Double Imaging Photoelectron Photoion Coincidence Sheds New

Jul 19, 2017 - Especially for the dissociation along the CH3+ + F fragmentation channel the ... A photodiode (AXUV100, IRD) just located behind the ph...
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Double Imaging Photoelectron Photoion Coincidence Sheds New Light on the Dissociation of State-Selected CHF Ions 3

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Xiaofeng Tang, Gustavo A. Garcia, and Laurent Nahon J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b06038 • Publication Date (Web): 19 Jul 2017 Downloaded from http://pubs.acs.org on July 25, 2017

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Double Imaging Photoelectron Photoion Coincidence Sheds New Light on the Dissociation of State-Selected CH3F+ Ions Xiaofeng Tang,*a,b Gustavo A. Garciab and Laurent Nahonb a, Laboratory of Atmospheric Physico-Chemistry, Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei, 230031 Anhui, China. b, Synchrotron SOLEIL, L’Orme des Merisiers, St. Aubin BP 48, 91192 Gif sur Yvette, France. ABSTRACT The vacuum ultraviolet (VUV) photoionization and dissociative photoionization of methyl fluoride (CH3F) in the 12.2-19.8 eV energy range were investigated by using synchrotron radiation coupled to a double imaging photoelectron photoion coincidence (i2PEPICO) spectrometer. The production of several fragment ions including CH2F+, CHF+, CH3+ and CH2+ as a function of state and internal energy of CH3F+ ions was identified and analyzed, with their individual appearance energies measured through threshold photoelectron spectroscopy. Dynamical information was inferred from electron and ion kinetic energy correlation diagrams measured at chosen fixed photon energies. The detailed mechanisms governing the dissociation of state-selected CH3F+ ions prepared in the X2E, A2A1 and B2E low-lying electronic states as well as outside the Franck-Condon region have been inferred based on the present experimental results and existing theoretical calculations. Both the CH2F+ and CH3+ primary fragment ions have three different channels of production from different electronic states of CH3F+. The spinorbit splitting states of the F fragment, 2P3/2 and 2P1/2, in the CH3+ + F dissociation channels were assigned and adiabatically correlate to the X2E ground state and the A2A1 electronic state, respectively, with the aid of previous theoretical results. The CH3F+ ions in the high energy part of the X2E ground state are unstable and statistically dissociate to the CH2F+(11A1) and H(2S) fragments along the potential energy curve of the X2E state. The A2A1 electronic state is a repulsive state and exclusively dissociates to the CH3+(11A1’) and F(2P1/2) fragments. In addition, the CH2F+, CHF+, CH3+ and CH2+ fragment ions are also produced in the B2E state and in the Franck-Condon gap by indirect processes, such as internal conversion or dissociative autoionization.

* E-mail: [email protected]. Tel: +86 551 65590357

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1. INTRODUCTION Methyl halides (CH3X, X= F, Cl, Br, I) are among the most abundant organic gases in the Earth’s atmosphere and play essential roles in the atmospheric and environmental reactions.1,2 They are also considered as model polyatomic systems with high-symmetry and have attracted a great deal of attention in the past decades. Specifically methyl halides have a C3V symmetry in the X1A1 ground state and their valence-shell electron configurations are (1a1)2(2a1)2(1e)4(3a1)2(2e)4, where 1a1 and 2a1 are inner-valence orbitals, and 1e, 3a1 and 2e are outer-valence orbitals. Removing an electron from the three outer orbitals leads to the three low-lying electronic states of methyl halide cations X2E, A2A1 and B2E.3,4 The Jahn-Teller effect will split the high-symmetry degenerate X2E or B2E electronic state into two 2A’ and 2A’’ states with Cs symmetry.5-7 The dissociation of methyl halide ions is of fundamental interest as they undergo specific reactions into different products depending on the cations’ state and the halide substituent.8 Recently we have initiated a systematic research on the dissociation dynamics of state/energy-selected methyl halide cations by combining vacuum ultraviolet (VUV) synchrotron radiation as ionizing source and double imaging photoelectron photoion coincidence (i2PEPICO) set-ups.9-15 Methyl halide ions CH3X+(X=F, Cl, Br) in the above three low-lying electronic states were prepared and analyzed and fragment ions such as CH2X+, CHX+, CH3+ and CH2+ were observed in the experiments, leading to valuable information on the energetics and dynamics of the dissociative ionization processes. For example, high-resolution kinetic energy release distributions (KERDs) were obtained from electron and ion kinetic energy correlation diagrams or threshold PEPICO (TPEPICO) ion images. Especially the detailed dissociation mechanisms of state/energyselected CH3X+ ions, prepared in the three low-lying electronic states, as well as outside the Franck-Condon region, along the CH3+ and X fragmentation pathway have been revealed and exhibit state-specific characters. The A2A1 electronic state is a direct dissociation state, the dissociation of the B2E state goes through the X2E state, and dissociative autoionization is invoked to explain the production of CH3+ in the FranckCondon gap. As for the target of this study, methyl fluoride (CH3F), its VUV photodynamics has already been studied by a great deal of experimental methods, such as photo-absorption spectroscopy,16-18 photoelectron spectroscopy (PES),3,5,19-22 electron impact ionization,2325 photoionization mass spectrometry (PIMS)26-28 and PEPICO spectroscopy8,21. The potential energy curves of the low-lying electronic states of CH3F+ along the C-H and CF coordinates were also theoretically calculated by using the methods of complete active 2 ACS Paragon Plus Environment

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space self-consistent field and multi-configuration second-order perturbation theory (CASSCF/CASSCF).6 In addition, just very recently, i2PEPICO experiments performed by the authors identified three channels of production of CH3+ fragment ions with different KERDs which correlated to the three low-lying electronic states of CH3F+.11 The first two electronically excited states A2A1 and B2E—which cannot be separated on their energetics alone due to their closeness and naturally broad energy profile—were firstly separated in the electron and ion kinetic energy correlation diagram based on their different dissociation dynamics.12 For the sake of completeness and in order to provide a global picture of methyl halides photodynamics, we reinvestigate here the dissociation of CH3F+ ion in more details, not only along the CH3+ and F fragmentation pathway, but also including the channels to produce CH2F+, CHF+ and CH2+ fragment ions, by using the method of i2PEPICO15 at Synchrotron SOLEIL. The mass-selected slow photoelectron spectra (SPES)29,30 and the photoionization efficiency (PIE) spectra corresponding to each species were measured by scanning the synchrotron photon energy yielding precise fragment appearance energies. Dynamical information on the observed dissociation channels was inferred from high-resolution electron and ion kinetic energy correlation diagrams recorded at several fixed photon energies that, combined with the energetics, lead to the detailed dissociation mechanisms of state-selected CH3F+ ions prepared in the X2E, A2A1 and B2E electronic states, as well as outside the Franck-Condon region. Especially for the dissociation along the CH3+ + F fragmentation channel the spin-orbit splitting states of the F fragment, 2P3/2 and 2P1/2, which adiabatically correlate to the X2E ground state and the A2A1 electronic state respectively were assigned. The A2A1 electronic state is a repulsive state and totally dissociates to the CH3+(11A1’) and F(2P1/2) fragments. To explain the productions of the CHF+ and CH2+ fragment ions, the noncrossing of the potential energy curves with lower symmetry geometries should be involved. 2. METHODS The experiments were performed with an i2PEPICO spectrometer, DELICIOUS III,15,31 on the VUV beamline DESIRS32 at Synchrotron SOLEIL, the French third generation synchrotron facility located in Gif sur Yvette, France. The configurations of the synchrotron beamline and the DELICIOUS III spectrometer have already been introduced in detail previously and so only a brief description is presented here. Synchrotron photons emitted from a variable polarization undulator were dispersed with a 6.65 m normal incidence monochromator. A 200 l mm-1 grating covering the photon energy range of 5~25 eV was employed and the entrance and exit slits of the 3 ACS Paragon Plus Environment

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monochromator were set to provide a photon energy resolution of ~3 meV. A gas filter located upstream of the beamline was filled with argon for hν < 15.6 eV to suppress high harmonic photons emitted from the undulator. The absolute photon energy was calibrated with the absorption lines of argon in the gas filter seen as dips in the photoionization spectra during the energy scans. Synchrotron photons were focused in the photoionization region with a spot size of 100 × 200 µ m (vertical × horizontal) at full width at half maximum (FWHM). A photodiode (AXUV100, IRD) just located behind the photoionization region was used to measure the photon flux to normalize the photon energy scans. Commercial CH3F gas (99% purity) seeded in helium carrier gas (1.2 atm) with a volume ratio of 1:49 was expanded through a nozzle (50 µ m diameter) and then traversed a skimmer (0.7 mm diameter) in the SAPHIRS vacuum chambers31. The synchrotron photon beam, molecular beam and the axis of the DELICIOUS III spectrometer installed inside the SAPHIRS chambers crossed at right angles in the photoionization region. The DELICIOUS III spectrometer is composed of an electron velocity map imaging (VMI) device33 coupled to a modified Wiley-McLaren time-offlight (TOF) ion imaging analyzer34 to measure electrons and ions in coincidence. The coincidence scheme yielded photoelectron images correlated to a particular mass, which were then processed with an Abel inversion algorithm35 to recover photoelectron spectra (PES). The electron and ion kinetic energy correlation diagrams can be obtained from the coincidence of photoelectron and ion images and then the dynamic information in the dissociation can be inferred. For recording the spectroscopy and state-selected fragmentation, the mass-selected threshold photoelectrons were measured as a function of the photon energy, using the SPES method previously described.29,30 3. RESULTS & DISCUSSION 3.1 Time-Of-Flight Mass Spectra TOF mass spectra were recorded at different fixed photon energies: hν = 13.00, 13.65, 15.50, 18.50 and 21.22 eV, and are shown in Figure 1. The adiabatic ionization energy (AIE) of CH3F is located at 12.533 eV.3 As shown in Table 1, many dissociation channels of CH3F+ leading to CH2F+, CHF+, CH3+ and CH2+ fragment ions are open in the present excitation energy range. The CH2F+(1A1) + H(2S) fragmentation channel is the lowest dissociation channel and its adiabatic appearance energy (dissociation limit) was given at 13.358 eV by modeling the breakdown diagram.36

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Figure 1. Time-of-flight mass spectra recorded at several fixed photon energies of (a) hν= 13.00 eV, (b) hν= 13.65 eV, (c) hν= 15.50 eV, (d) hν= 18.50 eV and (e) hν= 21.22 eV with 20-timesmagnified data in blue to clearly show the weak signals of some fragment ions.

In the mass spectrum of Figure 1a at hν= 13.00 eV, well below all the dissociation limits of the CH3F+ ion, the intense and narrow (=cold) peak at m/z= 34 exists and is assigned to the parent CH3F+ ion. Also another peak at m/z = 35 can be identified in the mass spectrum and assigned to 13CH3F+ isotopic molecular ion with an intensity of only about 1% of that of the CH3F+ peak. In Figure 1b at hν= 13.65 eV, besides the peak of CH3F+ molecular ion, another peak appears at m/z= 33 in the mass spectrum and is attributed to CH2F+ fragment ion. At the other higher photon energies additional peaks at m/z= 14, 15 and 32 can be discerned and are assigned to CH2+, CH3+, and CHF+ fragment ions in the mass spectra. In addition, similar to previous electron impact ionization and TPEPICO studies,21,37 the CF+ fragment ions which should involve three-body decomposition can be identified with very weak signal in the mass spectra too. Because of the released kinetic energy in the dissociation, the peak widths of CH2F+, CHF+, CH3+ and CH2+ fragment ions are larger than that of CH3F+ molecular ion. The CH3+ and CH2F+ fragments are the predominant fragment ions over the whole energy range studied. Interestingly, production of CH2+ and CHF+ fragment ions at hν= 15.50 eV (Figure 1c), lying in the Franck-Condon gap, is enhanced with respect to the other photon energies. 5 ACS Paragon Plus Environment

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We note also that the peak shape of CH3+ fragment ion in the mass spectra broadens with increasing photon energy, indicative of a changing KERD, as expected from previous measurements.11 Table 1 Appearance energies and resulting states in dissociation of CH3F+ ions.

+ 1

2

CH2F ( A1) + H( S)

13.358 b CHF+(2A1) + H2(1Sg+) 13.97 + 2

1

+

CH2 ( A1) + HF( S ) + 1

2

Resulting states f

Appearance energies (eV) Dissociation limits (eV) Present d Ref. 21 Ref. 6

Channels

CH3 ( A1) + F( P3/2) CH3+(1A1) + F(2P1/2) CH3+(3A’’) + F(2P) CH2F+(3A’’) + H(2S)

13.937

a

13.28

13.20±0.08 13.52

13.94 b b

14.530 14.580c 18.452b --

C3V

13.94 14.51 ----

13.91±0.05 14.04

e

13.93±0.05 14.00

e

14.51±0.03 ----

14.42 14.51 18.01 17.75

2

---

2

--

2

2

E, A1 E, 2A1 2 E --

2

Cs 2

A’ A’

A’

2

A’, 2A’’ 2 A’ 2 A’’ 2 A’’

a. from ref. 36; b, derived values from heat of formations and ionization energies cited from references 36,38-40; c. the spin-orbit splitting energy of F(2P3/2,1/2)= 0.050 eV, from NIST Atomic Spectra Database41; d. the errors of the present data are ±0.02 eV; e. from ref. 24; f. from ref. 6,27.

3.2 Total Slow Photoelectron Spectrum & Photoionization Efficiency Spectrum Similar to the traditional threshold photoelectron spectrum (TPES) acquired by scanning synchrotron photon energy, SPES29,30 also records the signal of photoelectrons with near-zero kinetic energies and its energy resolution can be comparable to the TPES obtained with a subtraction method42. In addition, as an Abel inversion algorithm35 was employed to process photoelectron images, SPES overcomes the problem of hot electron contamination found in Ref. 42, where only an empirical parameter is used to remove it. The total SPES of CH3F and the total photoionization efficiency (PIE) spectrum in the 12.2-19.8 eV energy range were measured by scanning the photon energy with a 10 meV step size and are displayed as a black solid line and a blue dotted line respectively in Figure 2a. The extraction electric field of the DELICIOUS III spectrometer was set at 53 V cm-1 and the total energy resolution of SPES is about 20 meV. Note that under these conditions photoelectrons with kinetic energies (eKE) larger than 2.2 eV will only be partially collected and so the PIE spectrum shown here does not correspond to the total ion yield spectrum for hν > AIE + 2.2 eV.13 Three broad bands with centers at 13.9, 15.2 and 17.8 eV can be discerned in the PIE spectrum and the first two bands are ascribed to the autoionization of the (3a1/1e)  3s/3p and (3a1/1e)  4s/3d Rydberg states based on the previous photo-absorption results16-18. In addition, several dips with a very sharp width can be identified in the PIE spectrum and are due to the resonant excitation of neutral argon in the gas filter, which have been utilized to calibrate the absolute photon energy. 6 ACS Paragon Plus Environment

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Figure 2. Mass-selected slow photoelectron spectra (SPES, black solid lines, with 10-timesmagnified data in red) and photoionization efficiency (PIE, blue dotted lines) spectra corresponding to (a) all ions, (b) CH3F+, (c) CH2F+, (d) CHF+, (e) CH3+ and (f) CH2+ ions in the photon energy range of 12.1–19.8 eV.

Similar to the previous PES and TPES results,3,11,21 two bands corresponding to the X2E, A2A1 and B2E low-lying electronic states of CH3F+ are observed in the SPES. The first band ranging from 12.5 to 14.4 eV is attributed to the X2E ground state and can be divided into two parts due to the Jahn-Teller splitting. Vibrational structure is evident in the low-energy part of the X2E state and has been assigned to the excitations of the C-F stretching, the H-C-F bending and the CH3 deformation vibrational modes of CH3F+ ion.3 The first peak located at hν= 12.54 ± 0.01 eV is attributed to the adiabatic ionization energy of CH3F molecule. In contrast, the high-energy part of the X2E state is structureless and presents a long tail towards higher photon energy. The second band of the SPES ranging from 16 to 18 eV belongs to the A2A1 and B2E overlapped electronic states, which cannot be separated even with higher energy resolution, and no fine structures can be discerned in it. Recently, taking advantage of the method of i2PEPICO, the overlapped A2A1 and the B2E electronic states were successfully separated in the electron and ion kinetic energy correlation diagram based on their different kinetic 7 ACS Paragon Plus Environment

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energies released in the dissociation, and their adiabatic ionization energies were measured at 16.08 ± 0.03 and 17.00 ± 0.05 eV, respectively.12 Contrary to the previous PES,3 in the SPES a noticeable signal also appears in the Franck-Condon gap between the two bands and is ascribed to the resonant autoionization of Rydberg states upon scanning the photon energy. The neutral Rydberg states of (3a1/1e)3s/3p and (3a1/1e)4s/3d observed in the photo-absorption spectra16-18 are located in the Franck-Condon gap and can decay to the lower X2E ionic ground state via resonant or near-resonant autoionization, leading to the production of photoelectrons with a priori a broad range of kinetic energy, including slow photoelectrons. 3.3 CH3F+ Molecular Ion The corresponding mass-selected SPES and the PIE spectrum of the CH3F+ molecular ion are displayed in Figure 2b. Interestingly, in the SPES it is clear that the production of the parent ion is strictly correlated to the left side of the X band, where the vibrational structure is seen. Note that in a previous TPEPICO study,21 Weitzel et al. found higher energy states correlated to the production of parent ion (non-dissociative) and even a metastable state of the CH3F+ ion was suggested to exist in this energy range, which is in stark disagreement with the mass-selected SPES in Figure 2b. This discrepancy might be ascribed to the better treatment of the hot electron contribution in the SPES method, as discussed in Section 3.2. To explore the photoionization and dissociative photoionization of CH3F in more detail, PEPICO experiments at several fixed photon energies were also performed. For example, to discriminate the different effects of the direct photoionization and the resonant autoionization, we have carried out PEPICO experiments at hν= 21.22 eV, the He(I) resonant wavelength. Note that when working at a fixed photon energy the resonant autoionization channels will be absent. The mass-selected photoelectron image corresponding to CH3F+ molecular ion recorded at hν= 21.22 eV is presented in Figure 3a. The mass-selected PES obtained from the photoelectron image is very similar to the mass-selected SPES of Figure 2b and neither has populations in the high-energy part of the X2E ground state. However, due to the restriction of energy resolution of electron image,15 the fine vibrational peaks in the low-energy part of the X2E state observed in the mass-selected SPES are not resolved in the PES and the high-energy side fall is less steep. The coincident CH3F+ molecular ion image was also measured (not shown here) which allowed the translational temperature of the continuous molecular beam to be estimated at ~25 K.

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Figure 3. Mass-selected electron images (a) CH3F+, (b) CH2F+ and (c) CH3+ ions recorded at fixed photon energy of hν= 21.22 eV. The upper half of the electron image represents the raw data and the lower one corresponds to the result from the pBasex inversion algorithm35. The polarization of synchrotron photons is linearly horizontal and parallel to the east-west direction of the image. The correspondent mass-selected PES extracted from the inversion of the electron image is presented in the right panels, with 10-times-magnified data in red.

3.4 CH2F+ Fragment Ion The lowest dissociation channel of the CH3F+ ion leads to the production of CH2F+(1A1) and H(2S) fragments with an adiabatic appearance energy at 13.358 eV.36 The adiabatic appearance energy was given by the disappearance energy of the parent ion and modeling the breakdown diagram with the internal energy distribution of the neutral precursor. As shown in Figure 1, CH2F+ is the primary fragment ion with a sharp appearance threshold at hν= 13.28 ± 0.02 eV and a maximum at hν= 13.46 eV, as seen in the mass-selected SPES of Figure 2c. The mass-selected SPES of the CH2F+ fragment ion can be divided into three components, an intense component ranging from 13.2 to 14.4 eV in the high-energy part 9 ACS Paragon Plus Environment

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of the X2E ground state, a long tail ranging from 14.4 to 16.0 eV in the Franck-Condon gap and a very weak component in the energy range of the A2A1 and B2E electronic states. In the high-energy part of the X2E ground state the intensity of the mass-selected SPES is almost the same as that of the total SPES in Figure 2a, indicating that the CH3F+ molecular ion prepared in the high-energy part of the X2E ground state predominately dissociates into CH2F+ and H fragments.

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Figure 4. Electron and ion kinetic energy correlation diagrams of (a) CH2F+, (b) CHF+ and (c) CH2+ fragment ions recorded at a fixed photon energy of hν= 15.50 eV. The signal intensity increases from yellow to white, black representing zero.

To elucidate the origin of the CH2F+ fragment ion produced in the Franck-Condon gap, the mass-selected electron image and PES corresponding to CH2F+ fragment ion were also recorded in the PEPICO experiment at hν= 21.22 eV and are presented in Figure 3b. In accordance with the mass-selected SPES of CH2F+ fragment ion in Figure 2c, the high-energy part of the X2E ground state has also been populated in the massselected PES of Figure 3b, implying that here the production of CH2F+ fragment ion is mainly from a direct process. The signal then disappears in the Franck-Condon gap between the X2E and the A2A1 electronic states. This is in contrast to the CH2F+ production seen in the mass-selected SPES of Figure 2c, which must now be attributed to the resonant dissociative autoionization of neutral Rydberg states during the photon energy scan. This is further validated by the two broad absorptions observed in the PIE spectrum of CH2F+ shown in Figure 2c, which appear in the energy range of the FranckCondon gap and that are assigned to the autoionization of the (3a1/1e)  3s/3p and (3a1/1e)  4s/3d Rydberg states, according to a previous photo-absorption study16-18. In addition, as shown in Figures 2c and 3b, both the mass-selected SPES and PES of the CH2F+ fragment ion still show a weak signal in the energy range of the A2A1 and B2E electronic states, indicating that the CH3F+ molecular ions prepared in this energy range can dissociate into CH2F+ and H fragments too. Electron and ion kinetic energy correlation diagrams can be constructed from the correlation of electron and ion images obtained in coincidence, and are displayed in Figure 4a for the CH2F+ fragment ion at the fixed photon energy of hν= 15.5 eV, lying in the Franck-Condon gap. For a more intuitive comparison with the above mass-selected SPES and PES, the horizontal axis of the correlation diagram has been converted to electron binding energy (eBE, or the parent ion energy relative to the neutral CH3F molecule) according to the relation eBE= hν – eKE. In the correlation diagram, CH2F+ fragment ions can be produced in the eBE range of 13.3 ~ 15.5 eV, covering the energy range of the high-energy part of the X2E ground state and the Franck-Condon gap, with the hν= 15.5 eV photons. As most of the kinetic energy released in the dissociation has been carried away by the accompanied H fragment, the kinetic energy of the CH2F+ fragment ion is very small, and its shape can be fitted with a thermal Boltzmann function. The dissociation mechanisms of CH3F+ ion to produce CH2F+ and H fragments can be discussed with the aid of theoretical potential energy curves. The potential energy curves of the low-lying electronic states of CH3F+ ion along the C-H coordinate adapted 11 ACS Paragon Plus Environment

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from references 6,8,27 are presented in Figure 5a. The previous CASPT2/CASSCF calculations show that the 12A’ and 12A” Jahn-Teller splitting states (Cs symmetry) of the X2E ground state are bound and adiabatically correlate to the dissociation limits of CH2F+(11A1) + H and CH2F+(13A”) + H, respectively. The A2A1(22A’) electronic state would not lead to the CH2F+ and H dissociation products. The 22A” Jahn-Teller split state of the B2E state is bound too and correlates to the CH2F+(11A”) + H dissociation limit. The energy levels of the excited CH2F+(13A”) + H and CH2F+(11A”) + H dissociation limits are too high to be involved in the production of CH2F+ and H fragments in the Figure 4 energy range (below 15.5 eV).

Figure 5. Potential energy curves of low-lying electronic states of CH3F+ ions along the (a) C–H and (b) C-F coordinates adapted with permission from ref. 6 (Copyright (2017) American Chemical Society), together with the Franck–Condon region in photoionization marked in purple. Note that the 12A” and 12A’ states resulting from the Jahn-Teller split of the X2E state in panel (b) are not distinguishable above RC-F>1.6 Å.

The combination of the experimental data and the theoretical potential energy curves point to several mechanisms for production of CH2F+ + H fragments summarized below.

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(1) In the high-energy part of the X2E ground state, the production of CH2F+ and H fragments is via vibrational dissociation, ie intramolecular vibrational redistribution (IVR) leading to the production of hot CH3F+ ions in the ground state undergoing statistical dissociation along the potential energy curve of the 12A’ state as supported by the statistical kinetic energy distribution released in the dissociation: CH3F + hν  CH3F+(X2E, v) + e-  CH2F+(11A1) + H(2S) + e-

(R1);

(2) In the Franck-Condon gap, the production of CH2F+ and H fragments can be explained through the autoionization of the (3a1/1e)  3s/3p and (3a1/1e)  4s/3d Rydberg states to a highly-excited vibrational ground state followed by statistical dissociation along the potential energy curve of the X2E ground state: CH3F + hν  CH3F*  CH3F+(X2E, v) + e-  CH2F+(11A1) + H(2S) + e-

(R2);

(3) As we will discuss in the next part, the A2A1 electronic state is a repulsive and directly dissociative state to produce CH3+ and F fragments. This dissociation is very fast and so the other competition pathways such as the production of CH2F+ fragment ion from the A2A1 state should be quenched21, and indeed the CH2F+ signal seen in the A2A1 state region is negligible. (4) In the B2E electronic state, CH3F+ ions first perform a relaxation process such as internal conversion to the high vibrational X2E ground state and then statistically dissociate to the CH2F+(11A1) and H(2S) fragments: CH3F + hν  CH3F+(B2E) + e-  CH3F+(X2E, v) + e-  CH2F+(11A1) + H(2S) + e- (R3). The productions of CH2F+ fragment ion from the above R1 ~ R3 three reactions can be used to explain and agree very well with the three components in the mass-selected SPES of CH2F+ ion in Figure 2c. 3.5 CH3+ Fragment Ion The mass-selected SPES of the CH3+ fragment ion is shown in Figure 2e and can be divided into two parts, the weak part in the Franck-Condon gap with an onset at hν= 14.51 ± 0.02 eV and the intense part in the energy range of the A2A1 and B2E electronic states where the CH3F+ ions predominately dissociate to CH3+ and F fragments. In contrast, no counts in the Franck-Condon gap can be observed in the mass-selected PES of CH3+ recorded at hν= 21.22 eV (see Figure 3c). Therefore, and as seen for the CH2F+ fragment, the population of the CH3+ channel in the Franck-Condon gap should be ascribed to the dissociative autoionization of the (3a1/1e)  3s/3p and (3a1/1e)  4s/3d Rydberg states too17.

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The electron and ion kinetic energy correlation diagram of CH3+ fragment ions recorded at hν= 15.50 eV is presented in Figure 6a.11 It is shown that CH3F+ ions can be prepared in the electron binding energy range of 14.5~15.5 eV with the hν= 15.5 eV photons and then dissociate to CH3+ and F fragments. In the correlation diagram the kinetic energy of CH3+ fragment ion increases with electron binding energy but still has a maximal population at low kinetic energy. The kinetic energy distribution can be fitted well with a Boltzmann function, implying a statistical dissociation.

Figure 6. Electron and ion kinetic energy correlation diagrams of CH3+ fragment ions recorded at fixed photon energies of (a) hν= 15.50 eV and (b) hν= 21.22 eV. The signal intensity increases from yellow to white, black representing zero.

The electron and ion kinetic energy correlation diagram of CH3+ fragment ion was also recorded at hν= 21.22 eV and is presented in Figure 6b. In agreement with the massselected PES in Figure 3c, here the CH3F+ ions were also only prepared in the A2A1 and B2E electronic states, without populations in the Franck-Condon gap, and then dissociate into CH3+ and F fragments. In agreement with our previously reported results, the contour of the correlation diagram can be divided into two parts.11,12 The intense part with a large kinetic energy of KE(CH3+) > 0.4 eV can be fitted with a Gaussian function and correlates to the direct dissociation along the A2A1 electronic state. The weak part with a small kinetic energy of KE(CH3+) < 0.4 eV has a Boltzmann distribution and is attributed to the statistical dissociation of the B2E electronic state. The potential energy curves of CH3F+ along the C-F coordinate adapted from reference 6 are presented in Figure 5b. The two Jahn-Teller split states of the X2E ground state, 12A” and 12A’, are bound and adiabatically correlate to the CH3+(11A1) + F dissociation limit. The A2A1 electronic state is a repulsive state and correlates to the CH3+(11A1) + F dissociation limit too. But the dissociation limit correlating to the A2A1 electronic state is calculated to be slightly higher (~ 0.09 eV) than that of the X2E ground state. So similar to the cases of CH3Cl+ and CH3Br+ and after taking into account the spin-orbit splitting energy of the 2P state of F atom, 0.05 eV, 10,13,41 the X2E ground state 14 ACS Paragon Plus Environment

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should correlate to the CH3+(11A1) + F(2P3/2) dissociation limit and the A2A1 excited state to the CH3+(11A1) + F(2P1/2) limit. For the B2E electronic state, its two Jahn-Teller split states, 22A” and 32A’, are bound along the C-F coordinate and correlate to the CH3+(13A”) + F and CH3+(13A’) + F dissociation limits, respectively, both of which are much higher than the ionization energies of the A2A1 and B2E electronic states. The detailed dissociation mechanisms of CH3F+ ions to produce CH3+ and F fragments are summarized below. (1) In the Franck-Condon gap, the production of CH3+(11A1’) and F(2P3/2) fragments is via dissociative autoionization of the (3a1/1e)  3s/3p and (3a1/1e)  4s/3d Rydberg states along the potential energy curve of the X2E ground state: CH3F + hνCH3F* CH3F+(X2E, v) + e-CH3+(11A1’) + F(2P3/2) + e-

(R4);

(2) The CH3F+ ions prepared in the A2A1 electronic state directly dissociate to CH3+(11A1’) and F(2P1/2) fragments along the potential energy curve of the A2A1 state: CH3F + hν  CH3F+(A2A1) + e-  CH3+(11A1’) + F(2P1/2) + e-

(R5);

(3) In the B2E state, the CH3F+ ions perform internal conversion to the high vibrational levels of the X2E ground state and then statistically dissociate to the CH3+(11A1’) and F(2P3/2) fragments: CH3F + hν  CH3F+(B2E) + e-  CH3F+(X2E, v) + e-  CH3+(11A1’) + F(2P3/2) + e- (R6). As shown in Figure 6b, the signal level of the slow CH3+ fragment ion is rather low in the energy range of the A2A1 and B2E states. So if the cross-sections to both electronic states are comparable, some part of the B2E states may also cross over to the A2A1 state and then dissociates impulsively. 3.6 CHF+ & CH2+ Fragment Ions As shown in the mass-selected SPES in Figures 2d and 2f, CHF+ and CH2+ are the minor fragment ions in the dissociation of CH3F+. From their SPES, their respective appearance energies are identical, 13.94 ± 0.02 eV, lying in the Franck-Condon gap, with a sharp rise towards the maximum located at ~ 14 eV followed by a monotonous decline with increasing photon energy, although they are still produced in the energy range of the A2A1 and B2E electronic states. The mass-selected SPES and PIE spectrum of the CF+ fragment ion were also acquired and are presented in Figure S1 and its appearance energy is measured to be at ~ 17 eV. The electron and ion kinetic energy correlation diagrams of CHF+ and CH2+ fragment ions obtained at fixed photon energy of hν= 15.5 eV are presented in Figures 4b 15 ACS Paragon Plus Environment

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and 4c. For the production of CHF+ fragment ions, as most of the kinetic energy released in the dissociation was carried away by the accompanied H2 fragment, the kinetic energy of the CHF+ fragment ion is small and can be fitted with a Boltzmann function, indicating a statistical dissociation mechanism. In the correlation diagram of Figure 4c, the CH2+ fragment ion exhibits a large kinetic energy, which can also be modeled with a Boltzmann distribution. Note that due to the very weak signals from these two fragments, the PEPICO data at hν= 21.22 eV are too noisy to be useable. According to the potential energy curves of the CH3F+ ion along the C-H coordinate shown in Figure 5a, the CH2+(2A1) + HF(1S+) dissociation limit should adiabatically correlate to the A2A1(22A’) repulsive state.8,27 But after taking into account the potential energy curves non-crossing rule (the geometry of CH3F+ may change from Cs to C1 symmetry in the production of CH2+ and HF fragments),43 the 12A’’(X2E) state should correlate to the CH2+(2A1) + HF(1S+) dissociation limit and the A2A1(22A’) state to the CH2F+(13A”) + H dissociation limit. Again, in the Franck-Condon gap, the production of CH2+ fragment ion is via dissociative autoionization of the (3a1/1e)  3s/3p and (3a1/1e)  4s/3d Rydberg states along the potential energy curve of the X2E ground state, CH3F + hνCH3F* CH3F+(X2E, v) + e- CH2+(2A1) + HF(1S+) + e-

(R7);

As we discussed above, the A2A1 electronic state is repulsive and directly dissociates to CH3+ and F fragments, so other competing pathways from the A2A1 state should be quenched. The CH3F+ ions prepared in the B2E electronic state can dissociate to CH2+ and HF fragments via internal conversion to the highly-excited vibrational levels of the X2E ground state, CH3F + hν  CH3F+(B2E) + e- CH3F+(X2E, v) + e- CH2+(2A1) + HF(1S+) + e-

(R8).

In addition, previous calculations44 show that the CH2FH+ isomer of CH3F+ also adiabatically correlates to the CH2+ and HF fragments and may be involved in the dissociation. Similar to the case of the CH2+(2A1) + HF(1S+) dissociation limit, the CHF+(2A1) + H2(1Sg+) dissociation limit originally correlates to a 2A’ electronic state.45 Taking into account the non-crossing rule of the potential energy curves,43 the CHF+(2A1) + H2(1Sg+) dissociation limit should also correlate to the X2E ground state. The appearance of CHF+ fragment ions in the Franck-Condon gap should also involve the dissociative autoionization of the (3a1/1e)  3s/3p and (3a1/1e)  4s/3d Rydberg states, 16 ACS Paragon Plus Environment

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CH3F + hνCH3F* CH3F+(X2E, v) + e-  CHF+(2A1) + H2(1Sg+) + e-

(R9);

In addition, the dissociation mechanism of internal conversion to the high vibrational levels of the X2E ground state can also be employed to explain the production of CHF+ and H2 fragments in the dissociation of the B2E state, CH3F + hν  CH3F+(B2E) + e-CH3F+(X2E, v) + e-  CHF+(2A1) + H2(1Sg+) + e- (R10). 4. CONCLUSIONS The VUV photoionization and state-selected dissociative photoionization of CH3F in the 12.2-19.8 eV energy range have been investigated by i2PEPICO coupled to tunable synchrotron radiation. Three low-lying electronic states of CH3F+ ion, X2E, A2A1 and B2E, as well as outside the Franck-Condon region, have been prepared and analyzed. CH2F+, CHF+, CH3+ and CH2+ fragment ions in the dissociation of CH3F+ were observed, with their individual appearance energies measured through threshold photoelectron spectroscopy. In addition, to explore the dissociation dynamics in more detail, and to judge the effect of resonant autoionization, PEPICO experiments were also performed at several fixed photon energies. The mass-selected PES and the electron and ion kinetic energy correlation diagrams corresponding to each fragment ions were obtained. Based on the present experimental data and the previous theoretical results, the detailed dissociation mechanisms of state-selected CH3F+ ions prepared in the X2E, A2A1 and B2E, as well as outside the Franck-Condon region have been discussed and revealed. Up to three different pathways for production of CH3+ and CH2F+ fragments have been determined below 20 eV photon energy. In the high-energy part of the X2E ground state, the production of CH2F+(11A1) and H(2S) fragments is via vibrational dissociation of CH3F+ ions along the potential energy curve of the X2E state. The productions of CH2F+, CHF+, CH3+ and CH2+ fragment ions in the Franck-Condon gap between the X2E and the A2A1 states arise from the dissociative autoionization of the (3a1/1e)  3s/3p and (3a1/1e)  4s/3d Rydberg states via the X2E ground state. The spin-orbit splitting states of the F fragment, 2P3/2 and 2P1/2, in the CH3+ + F dissociation channels were assigned and adiabatically correlate to the X2E ground state and the A2A1 electronic state respectively. The A2A1 electronic state is a repulsive state along the C-F coordinate and this dissociation is a direct and fast process. The CH3F+ ion prepared in the A2A1 state will predominantly dissociate to CH3+(11A1’) and F(2P1/2) fragment. The B2E electronic state is a bound state and will undergone internal conversion to the high vibrational states of the X2E ground state and then statistically dissociates to CH2F+, CHF+, CH3+ and CH2+ fragment ions.

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Similar to the CH3Cl+ and CH3Br+ ions we have analyzed before, the dissociation of CH3F+ ion to different products is also shown to be state-specific.9-13 In particular, the primary fragment ion in the dissociation of the CH3X+(X=F, Cl, Br) ions, the production of CH3+, is very rich and involves direct and indirect processes such as dissociative autoionization, direct dissociation and internal conversion etc. The i2PEPICO method has proven to be an adequate tool to investigate state/energy-selected CH3X+ (X=F, Cl, Br) ions providing valuable and detailed information. Further studies involving CH3I+ where the presence of a heavy atom might affect the fragmentation pathways will be undertaken in future experiments. ACKNOWLEDGEMENTS X. T. would like to thank financial supports from National Natural Science Foundation of China (91644109), National Key Research and Development Program of China (2016YFC0200300) and Natural Science Foundation of Anhui Province (1608085MB35). The authors are grateful to J.-F. Gil for his technical support during the experiments and the SOLEIL general staff for smoothly running the synchrotron facility and providing beamtime under Projects 20140090 and 20130969. REFERENCES (1) Molina, M. J.; Molina, L. T.; Kolb, C. E. Gas-phase and heterogeneous chemical kinetics of the troposphere and stratosphere. Annu. Rev. Phys. Chem. 1996, 47, 327-367. (2) Daniel, J. S.; Solomon, S.; Portmann, R. W.; Garcia, R. R. Stratospheric ozone destruction: The importance of bromine relative to chlorine. J. Geophys. Res. 1999, 104, 23871-23880. (3) Karlsson, L.; Jadrny, R.; Mattsson, L.; Chau, F. T.; Siegbahn, K. Vibrational and vibronic structure in the valence electron spectra of CH3X molecules (X= F, Cl, Br, I, OH). Phys. Scr. 1977, 16, 225-234. (4) Hikosaka, Y.; Eland, J. H. D.; Watson, T. M.; Powis, I. Molecule frame photoelectron angular distributions from oriented methyl chloride and methyl fluoride molecules. J. Chem. Phys. 2001, 115, 4593-4603. (5) Grutter, M.; Qian, X.; Merkt, F. Photoelectron spectroscopic study of the Ee JahnTeller effect in the presence of a tunable spin-orbit interaction. III. Two-state excitonic model accounting for observed trends in the X2E ground state of CH3X+ (X = F, Cl, Br, I) and CH3Y (Y = O, S). J. Chem. Phys. 2012, 137, 084313. (6) Xi, H. W.; Huang, M. B.; Chen, B. Z.; Li, W. Z. F-loss and H-loss dissociations in low-lying electronic states of the CH3F+ ion studied using multiconfiguration secondorder perturbation theory. J. Phys. Chem. A 2005, 109, 9149-9155. (7) Shao, Z.; Li, H.; Zhang, S. Y.; Li, J.; Dai, Z. Y.; Mo, Y. X.; Bae, Y. J.; Kim, M. S. The Jahn-Teller effect in CH3Cl+(X2E): A combined high-resolution experimental measurement and ab initio theoretical study. J. Chem. Phys. 2012, 136, 064308.

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(8) Eland, J. H. D.; Frey, R.; Kuestler, A.; Schulte, H.; Brehm, B. Unimolecular dissociations and internal conversions of methyl halide ions. Int. J. Mass Spectrom. Ion Phys. 1976, 22, 155-170. (9) Tang, X.; Zhou, X. G.; Wu, M. M.; Liu, S. L.; Liu, F. Y.; Shan, X. B.; Sheng, L. S. Dissociative photoionization of methyl chloride studied with threshold photoelectronphotoion coincidence velocity imaging. J. Chem. Phys. 2012, 136, 034304. (10) Tang, X.; Zhou, X. G.; Sun, Z. F.; Liu, S. L.; Liu, F. Y.; Sheng, L. S.; Yan, B. Dissociation of internal energy-selected methyl bromide ion revealed from threshold photoelectron-photoion coincidence velocity imaging. J. Chem. Phys. 2014, 140, 044312. (11) Tang, X.; Garcia, G. A.; Nahon, L. CH3+ formation in the dissociation of energyselected CH3F+ studied by double imaging electron/ion coincidences. J. Phys. Chem. A 2015, 119, 5942-5950. (12) Tang, X.; Garcia, G. A.; Nahon, L. Adiabatic ionization energies of the overlapped A2A1 and B2E electronic states in CH3Cl+/CH3F+ measured with double imaging electron/ion coincidence. Phys. Chem. Chem. Phys. 2015, 17, 16858-16863. (13) Tang, X.; Lin, X.; Zhang, W.; Garcia, G. A.; Nahon, L. Double imaging photoelectron photoion coincidence sheds new light on the dissociation of energyselected CH3Cl+ ions. Phys. Chem. Chem. Phys. 2016, 18, 23923-23931. (14) Tang, X.; Zhou, X. G.; Niu, M. L.; Liu, S. L.; Sun, J. D.; Shan, X. B.; Liu, F. Y.; Sheng, L. S. A threshold photoelectron-photoion coincidence spectrometer with double velocity imaging using synchrotron radiation. Rev. Sci. Instrum. 2009, 80, 113101. (15) Garcia, G. A.; Miranda, B. K. C.; Tia, M.; Daly, S.; Nahon, L. DELICIOUS III: A multipurpose double imaging particle coincidence spectrometer for gas phase vacuum ultraviolet photodynamics studies. Rev. Sci. Instrum. 2013, 84, 053112. (16) Stokes, S.; Duncan, A. B. F. Electronic transitions in methyl fluoride and in fluoroform. J. Am. Chem. Soc. 1958, 80, 6177-6181. (17) Locht, R.; Leyh, B.; Hoxha, A.; Dehareng, D.; Jochims, H. W.; Baumgartel, H. About the vacuum UV photoabsorption spectrum of methyl fluoride (CH3F): the fine structure and its vibrational analysis. Chem. Phys. 2000, 257, 283-299. (18) Olney, T. N.; Cooper, G.; Chan, W. F.; Burton, G. R.; Brion, C. E.; Tan, K. H. Quantitative studies of the photoabsorption, photoionization, and ionic photofragmentation of methyl fluoride at VUV and soft X-ray energies (7-250 eV) using dipole electron scattering and synchrotron radiation. Chem. Phys. 1994, 189, 733-756. (19) Brundle, C. R.; Robin, M. B.; Basch, H. Electronic energies and electronic structures of the fluoromethanes. J. Chem. Phys. 1970, 53, 2196-2213. (20) Pullen, B. P.; Carlson, T. A.; Moddeman, W. E.; Schweitzer, G. K.; Bull, W. E.; Grimm, F. A. Photoelectron spectra of methane, silane, germane, methyl fluoride, difluoromethane, and trifluoromethane. J. Chem. Phys. 1970, 53, 768-782. (21) Weitzel, K. M.; Guthe, F.; Mahnert, J.; Locht, R.; Baumgartel, H. Statistical and non-statistical reactions in energy selected fluoromethane ions. Chem. Phys. 1995, 201, 287-298. (22) Gao, S. M.; Dai, Z. Y.; Sun, W.; Li, H.; Wang, J.; Mo, Y. X. Tunneling splittings in vibronic energy levels of CH3F+ (X2E) studied by high resolution photoelectron spectroscopy and ab initio calculation. J. Chem. Phys. 2013, 139, 064302. (23) Locht, R.; Momigny, J. The dissociative ionization of methyl fluoride. The formation of CH2+ and CH3+. Int. J. Mass Spectrom. Ion Proc. 1986, 71, 141-157. 19 ACS Paragon Plus Environment

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(24) Torres, I.; Martinez, R.; Castano, F. Electron-impact dissociative ionization of the CH3F molecule. J. Phys. B: At. Mol. Opt. Phys. 2002, 35, 4113-4123. (25) Harshbarger, W. R.; Robin, M. B.; Lassettre, E. N. The electron impact spectra of the fluoromethanes. J. Electron Spectrosc. Relat. Phenom. 1972-1973, 1, 319-332. (26) Krauss, M.; Walker, J. A.; Dibeler, V. H. Mass spectrometric study of photoionization. X. Hydrogen chloride and methyl halides. J. Res. Natl. Bur. Stand. Section A 1968, 72, 281-293. (27) Momigny, J.; Locht, R.; Caprace, G. Translational energy disposal and mechanisms of unimolecular dissociative photoionization with He(I) and Ne(I) resonance lines. A surprisal analysis of the CH3F --> CH3+ + F process. Int. J. Mass Spectrom. Ion Proc. 1986, 71, 159-168. (28) Locht, R.; Momigny, J.; Ruhl, E.; Baumgartel, H. A mass spectrometric photoionization study of CH3F. The CH2+, CH3+ and CH2F+ ion formation. Chem. Phys. 1987, 117, 305-313. (29) Briant, M.; Poisson, L.; Hochlaf, M.; de Pujo, P.; Gaveau, M.-A.; Soep, B. Ar2 photoelectron spectroscopy mediated by autoionizing states. Phys. Rev. Lett. 2012, 109, 193401. (30) Poully, J. C.; Schermann, J. P.; Nieuwjaer, N.; Lecomte, F.; Gregoire, G.; Desfrancois, C.; Garcia, G. A.; Nahon, L.; Nandi, D.; Poisson, L.; Hochlaf, M. Photoionization of 2-pyridone and 2-hydroxypyridine. Phys. Chem. Chem. Phys. 2010, 12, 3566-3572. (31) Tang, X.; Garcia, G. A.; Gil, J.-F.; Nahon, L. Vacuum upgrade and enhanced performances of the double imaging electron/ion coincidence end-station at the vacuum ultraviolet beamline DESIRS. Rev. Sci. Instrum. 2015, 86, 123108. (32) Nahon, L.; Oliveira, N.; Garcia, G. A.; Gil, J. F.; Pilette, B.; Marcouille, O.; Lagarde, B.; Polack, F. DESIRS: a state-of-the-art VUV beamline featuring high resolution and variable polarization for spectroscopy and dichroism at SOLEIL. J. Synchrotron Rad. 2012, 19, 508-520. (33) Eppink, A.; Parker, D. H. Velocity map imaging of ions and electrons using electrostatic lenses: Application in photoelectron and photofragment ion imaging of molecular oxygen. Rev. Sci. Instrum. 1997, 68, 3477. (34) Wiley, W. C.; McLaren, I. H. Time-of-flight mass spectrometer with improved resolution. Rev. Sci. Instrum. 1955, 26, 1150-1157. (35) Garcia, G. A.; Nahon, L.; Powis, I. Two-dimensional charged particle image inversion using a polar basis function expansion. Rev. Sci. Instrum. 2004, 75, 4989-4996. (36) Harvey, J.; Tuckett, R. P.; Bodi, A. A halomethane thermochemical network from iPEPICO experiments and quantum chemical calculations. J. Phys. Chem. A 2012, 116, 9696-9705. (37) Torres, I.; Martinez, R.; Rayo, M. N. S.; Castano, F. Nascent kinetic energy distributions of the ions produced by electron-impact on the CH3F molecule. Chem. Phys. Lett. 2000, 328, 135-141. (38) Csontos, J.; Rolik, Z.; Das, S.; Kallay, M. High-accuracy thermochemistry of atmospherically important fluorinated and chlorinated methane derivatives. J. Phys. Chem. A 2010, 114, 13093-13103. (39) Chase, M. W. J. NIST-JANAF thermochemical tables, Fourth eidtion. J. Ref. Chem. Ref. Data 1998, 9, 1-1951. 20 ACS Paragon Plus Environment

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(40) Lias, S. G.; Liebman, J. F. Gas Phase Ion Energetics Data. In NIST Chemistry WebBook; P. J. Linstrom, Mallard, W. G., Eds; NIST Standard Reference Database Number 69; National Institute of Standards and Technology: Gaithersburg, MD, http://webbook.nist.gov/chemistry/ (retrieved May 1, 2017). (41) Kramida, A.; Ralchenko, Y.; Reader, J. In NIST Atomic Spectra Database; National Institute of Standards and Technology: Gaithersburg MD, http://physics.nist.gov/asd (retrieved May 1, 2017). (42) Sztaray, B.; Baer, T. Suppression of hot electrons in threshold photoelectron photoion coincidence spectroscopy using velocity focusing optics. Rev. Sci. Instrum. 2003, 74, 3763-3768. (43) Herzberg, G., Molecular Spectra and Molecular Structure. III. Electronic Spectra and Electronic Structure of Polyatomic Molecules; Litton Educational Publishing Inc.: New York, 1966. (44) Yates, B. F.; Bouma, W. J.; Radom, L. Ylides and ylidions: A comparative study of unusual gas-phase structures. J. Am. Chem. Soc. 1987, 109, 2250-2263. (45) Tsuji, M.; Funatsu, T.; Kouno, H.; Nishimura, Y. Dissociative charge-transfer reactions of Ar+ with fluoromethanes at thermal energy. J. Chem. Phys. 1992, 97, 82168222.

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