Quantum-state-selected integral cross sections for the charge transfer collision of O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1–2; J⁺) [O₂⁺(X²Π_g3/2,1/2: v⁺ = 22–23; J⁺)] + Ar at center-of-mass collision energies of 0.05–10.00 eV

Abstract

By employing the sequential electric field pulsing scheme for vacuum ultraviolet (VUV) laser pulsed field ionization-photoion (PFI-PI) detection, we have successfully recorded the spin–orbit and rovibronic state resolved VUV-PFI-PI spectra for O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: ν⁺ = 0–2; J⁺) and O₂⁺(X²Π_g3/2,1/2: ν⁺ = 21–23; J⁺), indicating that O₂⁺(a⁴Π_u) and O₂⁺(X²Π_g) ions in these spin–orbit and rovibronic states can be prepared for ion–molecule collision studies. The present experiment is concerned with the measurement of absolute integral cross sections (σ's) of the charge transfer reactions, O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: ν⁺ = 1, 2; J⁺) [O₂⁺(X²Π_g1/2,3/2: ν⁺ = 22, 23)] + Ar → Ar⁺ + O₂. The fact that the O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: ν⁺ = 1) and O₂⁺(X²Π_g3/2,1/2: ν⁺ = 22) [O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: ν⁺ = 2) and O₂⁺(X²Π_g3/2,1/2: ν⁺ = 23)] states are in close energy resonance, makes these reactions ideal model systems for investigating the energy resonance and Franck–Condon factor (FCF) effects on the charge transfer reactivity of O₂⁺. The σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: ν⁺ = 1, 2) values are found to be about ten-fold higher than the σ(X²Π_g3/2,1/2: ν⁺ = 22, 23) values at E_cm = 0.05–10.00 eV, indicating that the FCFs play a predominant role in promoting these charge transfer reactions. The present ion–molecule reaction study also shows that σ(a⁴Π_u) depends strongly on the spin–orbit as well as the vibrational states with the order: σ(a⁴Π_u: v⁺ = 2) > σ(a⁴Π_u: v⁺ = 1), and σ(a⁴Π_u5/2: v⁺) > σ(a⁴Π_u3/2: v⁺) > σ(a⁴Π_u1/2: v⁺) > σ(a⁴Π_u−1/2: v⁺), where v⁺ = 1 and 2. The high σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1, 2) values, along with their decreasing trend with increasing E_cm, are consistent with those expected for a long range charge transfer mechanism. However, the low σ(X²Π_g3/2,1/2: ν⁺ = 22, 23) values and the lack of E_cm-dependence observed in the E_cm range of 0.05–10.00 eV point to the involvement of short-range collision dynamics.

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I. Introduction

State-selected studies of ion–molecule collisions have played an important role in the fundamental understanding of chemical reaction dynamics.^1–4 The most outstanding merit of ion-neutral reaction studies is that ions in metastable and long-lived quantum states, which cannot be prepared by direct photoexcitation of ions, can be readily generated by single-photon vacuum ultraviolet (VUV) or two-color laser photoionization schemes.^5–12 This capability makes possible the systematic examination of ion reactivity as a function of not only center-of-mass collision energy (E_cm), but also internal spin–orbit, rotational, vibrational, and electronic states of ions.

The photoionization techniques required for ion-state preparations depend on the properties of the VUV light source used.⁸ It has been well established that the use of a pseudo-continuous VUV synchrotron source requires the application of the photoelectron–photoion coincidence method for state-selected studies, whereas the use of a pulsed VUV laser source necessitates the application of the PFI-PI or MATI (mass analyzed threshold ion)¹³ detection scheme.^8,14–16

In early state-selected ion–molecule experiments using a continuous VUV discharge source, Koyano and coworkers applied the threshold electron-secondary-ion coincidence (TESICO) method and have examined the E_cm and vibrational and electronic state effects on an array of prototypical ion–molecule reaction systems, including the charge transfer reactions, O₂⁺(a⁴Π_u: v⁺ = 0–7) [O₂⁺(X²Π_g: v⁺ = 19, 20)] + Ar → Ar⁺ + O₂.^17,18 Limited by the TPE energy resolution of ≈30 meV (full-width at half-maximum, FWHM), the TESICO study was not able to investigate the rotational and spin–orbit state dependences on these charge transfer reactions.

Taking advantage of the dark-gap existing in the synchrotron ring period at the Advanced Light Source, we have previously introduced the dark-gap VUV-pulsed field ionization-photoelectron (VUV-PFI-PE) scheme for high-resolution photoelectron measurements.^19,20 This scheme was further developed into the VUV-PFI-PE-photoion coincidence (VUV-PFI-PEPICO) method²¹ for state-selected unimolecular dissociation studies and the VUV-PFI-PE-secondary ion coincidence (VUV-PFI-PESICO) technique²² for state-selected bimolecular ion–molecule reaction measurements. The dark-gap VUV-PFI-PE method has demonstrated a practical energy resolution of 5–8 cm⁻¹ (FWHM). The successful application of the synchrotron based VUV-PFI-PESICO method for rovibrational-state selected σ-measurements of a series of proton transfer reactions, H₂⁺(X²Σ_g⁺: v⁺ = 0–15; N⁺ = 1) + He → HeH⁺ + H;²³ HD⁺(X²Σ⁺: v⁺ = 0–15; N⁺ = 1) + He → HeH⁺ (HeD⁺) + D(H);²⁴ H₂⁺(X²Σ_g⁺: v⁺ = 0–17; N⁺ = 1) + Ne → NeH⁺ + H;²⁵ and H₂⁺(X²Σ_g⁺: v⁺ = 0–17; N⁺ = 1) + Ar → ArH⁺ + H,²⁶ can be taken as strong evidence of the superior energy resolution and detection sensitivity achieved by the VUV synchrotron based PFI-PESICO detection approach. Nevertheless, the practical application of the VUV synchrotron based PFI-PEPISICO and TPESICO schemes remains very challenging as limited by the formidable data accumulation time required to achieve acceptable signal-to-noise ratios for quantum-state-selected σ-measurements. For more complex ion–molecule reactions, it is highly desirable to develop an alternative detection scheme with higher detection sensitivity for quantum-state-selected ion–molecule collision studies.

The recent development of the VUV laser PFI-PI ion source, along with its implementation with the double-quadrupole–double-octopole (DQDO) mass spectrometer, represents a significant experimental advance for quantum-state-selected ion–molecule reaction studies. The array of successful state-selected ion–molecule reaction studies^27–37 has shown that the VUV laser PFI-PI-DQDO approach achieves exceptional detection sensitivity and energy resolution unmatched by the VUV-TPESICO and VUV-PFI-PESICO schemes, allowing not only vibrational but also rotational state selections for ion–molecule reactions of H₂O⁺(X²B₁: v₁⁺v₂⁺v₃⁺; N_Ka+Kc+⁺) + H₂ (D₂, HD, and CO),^27–32 N₂⁺(X²Σ_g⁺: v⁺ = 0–2, N⁺ = 0–9) + Ar (CH₄ and C₂H₂),^33–36 and H₂⁺(X²Σ_g⁺: v⁺ = 1–3, N⁺ = 0–3) + Ne,³⁷ covering the E_cm range from thermal energies (0.03 eV) to 10.00 eV. Simple signal-to-noise analysis also shows that the PFI-PI and PFI-PI-DQDO methods are superior to the photoelectron–photoion coincidence schemes. In a photoelectron–photoion coincidence experiment, the coincidence-counting rate is proportional to the product of the detection efficiency for photoelectrons and that for photoions.⁵ The low photoelectron detection efficiency often makes coincidence experiments very challenging. The PFI-PI approach does not involve the detection of photoelectrons. The fact that prompt ions are completely rejected before reactant PFI-PI ions enter the reaction gas cell makes coincidence background corrections unnecessary.

The present study is concerned with the σ measurement of reactions (1) and (2) using the VUV laser PFI-PI-DQDO approach.

O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1, 2; J⁺) + Ar → Ar⁺ + O₂, (1)

O₂⁺[(X²Π_g3/2,1/2: v⁺ = 22, 23; J⁺)] + Ar → Ar⁺ + O₂. (2)

In addition to examining the v⁺-vibrational and electronic state effects, we have also observed significant spin–orbit-state and E_cm effects on these reactions, which have not been measured previously. Our decision to pursue a more detailed study of reactions (1) and (2) is partly motivated by the availability of highly precise ionization energies (IEs) for the formation of these rovibronic and spin–orbit states, O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 0–2; J⁺) and O₂⁺[(X²Π_g3/2,1/2: v⁺ = 21–23; J⁺)], which have been determined in previous VUV synchrotron and laser based PFI-PE studies.^38,39

Fig. 1 shows the energy level diagram for the reactant states, O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 0–2) + Ar and O₂⁺[(X²Π_g3/2,1/2: v⁺ = 21–23)] + Ar, and the product states, Ar⁺(²P_1/2,3/2) + O₂(X³Σ_g⁻: v = 0–2). The O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 0–2) states are well known metastable states as the radiative decay of these states is spin-disallowed.^40–42 Since O₂ has no dipole moment, the radiative decay of O₂⁺[(X²Π_g3/2,1/2: v⁺ = 21–23)] is also electric dipole disallowed. Thus, the preparation of these long-lived states cannot be made by direct photoexcitation.

Fig. 1 Schematic energy diagram showing the reactant states: O₂⁺(X²Π_g: ν⁺ = 20–23) + Ar (blue levels) and O₂⁺(a⁴Π_u: ν⁺ = 0–2) + Ar (red levels); and the product states: O₂(X²Σ_g⁻: ν = 0–3) + Ar⁺(²P_3/2) (green levels) and O₂(X²Σ_g⁻: ν = 0–3) + Ar⁺(²P_1/2) (black levels).

According to previous charge transfer studies of the [Ar + H₂]⁺ and [Ar + N₂] ion–molecule reaction systems,^1,43,44 where both the forward and backward reaction cross sections were examined, the energy resonance factor was found to be highly important in promoting charge transfer processes. It is clear from the energy diagram of Fig. 1 that both charge transfer reactions (1) and (2) are exothermic, and that O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1) and O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 2) states are in near energy resonance with their respective O₂⁺(X²Π_g3/2,1/2: v⁺ = 22) and O₂⁺(X²Π_g3/2,1/2: v⁺ = 23) states. Thus, reactions (1) and (2) are naturally interesting model reactions for a detailed investigation of the energy resonance factor in charge transfer collisions. Another interesting aspect that can be examined in the present study is the influence of the Franck–Condon factor (FCF) effect for electron capture by the O₂⁺(a⁴Π_u: v⁺ = 1, 2) and O₂⁺(X²Π_g: v⁺ = 22, 23) ions.⁴⁵

II. Experiment

The σ-measurements of reactions (1) and (2) are made using the VUV laser PFI-PI-DQDO ion–molecule reaction apparatus, which has been described previously in detail.³⁴Fig. 2 shows the schematic diagram of the apparatus, aiming to facilitate the description of the general experimental features and procedures used. Briefly, the apparatus consists of three major components, i.e., the tunable VUV laser system, the PFI-PI ion source, and the DQDO mass spectrometer.

Fig. 2 Schematic diagram showing the arrangement of the VUV laser and PFI-PI-DQDO apparatus. Ion lenses E1, I1, and I2 are important elements of the ion source, which are marked in the figure.

The VUV laser radiation was generated by resonance-enhanced four-wave sum-frequency (2ω₁ + ω₂) mixing (as shown in the inset of Fig. 2) using Kr gas in the form of a free jet as the nonlinear medium. The fundamental ω₁ and ω₂ frequencies were generated by two independently tunable dye lasers (Sirah Cobra Stretch), which were pumped by an identical Nd:YAG laser (Quanta Ray PRO-290, 30 Hz) at the third harmonic output (355 nm). The ω₁ output was fixed at 47046.43 cm⁻¹, where 2ω₁ matches the 5p ← 4p resonance transition of Kr at 94092.85 cm⁻¹. An autotracker with a BBO crystal and beam path compensator was used to scan ω₂ in the range of 33 749–36 697 cm⁻¹ to generate the VUV (2ω₁ + ω₂) range (129 750–132 366 cm⁻¹) required for the present experiment. The outputs of the two dye lasers, ω₁ and ω₂, were merged by a dichroic mirror before intersecting with a Kr gas jet in the four-wave mixing chamber. In this experiment, the sum-frequency (2ω₁ + ω₂) along with the ω₁, ω₂, (2ω₁ − ω₂), and 3ω₁ frequencies, entered the photoionization/photoexcitation (PI/PEX) region without passing through any windows or dispersive devices. As shown below, the analysis of the VUV laser PFI-PI spectra for O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 0–2) and O₂⁺(X²Π_g3/2,1/2: v⁺ = 21–23) obtained here shows no background contributions from the unwanted laser frequencies.

The precursor O₂ molecules were introduced into the beam source chamber as a pulsed molecular beam by supersonic expansion through a pulsed valve (operated at 30 Hz) at a stagnation pressure of 35 psi. The O₂ beam traveled along the central axis of the ion lenses of the ion source. After passing through two conical skimmers, the O₂ beam intersected the VUV laser perpendicularly at the PI/PEX center, resulting in excited O₂ molecules in high-n Rydberg states [O₂*(n)], along with the production of O₂⁺ prompt ions by direct photoionization. The most essential elements of the ion source are ion lenses E1, I1, and I2 as marked in Fig. 2. The PI/PEX region is defined by the spacing between lenses E1 and I1, and was maintained field free during VUV laser excitation. After a delay of 100 ns relative to the VUV laser pulse, prompt ions were retarded by a pulsed electric field (2.3 V cm⁻¹, duration = 2.2 μs) applied to lens I1, such that prompt ions were forced to travel in the opposite direction of the O₂ molecular beam. Immediately at the end of the retarding pulsed field, a second pulsed electric field (14.4 V cm⁻¹, duration = 0.76 μs) was applied to lens E1 to field ionize the O₂*(n) species as well as extract the PFI-PIs thus formed out of the ion source. The duration of the second pulsed electric field was set so that all the O₂⁺ PFI-PIs gained the same momentum from the PFI pulsed field before they exited the PI/PEX region. As a result, O₂⁺ PFI-PIs retain the same high kinetic energy resolution or laboratory kinetic energy spread (ΔE_cm) of the O₂ beam achieved in the supersonic expansion.

Fig. 3(a) shows a typical TOF spectrum for O₂⁺ ions formed in the ion source recorded using the microchannel-plate (MCP) ion detector associated with the dc quadrupole ion bender. As expected, the O₂⁺ PFI-PI peak appeared as a fast, narrow TOF peak at 29.5 μs, and the prompt ion peak appeared as a broad TOF structure at >35 μs, indicating that the prompt ions have lower kinetic energies compared to those for the PFI-PIs. Thus, by applying an appropriate dc retarding voltage at ion lens I2 situated between the PFI-PI ion source and the reactant quadrupole mass spectrometer (QMS), we can reject all prompt ions, but transmit all PFI-PIs to the MCP ion detector. Such a scenario is shown by the TOF spectrum of Fig. 3(b), showing only the O₂⁺ PFI-PI peak at 29.5 μs. Here, all other ion lenses along with the reactant QMS were used to optimize the transmission of O₂⁺ PFI-PIs into the rf-octopole ion-guide reaction gas cell, where the charge transfer collision with Ar occurred.

Fig. 3 (a) The TOF spectrum (black curve) for O₂⁺ PFI-PIs and prompt ions observed by means of the MCP ion detector associated with a DC quadrupole ion-bender. By employing the sequential electric field pulsing scheme for PFI-PI detection, we find that the O₂⁺ PFI-PI peak at 29 μs is cleanly separated from the prompt ion peak centered at 40 μs. (b) The TOF spectrum (red curve) for O₂⁺ PFI-PIs shows a single, clean O₂⁺ PFI-PI peak after rejecting the prompt ions by applying a sufficiently high dc potential barrier at lens I2 to block out the prompt ions.

The E_lab of reactant O₂⁺ PFI-PIs is measured with respect to the rf-octopole reaction gas cell, and thus is determined by the retarding potential method, which involves the measurement of the O₂⁺ PFI-PI intensity as a function of dc voltage applied to the rf-octopole ion guide. As an example, we show in Fig. 4 the retarding potential energy curve for the reactant O₂⁺ PFI-PI beam with E_lab = 1.20 ± 0.05 eV, which was determined by the steep drop identified with an error limit of 0.05 eV (FWHM).

Fig. 4 A typical retarding potential energy curve for reactant O₂⁺ PFI-PIs at E_lab = 1.20 ± 0.05 eV measured with respect to the reaction gas cell. The red dashed curve is shown to guide the eyes.

The Ar gas used in this experiment has a quoted purity of 99.999%; and the Ar pressure used in the reaction gas cell was maintained at 1.0 × 10⁻⁴ Torr as monitored by an MKS Baratron. The intensity of O₂⁺ PFI-PIs together with product Ar⁺ ions formed in the reaction gas cell were guided by the rf-octopole to enter the product QMS for the measurements of O₂⁺ and Ar⁺ ion intensities by using the Daly ion detector. As an example, we show in Fig. 5(a) and (b) the TOF spectra for respective O₂⁺ PFI-PIs and charge transfer Ar⁺ ions formed at E_lab = 0.50 eV (or E_cm = 0.28 eV), respectively. These spectra were recorded by using the product QMS and a multichannel scalar (FAST ComTec P7888). We found that the charge transfer channel is the overwhelming product channel of reactions (1) and (2) in the E_cm range of 0.05–10.0 eV. Fig. 5(a) shows that the O₂⁺ PFI-PIs arrived at the Daly detector at ∼240 μs, whereas the product Ar⁺ ions arrived at the ion detector over a wide TOF range of 240–1040 μs as shown in Fig. 5(b). The product Ar⁺ TOF profile appears to be bimodal. This feature possibly corresponds to forward–backward scattered Ar⁺ ions in the center-of-mass frame. Some Ar⁺ ions are expected to be formed with near thermal energies in the laboratory-frame. We note that at lower E_cm, the charge-transfer Ar⁺ ions are often found to cover a TOF range up to 2000 μs. The reactant O₂⁺ and product Ar⁺ ion counts are measured as the respective sums of ion counts covered by the TOF peaks of Fig. 5(a) and (b), respectively. Assuming that the rf-octopole ion guide allows the collection of all product Ar⁺ ions, the absolute integral cross sections were calculated based on the Beer–Lambert law.

Fig. 5 The TOF spectrum (black curve) for (a) reactant O₂⁺ and that (blue curve) for (b) product Ar⁺ ions measured by the Daly-type ion detector of the product QMS. The observed TOF spectra correspond to E_lab = 0.50 eV (or E_cm = 0.28 eV). The spectra show that O₂⁺ PFI-PIs arrived at the Daly detector at ∼240 μs, whereas the product Ar⁺ ions arrived at the ion detector over a wide TOF range of 240–1040 μs, indicative of the formation of Ar⁺ ions at near thermal energies.

As pointed out previously, the absolute integral cross sections determined here are estimated to have error limits of ≤30%. However, the error limits for relative integral cross sections of different reactant quantum states can reach the precision of 3–5%. In addition to absolute integral cross sections, we believe that the relative values for the σ[(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺; J⁺)] and σ(X²Π_g3/2,1/2; v⁺; J⁺) curves obtained by plotting σ as a function of E_cm are reliable experimental measurements for benchmarking theoretical dynamics predictions.

III. Results and discussion

As pointed out above, the present quantum-state-selection study is based on VUV-PFI-PI detection. Thus, the first step of this experiment necessarily involves the measurement and assignment of the VUV-PFI-PI spectra for the ion states of interest. Although the VUV-PFI-PE spectra for O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺; J⁺) and O₂⁺(X²Π_g3/2,1/2; v⁺; J⁺) with detailed simulation have been reported previously, measurements of the corresponding VUV-PFI-PI spectra have not been made. All VUV-PFI-PI spectra presented here represent the average of at least three independent scans.

As expected, the PFI-PI spectra for O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 0–2; J⁺) and O₂⁺(X²Π_g3/2,1/2; v⁺ = 21–23; J⁺) in the VUV energy [hν(VUV)] range of 129 750–132 366 cm⁻¹ are similar to those reported in previous VUV-PFI-PE studies. Some differences in rotational transition intensities observed here compared to the result of the previous synchrotron based study can be attributed to the different rotational temperatures of O₂ used in the PFI-PI and PFI-PE experiments. As shown in the spectral simulation below, O₂ molecules used in the form of a supersonic beam achieve a rotational temperature of 30 K, whereas O₂ molecules used in the form of an effusive beam in the VUV synchrotron PFI-PE study have a rotational temperature close to room temperature at 298 K.

A. VUV-PFI-PI spectra and spectral simulation

The spin–orbit and rovibronic state resolved VUV-PFI-PI spectra (top black curves) for O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 0; J⁺) and O₂⁺(X²Π_g3/2,1/2; v⁺ = 21; J⁺) at hν(VUV) = 129 750–130 025 cm⁻¹ are depicted in Fig. 6. Based on previous VUV-PFI-PE measurements, we have assigned the two strong VUV-PFI-PI bands at the high and low energy ends of Fig. 6 as the spin–orbit bands of O₂⁺(X²Π_g3/2: v⁺ = 21; J⁺) and O₂⁺(X²Π_g1/2; v⁺ = 21; J⁺). The four spin–orbit PFI-PI bands for O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 0; J⁺) fall in between the O₂⁺(X²Π_g3/2,1/2; v⁺ = 21; J⁺) spin–orbit bands. The very weak PFI-PI intensities for the O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 0; J⁺) bands compared to that for the O₂⁺(X²Π_g3/2,1/2: v⁺ = 21; J⁺) bands observed are consistent with previous VUV-PFI-PE measurements. This PFI-PI measurement indicates that the PFI-PI intensities for O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 0; J⁺) are likely too low for an ion–molecule collision study.

Fig. 6 Partially rotational resolved VUV PFI-PI spectrum (black curve) for O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: ν⁺ = 0) and O₂⁺(X²Π_g1/2,3/2: ν⁺ = 21) observed in the energy range of 129 750–130 025 cm⁻¹. The rotational assignments based on spectral simulations are marked by downward pointing drop lines. The numbers above the markings denote the J⁺ states of O₂⁺ PFI-PIs. Individual simulated spectra for ΔJ transitions are shown at the bottom of the figure. The overall simulated spectrum obtained by summing the corresponding ΔJ transitions is depicted as the red curve below the PFI-PI spectra.

The spin–orbit and rovibronic state resolved VUV-PFI-PI spectra (top black curves) for O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1; J⁺) and O₂⁺(X²Π_g3/2,1/2: v⁺ = 22; J⁺) at hν(VUV) = 130 800–131 225 cm⁻¹ are depicted in Fig. 7. The four spin–orbit PFI-PI bands for O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1; J⁺) are discernible, and have significantly higher intensities than those for the O₂⁺(X²Π_g3/2,1/2: v⁺ = 22; J⁺) bands. While the O₂⁺(X²Π_g3/2: v⁺ = 22; J⁺) band is well separated from other bands, the O₂⁺(X²Π_g1/2: v⁺ = 22; J⁺) band is in strong overlap with the O₂⁺(a⁴Π_u−1/2: v⁺ = 1; J⁺) band.

Fig. 7 Partially rotational resolved VUV PFI-PI spectrum of O₂⁺ (a⁴Π_{u5/2,3/2,1/2,−1/2}, ν⁺ = 1) and O₂⁺(X²Π_g1/2,3/2, ν⁺ = 22) observed in the energy range of 130 800–131 225 cm⁻¹. The rotational assignments based on spectral simulations are marked below the experimental spectra. The numbers above the markings denote the J⁺ states of O₂⁺. PFI-PIs. Individual simulated spectra for ΔJ transitions are shown at the bottom of the figure. The overall simulated spectrum obtained by summing the corresponding ΔJ transitions is shown as the red curve below the PFI-PI spectrum.

Fig. 8 depicts the spin–orbit resolved VUV-PFI-PI spectra (top black curves) for O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 2; J⁺) and O₂⁺(X²Π_g3/2,1/2: v⁺ = 23; J⁺) bands at hν(VUV) = 131 775–132 366 cm⁻¹. All PFI-PI spectra for these spin–orbit bands are well resolved. The intensities for the O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 2; J⁺) bands are found to be higher than those for the O₂⁺(X²Π_g3/2,1/2: v⁺ = 23; J⁺) bands. This observation is also consistent with the previous VUV synchrotron PFI-PE measurement.

Fig. 8 Partially rotational resolved VUV PFI-PI spectrum of O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: ν⁺ = 2) and O₂⁺(X²Π_g1/2,3/2, ν⁺ = 23) observed in the energy range of 131774.2–132366.1 cm⁻¹. The rotational assignments are marked below the experimental spectra. The numbers above the markings denote the J⁺ states of O₂⁺ PFI-PIs. Individual simulated spectra for ΔJ transitions are shown at the bottom of the figure. The overall simulated spectrum obtained by summing the corresponding ΔJ transitions is shown as the red curve below the PFI-PI spectrum.

In order to assign overlapping rotational and spin–orbit transitions of the O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 0–2; J⁺) and O₂⁺(X²Π_g3/2,1/2: v⁺ = 21–23; J⁺) bands, it is necessary to perform spectral simulations. The ground O₂⁺(X²Π_g) state is formed by the removal of an electron from the anti-bonding 1π_g orbital, whereas the O₂⁺(a⁴Π_u) state resulted from the ejection of one electron from the bonding 1π_u orbital. The spin–orbit interaction, i.e., the coupling between Λ and Σ, gives rise to four spin–orbit components F₁(⁴Π_5/2), F₂(⁴Π_3/2), F₃(⁴Π_1/2), and F₄(⁴Π_−1/2) for the O₂⁺(a⁴Π_uΩ) state, where the quantum number Ω = Λ + Σ = 5/2, 3/2, 1/2, and −1/2. Similarly, the O₂⁺(X²Π_g) state splits into two spin–orbit components: ²Π_g1/2 and ²Π_g3/2. The interaction of spin–orbit components can be expressed as ΔE_so = AΛΣ, where A is the spin–orbit coupling constant, and Λ and Σ are the projection of electronic orbital angular momentum (L) and electron spin angular momentum (S), respectively, along the molecular axis.

The electronic energies of spin–orbit states can be expressed as T_e = T₀ + ΔE_SO + T₀ + AΛΣ. The energy of O₂(X³Σ_g⁺: v′′ = 0; N′′) can be expressed by eqn (3):

E(X,v′′ = 0,N′′) = 1/2ω_e′′ − 1/4ω_e′′χ_e′′ + B₀′′N′′(N′′ + 1). (3)

The energy of the O₂⁺(a⁴Π_uΩ: v⁺; N⁺) or O₂⁺(X²Π_gΩ: v⁺, N⁺) state can be expressed by eqn (4):

E⁺(a,v⁺,N⁺) = T_e⁺ + ω_e⁺(v⁺ + 1/2) − ω_e⁺χ_e⁺ + (v⁺ + 1/2)² + B⁺[N⁺(N⁺ + 1) − v⁺Ω²] + AΛΣ. (4)

Rovibronic photoionization transition energies can thus be calculated by eqn (5):

ΔE = E⁺(a,v⁺,N⁺) − E(X,v′′ = 0,N′′) = T_0v⁺ + B⁺[N⁺(N⁺ + 1) − v⁺Ω²] + AΛΣ − B₀′′N′′(N′′ + 1). (5)

Here, T_0v⁺ = T_e⁺ + [ω_e⁺(v⁺ + 1/2) − ω_e⁺χ_e⁺ (v⁺ + 1/2)²] − (ω_e′′/2 − ω_e′′χ_e′′/4) represents the band origin of the rovibronic transitions. To simulate the spectra, T_0v⁺, B⁺, A, and B₀′′ are parameters that need to be specified and input to eqn (5) to predict transition peaks observed in the PFI-PI spectra. Molecular constants, including the rotational constant (B′′) of the O₂(X³Σ_g⁺: v′′ = 0; N′′) state, as well as the band origin (T₀₀⁺), rotational constant (B⁺), and spin–orbit coupling constants (A) of O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 21–23) and O₂⁺(X²Π_g3/2,1/2: v⁺ = 0–2) have been reported by Song et al.,^38,39 Kong and Hepburn,⁴⁶ and Cosby et al.⁴⁷ We have adopted these reported molecular constants for spectral simulations. In order to achieve the best simulation, minor adjustments (within the specified experimental uncertainties) to the previous reported spectroscopic constants were made.

For the O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}) states, the spin–orbit splitting of individual components are given in eqn (6a)–(6d).

⁴Π_5/2, ΔE_so = (3/2) A, Λ = 1, Σ = 3/2, (6a)

⁴Π_3/2, ΔE_so = (1/2) A, Λ = 1, Σ = 1/2, (6b)

⁴Π_1/2, ΔE_so = (−1/2) A, Λ = 1, Σ = −1/2, (6c)

⁴Π_−1/2, ΔE_so = (−3/2) A, Λ = 1, Σ = −3/2. (6d)

In the case of the O₂⁺(X²Π_g3/2,1/2) states, the spin–orbit splitting energies of individual components are given in eqn (7a) and (7b).

²Π_3/2, ΔE_so = (1/2) A, Λ = 1, Σ = 1/2, (7a)

²Π_1/2, ΔE_so = (−1/2) A, Λ = 1, Σ = −1/2. (7b)

Due to the nuclear-spin statistics, the O₂(X³Σ_g⁺) ground state does not contain even N′′ rotational levels.⁴⁸ Therefore, only odd N′′ levels were considered in the simulation. The simulation has taken into account the three sublevels F₁, F₂, and F₃ of O₂(X³Σ_g⁺: v′′ = 0); but we have ignored the fine sublevels because the optical bandwidth (0.4 cm⁻¹) of the VUV laser used here is larger than the spin-rotation splitting in the range of 0.1–0.2 cm⁻¹.

The spectral simulation of the VUV-PFI-PI spectra assume a Gaussian instrumental transition line profile with a FWHM = 4.0 cm⁻¹. We also assume that the N′′ (odd) rotational populations for the O₂(X³Σ_g⁺: v′′ = 0) ground state are governed by the Boltzmann rotational temperature achieved in the O₂ pulsed supersonic expansion. In previous rotational resolved PFI-PE studies of diatomic and small molecular ions, the intensities for rotational transitions are found to fall in a pattern that favors the smaller |ΔJ| (= |J⁺ − J′′|) value.^49–52 That is, the most intense rotational transition usually has the smallest |ΔJ| value, and the intensity for rotational transition decreases as |ΔJ| increases. The maximum |ΔJ| value identified can be in the range of 5–10. Furthermore, the ΔJ < 0 transitions are often found to be more intense than the ΔJ > 0 transitions. The present simulation assumes that the ΔJ transitions have an intensity profile as described above; and fine adjustment of the simulated intensities for individual ΔJ transitions were made to give the best fit to the PFI-PI spectra.

Since the spacing between adjacent rotational lines is generally 0.1–0.2 cm⁻¹, the present experiment was not able to fully resolve individual rotational transitions. The simulation of the VUV-PFI-PI spectra identified six ΔJ-branches, i.e., ΔJ = +5/2, +3/2, +1/2, −1/2, −3/2, and −5/2, which are marked by bars with downward or upward pointing strikes in Fig. 6–8. The individual simulated ΔJ-branch transition spectra are shown at the bottom of these figures. The markings of ΔJ-branch transitions in these figures are color coded in pink, green, red, blue, yellow, and black, for the ΔJ = +5/2, +3/2, +1/2, −1/2, −3/2, and −5/2 branches, respectively. The sums of the simulated ΔJ-transition spectra give the overall simulated spectra (red curves) shown below the PFI-PI spectra (top black curves) in Fig. 6–8. The PFI-PI spectra exhibit quite complicated rotational structures due to the high multiplicity of the O₂⁺(a⁴Π_u) and O₂⁺(X²Π_g) states. The numbers above the ΔJ branch transition markings are the J⁺ quantum numbers of O₂⁺ ions, which are defined as J⁺ = N⁺ + Ω⁺. Since the rotational transitions of nearby spin–orbit components have some overlap, the simulation is necessary for determining the purities of selected rovibronic states; and ensuring the PFI-PI transition peaks selected have no spectral overlaps between adjacent spin–orbit components.

In the VUV-PFI-PI spectra of O₂⁺(a⁴Π_u: v⁺ = 0) and O₂⁺(X²Π_g: v⁺ = 21) shown in Fig. 6, the four spin–orbit components O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 0) fall in between the two spin–orbit components O₂⁺(X²Π_g3/2,1/2: ν⁺ = 21). As pointed out above, due to very small FCFs for the formation of the O₂⁺(a⁴Π_u: v⁺ = 0) state from the O₂(X³Σ_g⁺) ground state,⁵³ the VUV-PFI-PI intensities for O₂⁺(a⁴Π_u: v⁺ = 0) are too weak for ion-neutral collision studies. Thus, we have not devoted much effort for a detailed simulation of the VUV-PFI-PI spectrum for O₂⁺(a⁴Π_u: v⁺ = 0).

Nonetheless, the O₂⁺(X²Π_g3/2,1/2: v⁺ = 21) VUV-PFI-PI spectra have been successfully analyzed with satisfactory rotational assignments as marked in Fig. 6. Based on the spectral simulation of the VUV-PFI-PI spectra for O₂⁺(a⁴Π_u, v⁺ = 0) and O₂⁺(X²Π_g, v⁺ = 21), we have identified two PFI-PI peaks at hν (VUV) = 129807.6 and 129982.4 cm⁻¹ (marked by downward pointing red arrows in Fig. 6 and listed in Table 1) for the spin–orbit state selections of O₂⁺(X²Π_g1/2: v⁺ = 21) and O₂⁺(X²Π_g3/2: v⁺ = 21), respectively. The spin–orbit components thus prepared consist of the three J⁺ = 1.5, 3.5, and 5.5 states (as listed in Table 1) with the J⁺ = 5.5 state (highlighted in red) predicted to have the highest population.

Table 1 Selected VUV photoionization energies (marked by downward pointing red arrows in Fig. 6–8) and the corresponding electronic, vibrational, Ω⁺, and J⁺ states of O₂⁺ PFI-PIs prepared for the charge transfer collision of O₂⁺ + Ar. The J⁺ states indicated in italic in the table are the dominant states

Spin–orbit and vibronic O2^+ states	Ω ^+	J ^+	hν(VUV) (cm^−1)
X^2Πg, v^+ = 21	1/2	1.5, 3.5, 5.5	129807.6
	3/2	1.5, 3.5, 5.5	129982.4
X^2Πg, v^+ = 22	1/2	5.5	131012.3
	3/2	1.5, 3.5, 5.5	131158.3
a^4Πu, v^+ = 1	5/2	2.5, 4.5	130840.7
	3/2	1.5, 3.5	130885.0
	1/2	2.5, 4.5	130943.5
	−1/2	1.5	130971.8
X^2Πg, v^+ = 23	1/2	1.5, 3.5	132129.8
	3/2	1.5, 3.5	132301.6
a^4Πu, v^+ = 2	5/2	2.5, 4.5, 6.5	131835.4
	3/2	2.5, 4.5, 6.5	131888.2
	1/2	2.5, 4.5, 6.5	131939.4
	−1/2	0.5, 1.5, 3.5	131979.6

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B. Spin–orbit state selected integral charge transfer cross sections

By tuning the VUV laser to selected PFI-PI peaks as marked by the downward pointing red arrows in Fig. 7 and 8, we can prepare reactant O₂⁺ ions in single spin–orbit states of O₂⁺(a⁴Π_uΩ: v⁺ = 1 and 2) and O₂⁺(X²Π_gΩ: ν⁺ = 22 and 23) for the ion–molecule collision study with Ar. The selection of these PFI-PI peaks with high spin–orbit purities and high intensities were guided by spectral simulation of the VUV-PFI-PI spectra as described above. The hν(VUV) values of twelve selected PFI-PI peaks, together with their spectroscopic assignments are given in Table 1. Six of the PFI-PI peaks selected at hν(VUV) = 131012.3, 131158.3, 130840.7, 130885.0, 130943.5, and 130971.8 cm⁻¹ are assigned as the spin–orbit states: O₂⁺(X²Π_g1/2: v⁺ = 22), O₂⁺(X²Π_g3/2: v⁺ = 22), O₂⁺(a⁴Π_u5/2: v⁺ = 1), O₂⁺(a⁴Π_u3/2: v⁺ = 1), O₂⁺(a⁴Π_u1/2: v⁺ = 1), and O₂⁺(a⁴Π_u−1/2: v⁺ = 1), respectively. The other six PFI-PI peaks situated at hν(VUV) = 132129.8, 132301.6, 131835.4, 131888.2, 131939.4, and 131979.6 cm⁻¹ are associated with the formation of their respective spin–orbit states: O₂⁺(X²Π_g1/2: ν⁺ = 23), O₂⁺(X²Π_g3/2: ν⁺ = 23), O₂⁺(a⁴Π_u5/2: ν⁺ = 2), O₂⁺(a⁴Π_u5/2: ν⁺ = 2), O₂⁺(a⁴Π_u5/2: ν⁺ = 2), and O₂⁺(a⁴Π_u5/2: ν⁺ = 2). The spectral simulations show that these PFI-PI peaks for the assigned spin–orbit states consist of contributions from one to three low J⁺ states with values ≤6.5. The J⁺ states highlighted in red are predicted to have the major populations.

The primary goal of this experiment is to measure and compare the σ values with reactant O₂⁺ ions prepared in two distinct vibronic states, i.e., O₂⁺(a⁴Π_u: v⁺ = 1) and O₂⁺(X²Π_g: v⁺ = 22) as well as O₂⁺(a⁴Π_u: v⁺ = 2) and O₂⁺(X²Π_g: ν⁺ = 23), which are in near energy resonance with energy separations in the range of 200–300 cm⁻¹. A comparison of σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1) with σ(X²Π_g3/2,1/2: v⁺ = 22) is shown in Fig. 9, and that of σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 2) with σ(X²Π_g3/2,1/2: v⁺ = 23) is given in Fig. 10. Both comparisons reveal that O₂⁺ ions in the a⁴Π_u state are overwhelmingly more reactive toward Ar via charge transfer than in the X²Π_g state. The high σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1, 2), and their increasing trend with decreasing E_cm are indicative of the involvement of a long range charge transfer mechanism.^35,36

Fig. 9 Comparison of spin–orbit state selected integral cross sections for the charge transfer reactions of O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}, v⁺ = 1) [O₂⁺(X²Π_g1/2,3/2: v⁺ = 22)] + Ar → Ar⁺ + O₂ in the E_cm range of 0.05–3.00 eV. Strong spin–orbit state enhancements in O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}) states are observed as the Ω⁺ quantum number is increased. For the O₂⁺(X²Π_g3/2,1/2) spin–orbit states, no significant spin–orbit state dependence was observed for the σ value.

Fig. 10 Comparison of integral cross section of charge transfer reaction O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}, v⁺ = 2) and [O₂⁺(X²Π_g1/2,3/2: v⁺ = 23)] + Ar → Ar⁺ + O₂ in the E_cm range of 0.05–10.0 eV. The a⁴Π_u state cross sections decrease with increasing kinetic energy, but rise at around 1 eV and peak at around 2 eV. The reaction cross section follows a decreasing trend with collision energy, dropping to about half from 0.05 eV to 1 eV. With collision energy reaching 1 eV, we observed a “bump” like structure and it peaks at around 2 eV. After that, the cross sections again follow a decreasing pattern.

As shown in Fig. 9, the σ(a⁴Π_u: v⁺ = 1) values obtained in the E_cm range of 0.05–3.00 eV reveal that the σ(a⁴Π_u) depends strongly on the spin–orbit state with the order: σ(a⁴Π_u5/2: v⁺ = 1) > σ(a⁴Π_u3/2: v⁺ = 1) > σ(a⁴Π_u1/2: v⁺ = 1) > σ(a⁴Π_u−1/2: v⁺ = 1). The σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1) values were found to decrease rapidly from thermal (0.05 eV) to E_cm ≈ 0.70 eV and level off at E_cm = 0.70–3.00 eV. The σ(a⁴Π_u5/2: v⁺ = 1) value is higher than the σ(a⁴Π_u−/2: v⁺ = 1) value by a factor of 1.5–2.2 in the E_cm = 0.05–3.00 eV range. Interestingly, the σ(X²Π_g3/2,1/2: v⁺ = 22) values obtained at E_cm = 0.05–3.00 eV were found to be essentially independent of E_cm. This observation, together with the low σ(X²Π_g3/2,1/2: v⁺ = 22) values observed, indicates that the formation of Ar⁺ from the charge transfer collision of O₂⁺(X²Π_g3/2,1/2: v⁺ = 22) + Ar is unlikely to result from a long-range electron jump mechanism. Instead, a short-range collision pathway must be involved in the latter reaction. It appears that σ(X²Π_g3/2: v⁺ = 22) is slightly larger than σ(X²Π_g1/2: v⁺ = 22).

Fig. 10 compares the σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 2) and the σ(X²Π_g3/2,1/2: v⁺ = 23) obtained at E_cm = 0.05–10.00 eV. The σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 2) curves at E_cm = 0.05–1.00 eV are found to be high and have an E_cm dependence similar to the σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1) of Fig. 9. The σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1) curves exhibit a broad hump peaked at E_cm ≈ 2.0 eV. At E_cm > 4.0 eV, the σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 2) curves were found to drop rapidly with increasing E_cm. The nature of this hump is not known, and would require theoretical interpretation. The spin–orbit state dependences for σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 2) observed are also similar to those for σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1), i.e., σ(a⁴Π_u5/2: v⁺ = 2) > σ(a⁴Π_u3/2: v⁺ = 2) > σ(a⁴Π_u1/2: v⁺ = 2) > σ(a⁴Π_u−1/2: v⁺ = 2) for the full E_cm range of 0.05–10.00 eV. The difference between adjacent σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 2) curves is ≈10%. The comparison of the σ(a⁴Π_u: v⁺ = 1) of Fig. 9 and the σ(a⁴Π_u: v⁺ = 2) of Fig. 10 has also shown that σ(a⁴Π_u: v⁺ = 2) > σ(a⁴Π_u: v⁺ = 1).

The low values and the lack of E_cm dependence observed for σ(X²Π_g3/2,1/2: v⁺ = 23) as shown in Fig. 10 are in close resemblance with that observed for the σ(X²Π_g3/2,1/2: ν⁺ = 22) of Fig. 9. Although the O₂⁺(X²Π_g3/2,1/2: v⁺ = 23) states are only slightly higher (≈300 cm⁻¹) than the O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 2) states, these states are found to have significantly different charge transfer reactivity with Ar.

Koyano and co-workers have previously reported relative values for σ(a⁴Π_u: v⁺ = 0–7) and σ(a²Π_g: v⁺ = 19, 20) at E_cm = 1.4 and 5.8 eV using the TESICO technique.¹⁷ Their results show that σ(a⁴Π_u: v⁺ = 2) is significantly higher than σ(a²Π_u: v⁺ = 1). The latter observation is in accordance with the result of the present study. Since the charge transfer collision of O₂⁺(X²Π_g: v⁺ = 19) + Ar is endothermic, we have not examined the reactivity of this state. We note that the TPE resolution of 30 meV (240 cm⁻¹) used in the previous TESICO measurements cannot resolve the O₂⁺(X²Π_g: v⁺ > 19) states from the O₂⁺(a⁴Π_u: v⁺ = 0–7) states, as well as from different spin–orbit states of interest in the present study. In order to compare the relative integral cross sections of Koyano and co-workers¹⁷ with the spin–orbit state-selected σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺) values obtained here, we have taken the average of σ(a⁴Π_u: v⁺) as 〈σ(a⁴Π_u: v⁺)〉 = (1/4)[σ(a⁴Π_u5/2: v⁺) + σ(a⁴Π_u3/2: v⁺) + σ(a⁴Π_u1/2: v⁺) + σ(a⁴Π_u−1/2: v⁺)], where v⁺ = 1 and 2. The 〈σ(a⁴Π_u: v⁺ = 1)〉 and 〈σ(a⁴Π_u: v⁺ = 2)〉 curves thus obtained are shown in Fig. 11, confirming the observation of Fig. 9 and 10 that the σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 2) values are significantly higher that the corresponding σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1) values. This conclusion is also in qualitative agreement with the results of the TPESICO study. We have also taken the averages 〈σ(X²Π_g: ν⁺ = 22)〉 and 〈σ(X²Π_g: v⁺ = 23)〉 as depicted in Fig. 11, revealing that 〈σ(X²Π_g: ν⁺ = 23)〉 is higher than 〈σ(X²Π_g: ν⁺ = 22)〉. Based on the HeI photoelectron study of O₂, it is well known that the FCFs for the formation of O₂⁺(a⁴Π_u: v⁺ ≥ 1) are significantly greater than those for O₂⁺(X²Π_g: v⁺ > 20) from O₂(X³Σ_g⁻).⁵³ Koyano and co-workers first suggested that the finding of σ(a⁴Π_u: v⁺ = 1) > σ(X²Π_g: v⁺ = 22) and σ(a⁴Π_u: ν⁺ = 2) > σ(X²Π_g: v⁺ = 23), along with the fact that σ(a⁴Π_u: v⁺ = 2) > σ(a⁴Π_u: v⁺ = 1), can be attributed to the difference in FCFs for the formation of the O₂⁺(a⁴Π_u: v⁺) and O₂⁺(X²Π_g: v⁺) electronic states from the O₂ ground state.

Fig. 11 Comparison of averaged integral cross section for the charge transfer reactions O₂⁺(a⁴Π_u: v⁺ = 1, 2) [O₂⁺(X²Π_g: v⁺ = 22, 23)] + Ar. The average σ(a⁴Π_u: v⁺) is taken as 〈σ(a⁴Π_u: v⁺)〉 = (1/4)[σ(a⁴Π_u5/2: v⁺) + σ(a⁴Π_u3/2: v⁺) + σ(a⁴Π_u1/2: v⁺) + σ(a⁴Π_u−1/2: v⁺)], where v⁺ = 1 and 2. Similarly the 〈σ(X²Π_g: ν⁺)〉 values are calculated as (1/2)[σ(X²Π_g3/2: ν⁺) + σ(X²Π_g1/2: ν⁺)], where v⁺ = 22 and 23. The 〈σ(a⁴Π_u: v⁺ = 1)〉, 〈σ(a⁴Π_u: v⁺ = 2)〉, 〈σ(X²Π_g: v⁺ = 22)〉 and 〈σ(X²Π_g: v⁺ = 23)〉 curves thus obtained are depicted in the figure.

The charge-transfer reactions (1) and (2) necessarily involve the crossing of the reactant state [O₂⁺⋯Ar] to the product state [Ar⁺⋯O₂] along the reaction coordinate. As pointed out above, the ground O₂⁺(X²Π_g) state is formed by the removal of an electron from the anti-bonding 1π_g orbital, whereas the O₂⁺(a⁴Π_u) state resulted from the ejection of one electron from the bonding 1π_u orbital. Thus, the interaction of Ar with O₂⁺(a⁴Π_u) in the long range by donating an electron to the 1π_u orbital from Ar is expected to be more attractive compared to the interaction of Ar with O₂⁺(X²Π_g), where the electron from Ar would be donated into the anti-bond 1π_g orbital. The more favorable bonding interaction for [O₂⁺(a⁴Π_u)⋯Ar] could partly account for the higher σ(a⁴Π_u: ν⁺ = 1 and 2) compared to the σ(X²Π_g: v⁺ = 22 and 23). The spin–orbit interaction and vibrational excitation can alter the crossing region for the [O₂⁺⋯Ar] and [Ar⁺⋯O₂] states, and thus the σ values for reactions (1) and (2). The extended O–O distance for highly vibrational states O₂⁺(X²Π_g: v⁺ = 21–23) may not favor the curve crossing between the reactant and product charge transfer states. We hope that the extensive high-quality spin–orbit, rotational, vibrational, and electronic state-selected integral cross sections reported here will motivate state-of-the-art theoretical dynamics calculations.

IV. Conclusion and summary

We have succeeded in preparing spin–orbit and rovibronic state selected O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 0–2; J⁺) and O₂⁺(X²Π_g3/2,1/2: v⁺ = 21–23; J⁺) ions in the form of a pulsed beam by employing the sequential electric field VUV laser PFI-PI detection scheme. These quantum state-selected ions thus generated have a narrow ΔE_lab spread of 50 meV, allowing σ measurements of reactions (1) and (2) from thermal energies (50 meV) to 10 eV. Since the O₂⁺(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1 and 2) and O₂⁺(X²Π_g3/2,1/2: v⁺ = 22 and 23) states are in close energy resonance, these reactions represent ideal model systems for investigating the energy resonance and FCF effects on charge transfer reactivity of O₂⁺. We found that the σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1 and 2) values are overwhelmingly higher than the σ(X²Π_g3/2,1/2: v⁺ = 22 and 23) values at E_cm = 0.05–10.00 eV, indicating that the FCFs play the dominant role in promoting these charge transfer reactions. The σ(a⁴Π_u) was also found to depend strongly on the spin–orbit as well as the vibrational states with the order: σ(a⁴Π_u: v⁺ = 2) > σ(a⁴Π_u: v⁺ = 1), and σ(a⁴Π_u5/2: v⁺) > σ(a⁴Π_u3/2: v⁺) > σ(a⁴Π_u1/2: v⁺) > σ(a⁴Π_u−1/2: v⁺), where v⁺ = 1 and 2. While the high σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺ = 1 and 2) values along with their E_cm dependences are consistent with that for exothermic long range charge exchange processes, the low σ(X²Π_g3/2,1/2: v⁺ = 22 and 23) and the lack of E_cm dependence observed in the full E_cm range of 0.05–10.00 eV point to the involvement of short-range collision dynamics. The spin–orbit state and E_cm dependences for σ(a⁴Π_{u5/2,3/2,1/2,−1/2}: v⁺) were not observed previously. The quantum-state-selected σ values presented here require the interpretation of rigorous theoretical calculations.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This material is based upon work supported by the National Science Foundation under grant CHE-1462172 and CHE-1642172. C. Y. N. is also grateful to Dr Huie Tarng Liou for his generous donation of research support for the Ng Laboratory.

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