Incident electrons are derived from the hairpin tungsten filament (cathode) by thermoelectronic emission. The electron beam is then extracted and focused into the interaction volume by seven electrodes of the electron gun. Electron energy can vary in the range from 40 to 300 eV and is determined by the potential difference between the filament and the last, grounded, electrode, with energy resolution about 0.5 eV. When the current through the cathode filament was about 2.22 A, the electron current, measured with the Faradays cup without gas in the chamber, was approximately 100 nA. The electron gun can be rotated around the fixed detection system in the angular range from −40◦ to 126◦ .

Atomic/molecular beam is formed by stainless-steel gas needle. The length of the needle is *l* = 40 mm and its diameter, *d* = 0.5 mm. According to Lucas [40], beam properties can be predicted and optimized. Optimum atomic beam is obtained when *I*(0) 2/ *NH*2 , where *I*(0) is axial intensity, *N* throughput and *H* beam halfwidth, is maximum. It is shown that *I*(0) 2/ *NH*2 ∝ *l* 2/*d* [41]. So, the optimum beam is acquired when the ratio of square of single tube length and its diameter is maximum, which is in our case 3200. These expressions can be employed for tubes where *γ* = *d*/*l* (true dimensionless ratio of length and diameter) is below 10 (γ < 10) and gas pressure is low enough so that the mean free path of a particle is larger or equal than *d* (*λ* ≥ *d*). In our experimental setup γ = 80 and *λ* ≈ *d*.

After the interaction with the molecular beam, scattered electrons are entering the detection system. First, they are focused and slowed down to the constant pass energy of the analyzer by the four-electrode lens. Then, they are energy-analyzed by the double cylindrical mirror analyzer (DCMA). After that, elastically scattered electrons are focused by the three-electrode lens into the detector (single channel electron multiplier).

The intensity of elastically scattered electrons from methane molecule is measured as a function of scattering angle, from 25◦ to 125◦ (in 5◦ steps), at given incident electron energy, from 50 to 300 eV (in 50 eV steps). Experimental parameters were adjusted so that the interaction volume was kept constant. Deviations that can occur at small angles are corrected by comparing cross-sections from Ar at given energy with other authors' data [42,43]. During the measurements, working pressure in the chamber was about 4 × 10−6 mbar. For each electron energy, scattering intensities are measured at least three times. To discount background scattering contributions, a gas beam was introduced to the chamber through a side leak, away from the collision area. Scattering intensities are measured and subtracted from apparent signal for each angle.

The obtained relative DCSs are converted to the absolute DCSs using relative flow method (RFM) [44]. Briefly, the signal of scattered electrons from the target molecule is compared with elastically scattered electron intensity from reference gas, at the same scattering angle, for the same electron energy and experimental conditions. The same experimental conditions for both gasses implies that their beam profiles must be closely equal, which is acquired, according to Olander and Kruger [45], under two conditions: the mean free paths (λ) behind the gas needle for both gasses must be the same and the Knudsen number, *KL*, defined as λ/*l*, must be in the appropriate range, *γ* ≤ *KL* ≤ 10. The first condition is fulfilled when pressure ratio of test molecule and reference gas is inversely proportional to the ratio of squares of their gas kinetic diameters. In this study, Ar is used as a reference, with its diameter of approximately 3.58 Å. The gas kinetic diameter of the target gas, methane is approximately 3.8 Å, which gives ratio 1.13; almost the same gas pressure behind gas needle for both gasses must be applied. As for the second condition, gas pressures were low enough so that *KL* is approximately equal to γ, although some studies have shown that even when *KL* is much lower than γ, beam profiles for most gasses can still be very alike [46,47]. Besides scattering intensities of both gasses, relative flow rate is determined by measuring pressure increase in time by admitting gas into the constant volume, while a chamber outlet was closed.

The known absolute DCSs for Ar are taken from Rankovi´c et al. [42] for incident electron energies 50–200 eV and 300 eV and from Williams and Willis [43] for electron energy of 250 eV. In both papers, the absolute values were derived by measurements of angular dependences of elastically scattered electrons using electron spectrometers, two 127◦ cylindrical electrostatic energy analyzer in [43], and a double cylindrical mirror analyzer in [42] but employing different normalization procedures. While in [42] the relative flow method with He as a reference gas was used, in [43] a phaseshift analysis of the relative angular distributions of electrons elastically scattered in the energy region of the resonances 2P3/2,1/2 of Ar, i.e., between 11.0 and 11.4 eV, were used. Nevertheless, the absolute DCS values for Ar agree within mutual uncertainties as discussed in [42]. Since our normalization is based upon relative flow method, we prefer to use values from the most recent paper [42] and only for the energy of 250 eV, which is not available in [42] we used those from [43].

Since our experimental DCSs are obtained in the limited angular range, in order to obtained elastic integral (ICSs) and momentum transfer (MTCSs) cross-sections, our DCSs must be extrapolated to the smallest (0◦ ) and the highest (180◦ ) scattering angles. Our extrapolation takes into account the theoretically obtained shapes of DCSs (present model 2, at small (0–25◦ ) and high (120–180◦ ) scattering angles and present experimental values of DCSs near 25◦ and 120◦ . Thereafter, ICSs and MTCSs were obtained using extrapolated DCSs and appropriate integration defined as:

$$ICS = 2\pi \int\_0^{\pi} DCS(\theta) \sin \theta d\theta \tag{14}$$

$$\text{MTCS} = 2\pi \int\_0^{\pi} \text{DCS}(\theta) (1 - \cos \theta) \sin \theta d\theta \tag{15}$$

The uncertainties of the relative DCSs consisted of statistical uncertainties and shortterm stability uncertainties, caused by instability of the system. This uncertainty is increased by 20% for small scattering angles, due to the potential alteration of the interaction volume. Dominant uncertainties for absolute DCSs are those from reference cross-sections for Ar [42,43], and are taken to be about 20%. The DCS uncertainties obtained in such a manner, ∆, are presented in parenthesis within Table 2. The total uncertainties for absolute DCSs are about 30% for small angles and about 20% for the rest of the angular range. The total uncertainties of ICSs and MTCs arise from the DCSs uncertainties mentioned above and uncertainties of the extrapolation of DCSs to 0◦ and to 180◦ and numerical integration (10%).

#### **4. Results**

Measured results of the absolute differential cross-sections, integral cross-sections, and momentum transfer cross-sections, together with their corresponding uncertainties, are shown in Table 2. The results cover six incident electron energies, from 50 eV to 300 eV and angular range from 25◦ to 125◦ . In Figure 1, the present theoretical and experimental DCSs for all six incident electron energies are shown graphically. For the sake of comparison, other authors' data [16,23,24,27–31], listed in Table 1, are shown in the same figure.

Theoretical results are shown in two approximations: the simple sum of individual atomic cross-sections (model 1, dashed black line) and with molecular effects taken into account (model 2, solid black line). It can be seen that those effects significantly modify DCSs. One of them, the absorption potential, plays a dominant role in this modification of cross-sections. In comparison with present experiment and other authors' results, theory with included molecular effects showed better agreement, both qualitatively and quantitatively, as expected.

Obtained ICSs, together with other authors' results [17,25,29–31,33,34], are presented in Figure 2. *Int. J. Mol. Sci.* **2021**, *22*, x FOR PEER REVIEW 9 of 14

**Figure 1.** *Cont*.

**Figure 1.** Angle differential cross-sections for elastic electron scattering from methane molecule, for six incident electron energies, from 50 eV to 300 eV. The present results include experiment (blue circles), relative flow absolute data (red stars), theory with molecular effects (full line) and simple sum theory (dashed line). Previous results, tabulated in Table 1,

are also shown for the sake of comparison.

**Figure 1.** Angle differential cross-sections for elastic electron scattering from methane molecule, for six incident electron energies, from 50 eV to 300 eV. The present results include experiment (blue circles), relative flow absolute data (red stars), theory with molecular effects (full line) and simple sum theory (dashed line). Previous results, tabulated in Table 1, are also shown for the sake of comparison. **Figure 1.** Angle differential cross-sections for elastic electron scattering from methane molecule, for six incident electron energies, from 50 eV to 300 eV. The present results include experiment (blue circles), relative flow absolute data (red stars), theory with molecular effects (full line) and simple sum theory (dashed line). Previous results, tabulated in Table 1, are also shown for the sake of comparison. *Int. J. Mol. Sci.* **2021**, *22*, x FOR PEER REVIEW 10 of 14 Obtained ICSs, together with other authors' results [17,25,29–31,33,34], are pre-

sented in Figure 2.

**Figure 2.** Integral cross-sections for elastic electron-methane collision, presented in energy range from 35 eV to 1000 eV. Present experimental (blue circles) and theoretical (solid black line) results are shown together with previous experimental, as well as the theoretical results, for comparison. **5. Discussion Figure 2.** Integral cross-sections for elastic electron-methane collision, presented in energy range from 35 eV to 1000 eV. Present experimental (blue circles) and theoretical (solid black line) results are shown together with previous experimental, as well as the theoretical results, for comparison.

estimate absolutes values or do so at certain angular ranges.

Experimental DCS at 50 eV exhibits wide minimum at 100° scattering angle, for which position and depth are in good agreement with other authors' results

There are many experimental and theoretical data for DCS at 100 eV. This cross-section shows a wide and shallow local minimum at 80° scattering angle, which vanishes for incident electron energies above 150 eV. Its position is the same or similar for every shown result. Our measurement and calculation are in strong agreement with the experimental result of Iga et al. [31] and with the theories of Jain (SEP) [32] and Mahato et al. [33], except at higher scattering angles (from 105°). Other results are in good agreement with the shape, but quantitatively are underestimated in comparison with the present result. It seems that there are two classes of experimental values that differ in absolute values, one by Boesten and Tanaka [25] and Cho et al. [29] and the other by Iga et al. [31] and the present measurements. One of the significant differences between these two sets of data lie in the choice of the reference gas, the former used He while the later used Ne and Ar as a reference. Nevertheless the cross-sections for He are known with better accuracy than those of Ne and Ar, it seems plausible to conclude that more similar flow conditions between the reference gas and the target one give more reliable data. If it has been possible to obtain perfectly the same all conditions necessary for applying the rela-

theories [29,32] at high scattering angles, above 110°. It is interesting to note that all existing experimental values at 50 eV impact energy agree among themselves within the estimated uncertainties. It is rather a problem with theories, which, in most cases, over-

#### **5. Discussion**

Experimental DCS at 50 eV exhibits wide minimum at 100◦ scattering angle, for which position and depth are in good agreement with other authors' results [17,25,29,32,33], especially experimental ones [17,25,29]. Our calculations overestimate the measured DCS, but it matches with shape and is in a good agreement with other theories [29,32] at high scattering angles, above 110◦ . It is interesting to note that all existing experimental values at 50 eV impact energy agree among themselves within the estimated uncertainties. It is rather a problem with theories, which, in most cases, overestimate absolutes values or do so at certain angular ranges.

There are many experimental and theoretical data for DCS at 100 eV. This cross-section shows a wide and shallow local minimum at 80◦ scattering angle, which vanishes for incident electron energies above 150 eV. Its position is the same or similar for every shown result. Our measurement and calculation are in strong agreement with the experimental result of Iga et al. [31] and with the theories of Jain (SEP) [32] and Mahato et al. [33], except at higher scattering angles (from 105◦ ). Other results are in good agreement with the shape, but quantitatively are underestimated in comparison with the present result. It seems that there are two classes of experimental values that differ in absolute values, one by Boesten and Tanaka [25] and Cho et al. [29] and the other by Iga et al. [31] and the present measurements. One of the significant differences between these two sets of data lie in the choice of the reference gas, the former used He while the later used Ne and Ar as a reference. Nevertheless the cross-sections for He are known with better accuracy than those of Ne and Ar, it seems plausible to conclude that more similar flow conditions between the reference gas and the target one give more reliable data. If it has been possible to obtain perfectly the same all conditions necessary for applying the relative flow method, then the choice of reference gas would be the one with the best-known cross-sections, i.e., He gas. However, since the method itself introduces additional uncertainties, in our opinion, it would be the best procedure to compare cross-sections with relatively similar flows within gas inlet system.

As for DCSs for 150 eV, there are only results by Fuss et al. [34] available for comparison. At this energy, there are no local minima, like for 50 eV and 100 eV. Instead, there is a wide plateau from 70◦ scattering angle. Experiment and theory are in good agreement by the shape, but the experiment is, on average, about 30% quantitatively lower.

DCSs for 200 eV (both measured and calculated) show good agreement (within experimental uncertainty) with experimental results of Iga et al. [31], recommended data by Song et al. [17] and theoretical results by Jain (SEP) [32] and Mahato et al. [33] for smaller scattering angles (below 70◦ ). Results by Vuškovi´c and Trajm ar [26] are good by shape but higher in absolute value.

For DCS for 250 eV incident electron energy, to the best of our knowledge, there are no published experimental or theoretical results. In the graph, it can be seen that our theory is slightly higher than the measured results, but both are similar qualitatively.

At 300 eV, the shapes and values of present theory and previous results by Iga et al. [31] and Song et al. [17] are in almost perfect agreement. The experimental result is just slightly lower on the absolute scale. Same as for every other energy, calculations by Jain [32] and Mahato et al. [33] agree good for smaller scattering angles, but for higher, they little overestimate other results.

The values of DCSs span over three and four orders of magnitude in presented energy range, what is the characteristic behavior for molecular targets and noticed also in the previous targets [42,48]. The general agreement among different experimental datasets and calculations is very good, and that is what one may expect at the present level of advanced experiments and sophisticated calculations [49].

The present experimental integral cross-sections ICSs are shown in Table 1 and together with other available results in Figure 2. Our experimental ICSs are placed between recommended Fuss et al. [34] and theoretical results Mahato et al. [33]. In the electron energy range from 50 eV to 300 eV most of the other experimental ICSs, like those by

m2

Boesten and Tanaka [25], Sakae et al. [30], Iga et al. [31], Song et al. [17], lie within the same uncertainty limits. Our experimental DCS data are obtained in rather limited angular range, and that is why the presented integral cross-sections depend strongly upon the extrapolation procedure. We have normalized our calculated DCS (model 2) to our measured absolute data to best match in shape and then used these values for integration. These values are presented in Table 2 with the uncertainty of 30% that arises from different plausible extrapolations. The absolute uncertainties of ICS and MTCS values are obtained from the difference of the corridor that is represented by maximal, DCS + ∆/2, and minimal DCS − ∆/2 values.

If total cross-section (TCS) we calculate as the sum of our measured ICSs, and ionization cross-sections obtained by Djuri´c et al. [50] plus the recommended neutral dissociation cross-sections by Fuss et al. [34], the TCS values obtained in such way agree well, within experimental uncertainties, with previously published experimental values by Zecca et al. [51] and recommended values by Song et al. [17]. Furthermore, for electron energies greater than 150 eV present TCS well agree with the semiempirical TCS by García and Manero [52] extrapolated in the interval energies of this paper. Total cross-sections for electron-methane collision in the energy range from 45 eV to 300 eV are contrasted in Figure 3a, while the corresponding Fano-Bethe plot is shown in Figure 3b. For electron energies from 150 eV to 300 eV Bethe plot of present TCS, References [17,51] and extrapolated semiempirical TCS García and Manero [52], agree within the limits of experimental uncertainties. This, under the given conditions, suggests that Born-Bethe approximation is valid in the electron energy range from 150 eV to 300 eV. *Int. J. Mol. Sci.* **2021**, *22*, x FOR PEER REVIEW 12 of 14 *Int. J. Mol. Sci.* **2021**, *22*, x FOR PEER REVIEW 12 of 14 *Int. J. Mol. Sci.* **2021**, *22*, x FOR PEER REVIEW 12 of 14 *Int. J. Mol. Sci.* **2021**, *22*, x FOR PEER REVIEW 12 of 14 *Int. J. Mol. Sci.* **2021**, *22*, x FOR PEER REVIEW 12 of 14

**Figure 3.** Total cross-sections for electron-methane collision in energy range from 45 eV to 300 eV. , present; , Song et al. (recommended values) [17]; , Zecca et al. (experiment) [51]; - - - , García and Manero (Born-Bethe approach) [52]: (**a**) Absolute values; (**b**) The Fano-Bethe plot: , linear fit of present; • • •, linear fit of Song et al. [17]; ̶∙ ̶∙ linear fit of Zecca et al.[51]. **Figure 3.** Total cross-sections for electron-methane collision in energy range from 45 eV to 300 eV. **Figure 3.** Total cross-sections for electron-methane collision in energy range from 45 eV to 300 eV. , present; , Song et al. (recommended values) [17]; , Zecca et al. (experiment) [51]; - - - , García and Manero (Born-Bethe approach) [52]: (**a**) Absolute values; (**b**) The Fano-Bethe plot: , linear fit of present; • • •, linear fit of Song et al. [17]; ̶∙ ̶∙ linear fit of Zecca et al.[51]. , present; **Figure 3.** Total cross-sections for electron-methane collision in energy range from 45 eV to 300 eV. , present; , Song et al. (recommended values) [17]; , Zecca et al. (experiment) [51]; - - - , García and Manero (Born-Bethe approach) [52]: (**a**) Absolute values; (**b**) The Fano-Bethe plot: , linear fit of present; • • •, linear fit of Song et al. [17]; ̶∙ ̶∙ linear fit of Zecca et al.[51]. , Song et al. (recommended values) [17]; **Figure 3.** Total cross-sections for electron-methane collision in energy range from 45 eV to 300 eV. , present; , Song et al. (recommended values) [17]; , Zecca et al. (experiment) [51]; - - - , García and Manero (Born-Bethe approach) [52]: (**a**) Absolute values; (**b**) The Fano-Bethe plot: , linear fit of present; • • •, linear fit of Song et al. [17]; ̶∙ ̶∙ linear fit of Zecca et al.[51]. , Zecca et al. (experiment) [51]; - - -, García and Manero (Born-Bethe approach) [52]; (**a**) Absolute values; (**b**) The Fano-Bethe plot: **Figure 3.** Total cross-sections for electron-methane collision in energy range from 45 eV to 300 eV. , present; , Song et al. (recommended values) [17]; , Zecca et al. (experiment) [51]; - - - , García and Manero (Born-Bethe approach) [52]: (**a**) Absolute values; (**b**) The Fano-Bethe plot: , linear fit of present; • • •, linear fit of Song et al. [17]; ̶∙ ̶∙ linear fit of Zecca et al.[51]. , linear fit of present; • • •, linear fit of Song et al. [17]; –·–· linear fit of Zecca et al. [51].

#### **6. Conclusions**  In order to provide the insight into methane/electron interaction, measurements and In order to provide the insight into methane/electron interaction, measurements and **6. Conclusions 6. Conclusions 6. Conclusions**

**6. Conclusions**

**6. Conclusions**

larger organic molecules.

larger organic molecules.

larger organic molecules.

larger organic molecules.

larger organic molecules.

lished version of the manuscript.

lished version of the manuscript.

lished version of the manuscript.

lished version of the manuscript.

lished version of the manuscript.

In order to provide the insight into methane/electron interaction, measurements and calculations of elastic electron scattering from methane target were performed. To summarize, calculated and measured cross-sections for elastic CH4-electron scattering in (50–300) eV incident electron energy range are reported and, conceivably, they will serve as a dependable standard for related investigations in the future. Good agreement between present theory and experiment and results available in the literature is noticed. Also, it is shown that molecular effects (especially absorption effects) play a crucial role on calculated cross-sections, particularly for very small scattering angles (below 20°). The experiment calculations of elastic electron scattering from methane target were performed. To summarize, calculated and measured cross-sections for elastic CH4-electron scattering in (50–300) eV incident electron energy range are reported and, conceivably, they will serve as a dependable standard for related investigations in the future. Good agreement between present theory and experiment and results available in the literature is noticed. Also, it is shown that molecular effects (especially absorption effects) play a crucial role on calculated cross-sections, particularly for very small scattering angles (below 20°). The experiment was performed in two independent steps. First was measuring relative DCSs for fixed calculations of elastic electron scattering from methane target were performed. To summarize, calculated and measured cross-sections for elastic CH4-electron scattering in (50–300) eV incident electron energy range are reported and, conceivably, they will serve as a dependable standard for related investigations in the future. Good agreement between present theory and experiment and results available in the literature is noticed. Also, it is shown that molecular effects (especially absorption effects) play a crucial role on calculated cross-sections, particularly for very small scattering angles (below 20°). The experiment was performed in two independent steps. First was measuring relative DCSs for fixed In order to provide the insight into methane/electron interaction, measurements and calculations of elastic electron scattering from methane target were performed. To summarize, calculated and measured cross-sections for elastic CH4-electron scattering in (50–300) eV incident electron energy range are reported and, conceivably, they will serve as a dependable standard for related investigations in the future. Good agreement between present theory and experiment and results available in the literature is noticed. Also, it is shown that molecular effects (especially absorption effects) play a crucial role on calculated cross-sections, particularly for very small scattering angles (below 20°). The experiment was performed in two independent steps. First was measuring relative DCSs for fixed In order to provide the insight into methane/electron interaction, measurements and calculations of elastic electron scattering from methane target were performed. To summarize, calculated and measured cross-sections for elastic CH4-electron scattering in (50–300) eV incident electron energy range are reported and, conceivably, they will serve as a dependable standard for related investigations in the future. Good agreement between present theory and experiment and results available in the literature is noticed. Also, it is shown that molecular effects (especially absorption effects) play a crucial role on calculated cross-sections, particularly for very small scattering angles (below 20°). The experiment was performed in two independent steps. First was measuring relative DCSs for fixed In order to provide the insight into methane/electron interaction, measurements and calculations of elastic electron scattering from methane target were performed. To summarize, calculated and measured cross-sections for elastic CH4-electron scattering in (50–300) eV incident electron energy range are reported and, conceivably, they will serve as a dependable standard for related investigations in the future. Good agreement between present theory and experiment and results available in the literature is noticed. Also, it is shown that molecular effects (especially absorption effects) play a crucial role on calculated cross-sections, particularly for very small scattering angles (below 20◦ ). The experiment

was performed in two independent steps. First was measuring relative DCSs for fixed

electron energy in function of scattering angle. Second was obtaining pair of absolute points for every energy, by relative flow method and Ar as reference gas. These absolute

electron energy in function of scattering angle. Second was obtaining pair of absolute points for every energy, by relative flow method and Ar as reference gas. These absolute

electron energy in function of scattering angle. Second was obtaining pair of absolute

electron energy in function of scattering angle. Second was obtaining pair of absolute

well, which is confirmation of the reliability of the experimental method. DCSs for the in-

well, which is confirmation of the reliability of the experimental method. DCSs for the in-

well, which is confirmation of the reliability of the experimental method. DCSs for the in-

well, which is confirmation of the reliability of the experimental method. DCSs for the in-

points were then used for normalization of relative DCSs. These independent results agree well, which is confirmation of the reliability of the experimental method. DCSs for the in-

Nevertheless there are many studies of electron elastic scattering by methane molecule, our impression is that the present study is important to pinhole the absolute cross-sections, to confirm recommended sets of data for this process given by Song et al. [17] and to bring new results at one impact energy. Last but not the least, we stress the problem of the choice of a reference gas in the relative flow measurements and the necessity of choosing gases with similar flowing conditions. That could bring methane molecule to be a new standard for cross-sections measurements of other hydrocarbons or

Nevertheless there are many studies of electron elastic scattering by methane molecule, our impression is that the present study is important to pinhole the absolute cross-sections, to confirm recommended sets of data for this process given by Song et al. [17] and to bring new results at one impact energy. Last but not the least, we stress the problem of the choice of a reference gas in the relative flow measurements and the necessity of choosing gases with similar flowing conditions. That could bring methane molecule to be a new standard for cross-sections measurements of other hydrocarbons or

Nevertheless there are many studies of electron elastic scattering by methane molecule, our impression is that the present study is important to pinhole the absolute cross-sections, to confirm recommended sets of data for this process given by Song et al. [17] and to bring new results at one impact energy. Last but not the least, we stress the problem of the choice of a reference gas in the relative flow measurements and the necessity of choosing gases with similar flowing conditions. That could bring methane molecule to be a new standard for cross-sections measurements of other hydrocarbons or

**Author Contributions:** Conceptualization, all uthors; methodology, J.B.M., B.P. and B.P.M.; software, K.T.; validation, all authors; experimental investigation, J.V. and J.B.M.; resources, B.P.M.; data curation, B.P.M.; writing—original draft preparation, J.V. and K.T.; writing—review and editing, B.P. and B.P.M.; visualization, J.V. and B.P.; supervision, B.P. and B.P.M.; project administration, B.P.M.; funding acquisition, B.P. and B.P.M. All authors have read and agreed to the pub-

**Funding:** This research was funded by the Institute of Belgrade, through the grant by the Ministry

**Funding:** This research was funded by the Institute of Belgrade, through the grant by the Ministry

**Funding:** This research was funded by the Institute of Belgrade, through the grant by the Ministry

**Funding:** This research was funded by the Institute of Belgrade, through the grant by the Ministry

**Author Contributions:** Conceptualization, all uthors; methodology, J.B.M., B.P. and B.P.M.; software, K.T.; validation, all authors; experimental investigation, J.V. and J.B.M.; resources, B.P.M.; data curation, B.P.M.; writing—original draft preparation, J.V. and K.T.; writing—review and editing, B.P. and B.P.M.; visualization, J.V. and B.P.; supervision, B.P. and B.P.M.; project administration, B.P.M.; funding acquisition, B.P. and B.P.M. All authors have read and agreed to the pub-

**Author Contributions:** Conceptualization, all uthors; methodology, J.B.M., B.P. and B.P.M.; software, K.T.; validation, all authors; experimental investigation, J.V. and J.B.M.; resources, B.P.M.; data curation, B.P.M.; writing—original draft preparation, J.V. and K.T.; writing—review and editing, B.P. and B.P.M.; visualization, J.V. and B.P.; supervision, B.P. and B.P.M.; project administration, B.P.M.; funding acquisition, B.P. and B.P.M. All authors have read and agreed to the pub-

**Author Contributions:** Conceptualization, all uthors; methodology, J.B.M., B.P. and B.P.M.; software, K.T.; validation, all authors; experimental investigation, J.V. and J.B.M.; resources, B.P.M.; data curation, B.P.M.; writing—original draft preparation, J.V. and K.T.; writing—review and editing, B.P. and B.P.M.; visualization, J.V. and B.P.; supervision, B.P. and B.P.M.; project administration, B.P.M.; funding acquisition, B.P. and B.P.M. All authors have read and agreed to the pub-

**Author Contributions:** Conceptualization, all uthors; methodology, J.B.M., B.P. and B.P.M.; software, K.T.; validation, all authors; experimental investigation, J.V. and J.B.M.; resources, B.P.M.; data curation, B.P.M.; writing—original draft preparation, J.V. and K.T.; writing—review and editing, B.P. and B.P.M.; visualization, J.V. and B.P.; supervision, B.P. and B.P.M.; project administration, B.P.M.; funding acquisition, B.P. and B.P.M. All authors have read and agreed to the pub-

**Funding:** This research was funded by the Institute of Belgrade, through the grant by the Ministry

for Education, Science and Technological Development of the Republic of Serbia.

for Education, Science and Technological Development of the Republic of Serbia.

for Education, Science and Technological Development of the Republic of Serbia.

for Education, Science and Technological Development of the Republic of Serbia.

for Education, Science and Technological Development of the Republic of Serbia.

**Institutional Review Board Statement:** Not applicable.

**Institutional Review Board Statement:** Not applicable.

**Institutional Review Board Statement:** Not applicable.

**Institutional Review Board Statement:** Not applicable.

**Institutional Review Board Statement:** Not applicable.

Nevertheless there are many studies of electron elastic scattering by methane molecule, our impression is that the present study is important to pinhole the absolute cross-sections, to confirm recommended sets of data for this process given by Song et al. [17] and to bring new results at one impact energy. Last but not the least, we stress the problem of the choice of a reference gas in the relative flow measurements and the necessity of choosing gases with similar flowing conditions. That could bring methane molecule to be a new standard for cross-sections measurements of other hydrocarbons or

cident energy 250 eV is given without previous results known to the authors.

Nevertheless there are many studies of electron elastic scattering by methane molecule, our impression is that the present study is important to pinhole the absolute cross-sections, to confirm recommended sets of data for this process given by Song et al. [17] and to bring new results at one impact energy. Last but not the least, we stress the problem of the choice of a reference gas in the relative flow measurements and the necessity of choosing gases with similar flowing conditions. That could bring methane molecule to be a new standard for cross-sections measurements of other hydrocarbons or

cident energy 250 eV is given without previous results known to the authors.

cident energy 250 eV is given without previous results known to the authors.

cident energy 250 eV is given without previous results known to the authors.

cident energy 250 eV is given without previous results known to the authors.

was performed in two independent steps. First was measuring relative DCSs for fixed electron energy in function of scattering angle. Second was obtaining pair of absolute points for every energy, by relative flow method and Ar as reference gas. These absolute points were then used for normalization of relative DCSs. These independent results agree well, which is confirmation of the reliability of the experimental method. DCSs for the incident energy 250 eV is given without previous results known to the authors.

Nevertheless there are many studies of electron elastic scattering by methane molecule, our impression is that the present study is important to pinhole the absolute cross-sections, to confirm recommended sets of data for this process given by Song et al. [17] and to bring new results at one impact energy. Last but not the least, we stress the problem of the choice of a reference gas in the relative flow measurements and the necessity of choosing gases with similar flowing conditions. That could bring methane molecule to be a new standard for cross-sections measurements of other hydrocarbons or larger organic molecules.

**Author Contributions:** Conceptualization, all uthors; methodology, J.B.M., B.P. and B.P.M.; software, K.T.; validation, all authors; experimental investigation, J.V. and J.B.M.; resources, B.P.M.; data curation, B.P.M.; writing—original draft preparation, J.V. and K.T.; writing—review and editing, B.P. and B.P.M.; visualization, J.V. and B.P.; supervision, B.P. and B.P.M.; project administration, B.P.M.; funding acquisition, B.P. and B.P.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Institute of Belgrade, through the grant by the Ministry for Education, Science and Technological Development of the Republic of Serbia.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study is contained within the aricle.

**Acknowledgments:** We are thankful to R. Srivastava for providing their data in tabular form.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Abbreviations**

#### **References**

## *Article* **Absolute Differential Cross-Sections for Elastic Electron Scattering from Sevoflurane Molecule in the Energy Range from 50–300 eV**

**Jelena Vukalovi´c 1,2, Jelena B. Maljkovi´c 1 , Francisco Blanco 3 , Gustavo García 4,5, Branko Predojevi´c 2 and Bratislav P. Marinkovi´c 1,\***

**Abstract:** We report the results of the measurements and calculations of the absolute differential elastic electron scattering cross-sections (DCSs) from sevoflurane molecule (C4H3F7O). The experimental absolute DCSs for elastic electron scattering were obtained for the incident electron energies from 50 eV to 300 eV, and for scattering angles from 25◦ to 125◦ using a crossed electron/target beams setup and the relative flow technique for calibration to the absolute scale. For the calculations, we have used the IAM-SCAR+I method (independent atom model (IAM) applying the screened additivity rule (SCAR) with interference terms included (I)). The molecular cross-sections were obtained from the atomic data by using the SCAR procedure, incorporating interference term corrections, by summing all the relevant atomic amplitudes, including the phase coefficients. In this approach, we obtain the molecular differential scattering cross-section (DCS), which, integrated over the scattered electron angular range, gives the integral scattering cross-section (ICS). Calculated cross-sections agree very well with experimental results, in the whole energy and angular range.

**Keywords:** sevoflurane; cross-section; elastic scattering; electrons

#### **1. Introduction**

Sevoflurane (SF) is sweet-smelling non-flammable highly fluorinated methyl isopropyl ether with a boiling point at a temperature of 58.5 ◦C. Molar mass is 200.055 g/mol, vapor pressure 197 mmHg at 26 ◦C, and dipole moment 2.33 D [1]. It is one of the most commonly used inhalational anaesthetics, and it has been widely investigated. The recent review on inhaled anaesthetics [2] covered their environmental role, occupational risk, and clinical use. Gaya da Costa and co-authors [2] extensively elaborated on the case of sevoflurane molecule and its contribution to the global warming effect as a volatile anaesthetic (especially in combination with the use with N2O), pointed out that its threshold has not yet been established in the workplace as waste anaesthetic gas, considering its side effects in a clinical context (epileptiform electroencephalogram patterns in both adults and paediatric populations; the cardio protective effect in patients with coronary artery disease undergoing vascular surgery, kidney transplantation or lung surgery). The atmospheric lifetimes of the halogenated anaesthetics, halothane, enflurane, sevoflurane, isoflurane, and desflurane to the reaction to the hydroxyl radical (OH) and UV photolysis have been determined from observations of OH reaction kinetics and UV absorption spectra [3]. Halothane, enflurane, and isoflurane showed distinct UV absorption in the range 200–350 nm, and no absorption in

**Citation:** Vukalovi´c, J.; Maljkovi´c, J.B.; Blanco, F.; García, G.; Predojevi´c, B.; Marinkovi´c, B.P. Absolute Differential Cross-Sections for Elastic Electron Scattering from Sevoflurane Molecule in the Energy Range from 50–300 eV. *Int. J. Mol. Sci.* **2022**, *2*, 10021. https://doi.org/10.3390/ ijms23010021

Academic Editor: Krzysztof Bobrowski

Received: 27 November 2021 Accepted: 15 December 2021 Published: 21 December 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

the wavelength range 200–350 nm was detected for sevoflurane. Tang et al. [1] analysed the effects of general anaesthetics on their potential targets by large-scale molecular simulation. The structural parameters and partial atomic charges of the anaesthetics, considered to be of great importance, were determined. Geometric optimizations using the Hartree–Fock and the B3LYP (Becke, 3-parameter, Lee–Yang–Parr) density functional theory methods with the large 6–311+G (2d,p) basis set were performed to determine the structures and charge distributions of two halogenated anaesthetics; sevoflurane and halothane. Lesarri and co-authors [4] investigated the conformational landscape of the volatile anaesthetic sevoflurane. The structure of the anaesthetic haloether sevoflurane (CH2F–O–CH(CF3)2) has been resolved using Fourier-transform microwave (FT-MW) spectroscopy in a supersonic-jet expansion. In isolated conditions, sevoflurane adopts a single conformation characterized by a gauche fluoromethoxy group and a near-symmetric orientation of the isopropyl group with respect to the ether plane (cis H–Cipr–O–CF). A schematic drawing of sevoflurane is shown in Figure 1. plane (cis H–Cipr–O–CF). A schematic drawing of sevoflurane is shown in Figure 1. Don et al. [5] proposed a vibrational assignment of sevoflurane and studied its interaction with the aromatic model compound benzene, using the vibrational spectroscopy of supersonic jet expansions and of cryo solutions in liquid xenon. Sevoflurane has been investigated from the medical point of view also. Shiraishi and Ikeda [6] studied an uptake and biotransformation of sevoflurane in humans and concluded that, despite its relatively large minimum alveolar concentration (MAC), sevoflurane has a small uptake due to its low solubility, but the degradation rate is shown to be high, resulting in a higher serum fluoride concentration than for other halogenated anaesthetics. Most recently, Dong et al. [7] assessed mice and neurons treated with anaesthetics sevoflurane and desflurane, and applied nanobeam-sensor technology, an ultrasensitive method, to measure tau/p-tau amounts. They showed that the sevoflurane induces tau trafficking from neurons to microglia.

*Int. J. Mol. Sci.* **2021**, *22*, x FOR PEER REVIEW 2 of 11

have been determined from observations of OH reaction kinetics and UV absorption spectra [3]. Halothane, enflurane, and isoflurane showed distinct UV absorption in the range 200–350 nm, and no absorption in the wavelength range 200–350 nm was detected for sevoflurane. Tang et al. [1] analysed the effects of general anaesthetics on their potential targets by large-scale molecular simulation. The structural parameters and partial atomic charges of the anaesthetics, considered to be of great importance, were determined. Geometric optimizations using the Hartree–Fock and the B3LYP (Becke, 3-parameter, Lee– Yang–Parr) density functional theory methods with the large 6–311+G (2d,p) basis set were performed to determine the structures and charge distributions of two halogenated anaesthetics; sevoflurane and halothane. Lesarri and co-authors [4] investigated the conformational landscape of the volatile anaesthetic sevoflurane. The structure of the anaesthetic haloether sevoflurane (CH2F–O–CH(CF3)2) has been resolved using Fourier-transform microwave (FT-MW) spectroscopy in a supersonic-jet expansion. In isolated conditions, sevoflurane adopts a single conformation characterized by a gauche fluoromethoxy group and a near-symmetric orientation of the isopropyl group with respect to the ether

**Figure 1.** Schematic drawing of sevoflurane. **Figure 1.** Schematic drawing of sevoflurane.

Lange et al. [8] have investigated the lowest-lying electronic states of isoflurane and sevoflurane in the 5.0–10.8 eV energy range by experimental and theoretical methods. Photoabsorption spectra of isoflurane and sevoflurane have been measured with synchrotron radiation over the photon range 5.0–10.8 eV. Low-lying excited singlet valence and Rydberg states are investigated, and the assignments supported by quantum chemical calculations, the latter also helping to identify the triplet states. The measured absolute Don et al. [5] proposed a vibrational assignment of sevoflurane and studied its interaction with the aromatic model compound benzene, using the vibrational spectroscopy of supersonic jet expansions and of cryo solutions in liquid xenon. Sevoflurane has been investigated from the medical point of view also. Shiraishi and Ikeda [6] studied an uptake and biotransformation of sevoflurane in humans and concluded that, despite its relatively large minimum alveolar concentration (MAC), sevoflurane has a small uptake due to its low solubility, but the degradation rate is shown to be high, resulting in a higher serum fluoride concentration than for other halogenated anaesthetics. Most recently, Dong et al. [7] assessed mice and neurons treated with anaesthetics sevoflurane and desflurane, and applied nanobeam-sensor technology, an ultrasensitive method, to measure tau/p-tau amounts. They showed that the sevoflurane induces tau trafficking from neurons to microglia.

Lange et al. [8] have investigated the lowest-lying electronic states of isoflurane and sevoflurane in the 5.0–10.8 eV energy range by experimental and theoretical methods. Photoabsorption spectra of isoflurane and sevoflurane have been measured with synchrotron radiation over the photon range 5.0–10.8 eV. Low-lying excited singlet valence and Rydberg states are investigated, and the assignments supported by quantum chemical calculations, the latter also helping to identify the triplet states. The measured absolute cross-sections have been used to calculate the photolysis lifetimes of isoflurane and sevoflurane in the Earth's atmosphere.

Electron collisions with sevoflurane have also been investigated. Very recently, Lozano et al. [9] reported total scattering cross-section from sevoflurane of 1–300 eV electrons. The experimental results, obtained from an implemented magnetic beam apparatus, are compared with theoretical results from the independent atom model, with a screening corrected additivity rule including interference effects and rotational excitation.

As pointed out by Tanaka et al. [10], the absolute electron-impact excitation crosssections could be obtained by normalization to elastic scattering cross-section (which is the subject of the present study), or in other ways to determine the binary encounter (BE) scaling curve, after measuring the DCSs at high-energy impact (>100 eV), and for small scattering angles. A comprehensive review of experimental techniques and calculation methods for determination of electron cross-sections from biomolecules, biofuels and their fragments, has been recently given by Brunger [11], covering extensive literature in the field.

In this paper, theoretical and experimental results for elastic electron scattering from sevoflurane, in the medium energy range, are shown, complementing the investigations of electron interaction with this molecule. According to our knowledge, these are the first reported results for absolute differential cross-sections in the energy range from 50–300 eV.

Experimentally obtained data include absolute differential cross-sections for elastic electron scattering for the incident electron energy range from 50 to 300 eV (with 50 eV steps) and an angular range from 25◦ to 125◦ (with 5◦ steps), and integral and momentum transfer cross-sections for every measured energy. The experiment was performed on a crossed-beam apparatus. Relative points were put on the absolute scale with the help of the relative flow method, using Ar as a reference gas. Theoretical results are obtained using the IAM-SCAR+I method (independent atom model (IAM) applying the screened additivity rule (SCAR) with interferences terms included (I)). A very good level of agreement has been found between the present experimental and theoretical data, within the experimental uncertainties.

The paper is organized as follows. The experimental setup and measurement procedure are given in Section 2. The theory and calculations of DCSs are explained in Section 3. Obtained results are shown graphically and in the table, and discussion is shown in Section 4. Section 5 is reserved for the conclusion.

#### **2. Experiment**

A schematic drawing of the experimental set-up is shown in Figure 2. Our beam profile has been determined in a previous set of measurements [12–14]. In our experiment, the source of molecular beam is a stainless steel gas needle, with a diameter of d = 0.5 mm and a tube length of l = 40 mm, which gives the ratio Γ = d/l = 80, while the input pressures were such that the free mean path (λ) was larger than the inner diameter of the tube. According to Lucas [15], the proposed conditions for Γ and λ are Γ > 10 and λ ≈ d, so we fulfil all the requirements for the well-collimated beam, and the derived expressions can be used in our experiment. Moreover, author [15] states that the beam properties will be optimized if the ratio of the square of single tube length and its diameter is maximized, which, in our case, is 3200.

The analysing system consists of a front four-electrode lens, energy analyser, and rear three-electrode lens. The four-electrode lens is used for collecting, directing, and focusing scattered electrons to the energy analyser after slowing them down to the constant analyser pass energy. Electron energy analyser is a double cylindrical mirror analyser (DCMA), which, essentially, represents two cylindrical analysers connected in series. Pass energy is determined by the potential difference between the cylinders. The three-electrode lens is used for focusing analysed electrons into the detector (single channel electron multiplier).

Since detecting particles are electrons, detector entrance is grounded, and exit is on a high positive potential. *Int. J. Mol. Sci.* **2021**, *22*, x FOR PEER REVIEW 4 of 11

**Figure 2.** Schematic drawing of the experimental set-up. **Figure 2.** Schematic drawing of the experimental set-up.

The anhydrous sevoflurane (C4H3F7O) used in this experiment had a declared purity better than 99%. Before starting the measurements a few freeze-thaw-pump cycles under vacuum have been made. Sevoflurane (SF) is a liquid at room temperature and was introduced into the scattering region from a glass container via a gas line system. SF molecule is characterized by vapor pressure (197 mm Hg at 26 °C) and relatively high dipole moment (2.33 D). Therefore, to provide stable experimental conditions, everything was heated to approximately 50 °C during the gas phase measurements in analogy with previously studied molecular targets [16,17]. In the present work, pipes and the needle were also heated providing a stable driving pressure behind the needle and also for avoiding the absorption effects [18]. In order to reduce magnetic disturbance, the experimental setup is placed in the The anhydrous sevoflurane (C4H3F7O) used in this experiment had a declared purity better than 99%. Before starting the measurements a few freeze-thaw-pump cycles under vacuum have been made. Sevoflurane (SF) is a liquid at room temperature and was introduced into the scattering region from a glass container via a gas line system. SF molecule is characterized by vapor pressure (197 mm Hg at 26 ◦C) and relatively high dipole moment (2.33 D). Therefore, to provide stable experimental conditions, everything was heated to approximately 50 ◦C during the gas phase measurements in analogy with previously studied molecular targets [16,17]. In the present work, pipes and the needle were also heated providing a stable driving pressure behind the needle and also for avoiding the absorption effects [18].

chamber shielded by the two concentric µ-metal layers. The pre-experimental pressure in the chamber was about 5·× 10−7 mbar and the working pressure was an order of magnitude higher. The experimental procedure for acquiring the absolute differential cross-sections for In order to reduce magnetic disturbance, the experimental setup is placed in the chamber shielded by the two concentric µ-metal layers. The pre-experimental pressure in the chamber was about 5·× 10−7 mbar and the working pressure was an order of magnitude higher.

elastic scattering of electrons from sevoflurane molecule consists of two main stages: • Stage 1: obtaining relative DCSs by measuring the intensity of electrons elastically The experimental procedure for acquiring the absolute differential cross-sections for elastic scattering of electrons from sevoflurane molecule consists of two main stages:

scattering angles from 20° to 125° (in 5° steps). At given electron energy, the relative crosssection has been derived as a function of scattering angle by measuring the elastic scattering In the present work, DCSs for elastic electron scattering from sevoflurane have been measured at selected incident electron energies, from 50 to 300 eV (in 50 eV steps), and at scattering angles from 20◦ to 125◦ (in 5◦ steps). At given electron energy, the relative cross-section has been derived as a function of scattering angle by measuring the elastic

scattering intensity at the maximum of the elastic peak. The background contributions of the elastic electron intensities, which were around 10% at higher energies, were subtracted from the measured electron yields. It should be noted that the background contributions were generally more important at low incident energies and scattering angles (around 15%). During the measurements, potentials on electron gun electrodes and DCMA were adjusted to keep interaction volume constant. Deviations that can occur at small angles are corrected by comparing cross-sections from Ar at given energy with other authors' data [14,21].

Measured relative DCSs were normalized to the absolute scale according to the absolute points (at 40◦ , 80◦ , 90◦ or 100◦ ), obtained by a Relative flow method (RFM) previously explained in detail [22]. In RFM we compare intensities of elastically scattered electrons on the target molecule (SF) and referent gas (we used Ar), under the same experimental conditions [19,20]. In order to obtain the same experimental conditions, the same beam profiles, for both target molecule and referent gas must be provided. According to Olander and Kruger [23], the same beam profiles can be obtained with two conditions: (1) the mean free paths for both gases must the same and (2) the mean free path is approximately equal to the diameter of stainless steel gas needle. λ ≈ d. In the experiment, the first condition is achieved by adjusting pressures behind the gas needle inversely proportional to the ratio of the squared gas kinetic diameters, and for second condition gas pressures need to be low, which is fulfilled in our experiment [14]. Gas kinetic diameter for Ar is 3.58 Å and for sevoflurane 5.51 Å, so the pressure ratio was PAr: PSF = D2 SF: D2 Ar ~ 2.4. When the same beam profiles for both, target molecule (*DCSx*) and referent gas (*DCSref*) are obtained, according to Nickel at al [19,20], absolute differential cross-sections for target molecule *DCSx* (*E*, *θ*) can be calculated, knowing absolute differential cross-sections for the referent gas *DCSref* (*E*, *θ*), at the same energy and angle, using a formula:

$$DCS\_{\rm x}(E,\theta) = DCS\_{ref}(E,\theta)\frac{\mathcal{N}\_{\rm x}F\_{ref}}{\mathcal{N}\_{ref}F\_{\rm x}}\sqrt{\frac{\mathcal{M}\_{ref}}{\mathcal{M}\_{\rm x}}}\tag{1}$$

Quantities that we measure in the experiment are: Flow rate (F) and intensity of elastically scattered electrons (N). *Mref* and *Mx* are molecular masses for referent gas and target molecule, respectively. The relative flow rate has been determined by closing an outlet to the chamber, admitting target gases into a closed constant volume, and then measuring the pressure increase in time. The flow is determined from the experimental curve of pressure versus time fitted by the least-squares method. The whole system was heated to minimize absorption effects [18], which can influence measuring flow rates and determining the flow.

Our experimental spectrometer UGRA is limited in performing angular dependent differential cross-sections measurements (25–125◦ ) and to obtain integral (*ICSs*) and momentum transfer cross-sections (*MTCSs*) we need to extrapolate measured *DCSs* to 0◦ and 180◦ . For extrapolation, from 0–25◦ , and 125–180◦ we used calculated results obtained by IAM + SCAR + I procedure (see section Theory) and appropriate integration. Our experimental *DCS* data are obtained in a rather limited angular range and that is why the presented integral cross-sections depend strongly upon the extrapolation procedure. The exact formulae used for the integration are in the form:

$$\text{LCS} = 2\pi \int\_0^{\pi} \text{DCS}(\theta) \sin \theta d\theta \tag{2}$$

$$\text{MTCS} = 2\pi \int\_0^{\pi} \text{DCS}(\theta) (1 - \cos \theta) \sin \theta d\theta \tag{3}$$

The uncertainties of the relative *DCSs* consist of statistical uncertainties and shortterm stability uncertainties, caused by the instability of the system. This uncertainty is increased by 20% for small scattering angles, due to the potential alteration of the interaction volume. Dominant uncertainty for absolute *DCSs* are those from reference cross-sections for Ar [14,21], and are taken to be about 20%. The total uncertainties, derived as the square

root of the sum of squares of individual independent uncertainties, for absolute *DCSs* are about 30% for small angles and about 22% for the rest of the angular range. The total uncertainties of *ICSs* and *MTCs* arise from the *DCSs* uncertainties mentioned above and uncertainties of the extrapolation of *DCSs* to 0◦ and 180◦ and numerical integration and were approximately 30%.

#### **3. Theory**

To calculate the differential elastic, integral elastic, and inelastic as well as the total cross-sections we have used the IAM-SCAR+I method (independent atom model (IAM) applying the screened additivity rule (SCAR) with interferences terms included (I)). This method has been described in detail in previous publications [9,24–28]. Briefly, the molecular target is described as an aggregate of its individual atoms (i.e., C, H, F, and O in this case). Each atomic target is represented by an ab initio interacting complex optical potential given by:

$$V\_{opt}(\stackrel{\rightarrow}{r'}) = V\_{\mathbb{R}}(\stackrel{\rightarrow}{r'}) + iV\_{abs}(\stackrel{\rightarrow}{r'}) \tag{4}$$

In Equation (4), the real part accounts for elastic scattering while the imaginary part represents the inelastic processes which are considered as the 'absorption part' following the procedure of Staszewska et al. [29]. The real part is divided into three terms that include:

$$V\_R(\overrightarrow{r'}) = V\_s(\overrightarrow{r'}) + V\_{ex}(\overrightarrow{r'}) + V\_{pol}(\overrightarrow{r'}),\tag{5}$$

where vs. represents a static term derived from a Hartree-Fock calculation of the atomic charge distribution [30], *Vex* an exchange term to account for the indistinguishability of the incident and target electrons [31], and *Vpol* a long-range polarization term [32].

The molecular cross-sections are obtained from the atomic data by using the screening corrected additivity rule (SCAR) procedure [33], incorporating interference (I) term corrections [25], by summing all the relevant atomic amplitudes, including the phase coefficients. In this approach, we obtain the molecular differential scattering cross-section (DCS), which integrated over all the scattered electron angular range gives the integral scattering crosssection (ICS). Moreover, by taking the sum of the ICS for all open channels (elastic ICS and inelastic ICS) the total cross-section (TCS) could be obtained. Note that we do not include at this stage any contribution from vibrational and rotational excitation processes.

Sevoflurane is a polar molecule with a permanent dipole moment of 2.22 D [1] and therefore rotational excitations, not accounted for by the above procedure, are relevant within the scattering scheme. In order to approximately include differential and integral rotational excitation cross-section in the present study, we used the first-Born approximation, following the procedure described in [27]. In these conditions, these cross-sections can easily be calculated by considering the molecule as a rigid rotor, with the initial rotational excited state distribution in equilibrium at 300 K, and calculating all the transitions ∆J = ±1 (J being the rotational quantum number) assuming the Born approximation but including the correction for the larger angles given by Dickinson (see ref. [34] and references therein).

#### **4. Results**

Experimental results for DCSs, together with experimental ICSs and MTCSs, for elastic electron scattering from sevoflurane, are presented in Table 1, all with corresponding absolute uncertainties. Experimentally measured and theoretically calculated DCSs are shown graphically in Figure 3. The experiment covers six energies of impact electrons, from 50 eV to 300 eV, and the angular range from 25◦ to 125◦ (theory covers all angles, from 0◦ to 180◦ ). Absolute uncertainties are about 22%, except for small angles, where uncertainties are increased to about 30% due to the potential interaction volume alterations.

**Table 1.** Experimental results for absolute differential cross-sections (DCSs), integral cross-sections (ICSs) and momentum transfer cross-sections (MTCSs) for elastic electron scattering from sevoflurane. In parentheses are given absolute uncertainties of the last two digits.

DCSs have characteristic behavior for molecular targets, noticed previously [12,13]. At 50 eV and 100 eV DCSs exhibit a wide minimum at 100◦ scattering angle, which disappears at higher incident electron energies. Experiment and theory are generally in good agreement, both in shape and on the absolute scale. There are systematic discrepancies at small angles for all electron energies, probably because of the instability of interaction volume at those angles during the experiment. Also, there are obvious declinations of DCSs for 150 eV electron energies at high scattering angles.

Concerning the normalization procedure of our results, in the relative flow measurements, absolute DCSs for Ar are taken from Rankovi´c et al. [14] for incident electron energies 50–200 eV and 300 eV and from Williams and Willis [22] for electron energy of 250 eV. In both papers, the absolute values were derived by measurements of angular dependences of elastically scattered electrons using electron spectrometers, two 127◦ cylindrical electrostatic energy analysers in [21], and a double cylindrical mirror analyser (DCMA) in [14]. Authors had different normalization procedures. Rankovi´c et al. [14] used He as a reference gas and Williams and Willis [21] a phaseshift analysis of the relative angular distributions of electrons elastically scattered in the energy region of the resonances 2P3/2.1/2 of Ar. Both absolute differential cross-sections agree within mutual uncertainties as discussed in [10]. Since our normalization is based upon RFM, we prefer to use values from the most recent paper [14] because they were obtained at the same electron spectrometer UGRA and only for the energy of 250 eV, which is not available from our apparatus [14], we used those from Williams and Willis [21].

**Figure 3.** Angularly dependent differential cross-sections for elastic electron scattering from sevoflurane molecule, for six incident electron energies, from 50 eV to 300 eV. The present results include: experiment (blue circles), relative flow absolute data (red stars) and theory (full line). **Figure 3.** Angularly dependent differential cross-sections for elastic electron scattering from sevoflurane molecule, for six incident electron energies, from 50 eV to 300 eV. The present results include: experiment (blue circles), relative flow absolute data (red stars) and theory (full line).

The shapes of the experimental and theoretical cross-section plots are in excellent agreement, but measured points are 25% lower than the calculated ones. Because our experiment is angularly limited, ICS depends on the used extrapolation method, which is consisted of the normalization of our theoretical DCSs to our measured absolute ones. We have normalized calculated DCS to the measured absolute data to best match in shape and then used these values for integration. These values are presented in Table 1 with an uncertainty of 30% that arises from different plausible extrapolations. The absolute uncertainties of ICS and MTCS values are obtained from the difference of the corridor that is The shapes of the experimental and theoretical cross-section plots are in excellent agreement, but measured points are 25% lower than the calculated ones. Because our experiment is angularly limited, ICS depends on the used extrapolation method, which is consisted of the normalization of our theoretical DCSs to our measured absolute ones. We have normalized calculated DCS to the measured absolute data to best match in shape and then used these values for integration. These values are presented in Table 1 with an uncertainty of 30% that arises from different plausible extrapolations. The absolute uncertainties of ICS and MTCS values are obtained from the difference of the corridor that is represented by maximal, DCS + ∆/2, and minimal DCS − ∆/2 values.

Measured and calculated absolute differential and integral cross-sections are graphically presented in Figures 3 and 4, and to the best of the authors knowledge, there are no

represented by maximal, DCS + Δ/2, and minimal DCS − Δ/2 values.

Measured and calculated absolute differential and integral cross-sections are graphically presented in Figures 3 and 4, and to the best of the authors knowledge, there are no other published results, neither experimental nor theoretical, for DCS or ICSs for elastic electron scattering from sevoflurane in this energy and angular range. *Int. J. Mol. Sci.* **2021**, *22*, x FOR PEER REVIEW 9 of 11

**Figure 4.** Integral cross-section for elastic electron collision with sevoflurane molecule in the energy range from 10 eV to 350 eV. Experiment (blue circles) and theory (solid black line) are presented. **Figure 4.** Integral cross-section for elastic electron collision with sevoflurane molecule in the energy range from 10 eV to 350 eV. Experiment (blue circles) and theory (solid black line) are presented.

#### **5. Conclusions**

the manuscript.

**5. Conclusions**  We performed the experimental and theoretical investigation of elastic electron collisions on sevoflurane molecule at intermediate incident electron energies in order to provide insight into electron/sevoflurane interaction. Two independent sets of measurements, relative differential cross-sections at fixed energy in the function of scattering angle and absolute differential cross-sections obtained by relative flow method were performed. The last one provides us with two absolute points for every incident energy, which were used for the normalization to the absolute scale. These two independent sets of measurements showed good agreement which gives reliability to our experimental procedure. We have shown good agreement between the present experiment and theory (IAM-SCAR+I method) on the absolute scale and also in the shape. Using Ar we stress the problem of the choice of the reference gas in the relative flow measurements, since conditions should be provided for the widths (shapes) of the target beam and the reference gas beam to be approximately the same, which is easier to achieve with Ar in relation to He or Ne, since they are much lighter. We performed the experimental and theoretical investigation of elastic electron collisions on sevoflurane molecule at intermediate incident electron energies in order to provide insight into electron/sevoflurane interaction. Two independent sets of measurements, relative differential cross-sections at fixed energy in the function of scattering angle and absolute differential cross-sections obtained by relative flow method were performed. The last one provides us with two absolute points for every incident energy, which were used for the normalization to the absolute scale. These two independent sets of measurements showed good agreement which gives reliability to our experimental procedure. We have shown good agreement between the present experiment and theory (IAM-SCAR+I method) on the absolute scale and also in the shape. Using Ar we stress the problem of the choice of the reference gas in the relative flow measurements, since conditions should be provided for the widths (shapes) of the target beam and the reference gas beam to be approximately the same, which is easier to achieve with Ar in relation to He or Ne, since they are much lighter. The importance of this investigation is that according to our knowledge these are the first reported results for absolute differential and integral cross-sections for elastic electron scattering on sevoflurane in the energy range from (50–300) eV.

The importance of this investigation is that according to our knowledge these are the first reported results for absolute differential and integral cross-sections for elastic electron scattering on sevoflurane in the energy range from (50–300) eV. **Author Contributions:** Conceptualization, all authors; methodology, J.B.M. and B.P.M.; software, F.B. and G.G.; validation, all authors; experimental investigation, J.V. and J.B.M.; resources, B.P.M.; **Author Contributions:** Conceptualization, all authors; methodology, J.B.M. and B.P.M.; software, F.B. and G.G.; validation, all authors; experimental investigation, J.V. and J.B.M.; resources, B.P.M.; data curation, B.P.M.; writing—original draft preparation, J.V., J.B.M. and G.G.; writing—review and editing, B.P.M. and J.V.; visualization, J.V. and B.P.; supervision, B.P.M.; project administration, B.P.M.; funding acquisition, B.P.M. All authors have read and agreed to the published version of the manuscript.

data curation, B.P.M.; writing—original draft preparation, J.V., J.B.M. and G.G.; writing—review and editing, B.P.M. and J.V.; visualization, J.V. and B.P.; supervision, B.P.M.; project administration, B.P.M.; funding acquisition, B.P.M. All authors have read and agreed to the published version of

**Funding:** This research was funded by the Institute of Physics Belgrade, through the grant by the Ministry for Education, Science and Technological Development of the Republic of Serbia. This study is partially supported by the Spanish Ministerio de Ciencia e Innovación (Project PID2019-

104727RB-C21) and CSIC (Project LINKA20085).

**Informed Consent Statement:** Not applicable.

**Institutional Review Board Statement:** Not applicable.

**Funding:** This research was funded by the Institute of Physics Belgrade, through the grant by the Ministry for Education, Science and Technological Development of the Republic of Serbia. This study is partially supported by the Spanish Ministerio de Ciencia e Innovación (Project PID2019-104727RB-C21) and CSIC (Project LINKA20085).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study is contained within the article. All data are possible to retrieve from the Belgrade Electron Atom/Molecule DataBase (BEAMDB) at http://servo.aob.rs/emol after the article has been published.

**Acknowledgments:** This article/publication is based upon work from COST Action CA18212— Molecular Dynamics in the GAS phase (MD-GAS), supported by COST (European Cooperation in Science and Technology.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

## *Article* **Total Electron Detachment and Induced Cationic Fragmentation Cross Sections for Superoxide Anion (O2** −**) Collisions with Benzene (C6H6) Molecules**

**Carlos Guerra 1 , Sarvesh Kumar 2 , Fernando Aguilar-Galindo 3 , Sergio Díaz-Tendero 4,5,6,\* , Ana I. Lozano 2 , Mónica Mendes 2 , Juan C. Oller 7 , Paulo Limão-Vieira 2 and Gustavo García 1,8,\***

**Abstract:** In this study, novel experimental total electron detachment cross sections for O2 − collisions with benzene molecules are reported for the impact energy range (10–1000 eV), as measured with a transmission beam apparatus. By analysing the positively charged species produced during the collision events, relative total ionisation cross sections were derived in the incident energy range of 160–900 eV. Relative partial ionisation cross sections for fragments with *m*/*z* ≤ 78 u were also given in this energy range. We also confirmed that heavier compounds (*m*/*z* > 78 u) formed for impact energies between 550 and 800 eV. In order to further our knowledge about the collision dynamics governing the fragmentation of such heavier molecular compounds, we performed molecular dynamics calculations within the framework of the Density Functional Theory (DFT). These results demonstrated that the fragmentation of these heavier compounds strongly supports the experimental evidence of *m*/*z* = 39–42, 50, 60 (u) cations formation, which contributed to the broad local maximum in the total ionisation observed from 550 to 800 eV. This work reveals the reactivity induced by molecular anions colliding with hydrocarbons at high energies, processes that can take place in the interstellar medium under various local conditions.

**Keywords:** anion–molecule collisions; electron detachment cross sections; positive ion-induced fragmentation; molecular dynamics

### **1. Introduction**

Benzene is one of the simplest and more stable aromatic ring molecules. It has been considered a prototype for the study of chemical reactions involving biomolecules, such as pyridine [1] and carbamates [2], a building block for the synthesis of carbon nano-cages [3] and a precursor of hydrocarbon structures (e.g., phenol, toluene, aniline, anthracene) with important technological applications [4]. The functionalization of fullerene-based nanostructures using the Density Functional Theory (DFT) has opened new investigations on their transport properties in biological media and their capability to be used as molecular sensors or drug carriers [5–7]. Additionally, oxygen superoxide anion, O2 −, is one of the

**Citation:** Guerra, C.; Kumar, S.; Aguilar-Galindo, F.; Díaz-Tendero, S.; Lozano, A.I.; Mendes, M.; Oller, J.C.; Limão-Vieira, P.; García, G. Total Electron Detachment and Induced Cationic Fragmentation Cross Sections for Superoxide Anion (O2 −) Collisions with Benzene (C6H6) Molecules. *Int. J. Mol. Sci.* **2022**, *23*, 1266. https://doi.org/10.3390/ ijms23031266

Academic Editor: Mihai V. Putz

Received: 31 December 2021 Accepted: 21 January 2022 Published: 23 January 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

reactive oxygen species (ROS) which are responsible for numerous biochemical processes leading to oxidative damage in living organisms [8] as well as in materials [9]. In particular, 8-oxoguanine is frequently formed by the interaction of ROS with the guanine base in DNA under conditions of oxidative stress, yielding an efficient way of damaging DNA [10].

Due to benzene's relevance for some of the applications listed above where charge transfer (electron transfer) is a pivotal mechanism in such reactions, electron scattering cross section data have been the subject of numerous theoretical and experimental studies. We recently reported an experimental and theoretical analysis of the total electron scattering cross section (TCS) with the aim of providing some reference data for modelling procedures connected with these applications [11]. Apart from TCS measurements and calculations, elastic scattering, vibrational excitation and electron attachment cross sections have also been published (see Ref. [11] and references therein). However, surprisingly, there is a lack of data on electron impact ionization and electronic excitation cross sections. Bull et al. in 2014 [12] evidenced this scarcity of data for aromatic molecules and provided new experimental data, which showed important discrepancies with the old measurements [13]. More recently, the double ionization of benzene by electron impact has been studied by Wolf et al. [14] and Sigaud and Montenegro [15], both presenting the remarkable probability of double ionization of benzene for increasing impact energies above 20 eV. Yet, being the projectile a superoxide anion, O2 −, collision-induced ionization of a target molecule is certainly more complex to describe from the dynamical point of view of the interaction. To our knowledge, except for our recent study on the anomalous oxidation of benzene in collisions with superoxide anions [16], no experimental or theoretical data for O2 − collision with benzene are available in the literature. Notwithstanding, we report on absolute total electron detachment cross sections for such collision processes in the impact energy range of 200–900 eV. Measurements were obtained with a beam attenuation technique which has been previously described [16,17]. The total uncertainty limits of these results are within 6 and 10%. Additional experimental information on the induced cationic fragmentation, i.e., positively charged fragments with a mass-tocharge ratio (*m*/*z*) less than 78 u, is also given in terms of relative cross sections normalized to that of the parent ion formation with uncertainty limits within 10 and 20%. These relative fragmentation probabilities were also obtained by means of molecular dynamics calculations carried out in the framework of the density functional (DFT) theory. The remainder of this paper has been divided into the following sections: in Section 2, we present our experimental and theoretical data together with details of their associated uncertainties. These results are discussed and compared in Section 3. A detailed description of the theoretical and experimental methods used in this study are presented in Section 4. Finally, some conclusions are drawn in Section 5.

#### **2. Results**

The theoretical and experimental results of this study are presented in this section and discussed in Section 3, and a full description of the Material and Methods utilized to obtain these results is provided in Section 4.

#### *2.1. Total Electron Detachment Cross Sections*

The experimental absolute total electron detachment cross sections (TEDCS) are presented in Table 1. Total uncertainty limits, according to the error estimation procedure described in Section 4, are also included in this table. These results are also plotted in Figure 1 together with their corresponding error bars.

As to the authors' knowledge, no previous experimental or theoretical TEDCS data have been reported in the literature. If we compare these results with our recent measurements for O2 − collisions with N2 [17], we see that the average magnitude of the TEDCS in the common energy range (50–1000 eV) is in concordance with their respective molecular masses, i.e., 3–4 times higher for benzene than for nitrogen. In addition, the energy dependence of the TEDCSs shows some similarities for both molecular targets. In both cases, the magnitude of the cross section has some local maxima/minima superimposed

to a relatively flat tendency. For N2, a prominent local maximum is shown around 200 eV (see Ref. [17]), while for benzene, two local maxima at 40 and 400 eV and a minimum around 320 eV are discernible. In contrast with nitrogen, these features are not well defined for benzene, and their respective magnitudes follow the flat tendency of the TEDCS if we consider their total uncertainty limits. These features should be connected with the excitation of specific energy levels of the target molecule. Figure 2 shows the time-of-flight spectra once calibrated in kinetic energy of the incident anion beam with and without benzene in the scattering region. As derived from this figure, the average energy loss by the primary beam after the collision with 1.2 mTorr of benzene was about 16 eV. This energy transferred was enough to induce single and double electronic excitations and/or ionisations to the benzene target molecule.

**Table 1.** Experimental total electron detachment cross sections in SI units (10−20 m2 ). Total uncertainty limits are also included.

#### *2.2. Induced Fragmentation of Benzene by O2* − *Impact*

The relative fragmentation yields of benzene cations formed after O2 − collisions in the energy range 160–900 eV were obtained by measuring the intensity of the TOF features, corresponding to identified fragments with *m*/*z* < 78 u, with respect to that of the parent ion (*m*/*z* = 78 u). A typical mass spectrum for an 850 eV impact energy is shown in Figure 3.

*Int. J. Mol. Sci.* **2022**, *23*, x FOR PEER REVIEW 4 of 15

**Figure 1.** Total electron detachment cross section (TEDCS) for O2− collisions with benzene (C6H6) as measured with the described transmission beam experimental setup (see Section 4 for details). **Figure 1.** Total electron detachment cross section (TEDCS) for O2 − collisions with benzene (C6H6 ) as measured with the described transmission beam experimental setup (see Section 4 for details). **Figure 1.** Total electron detachment cross section (TEDCS) for O2− collisions with benzene (C6H6) as measured with the described transmission beam experimental setup (see Section 4 for details). 0 200 400<PHONE_NUMBER> Anion impact energy (eV) 0 200 400<PHONE_NUMBER> Anion impact energy (eV)

**Figure 1.** Total electron detachment cross section (TEDCS) for O2− collisions with benzene (C6H6) as

0.2

3.

3.

3.

3.

the gas cell; ⎯ , 1.2 mTorr of benzene in the gas cell. **Figure 2***.* Intensity and energy of the transmitted anion beam with: ⎯ , no benzene gas (0 mTorr) in the gas cell; ⎯ , 1.2 mTorr of benzene in the gas cell. **Figure 2.** Intensity and energy of the transmitted anion beam with: **Figure 2***.* Intensity and energy of the transmitted anion beam with: ⎯ , no benzene gas (0 mTorr) in the gas cell; ⎯ , 1.2 mTorr of benzene in the gas cell. , no benzene gas (0 mTorr) in the gas cell; **Figure 2***.* Intensity and energy of the transmitted anion beam with: ⎯ , no benzene gas (0 mTorr) in the gas cell; ⎯ , 1.2 mTorr of benzene in the gas cell. , 1.2 mTorr of benzene in the gas cell.

**Figure 2***.* Intensity and energy of the transmitted anion beam with: ⎯ , no benzene gas (0 mTorr) in

corresponding to identified fragments with *m*/*z* < 78 u, with respect to that of the parent ion (*m*/*z* = 78 u). A typical mass spectrum for an 850 eV impact energy is shown in Figure

energy range 160–900 eV were obtained by measuring the intensity of the TOF features, corresponding to identified fragments with *m*/*z* < 78 u, with respect to that of the parent

*2.2. Induced Fragmentation of Benzene by O2− Impact*  The relative fragmentation yields of benzene cations formed after O2− collisions in the energy range 160–900 eV were obtained by measuring the intensity of the TOF features, *2.2. Induced Fragmentation of Benzene by O2− Impact*  The relative fragmentation yields of benzene cations formed after O2− collisions in the *2.2. Induced Fragmentation of Benzene by O2− Impact*  The relative fragmentation yields of benzene cations formed after O2− collisions in the *2.2. Induced Fragmentation of Benzene by O2− Impact*  The relative fragmentation yields of benzene cations formed after O2− collisions in the As described in Section 4, due to the specific anion formation process in the hollow cathode discharge, the time (mass) resolution was not enough to fully resolve each single fragment ion

energy range 160–900 eV were obtained by measuring the intensity of the TOF features, corresponding to identified fragments with *m*/*z* < 78 u, with respect to that of the parent

energy range 160–900 eV were obtained by measuring the intensity of the TOF features, corresponding to identified fragments with *m*/*z* < 78 u, with respect to that of the parent *J.* **2022**, *23*, x

*Int.* FOR PEER

produced, but allowed distinguishing different fragment series clearly characterised by the number of carbon atoms constituting each group of cations. Nonetheless, using a gaussian fitting analysis procedure, we could identify the mass of the fragments that mainly contributed to each fragment group. For the anion impact energy shown in Figure 3 (850 eV), the most intense feature corresponds to the parent ion (C6H6 + ), and other significative ion fragment peaks were identified as C4H2 + , C5H5 + , C2H6 + , C3H6 + , C2H2 + , C5 + , CH4 + , C+ and H/H2 + (in decreasing order of their relative intensities). Note that some features corresponding to ions heavier than the parent ion (*m*/*z* > 78 u) also appear in the mass spectrum. The formation of these heavy complexes can only be explained by the aggregation of oxygen molecules to some of the generated fragments, in particular [C6H6 + O] (m = 94 u) and [C6H6 + O2] (m = 110 u). The mechanisms by which these abducts are generated were investigated in a recent study, and the experimental evidence together with its theoretical justification can be found in Ref. [16]. We focused the present study on the formation of cationic fragments that were lighter than the parent ion, i.e., *m*/*z* < 78 u. *Int. J. Mol. Sci.* **2022**, *23*, x FOR PEER REVIEW 5 of 15

5 of 15

**Figure 3.** TOF mass spectrum of the positive ion-induced fragmentation of benzene in collisions with 850 eV oxygen anions (O2−). Gaussian fitting analysis: *m/z(u) =* 2 (⎯ ); 12 (⎯ ); 16 (⎯ ); 26 (⎯ ); 32 (⎯ ); 42 (⎯ ); 50 (⎯ ); 60 (⎯ ); 65 (⎯ ); 78 (⎯ ); 94 (⎯ ); 110 (⎯ ); fit sum (---). **Figure 3.** TOF mass spectrum of the positive ion-induced fragmentation of benzene in collisions with 850 eV oxygen anions (O2 −). Gaussian fitting analysis: *m*/*z*(*u*) = 2 ( **Figure 3.** TOF mass spectrum of the positive ion-induced fragmentation of benzene in collisions with 850 eV oxygen anions (O2−). Gaussian fitting analysis: *m/z(u) =* 2 (⎯ ); 12 (⎯ ); 16 (⎯ ); 26 (⎯ ); 32 (⎯ ); 42 (⎯ ); 50 (⎯ ); 60 (⎯ ); 65 (⎯ ); 78 (⎯ ); 94 (⎯ ); 110 (⎯ ); fit sum (---). ); 12 ( **Figure 3.** TOF mass spectrum of the positive ion-induced fragmentation of benzene in collisions with 850 eV oxygen anions (O2−). Gaussian fitting analysis: *m/z(u) =* 2 (⎯ ); 12 (⎯ ); 16 (⎯ ); 26 (⎯ ); 32 (⎯ ); 42 (⎯ ); 50 (⎯ ); 60 (⎯ ); 65 (⎯ ); 78 (⎯ ); 94 (⎯ ); 110 (⎯ ); fit sum (---). ); 16 ( **Figure 3.** TOF mass spectrum of the positive ion-induced fragmentation of benzene in collisions with 850 eV oxygen anions (O2−). Gaussian fitting analysis: *m/z(u) =* 2 (⎯ ); 12 (⎯ ); 16 (⎯ ); 26 (⎯ ); 32 (⎯ ); 42 (⎯ ); 50 (⎯ ); 60 (⎯ ); 65 (⎯ ); 78 (⎯ ); 94 (⎯ ); 110 (⎯ ); fit sum (---). ); 26 ( **Figure 3.** TOF mass spectrum of the positive ion-induced fragmentation of benzene in collisions with 850 eV oxygen anions (O2−). Gaussian fitting analysis: *m/z(u) =* 2 (⎯ ); 12 (⎯ ); 16 (⎯ ); 26 (⎯ ); 32 (⎯ ); 42 (⎯ ); 50 (⎯ ); 60 (⎯ ); 65 (⎯ ); 78 (⎯ ); 94 (⎯ ); 110 (⎯ ); fit sum (---). ); 32 ( **Figure 3.** TOF mass spectrum of the positive ion-induced fragmentation of benzene in collisions with 850 eV oxygen anions (O2−). Gaussian fitting analysis: *m/z(u) =* 2 (⎯ ); 12 (⎯ ); 16 (⎯ ); 26 (⎯ ); 32 (⎯ ); 42 (⎯ ); 50 (⎯ ); 60 (⎯ ); 65 (⎯ ); 78 (⎯ ); 94 (⎯ ); 110 (⎯ ); fit sum (---). ); 42 ( TOF mass of the ion-induced fragmentation of benzene with 850 oxygen anions analysis: *m/z(u) =* 2 ); 12 ); 16 ⎯ ); 26 (⎯ ); 60 ( **Figure 3.** TOF mass spectrum benzene in collisions −). fitting analysis: (⎯); 65 ( **Figure** positive ion-induced with (O2−*=* 2⎯spectrum of with 850 eV oxygen anions (O2−). Gaussian fitting analysis: *m/z(u) =* 2(⎯); 12 (); 16 (); 26 (); ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ sum

As described in Section 4, due to the specific anion formation process in the hollow cathode discharge, the time (mass) resolution was not enough to fully resolve each single fragment ion produced, but allowed distinguishing different fragment series clearly characterised by the number of carbon atoms constituting each group of cations. Nonetheless, using a gaussian fitting analysis procedure, we could identify the mass of the fragments that mainly contributed to each fragment group. For the anion impact energy shown in Figure 3 (850 eV), the most intense feature corresponds to the parent ion (C6H6+), and other As described in Section 4, due to the specific anion formation process in the hollow cathode discharge, the time (mass) resolution was not enough to fully resolve each single fragment ion produced, but allowed distinguishing different fragment series clearly characterised by the number of carbon atoms constituting each group of cations. Nonetheless, using a gaussian fitting analysis procedure, we could identify the mass of the fragments that mainly contributed to each fragment group. For the anion impact energy shown in Figure 3 (850 eV), the most intense feature corresponds to the parent ion (C6H6+), and other significative ion fragment peaks were identified as C4H2+, C5H5+, C2H6+, C3H6+, C2H2+, C5+, As described in Section 4, due to the specific anion formation process in the hollow cathode discharge, the time (mass) resolution was not enough to fully resolve each single fragment ion produced, but allowed distinguishing different fragment series clearly characterised by the number of carbon atoms constituting each group of cations. Nonetheless, using a gaussian fitting analysis procedure, we could identify the mass of the fragments that mainly contributed to each fragment group. For the anion impact energy shown in Figure 3 (850 eV), the most intense feature corresponds to the parent ion (C6H6+), and other significative ion fragment peaks were identified as C4H2+, C5H5+, C2H6+, C3H6+, C2H2+, C5+, As described in Section 4, due to the specific anion formation process in the hollow cathode discharge, the time (mass) resolution was not enough to fully resolve each single fragment ion produced, but allowed distinguishing different fragment series clearly characterised by the number of carbon atoms constituting each group of cations. Nonetheless, using a gaussian fitting analysis procedure, we could identify the mass of the fragments that mainly contributed to each fragment group. For the anion impact energy shown in Figure 3 (850 eV), the most intense feature corresponds to the parent ion (C6H6+), and other significative ion fragment peaks were identified as C4H2+, C5H5+, C2H6+, C3H6+, C2H2+, C5+, As described in Section 4, due to the specific anion formation process in the hollow cathode discharge, the time (mass) resolution was not enough to fully resolve each single fragment ion produced, but allowed distinguishing different fragment series clearly characterised by the number of carbon atoms constituting each group of cations. Nonetheless, using a gaussian fitting analysis procedure, we could identify the mass of the fragments that mainly contributed to each fragment group. For the anion impact energy shown in Figure 3 (850 eV), the most intense feature corresponds to the parent ion (C6H6+), and other significative ion fragment peaks were identified as C4H2+, C5H5+, C2H6+, C3H6+, C2H2+, C5+, As described in Section 4, due to the specific anion formation process in the hollow cathode discharge, the time (mass) resolution was not enough to fully resolve each single fragment ion produced, but allowed distinguishing different fragment series clearly characterised by the number of carbon atoms constituting each group of cations. Nonetheless, using a gaussian fitting analysis procedure, we could identify the mass of the fragments that mainly contributed to each fragment group. For the anion impact energy shown in Figure 3 (850 eV), the most intense feature corresponds to the parent ion (C6H6+), and other significative ion fragment peaks were identified as C4H2+, C5H5+, C2H6+, C3H6+, C2H2+, C5+, ); ); ); ); ); ); ); ); fit sum described Section 4, to the specific anion process the hollow cathode discharge, the time resolution was not enough to fully each single ion distinguishing series characterised by the number of carbon atoms constituting each group of cations. Nonetheless, a gaussian fitting procedure, we could identify mass the fragments mainly to fragment anion energy shown in eV), the most to the parent ion and other ion fragment were identified C5H5+, C2H2+, C5+, CH4+, C+ and H/H2+ (in decreasing order of their relative intensities). Note that some fea-= 78) intensity.); 50 ( using a gaussian fitting analysis procedure, we could identify the mass of the fragments 12 (⎯ 16 (); ); 110 (⎯ (---). As in due to specific anion formation process in the time (mass) fully resolve ion distinguishing fragment series clearly by of carbon atoms constituting of analysis could the of the that contributed each For energy 3 (850 intense feature corresponds ion fragment identified C4H2+, C2H6+, C3H6+, C2H2+, C+ and H/H2+ (in of relative intensities). Note tures corresponding to ions the parent ion *m*/*z* > 78 u) also appear in mass spectrum. The of heavy complexes can only by the of oxygen molecules the generated fragments, in O](m = and = 110 The mechanisms by which abducts were investigated in a recent with be [16]. the study formation of *m*/< 78 is the fragmentation induced beam to an beam in similar collision conditions. As Section experimental arrangement an electron the TOF spectrometer used species of generated 4 shows the fragmentation spectrum by eV anion (same shown in Figure 3) together with induced fragmentation mass 850 eV spectra are to the *z* ); ); 32 ); 42 ); 50 ); 60 ); 65 ); 78 ); 94 ); ); Section in cathode resolve each fragment but allowed different characterised by the number of carbon atoms constituting each group of cations. Nonetheless, using a fitting analysis procedure, we of that mainly the anion impact Figure most parent and significative were as CH4+, C+ and H/H2+ (in decreasing order of their relative intensities). Note that some feaduced in experimental incorporated an normal the anion front of the TOF spectrometer used to analyse ions species of the generated fragments. Figure shows (same that shown in 3) together with the generated are normalised = ); 78 ( fragment acterised number group using CH4+, feawith its theoretical justification can be found in Ref. [16]. We focused the present study on compare front the that ); 94 ( of by number atoms each group Nonetheless, on 4, spectrometer fragments. ); 110 ( formation cathode discharge, the time (mass) resolution was not enough to fully resolve each single fragment ion produced, but allowed distinguishing different fragment series clearly charthe mass the Figure 3 (850 eV), the most intense feature corresponds to the parent ion (C6H6+), and other significative ion fragment peaks were identified as C4H2+, C5H5+, C2H6+, C3H6+, C2H2+, C5+, CH4+, C+ and H/H2+ (in decreasing order of their relative intensities). Note that some feaeV = 78) intensity.); fit sum ( 26 enough to single by the number atoms each group Nonetheless, to H/H2+ order of relative Note feafound in of the used to collisions spectrum ).It is interesting to compare the fragmentation induced by the anion beam to that produced by an electron beam in similar collision conditions. As described in Section 4, the experimental arrangement incorporated an electron gun normal to the anion beam, just in front of the TOF spectrometer used to analyse ions species of the generated fragments. Figure 4 shows the cationic fragmentation spectrum induced by 850 eV anion collisions (same as that shown in Figure 3) together with the induced fragmentation mass spectrum generated by an 850 eV electron beam. Both spectra are normalised to the parent ion (*m*/*z* = 78) intensity.

significative ion fragment peaks were identified as C4H2+, C5H5+, C2H6+, C3H6+, C2H2+, C5+, CH4+, C+ and H/H2+ (in decreasing order of their relative intensities). Note that some features corresponding to ions heavier than the parent ion (*m*/*z* > 78 u) also appear in the CH4+, C+ and H/H2+ (in decreasing order of their relative intensities). Note that some features corresponding to ions heavier than the parent ion (*m*/*z* > 78 u) also appear in the mass spectrum. The formation of these heavy complexes can only be explained by the CH4+, C+ and H/H2+ (in decreasing order of their relative intensities). Note that some features corresponding to ions heavier than the parent ion (*m*/*z* > 78 u) also appear in the mass spectrum. The formation of these heavy complexes can only be explained by the CH4+, C+ and H/H2+ (in decreasing order of their relative intensities). Note that some features corresponding to ions heavier than the parent ion (*m*/*z* > 78 u) also appear in the mass spectrum. The formation of these heavy complexes can only be explained by the CH4+, C+ and H/H2+ (in decreasing order of their relative intensities). Note that some features corresponding to ions heavier than the parent ion (*m*/*z* > 78 u) also appear in the mass spectrum. The formation of these heavy complexes can only be explained by the CH4+, C+ and H/H2+ (in decreasing order of their relative intensities). Note that some features corresponding to ions heavier than the parent ion (*m*/*z* > 78 u) also appear in the mass spectrum. The formation of these heavy complexes can only be explained by the corresponding to ions heavier than the (> 78 u) also the spectrum. The formation of heavy the aggregation of some of [C6H6 + O](m 94 and [C6H6 + O2] (m = u). mechanisms these are generated study, and the experimental together its theoretical justification be found in [16]. We present on were lighter than the ion, i.e., *z* < 78 u. tures corresponding to ions heavier than the parent ion (*m*/*z* > 78 u) also appear in the tures heavier than parent ion (*m*/*z* appear the mass formation these can be aggregation molecules to fragments, + 94 u). The which generated were investigated and the evidence together with can be [16]. the present study the cationic fragments that were the parent i.e., *m*/*z* u.to compare the induced the anion prothese + O](m = 94 u) and [C6H6 + O2] (m = 110 u). The mechanisms by which these abducts are generated were investigated in a recent study, and the experimental evidence together A close inspection of Figure 4 shows that superoxide anion projectiles produced a higher fragmentation pattern relative to electrons as projectiles. At 850 eV, 60% of the electron impact ionization corresponded to the formation of the parent ion, while in the case of O2 −,

aggregation of oxygen molecules to some of the generated fragments, in particular [C6H6 + O](m = 94 u) and [C6H6 + O2] (m = 110 u). The mechanisms by which these abducts are

aggregation of oxygen molecules to some of the generated fragments, in particular [C6H6 + O](m = 94 u) and [C6H6 + O2] (m = 110 u). The mechanisms by which these abducts are

aggregation of oxygen molecules to some of the generated fragments, in particular [C6H6 + O](m = 94 u) and [C6H6 + O2] (m = 110 u). The mechanisms by which these abducts are

aggregation of oxygen molecules to some of the generated fragments, in particular [C6H6 + O](m = 94 u) and [C6H6 + O2] (m = 110 u). The mechanisms by which these abducts are

aggregation of oxygen molecules to some of the generated fragments, in particular [C6H6 + O](m = 94 u) and [C6H6 + O2] (m = 110 u). The mechanisms by which these abducts are

with its theoretical justification can be found in Ref. [16]. We focused the present study on the formation of cationic fragments that were lighter than the parent ion, i.e., *m*/*z* < 78 u. It is interesting to compare the fragmentation induced by the anion beam to that produced by an electron beam in similar collision conditions. As described in Section 4, the experimental arrangement incorporated an electron gun normal to the anion beam, just in front of the TOF spectrometer used to analyse ions species of the generated fragments. Figure 4 shows the cationic fragmentation spectrum induced by 850 eV anion collisions (same as that shown in Figure 3) together with the induced fragmentation mass spectrum generated by an 850 eV electron beam. Both spectra are normalised to the parent ion (*m*/*z*

with its theoretical justification can be found in Ref. [16]. We focused the present study on the formation of cationic fragments that were lighter than the parent ion, i.e., *m*/*z* < 78 u. It is interesting to compare the fragmentation induced by the anion beam to that produced by an electron beam in similar collision conditions. As described in Section 4, the experimental arrangement incorporated an electron gun normal to the anion beam, just in front of the TOF spectrometer used to analyse ions species of the generated fragments. Figure 4 shows the cationic fragmentation spectrum induced by 850 eV anion collisions (same as that shown in Figure 3) together with the induced fragmentation mass spectrum generated by an 850 eV electron beam. Both spectra are normalised to the parent ion (*m*/*z*

with its theoretical justification can be found in Ref. [16]. We focused the present study on the formation of cationic fragments that were lighter than the parent ion, i.e., *m*/*z* < 78 u. It is interesting to compare the fragmentation induced by the anion beam to that produced by an electron beam in similar collision conditions. As described in Section 4, the experimental arrangement incorporated an electron gun normal to the anion beam, just in front of the TOF spectrometer used to analyse ions species of the generated fragments. Figure 4 shows the cationic fragmentation spectrum induced by 850 eV anion collisions (same as that shown in Figure 3) together with the induced fragmentation mass spectrum generated by an 850 eV electron beam. Both spectra are normalised to the parent ion (*m*/*z*

It interesting by anion that by an beam similar conditions. described 4, the arrangement incorporated gun normal the anion beam, just in front of the TOF spectrometer used to analyse ions species of the generated fragments. 4 the cationic induced by 850 anion collisions

with its theoretical justification can be found in Ref. [16]. We focused the present study on the formation of cationic fragments that were lighter than the parent ion, i.e., *m*/*z* < 78 u.Figure 4 shows the cationic fragmentation spectrum induced by 850 eV anion collisions

formation duced by an electron beam in similar collision conditions. As described in Section 4, the experimental arrangement incorporated an electron gun normal to the anion beam, just in front

as the induced fragmentation mass spectrum generated by an 850 eV electron beam. Both spectra normalised to parent ion (*m*/*z*

with its theoretical justification can be found in Ref. [16]. We focused the present study on the formation of cationic fragments that were lighter than the parent ion, i.e., *m*/*z* < 78 u. It is interesting to compare the fragmentation induced by the anion beam to that produced by an electron beam in similar collision conditions. As described in Section 4, the experimental arrangement incorporated an electron gun normal to the anion beam, just in front of the TOF spectrometer used to analyse ions species of the generated fragments. Figure 4 shows the cationic fragmentation spectrum induced by 850 eV anion collisions (same as that shown in Figure 3) together with the induced fragmentation mass spectrum generated by an 850 eV electron beam. Both spectra are normalised to the parent ion (*m*/*z*

with its theoretical justification can be found in Ref. [16]. We focused the present study on the formation of cationic fragments that were lighter than the parent ion, i.e., *m*/*z* < 78 u. It is interesting to compare the fragmentation induced by the anion beam to that produced by an electron beam in similar collision conditions. As described in Section 4, the experimental arrangement incorporated an electron gun normal to the anion beam, just in front of the TOF spectrometer used to analyse ions species of the generated fragments. Figure 4 shows the cationic fragmentation spectrum induced by 850 eV anion collisions (same as that shown in Figure 3) together with the induced fragmentation mass spectrum generated by an 850 eV electron beam. Both spectra are normalised to the parent ion (*m*/*z*

mass spectrum. The formation of these heavy complexes can only be explained by the

generated were investigated in a recent study, and the experimental evidence together with its theoretical justification can be found in Ref. [16]. We focused the present study on the formation of cationic fragments that were lighter than the parent ion, i.e., *m*/*z* < 78 u.

It is interesting to compare the fragmentation induced by the anion beam to that produced by an electron beam in similar collision conditions. As described in Section 4, the experimental arrangement incorporated an electron gun normal to the anion beam, just in front of the TOF spectrometer used to analyse ions species of the generated fragments. Figure 4 shows the cationic fragmentation spectrum induced by 850 eV anion collisions (same as that shown in Figure 3) together with the induced fragmentation mass spectrum generated by an 850 eV electron beam. Both spectra are normalised to the parent ion (*m*/*z*

Ref.

= 78) intensity.

= 78) intensity.

= 78) intensity.

= 78) intensity.

= 78) intensity.

= 78) intensity.

it represented only 32.6% of the total ion yield. Thus, a clear enhancement of the target's fragmentation induced by the anion beam was noted. In general, the relative intensity of the observed peaks obtained with the superoxide anion beam increased with respect to those obtained with the electron beam, but in particular, those with *m*/*z* = 65, 50 and 42 were especially enhanced, showing also a double-peak structure. This seemed to indicate that losses of CH, C2H4 and C3 radicals from the benzene ring were favoured in anion collisions. *Int. J. Mol. Sci.* **2022**, *23*, x FOR PEER REVIEW 6 of 15 *Int. J. Mol. Sci.* **2022**, *23*, x FOR PEER REVIEW 6 of 15

*Int. J. Mol. Sci.* **2022**, *23*, x FOR PEER REVIEW 6 of 15

**Figure 4.** Positive ion-induced fragmentation by the superoxide anion beam (⎯) and the electron beam (⎯), respectively, both at 850 eV impact energy. **Figure 4.** Positive ion-induced fragmentation by the superoxide anion beam ( **Figure 4.** Positive ion-induced fragmentation by the superoxide anion beam (⎯) and the electron beam (⎯), respectively, both at 850 eV impact energy. ) and the electronbeam ( **Figure 4.** Positive ion-induced fragmentation by the superoxide anion beam (⎯) and the electron beam (⎯), respectively, both at 850 eV impact energy. ), respectively, both at 850 eV impact energy.

A close inspection of Figure 4 shows that superoxide anion projectiles produced a higher fragmentation pattern relative to electrons as projectiles. At 850 eV, 60% of the electron impact ionization corresponded to the formation of the parent ion, while in the case of O2−, it represented only 32.6% of the total ion yield. Thus, a clear enhancement of the target's fragmentation induced by the anion beam was noted. In general, the relative intensity of the observed peaks obtained with the superoxide anion beam increased with respect to those obtained with the electron beam, but in particular, those with *m*/*z* = 65, 50 and 42 were especially enhanced, showing also a double-peak structure. This seemed to indicate that losses of CH, C2H4 and C3 radicals from the benzene ring were favoured in anion collisions. In order to further our knowledge on the collision dynamics governing such cation formation, molecular dynamics calculations using the Density Functional Theory (DFT) were performed (see Section 4 for further details). In our previous work [16], we proposed a collision model with the formation of a stable complex in which O2 molecules remained bonded to the ionized benzene, [C6H6–O2]+. Non-associative collisions, where the O2 molecule did not remain bonded to benzene, might also occur. Therefore, we considered both A close inspection of Figure 4 shows that superoxide anion projectiles produced a higher fragmentation pattern relative to electrons as projectiles. At 850 eV, 60% of the electron impact ionization corresponded to the formation of the parent ion, while in the case of O2−, it represented only 32.6% of the total ion yield. Thus, a clear enhancement of the target's fragmentation induced by the anion beam was noted. In general, the relative intensity of the observed peaks obtained with the superoxide anion beam increased with respect to those obtained with the electron beam, but in particular, those with *m*/*z* = 65, 50 and 42 were especially enhanced, showing also a double-peak structure. This seemed to indicate that losses of CH, C2H4 and C3 radicals from the benzene ring were favoured in anion collisions. In order to further our knowledge on the collision dynamics governing such cation formation, molecular dynamics calculations using the Density Functional Theory (DFT) were performed (see Section 4 for further details). In our previous work [16], we proposed a collision model with the formation of a stable complex in which O2 molecules remained bonded to the ionized benzene, [C6H6–O2]+. Non-associative collisions, where the O2 molecule did not remain bonded to benzene, might also occur. Therefore, we considered both situations and we ran two sets of trajectory calculations. The first one assumed chemical interaction and thus formation of a stable [C6H6–O2]+ molecule; therefore, these simula-A close inspection of Figure 4 shows that superoxide anion projectiles produced a higher fragmentation pattern relative to electrons as projectiles. At 850 eV, 60% of the electron impact ionization corresponded to the formation of the parent ion, while in the case of O2−, it represented only 32.6% of the total ion yield. Thus, a clear enhancement of the target's fragmentation induced by the anion beam was noted. In general, the relative intensity of the observed peaks obtained with the superoxide anion beam increased with respect to those obtained with the electron beam, but in particular, those with *m*/*z* = 65, 50 and 42 were especially enhanced, showing also a double-peak structure. This seemed to indicate that losses of CH, C2H4 and C3 radicals from the benzene ring were favoured in anion collisions. In order to further our knowledge on the collision dynamics governing such cation formation, molecular dynamics calculations using the Density Functional Theory (DFT) were performed (see Section 4 for further details). In our previous work [16], we proposed a collision model with the formation of a stable complex in which O2 molecules remained bonded to the ionized benzene, [C6H6–O2]+. Non-associative collisions, where the O2 molecule did not remain bonded to benzene, might also occur. Therefore, we considered both situations and we ran two sets of trajectory calculations. The first one assumed chemical interaction and thus formation of a stable [C6H6–O2]+ molecule; therefore, these simula-In order to further our knowledge on the collision dynamics governing such cation formation, molecular dynamics calculations using the Density Functional Theory (DFT) were performed (see Section 4 for further details). In our previous work [16], we proposed a collision model with the formation of a stable complex in which O2 molecules remained bonded to the ionized benzene, [C6H6–O2] + . Non-associative collisions, where the O2molecule did not remain bonded to benzene, might also occur. Therefore, we considered both situations and we ran two sets of trajectory calculations. The first one assumed chemical interaction and thus formation of a stable [C6H6–O2] + molecule; therefore, these simulations started with the structure shown in Figure 5a. The starting point of the dynamics in the second one was a weakly bonded van der Waals complex [C6H6 ··· O2] + , shown in Figure 5b. Thus, both situations kept the same number of atoms but with a quite different bonding strength. Both initial structures were optimized and, thus, they were minima of the potential energy surfaces. The final results were obtained by computing statistics over the molecular dynamics simulations: 100 trajectories for each structure and each excitation energy value. Note that the excitation energy was randomly redistributed among the nuclear degrees of freedom in each trajectory. We considered that a fragment was created when the atoms forming this species were separated by at least 3 Å from other fragments in the last point of the trajectory.

situations and we ran two sets of trajectory calculations. The first one assumed chemical interaction and thus formation of a stable [C6H6–O2]+ molecule; therefore, these simulations started with the structure shown in Figure 5a. The starting point of the dynamics in the second one was a weakly bonded van der Waals complex [C6H6 ··· O2]+, shown in Figure 5b. Thus, both situations kept the same number of atoms but with a quite different bonding strength. Both initial structures were optimized and, thus, they were minima of

tions started with the structure shown in Figure 5a. The starting point of the dynamics in the second one was a weakly bonded van der Waals complex [C6H6 ··· O2]+, shown in Figure 5b. Thus, both situations kept the same number of atoms but with a quite different bonding strength. Both initial structures were optimized and, thus, they were minima of the potential energy surfaces. The final results were obtained by computing statistics over the molecular dynamics simulations: 100 trajectories for each structure and each excitation

tions started with the structure shown in Figure 5a. The starting point of the dynamics in the second one was a weakly bonded van der Waals complex [C6H6 ··· O2]+, shown in Figure 5b. Thus, both situations kept the same number of atoms but with a quite different bonding strength. Both initial structures were optimized and, thus, they were minima of the potential energy surfaces. The final results were obtained by computing statistics over the molecular dynamics simulations: 100 trajectories for each structure and each excitation

clear degrees of freedom in each trajectory. We considered that a fragment was created when the atoms forming this species were separated by at least 3 Å from other fragments

clear degrees of freedom in each trajectory. We considered that a fragment was created when the atoms forming this species were separated by at least 3 Å from other fragments

the molecular dynamics simulations: 100 trajectories for each structure and each excitation energy value. Note that the excitation energy was randomly redistributed among the nuclear degrees of freedom in each trajectory. We considered that a fragment was created when the atoms forming this species were separated by at least 3 Å from other fragments

In the simulated mass spectra in Figure 5, we included the percentage of trajectories where a given fragment appeared. In these spectra, we grouped all fragments with a different number of H atoms in a single peak, e.g., C6HX included trajectories in which C6H6,

In the simulated mass spectra in Figure 5, we included the percentage of trajectories where a given fragment appeared. In these spectra, we grouped all fragments with a different number of H atoms in a single peak, e.g., C6HX included trajectories in which C6H6,

In the simulated mass spectra in Figure 5, we included the percentage of trajectories where a given fragment appeared. In these spectra, we grouped all fragments with a different number of H atoms in a single peak, e.g., C6HX included trajectories in which C6H6,

in the last point of the trajectory.

in the last point of the trajectory.

in the last point of the trajectory.

higher than for the weakly bonded case.

corroborating the associative mechanism proposed in Ref. [16].

C6H5, C6H4, etc. molecules were produced. The spectra corresponding to the weakly bonded [C6H6 ··· O2]+ were dominated by a single peak that corresponded to C6HX+ molecules. Further fragmentation was observed only for Eexc = 40 eV, in which a slightly amount of C5HX+, C4HX+ and C3HX+ could be noted. In the case of [C6H6–O2]+, a much richer spectrum was obtained, where oxygenated species were of particular importance: C6HXO2+ and C6HXO+, together with C6HX+, were the most prominent peaks at low excitation energies. At the highest excitation energy here considered, mono-oxygenated fragments, C5HXO+, C4HXO+, C3HXO+, gained in relative intensity. It is worth stressing that for [C6H6–O2]+, the relative intensity of non-oxygenated species, i.e., C5HX+, C4HX+, and C3HX+, was much

In the experimental mass spectrum, we could also discern double-peak structures, which we assigned to oxygenated and non-oxygenated species, e.g., the double-peak structure shown in the region 40–50 u, corresponded to C3HX and C2HXO. Therefore, by only considering the fragmentation of [C6H6–O2]+, these double-peak structures can be explained. A comparison between the experimental measurements and the theoretical simulations is shown in Figure 6. For this purpose, we added both theoretical spectra obtained at 40 eV, i.e., we considered that both possibilities might occur, i.e., ionization and excitation of benzene (i) in a non-reactive collision and (ii) with formation of stable oxygenated

**Figure 5.** Simulated mass spectra for (**a**) [C6H6–O2]+ and (**b**) [C6H6 ··· O2]+ at different excitation energies derived from the molecular dynamics simulations. **Figure 5.** Simulated mass spectra for (**a**) [C6H6–O2 ] + and (**b**) [C6H6 ··· O2 ] + at different excitation energies derived from the molecular dynamics simulations.

In the simulated mass spectra in Figure 5, we included the percentage of trajectories where a given fragment appeared. In these spectra, we grouped all fragments with a different number of H atoms in a single peak, e.g., C6HX included trajectories in which C6H6, C6H5, C6H4, etc. molecules were produced. The spectra corresponding to the weakly bonded [C6H6 ··· O2] + were dominated by a single peak that corresponded to C6HX + molecules. Further fragmentation was observed only for Eexc = 40 eV, in which a slightly amount of C5HX + , C4HX + and C3HX + could be noted. In the case of [C6H6–O2] + , a much richer spectrum was obtained, where oxygenated species were of particular importance: C6HXO2 + and C6HXO+ , together with C6HX + , were the most prominent peaks at low excitation energies. At the highest excitation energy here considered, mono-oxygenated fragments, C5HXO+ , C4HXO+ , C3HXO+ , gained in relative intensity. It is worth stressing that for [C6H6–O2] + , the relative intensity of non-oxygenated species, i.e., C5HX + , C4HX + , and C3HX + , was much higher than for the weakly bonded case.

In the experimental mass spectrum, we could also discern double-peak structures, which we assigned to oxygenated and non-oxygenated species, e.g., the double-peak structure shown in the region 40–50 u, corresponded to C3HX and C2HXO. Therefore, by only considering the fragmentation of [C6H6–O2] + , these double-peak structures can be explained. A comparison between the experimental measurements and the theoretical simulations is shown in Figure 6. For this purpose, we added both theoretical spectra obtained at 40 eV, i.e., we considered that both possibilities might occur, i.e., ionization and excitation of benzene (i) in a non-reactive collision and (ii) with formation of stable oxygenated species. A qualitative agreement was obtained, showing the validity of the model and corroborating the associative mechanism proposed in Ref. [16].

**Figure 6.** Comparison of experimental (collision energy = 850 eV) and theoretical (internal excitation **Figure 6.** Comparison of experimental (collision energy = 850 eV) and theoretical (internal excitation energy = 40 eV) fragmentation spectra.

#### energy = 40 eV) fragmentation spectra. *2.3. Relative Partial and Total Ionization Cross Sections of Benzene by O2* − *Impact*

*2.3. Relative Partial and Total Ionization Cross Sections of Benzene by O2− Impact*  The relative intensities were normalised to the primary beam intensity and, according to Equation (2) (see Section 4, they accounted for the target gas pressure and geometry of the ion extraction region. However, as the ratio between the ion extracted beam and the actual primary beam intensity in the interaction region was not known, we could only provide relative values of the fragment yields. The energy dependence of these yields for The relative intensities were normalised to the primary beam intensity and, according to Equation (2) (see Section 4, they accounted for the target gas pressure and geometry of the ion extraction region. However, as the ratio between the ion extracted beam and the actual primary beam intensity in the interaction region was not known, we could only provide relative values of the fragment yields. The energy dependence of these yields for the identified cation fragments is shown in Figure 7 for the whole impact energy range considered in this study (160–900 eV).

the identified cation fragments is shown in Figure 7 for the whole impact energy range considered in this study (160–900 eV). The fragment cation intensity distributions shown in Figure 3 were analysed as a function of the incident energy. For a given m/z fragment, its production cross section was The fragment cation intensity distributions shown in Figure 3 were analysed as a function of the incident energy. For a given m/z fragment, its production cross section was given by the ratio between its detected ion intensity and the primary anion intensity divided by the target molecular density and the length of the ion extraction region (see Section 4 for technical details).

given by the ratio between its detected ion intensity and the primary anion intensity divided by the target molecular density and the length of the ion extraction region (see Section 4 for technical details). Following this procedure, we could in principle derive the absolute values of those partial ionisation cross sections. However, as already mentioned, we did not accurately know the ratio between the cation and the primary anion currents in the interaction region Following this procedure, we could in principle derive the absolute values of those partial ionisation cross sections. However, as already mentioned, we did not accurately know the ratio between the cation and the primary anion currents in the interaction region and therefore we could only report here on their relative cross section values. The error bars shown in Figure 7 correspond to the combination in quadrature of all the known uncertainty sources (ion intensity statistical uncertainties and those derived from the gas pressure and temperature determination, see Section 4 for details).

and therefore we could only report here on their relative cross section values. The error bars shown in Figure 7 correspond to the combination in quadrature of all the known uncertainty sources (ion intensity statistical uncertainties and those derived from the gas pressure and temperature determination, see Section 4 for details). The total ionisation cross sections (TICS) derived by adding the intensities of all detected cationic species generated by the anion–molecule collisions considered in this study are shown in Figure 8. In such figure, the TICS present a prominent feature from 550 eV to 800 eV. Note that these species included the heavier adducts (*m*/*z* = 94–95, *m*/*z* = 110), whose formation process is described in Ref. [16]. According to the fragmentation pattern shown in Figure 7 and the above theoretical justification, we deduced that this prominent peak was mainly due to the fragmentation of these heavier adducts which mainly formed for impact energies from 550 to 800 eV. The dashed red line in Figure 6 represents the contribution to the TICS of the fragments coming from the dissociation of the parent ion, i.e., the TICS values we would obtain if these adducts did not form.

**Figure 7.** Relative cation intensities for *m*/*z* 78 u fragments induced by collisions with oxygen anions in the impact energy range (160–900 eV). See legend for the different cation species **Figure 7.** Relative cation intensities for *m*/*z* 78 u fragments induced by collisions with oxygen anions in the impact energy range (160–900 eV). See legend for the different cation species. *Int. J. Mol. Sci.* **2022**, *23*, x FOR PEER REVIEW 10 of 15

The total ionisation cross sections (TICS) derived by adding the intensities of all de-

**Figure 8.** Relative total ionisation cross sections (TICS) accounting for all the cationic species generated by single O2—–C6H6 collisions for impact energies ranging from 160 up to 900 eV. **Figure 8.** Relative total ionisation cross sections (TICS) accounting for all the cationic species generated by single O2 —–C6H6 collisions for impact energies ranging from 160 up to 900 eV.

The energy dependence of the TEDCS showed a quite flat behaviour except for two relative maxima and a local minimum, cross section values which were not clearly defined