ion and H atom. This finding has an implication in atmospheric chemistry since these species can produce HF. The loss of the halogen atom is evident in all the mass spectra of halomethanes. Moreover, the CCl₄⁺ molecular ion is not observed due to the instability of this ion towards the exothermic loss of the chlorine atom. CH₂I₂ is the only dihalomethane that produces I₂⁺ ions. This fragmentation pathway is generally a high-energy process, which might be relevant in the upper atmosphere. In Figure 11, the photoionization curves for the I₂⁺, CH₂⁺, and I⁺ species are presented.

The results show that the appearance energy of I₂⁺ (AE_exp) is 12.76 ± 0.03 eV. Moreover, the PEPICO measurements (Figure 12) demonstrate that the I₂⁺ loss involves electronic states with B.E. >12.0 eV as well as the channel that produces CH₂⁺ (AE_exp = 15.34 ± 0.05 eV). In the latter case, theoretical calculations demonstrate that the formation of CH₂⁺ ions produce two iodine atoms and not the I₂ molecule. As clearly seen in Figure 12, the parent ion (m/z = 268) is present until BE~11 eV [62].

In Figure 13, the PEPICO spectra acquired in the BE region between 9 and 11 eV are shown to investigate the fragment ions generated from the lower ionic states. At the BE = 9.7 eV (Figure 13a), only the peak at m/z = 268 due to the molecular ion [CH₂I₂]^•+ is observed, while at the BE = 10.9 eV (Figure 13b) the fragment ion at m/z = 141 (CH₂I⁺) is also observed. This result clearly demonstrates that at an energy lower than 11 eV, the only pathway accessible by the electronic states of [CH₂I₂]^•+ is the I-loss channel, whereas the other fragments observed in the mass spectrum at hν = 40 eV are formed from higher excited states of [CH₂I₂]^•+.

A computational study has been carried out to investigate the mechanism of the I-loss channel from [CH₂I₂]^•+ [63]. In Figure 14, the optimized geometries of the minima (1, 2, and 3) found on the [CH₂I₂]^•+ potential energy surface, the transition states TS1 and TS2 connecting 1–2 and 2–3, respectively, and the optimized structure of the CH₂I⁺ fragment, are reported.

The results show that the isomerization of geminal [CH₂I₂]^•+ into iso-diiodomethane is a relevant process in the CH₂I₂ radical cation as well as in the CH₂I₂ molecule and it can have a role in the photochemical reactions. Moreover, this isomerization is not a key process for molecular I₂-loss at the lower electronic states of the cation. Recently, the transient [CH₂-I-I]⁺ isomeric ion 2 in the dissociation of the [CH₂I₂]^•+ molecular has been proven experimentally with the XUV FEL at Hamburg [64].

5. Perspectives

5.1. Planning Experiments at the FEL Facilities

The development of new radiation sources has undergone a notable increase in the last ten years starting from attosecond high-harmonic radiation source [65] to phase-stabilized few-cycle optical laser pulses [66], femtosecond electron beams [67], and lastly free-electron lasers (FELs) [68,69,70].

Unlike the conventional femtochemistry, which uses IR and UV laser pulses to trigger and interrogate molecular processes, FELs extend the pump–probe scheme into the regime of XUV and X-ray radiation.

By combining ultra-short pulse durations and never-before-seen pulse intensities, FELs offer the possibility to study completely new and largely unexplored very basic and fundamental molecular behavior.

The experiments at the FEL facilities aim to study the peculiarities of electronic dynamics, known to be active on attosecond time scales, and the formation/breaking of bonds that occur in the femtosecond regime. Particular attention is paid to the study of the electronic and nuclear motion in photoexcited molecules, the redistribution of the energy stored by the molecule as a result of photo-absorption, and the nuclear dynamics of chemical reactions involving highly excited states in cold molecular ions, in order to mimic the XUV photochemistry of higher planetary atmospheres and interstellar clouds [71].

For these purposes, FELs combine the key features of optical lasers, such as a short pulse duration at a high intensity, with those of synchrotron radiation sources delivering XUV and X-ray radiation.

The first laser operating in the XUV regime was FLASH in Hamburg in 2005 [72] followed by LCLS in Stanford in 2009 [73], which reached for the first time the hard X-ray range. To date, two other facilities are operating in the XUV regime, which are FERMI [74] in Italy and SCSS [75] in Japan, while SACLA [76] in Japan falls within the hard X-ray FELs. In the very near future, more FEL facilities will become online such as EUPRAXIA in Italy, where the ultrashort X-ray pulses, made available by the plasma accelerator-driven FEL, will open up to new possibilities of measuring ultrafast processes in nature that can be analyzed at the electronic level without perturbation.

In this section, the recent achievements in the field of molecular dynamics and gas-phase chemistry and possible future prospects in the field of gas phase ion–molecules reaction with FELs will be presented.

5.1.1. Ultrafast Reaction Dynamics

The main questions that generally arise in the ultrafast photodynamics of molecular systems concern the time scale and the mechanism of the reaction, how many steps it implies, whether it is possible to “photograph” some intermediate species, and whether it is possible to manipulate and control the system by varying some instrumental and temporal parameters.

The ability to observe the temporal evolution of a chemical reaction has often been called “molecular film making”, implying the need to capture consecutive images of bond breaking and formation with a temporal resolution ranging from femtoseconds to picoseconds and possibly electronic and/or geometric structural resolution for all species involved. With the new FEL sources, this possibility is gradually becoming a reality, although it must be emphasized that until recently, many FELs showed a jitter in photon energy generally too large to provide sufficiently resolved spectra without an accurate post-processing of the data and an average over different time delays, while HHG (high-harmonic generation) laser sources lose resolution due to the simultaneous presence of several harmonics. In the latter case, even with the application of suitable filters that generate single pulses, the resulting intensity is very low, and this limits the plethora of possible experiments to be performed and requiring a high density of molecules.

Unfortunately, there is still no suitable FEL source with a negligible photonic energy jitter and very short pulses (down to the attosecond) whose construction is mandatory if you want to reach another planned goal, i.e., the study of the electronic motion preceding bond breaking/formation on its “natural” timescale.

Attosecond laser technology has already proven to trace the electronic dynamics in small atoms and molecules, while for large molecules such as those involved in biological processes (photosynthesis, radiation damage, etc.) [77,78,79,80,81,82], the study is still in its infancy. Usually, attosecond pump–probe spectroscopy is used to study electron dynamics with a temporal resolution of a few femtoseconds and sub-femtoseconds [83,84,85,86]. It consists in the use of an extreme attosecond generally ultraviolet (XUV) pulse to excite/ionize the target molecule, followed by a delayed probe pulse ranging from the near infrared (NIR) to the X-ray domain capable of tracing the dynamics generated by the first pulse. In this way, the target molecule is ionized by an attosecond pulse, creating a delocalized electron hole that moves across the molecule on a time scale of sub-femtoseconds. The evolution of the hole depends on the interaction between electronic and nuclear motions, which can lead to a final localization of the charge on a specific molecular site or on a specific molecular fragment. So, depending on the initially created hole, fragmentation will occur leading to different chemical species, hence to a distinct reactivity. Full controllability would allow attosecond chemistry to synthesize any stoichiometrically allowed molecular structure or even a macroscopic object from a bunch of atoms in the ultimate realization of a molecular 3D printer [87]. The experimental approach generally used to trace charge migration is based on measuring the yield of photofragmentation as a function of the probe delay with respect to the pump. Reliable theoretical tools are required for the interpretation of attosecond spectroscopy experiments, but unfortunately, currently, a full dimensional quantum mechanical treatment of molecular ionization dynamics, which considers all electronic and nuclear degrees of freedom, is still difficult to obtain. One of the most tempting challenges of attosecond science is to induce ultra-fast electronic dynamics in molecules in order to selectively break and form chemical bonds, thus leading to new chemical reactions. In an ambitious vision, this approach could be applied to study and eventually control the chemical ion–molecule dynamics that occur in high atmosphere by inducing chemical reactions to counteract environmental pollution. The near-future technological frontier in attosecond science is the attosecond pump–attosecond probe measurement of electron motion that would allow us to specifically address and temporally resolve time-dependent processes in complex systems on the electronic time scale [88].

5.1.2. Study the Intermediate State of a Reaction: A Challenge Still Open

In the XUV/hard X-ray regime active in FELs, the dominant mechanism in the molecule radiation interaction is the absorption of photons with subsequent emission of photoelectrons. This process generates a molecular ion that remains in an energetically and vibrationally excited state, which can relax through different reaction pathways, sometimes passing through intermediate stages. The study of the lifetimes of reaction intermediates is still in its infancy. For this purpose, dedicated spectroscopic methods are needed that are able to isolate or label the population of the intermediate states, to follow their evolution as a function of time and to determine their essential characteristics. One way to do this is by leveraging pump–probe technology. The intermediate electronic state is populated by the ionization of a molecule through the pump pulse launching a nuclear wave packet due to the coherent population of several vibrational levels. During its motion along the internuclear axis, a second time-delayed probe pulse may further ionize the system promoting the molecule onto a repulsive Coulomb curve. As a result, the molecule may break up into two ions. In these conditions the Coulomb explosion imaging [89] can reconstruct the molecular geometry and the internuclear distances by analyzing the kinetic energies and emission directions of the repelling ionic constituents. Moreover, the momenta of electrons and the remaining ion can be measured in coincidence by Reaction Microscope/COLTRIMS [90]. In COLTRIMS experiments the emission directions of the ionic fragments coincide with the spatial orientation of molecular bonds at the instant of photoabsorption. One of the main challenges is to extend the acquisition of coincident electrons and ions to the time domain, which seems to be possible thanks to the advent of higher repetition rate lasers and FEL, but some technical challenges still persist. Up to now, only a few true ion-electron coincidence imaging experiments performed at a FEL have been reported [91]. Nevertheless, COLTRIMS coincidence experiments provide the most detailed and complete account of photon driven dynamics in the gas phase. They are the eyes that scan the many-body quantum world, providing images of otherwise invisible details.

5.1.3. Time-Resolved Ion-Molecule Reactions in Gas Phase

Looking at the recent experiments performed at FEL regarding molecular physics and photochemistry, we can report examples of photon-induced fragmentation dynamics of cold molecular ions with relevance of the XUV photochemistry in atmospheric clouds [92], time resolved measurements of van der Waals-bonded molecules called interatomic Coulombic decay (ICD) [93,94,95], real-time observations of electron migration and charge transfer in small dissociating molecules [96,97], temporal tracing of the isomerization dynamics in acetylene cations [98], and X-ray diffractive imaging of spatially aligned small- and medium-sized molecules in the gas phase [99]. The chemistry of upper planetary atmospheres and interstellar clouds is dominated by the dynamics of small and medium-sized molecular ions, and some of them are presumed to play a crucial role in the emergence of life. We found few examples of time-resolved bimolecular reactions such as Scherer et al. [100], who studied the collision dynamics between HI and CO₂ and Hu et al. [101], who studied the energy-rich intermediate collision complex K₂Rb₂* in the reaction KRb + KRb → K₂Rb₂* → K₂ + Rb₂. In the first example, Scherer et al. used the first pulse to liberate the H atom from HI with a known translational energy and a second pulse to probe the nascent OH products. The experiments established that the intermediate HOCO lives for a time of 1 ps, and for this reason, the OH bond making and the CO bond breaking happen in a non-concerted pathway. If the lifetime was found to be 10–100 fs, the picture would have been entirely different; bond making and breaking would occur as a result of the electron redistribution with the nuclei essentially “frozen” in configuration. This consideration is important, because it means that depending on the time duration of the pulse available, one can investigate different phenomena and distinguish in this context, reactions that occur in a concerted and non-concerted pathway.

In Hu et al. [101], they tuned the wavelength of the laser well below the lowest dissociative ionization channel of the intermediate complex K₂Rb₂* and recorded the mass spectrum where a visible K₂Rb₂⁺ signal was evident. It is important to note that in this case, the dynamics of the intermediate complex after photoionization is not followed. A possible step forward in this direction would be using the pump–probe approach.

In all gas phase experimental studies that have been addressed in Section 3, only information about the mass/charge ratio of the products and reactants involved in the reaction were obtained, but nothing about their reaction dynamics as well as the reactive intermediate. Hence, in our opinion, a step forward in this direction would be necessary. Gas phase studies have two main goals with respect to the condensed phase: (i) the investigation of the intrinsic nature of isolated species free from the effect of solvent and intermolecular forces, and (ii) models for processes occurring in planets’ atmospheres and the interstellar medium relevant in astrochemistry and becoming a benchmark for the development of new computational/theoretical models capable of explaining such reactions. The limit of the present studies could be overcome through an interdisciplinary approach by homemade instrumentations and advanced technologies that allow a more accurate and complete analysis of the processes. The fabrication of a versatile ion source that can interface with the FEL beamline to perform pump–probe experiments would be the case (Figure 15). The instrumentation should be able to accommodate several ion sources from electron impact ionization to an electrospray ionization source depending on the nature of the species to ionize. Then, the ion of interest should be selected with a mass filter, accumulated in an ion trap, and then analyzed with an intense ultrafast pump–probe spectroscopy better if interfaced with a reaction microscope/COLTRIMS.

Three different scenarios of possible studies open up: (i) studying the dynamic of the parent ion I₁⁺ produced in the ion source (path (a) in Figure 16); (ii) inserting the neutral molecule into the ion trap and studying the dynamic of the product ion I₂⁺ formed by the ion–molecule interaction (path (b) in Figure 16), and most important of all; (iii) applying the ultra-low temperature regime at the trap in order to greatly extend the lifetime of the reaction–intermediate complex [I₁N₁]⁺ that can be selected and studied by pump–probe spectroscopy (path (c) in Figure 16).

To follow the kinetics of the process inside the ion trap, it should be better to use a trap with a temperature control, to obtain the rate coefficients as a function of the temperature for the improvements of the theoretical models and the study of the ionic product dynamics and the energetics.

Obviously, the choice of the ion source, the pump–probe pulses, and the spectroscopy will depend on the species under investigations. This review aims to stress about the fundamental role of ions. Molecular ions were decisive in the cooling of the early universe, are ubiquitous in aqueous solutions, play an important role in the chemistry of upper planetary atmospheres, in interstellar space, and they seem to have been crucial for the beginning of life. The photochemistry of ions is not easy to study in the laboratories since it requires high-intensity VUV and X-ray sources and most of the time the ion density is too low, but with the improvement of technologies we can improve our knowledge. The goal would be to obtain relaxation lifetimes for ionic reagents, products, and intermediate states with high accuracy in order to gain reliable chemical networks for more realistic complex modelling. In this way, we could improve our predictive capability.

5.2. Improvement in Modeling the Ion–Molecule Reactions

A fundamental aspect, still poorly studied, is the role of cosmic rays (CRs) in increasing the reaction rate and modifying the type of chemical reactions by producing ions. Indeed, the reaction rate between an ion and a molecule can be up to 10 orders of magnitude higher than that with only neutrals. Moreover, the spatial distribution of the ions is extremely inhomogeneous, since it increases in particular in the neighbourhood of the passage area of the ionising radiation. Ions are leading actors in several atmospheric processes such as ion-induced nucleation, precipitation, and aerosol formation. However, the connection of CRs with ions and the climate parameters is a challenging topic. The amount and state of ionisation, as well as the spatial distribution of ions in the atmosphere, is one of the open questions for the atmosphere models that are fundamental to investigate also in the very low-energy range. To compute cosmic rays-induced ionisation (CRII), models of the new generation consider the atmospheric cascade initiated by cosmic rays to its full extent using a Monte Carlo numerical simulation by means of a toolkit such as FLUKA [102], CORSIKA [103], and Geant4 [104,105,106]. Over the years, several numerical models were created and validated via a comparison with direct observations and measurements of the cosmic rays-induced ionization, e.g., the Sofia model [107,108], the Bern model, also called ATMOCOSMIC/PLANETOCOSMIC [109], and the Oulu model, also called CRAC:CRII [110]. All these numerical CRII models allow us to simulate the 3D time-dependent ionisation rate in the atmosphere, down to the lower stratosphere (below∼20 km), providing a reliable tool to study ionisation effects due to cosmic rays. The ion pair production rates (ions·cm⁻³·s⁻¹) are the fundamental information to be considered in the atmospheric chemistry models, and they are calculated by taking into account the mean energy required to produce an ion–electron couple. Recently, a newly developed GEANT4-based code, atmospheric radiation interaction simulator AtRIS [111], has been developed, tailored specifically to enable parametric studies of radiation propagation through various planetary atmospheres.

However, the average approach used by current models cannot provide the exact interaction of low-energy secondary radiation with molecules, nor the exact concentration of the ions produced, their spatial distribution, and ionization state. Together with the ions produced in the initial ionisation, the low-energy secondary particles produce a large number of ions and excited atoms and molecules. In addition, the distribution of reactive chemical species, although present in very small amounts, cannot be underestimated as they trigger fast reactions that can alter the balance of important molecules and have a key role in fundamental reactions.

To precisely estimate these quantities, it is necessary to simulate particle–molecule interactions, following a step-by-step tracking down to very low energies. Interaction models that enable these simulations require interaction probabilities over a broad energy range and for all possible energetically allowed scattering processes.

Our work to find such models for each molecule relevant to climatology has just begun, and in the following we focus on electron impact interactions with N₂ and O₂ molecules, being the most abundant atmospheric chemical species. For these two molecules, we reviewed the state-of-the-art models needed to describe the interactions relevant to our purpose, namely ionization, elastic scattering, and electronic excitation cross sections.

In the next sections, we present some reliable theoretical models for differential (DCS) and integral (ICS) cross sections in the low-energy range up to few MeV, looking for a good compromise between accuracy and computational time. Models that provide an analytical expression for the cross section as a function of energy will be preferred, as they are ideally suited for future modeling applications and Monte Carlo simulations.

5.2.1. Ionisation

Many standard theoretical methods for ionisation cross sections work well at high-incident energies, but few are reliable at low-incident energies, particularly near the ionization threshold. Furthermore, theories requiring continuum wave functions are difficult to compute for molecules especially polyatomic ones. To date, major sources of ionization cross sections for molecules come from experimental data and theories, often semiempirical, that worked well only on limited types of targets and limited ranges of incident energies [112].

To treat electron impact ionisation for the case object of this review, we selected the binary encounter Bethe (BEB) model developed by Kim and Rudd [113]. It combines a modified form of the Mott cross section [114,115] with the high-energy behavior of the Bethe cross section [113,116,117]. The BEB model has been successfully used to calculate electron impact differential and total ionisation cross sections for a large number of atmospheric molecules [118,119,120,121,122]. The agreement with experimental data is excellent for small size molecules in the energy range from the ionization threshold up to hundreds of electron volts [123].

An extension of the BEB model to relativistic incident electrons (few MeV) is the relativistic BEB (RBEB) model, by Kim and Santos [124].

In the BEB and RBEB models, the scattering angle of the primary electron and the ejected angle of the secondary electron are considered to be isotropic. This approximation can be reduced by introducing a sampling of both angles determined by the kinematics of binary collisions [125].

Figure 17 shows the BEB cross sections for N₂ and O₂ calculated using orbital parameters provided by the NIST database [112] compared with the experimental data of Rapp and Englander-Golden [126], the data of Schram et al. [127,128], the data of Krishnakumar and Srivastava [129], and the more recent experimental data of Straub et al. [130]. As the plots show, the BEB cross sections for both molecules agree very well with the experiments, even near threshold. We expect the behavior at high energies of the RBEB model will be even more accurate than that obtained with the BEB model.

However, it can be noticed that BEB underestimates the cross section for O₂ near the peak compared with the experimental measurement of Rapp and Englander-Golden [126]. In this case, the theoretical binding energy values used for the outer valence orbitals do not agree well with the known experimental values, which can be interpreted as an indication of the need for a better wave function in the calculations.

5.2.2. Elastic Scattering

Elastic scattering, although it does not practically lead to energy loss, strongly influences the accuracy of the spatial distribution of energy deposition. The process is typically calculated with the additivity rule (AR), which is a simple sum of atomic cross sections, or with the single-scattering independent atom model (IAM), which is a coherent sum of atomic scattering amplitudes that takes into account relative atomic positions [131,132]. In the IAM model, the interaction of the projectile with each atom of a molecule is assumed to be given by the spherically complex symmetric potential due to a free atom, which is the sum of the electrostatic, exchange, correlation–polarization potentials, and absorption potential. This approximation prepares the ground for the application of partial-wave analysis of scattering.

Atomic scattering amplitudes can be calculated with the ELSEPA (ELastic Scattering of Electrons and Positrons by neutral Atoms) code, developed by Salvat et al. [133]. This code is based on Dirac partial-wave calculations for elastic scattering of electrons by an atom, with energies ranging from a few eV up to 100 MeV in a variety of materials. Another advantage of ELSEPA is the ability to easily modify the computational parameters and interaction potential models to optimize the results and get better agreement with experimental data. Details on these potentials are available in ref. [133].

It should be noted that the concept of independent scattering centers becomes invalid at relatively low energies (<100 eV) or for large molecules, since this approximation ignores the interactions of the incident electron with more than one atom at a time. Another reason for the low-energy failure of this model is its ignorance of the mutual overlapping of nearby atomic cross-sections, which leads to an overestimation of cross sections calculated with the IAM model. To make up for this lack, Blanco and García [134,135] proposed the screening corrected additivity rule method, derived from a semiclassical analysis of atomic geometrical overlapping. This method has been proved to be a powerful tool for calculating electron scattering cross sections down to about 30 eV for a wide variety of nonpolar molecules [136,137,138]. A more sophisticated model, which falls under the same optical potential formalism as the IAM model, is the modified independent atom model (MIAM). MIAM divides the elastic interaction into a short-range potential that describes multiple electrons scattering by individual atoms, and a long-range potential that can account for non-spherical effects such as polarization. This multicenter process is described within the Born approximation, with higher-order terms representing successive scattering events from different atoms within the molecule and does not make use of empirical correction factors.

For the N₂ and O₂ molecules under study, several results in the literature are in very good agreement with experimental data using the IAM method down to energies of 50 eV [139,140]. For this reason, and because of its simplicity, we consider it the best option for our application. The IAM approach has also proven to be successful for other polyatomic molecules down to energies of tens of eV [141,142,143]. For energies below 50 eV, the theoretical model can be supplemented with the large amount of experimental data in the literature for these two molecules [144,145,146,147,148].

5.2.3. Electronic Excitation

The electronic excitation process plays an important role in determining the internal energy and state distribution of the gaseous particles in the atmosphere.

The Born approximation is the most commonly used method for the calculation of electron impact excitation cross sections for optically allowed states at high collision energies. However, it does not account for electron exchange, polarization of the target electrons by the free electron, and distortion of the free electron by the target at lower energies, which are described by higher-order terms in the perturbation series. In order to approximately incorporate these effects, Kim extended the BEB method to electronic excitation by developing the new simple BEf-scaling theory described in detail by Kim [149]. This method aims to scale the first-order plane-wave Born cross sections for electron impact excitation of neutral atoms [149] and molecules [150], provided that the scaling is applicable only to integral cross sections for electric dipole-allowed transitions.

The scaling process has the effect of replacing the wave function used to calculate the Born cross section with an accurate one and correcting the well-known deficiency of the Born approximation at low energies, without losing its validity at high energies.

The use of the BEf method requires two initial ingredients: the Born integral cross sections and reliable optical oscillator strengths.

Once these quantities have been obtained theoretically or experimentally, a fairly reasonable cross section can be produced at any incident energy with the BEf-scaling approach. Indeed, the BEf-scaled method has been found to provide good agreement for the cross section in the energy range from threshold to about 10 keV for a large number of molecules, including N₂ and O₂ [151,152]. Full details on the method can be found in ref. [153].

Finally, it is important to point out that only advanced ab initio electron–molecule collision theories, such as complex Kohn [154], Schwinger multi-channel [155], and the R-matrix [156,157], although computationally demanding, are able to reproduce the existence of resonances, and accurately address the low-energy (<30 eV) scattering problem. All three methods are based on the variation principle, and the results obtained using each method with the same target and scattering models often exhibit good agreement.

The fixed-nuclei approximation R-matrix theory is by far the most widely used method. It is already implemented in the UK molecular R-matrix (UKRMol) codes [158] and executable through the Quantemol-N expert system [159], which uses the MOLPRO quantum chemistry code to provide the target molecular orbitals. This code has proven to be the most versatile tool for calculating both elastic and electronic cross sections from threshold up to about 100 eV in molecules dominated by resonances. Indeed, it has been successfully used to study a large number of molecules, including N₂ and O₂ [160,161,162,163].

The UKRmol code can be used, in conjunction with experimental data, to compensate for those energies or excited states not included in the previous BEf model.

In conclusion, the ionisation state and spatial distribution of ions produced by cosmic rays can significantly change chemical reaction rates by orders of magnitude. In this section, we reviewed models that could be used to simulate electron interactions with the most abundant species in the atmosphere, i.e., N₂ and O₂. Using these models, it would be possible to accurately simulate the interaction of electrons produced by primary and secondary cosmic rays in the atmosphere, thus allowing the calculations of the concentration of the ions produced, their spatial distribution, and their ionisation state. We are working on implementing, or interfacing, these models with Geant4-DNA [164,165,166,167], to perform such a simulation. Geant4-DNA is an extension of Geant4, the most widely used toolkit for performing Monte Carlo simulations of radiation–matter interactions. Geant4-DNA makes it possible to explicitly simulate every single electromagnetic particle interaction down to eV, as well as diffusion and chemical reactions, on some specific materials of interest in radiobiology. We are working to extend Geant4-DNA to simulate radiation transport in the atmosphere.

Our ultimate goal will be to obtain the ionisation effect in the Earth’s troposphere and stratosphere based on cosmic ray spectra, and subsequent Monte Carlo simulations of the cosmic ray-induced atmospheric cascade. The interaction of protons, photons, kaons, and muons with matter will be simulated using the Geant4 toolkit, while our cross-section models will be used to simulate the electron impact processes on N₂ and O₂ in small volumes at different altitudes in the atmosphere.

The development of the physics for each molecule of climatological interest may open the way to a better description of the physicochemical processes used in atmospheric prediction models, but also to new space-related studies regarding chemistry and exobiology.