Investigation of dissociative photoionization pathways for orientation-selected molecules by phase-controlled laser fields

Interaction between intense light and matter, such as nonlinear optical response, can be described by the conventional perturbation theory of quantum mechanics as multiphoton processes at a considerably high order. However, multiphoton processes involving more than tens of photons, which are easily induced by an intense ultrashort laser pulse with an intensity of more than 10¹² W/cm², cannot be described by conventional perturbation theory. Typical examples have been observed in tunneling ionization (TI) in which the sub-optical cycle dynamics of electrons in matter plays an essential role. The TI induced by intense laser fields occurs when the binding potential of an electron is reduced by the electric field of a laser so strongly that the wavefunction of the highest occupied electron penetrates the potential barrier and the electron is liberated from the binding potential.^1–5 Experimental studies have shown that TI is induced mainly in the sub-optical cycle of the attosecond time region, when the amplitude of the electric field of the laser peaks because of a high-order nonlinear optical response.^6–9 

In the case of molecules, the molecular orbital Ammosov–Delone–Krainov (MO-ADK) model,^10,11 which is a simple extension of the ADK model widely used for atoms,³ has revealed that the angular dependence of the TI rate between the electric field vector and the molecular axis reflects the geometric structure of the highest occupied molecular orbital (HOMO)^10,11 because photoelectrons are preferentially removed via the tunneling process from the large-amplitude lobe of the HOMO along the opposite direction of the electric field vector.^12,13 In addition to the influence of the orbital shape, the Stark effect,^14,15 orbital distortion in the presence of intense laser fields,^16,17 and the multi-electron effect^18–20 have been discussed in recent advanced theories.

We have investigated the sub-optical cycle control of laser waveforms and resultant orientation-selected molecular TI (OSM-TI) induced by phase-controlled two-color laser fields consisting of a fundamental light and its second harmonics in various molecules.^21–27 The OSM-TI that reflects the geometric structure of the HOMO has been observed in a broad range of molecules.^21–27 The electric field of a linearly polarized phase-controlled laser field consisting of a fundamental light and its second harmonics (hereafter ω+2ω laser fields) is given by E(t) = E₁ cos(ωt) + E₂ cos(2ωt + ϕ), where the E_n (n = 1, 2) are the amplitudes of the electric field of each component and ϕ is the relative phase difference between the ω and 2ω fields. The amplitude of the electric field in the positive (negative) direction is about twice that in the negative (positive) direction when ϕ = 0 (π) and E₂/E₁ = 0.5. Phase-controlled ω+2ω laser fields have a characteristic phase-dependent asymmetric waveform, in contrast to single-frequency laser fields, which have symmetric waveforms.

When TI of molecules with the asymmetric HOMO structure is induced by an asymmetric ω+2ω field, electrons are much more likely to be removed from the large-amplitude part of the HOMO in the direction opposite to that of the electric field vector at field maxima so that OSM-TI occurs among randomly oriented molecular ensembles. The ω+2ω laser fields can discriminate among molecular orientations with respect to head–tail ordering, which is impossible to achieve with a single-frequency laser field with a symmetric waveform.^21–27 

In this article, as an application of OSM-TI, we demonstrate the elucidation of dissociative ionization pathways of polyatomic molecules induced by phase-controlled laser fields.^28–30 Generally, photochemical reactions depend on the relative orientation between the molecular geometry and the polarization direction of the irradiating light. This orientational averaging can lead to loss of information in the gas or liquid phase with randomly orientated molecular ensembles. Observation and detection of molecules with orientation control have the potential to facilitate progress in molecular physics and analytical chemistry because loss of information due to orientational averaging can be eliminated. We demonstrate that OSM-TI is a powerful method for elucidating dissociation pathways, as well as for ion coincidence measurements and covariance mapping,^31–34 especially those dissociative ionization pathways that produce neutral photofragments, which are unable to be detected by ion detection techniques.

We selected two hydrofluorocarbons (HFCs), HFC-152a (1,1-difluoromethane, CHF₂–CH₃) and HFC-134a (1,1,1,2-tetrafluoromethane, CF₃–CH₂F) as target molecules. HFCs are known as replacement products for chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs). HFCs, CFCs, and HCFCs are recognized as refrigerants that are stable and harmless to animals; however, CFCs and HCFCs are well known ozone-depleting substances. The trigger of the chain reaction leading to ozone depletion is assumed to be the release of the chlorine radical by photolysis. An HFC molecule does not contain chorine, so HFC does not damage atmospheric ozone, but it remains a serious greenhouse gas with a global warming potential hundreds to thousands of times that of CO₂. These particular HFCs are studied from the viewpoint of the release of radicals in the same manner as for CFCs and many reactions with NO_x molecules and O atoms in previous studies.^35,36 The peaks of the photofragment ions produced from the HFC molecules in the mass spectrum do not interfere with each other, unlike hydrocarbon cations for which the mass spectrum is dense because of the difference in the number of hydrogen atoms. Therefore, HFC molecules are suitable for investigating dissociative ionization pathways clearly.

The experimental apparatus, which is described in a previous report,²³ consisted of a pulsed neodymium-doped yttrium-aluminum-garnet (Nd:YAG) laser, an interferometer-free phase-controlled laser field generator, and a time-of-flight mass spectrometer (TOF-MS) equipped with a supersonic molecular beam source. The output of the Q-switched Nd:YAG laser (Spectra-Physics, LAB150), which generates linearly polarized laser pulses with a 10-ns duration, a bandwidth of 1.0 cm⁻¹, and a 10-Hz repetition rate at a wavelength of 1064 nm, was introduced to an interferometer-free, phase-controlled ω+2ω laser field generator to ensure adjustment-free operation, high stability, and high reproducibility.^23,27 The generated phase-controlled ω+2ω beams were directed toward the TOF-MS and were focused on the supersonic molecular beam by a concave mirror with a focal length of 120 mm. The total intensity I = I₁ + I₂ was around 5.0 × 10¹² W/cm² at the focus, and the I₂/I₁ ratio was about 0.25, where I₁ and I₂ are the intensities of the ω and 2ω pulses, respectively. The polarization direction of the phase-controlled ω+2ω laser fields was set to be parallel to the TOF detection axis. We defined the relative phase difference ϕ = 0 to be the configuration in which the electric field maxima were pointing toward the ion detector. To calibrate ϕ and molecular mass, we performed simultaneous measurements using gas mixtures of target molecules and reference carbonyl sulfide (OCS) molecules.²³ 

A TOF-MS equipped with a pulsed supersonic molecular beam source was used to detect the ionized molecules and their photofragments. Target gases were expanded from a pulsed valve (General valve, Series 9) with a stagnation pressure of 6 × 10⁵ Pa. By operating the pulsed molecular beam at 10 Hz, the pressure in the TOF-MS was kept below 2.0 × 10⁻⁵ Pa. Photofragment ions generated by the phase-controlled ω+2ω laser pulses were detected with a microchannel plate detector. TOF spectra were recorded with a digital oscilloscope. The kinetic energies of photofragment ions were estimated by numerical calculations that took into account the configurations of the extraction electrodes and the ion detector in the TOF-MS and the applied voltages.

The optimized molecular structures and molecular orbitals were calculated at the MP2/aug-cc-pVTZ level by the GAUSSIAN 09 package.³⁷ The potential energy curves (PECs) were calculated at the M06-2X/aug-cc-pVTZ level. Note that the optimized structures of neutral species were used for singly charged cation calculations.

Figure 1(a) shows the molecular structure and isocontour of the HOMO of the HFC-152a molecule. The HOMO, in general, shows a less asymmetric structure than that of previously reported molecules.^21–26 Qualitative descriptions are that (1) the amplitude of the wavefunction is shrunk by the presence of F atoms, reflecting their large ionization potential, and (2) nodal structures originating from the p orbital of F atoms appear. Although the TI probability along the C–C bond is expected to decrease due to the shrinking and destructive interference at the nodal structures on the CHF₂ side,^10,11 at first glance, it is not apparent from which side the OSM-TI would be expected to remove an electron.

Figure 2(a) shows the TOF spectra of singly charged ions generated by dissociative ionization of HFC-152a from irradiation by phase-controlled ω+2ω pulses. We observed various singly charged photofragment ions, but we did not observe F⁺ nor parent C₂H₄F₂⁺ cations. In particular, CH₃⁺ and its counterpart CH₂F⁺ each exhibited a pair of peaks, the first resulting from ions emitted directly toward the detector and the second from those ions that were first emitted in the backward direction before being reversed by the extraction fields. The spacing of the forward and backward peaks reflects kinetic energy release. The kinetic energy of each photofragment ion was less than 0.2 eV.

Expanded views of typical TOF spectra of CH₃⁺ and the counterpart cation CHF₂⁺ with relative phase differences ϕ = 0, π/2, and π are shown in Figs. 2(b) and 2(c). When the molecules were irradiated by ω+2ω pulses with ϕ = 0 or π, breaking of the forward–backward symmetry was clearly observed in the TOF spectra. The backward peak of CH₃⁺ and the forward peak of its counterpart CHF₂⁺ predominated at ϕ = 0. This forward–backward asymmetry was reversed at ϕ = π. These results show that dissociative ionization was induced by the phase-controlled ω+2ω laser fields while discriminating between the head and tail orientations of the molecule. We defined the positive orientation of a molecule as the configuration in which the CHF₂⁺ side of the molecule points toward the ion detector. Other photofragment ions were not split into forward–backward peaks because of their small kinetic energy and broad energy distribution; therefore, phase-dependent behavior was not clearly discernible in the TOF spectra.

We analyzed the phase dependence of the observed photofragment ions by the yield asymmetry A_yield defined by (I_f − I_b)/(I_f + I_b), where I_f (I_b) is the ion yield of the forward (backward) photofragment emission. Figure 4(a) depicts A_yield as a function of ϕ. Clear sinusoidal patterns of A_yield were observed in CHF₂⁺ and counterpart CH₃⁺, and the A_yield values of CHF₂⁺ and CH₃⁺ were completely out of phase with each other. These results showed that phase-controlled ω+2ω fields could distinguish between head and tail orientations of a molecule and that the orientation was inverted between ϕ = 0 and ±π.

We performed simultaneous measurements using gas mixtures of target molecules and reference OCS molecules to calibrate ϕ. CH₃⁺ and S⁺ (large-amplitude side in the wavefunction) are in phase with each other (not shown). We have reported that the geometric structure of the HOMO dominates the orientation-selective molecular TI in a broad range of molecules.^21–26 We can qualitatively say that the geometric structure of the HOMO dominates the OSM-TI where the removal of an electron by the TI process occurs on the CH₃ side by the shrinkage and nodal structure of the HOMO on the CHF₂ side owing to the presence of F atoms.^10,11 However, the large orientation selectivity (large contrast in A_yield) observed for HFC-152a cannot be explained solely by the geometric nature of its HOMO because the HOMO of HFC-152a is not so prominently asymmetric, as shown in Fig. 1(a). Theoretical studies have pointed out that several contributions should be considered in molecular TI induced by intense laser fields such as the Stark effect,^14,15 orbital distortion in the presence of intense laser fields,^16,17 and the multi-electron effect.^18–20 Although each contribution remains unclear, the HFC-152a molecule could provide an opportunity to obtain an in-depth understanding of molecular TI while eliminating the influence of the geometric nature of the HOMO.

The Keldysh parameter, γ [γ > 1: multiphoton ionization (MPI) is dominant and γ < 1: TI is dominant], is used to judge whether a phenomenon involves MPI or TI. Because there is no absolute boundary between MPI and TI, phenomena that fall in the intermediate region (γ ∼ 1) can often be successfully explained by both MPI and TI. The ionization potentials of HFC-152a and HFC-134a are 11.87 eV and 12.64 eV, respectively.³⁸ Our experimental conditions correspond to γ ∼ 3. Recent theoretical³⁹ and experimental⁶ studies have shown that TI remains the dominant ionization mechanism even at γ ∼ 3 (non-adiabatic TI regime).

We mention the influence of dynamic orientation and alignment. Theoretical investigations showed that phase-controlled ω+2ω fields can induce dynamic molecular orientation (DMO), where molecules can be dynamically oriented along the laser polarization direction by the torque generated by the nonlinear interaction between a non-resonant laser field and the induced dipoles of the molecules.⁴⁰ A double-pulse experiment involving an orienting nanosecond ω+2ω pulse and a delayed femtosecond probe (ionization) pulse has been successfully reported.⁴⁰ However, the degree of orientation was modest. We have not yet succeeded in observing a prominent degree of DMO in the double-pulse experiment for HFC molecules, and experimental reports for other molecules have not been reported. The contribution of DMO can be expected to be very small. However, several researchers have confirmed that molecules can be dynamically aligned in intense nanosecond laser fields (without discriminating the head–tail order of the molecules) through the linear interaction between non-resonant laser fields and induced dipoles.⁴¹ Therefore, it is reasonable to conclude that our intense nanosecond ω+2ω laser field induces OSM-TI in dynamically aligned molecules, rather than in randomly oriented molecules, during the laser pulse.

We also note the influence of electronic excitation after TI from the HOMO. The dissociative ionization processes include several entangled processes such as (1) generation of the parent ion in the electronic ground state directly connected to dissociation channels (direct process) and (2) generation of the parent ion in the electronic ground state followed by electronic excitation toward dissociation channels (stepwise process). Although we cannot distinguish the direct process from the stepwise process in our experiments, electronic excitation after TI from HOMO could provide certain contributions that result in asymmetries of photofragment ions. In our experimental results, the ion yield asymmetries of each main photofragment ion were completely out of phase with each other. These results show that OSM-TI occurs in the first process; the fact is that the electronic excitation that contributes to ion yield asymmetries after TI is washed away causes other effects that induce ion yield asymmetries to appear to be minor.

We can elucidate the dissociation pathway from the phase dependencies of the respective cations by comparing the phase dependencies between the main photofragment ions (CHF₂⁺ and CH₃⁺) and other ones. In cases where the photofragment ions were not split into forward–backward peaks because of their small kinetic energy and broad energy distribution, we obtained the phase dependence of A_yield from the area of the forward (backward) side with respect to the peak center as I_f (I_b). Clear sinusoidal patterns of A_yield were observed for various photofragment ions except for H⁺, and there are two types of phase-dependent behaviors: CHF₂⁺-like and CH₃⁺-like. CHF₂⁺-like (CH₃⁺-like) behavior implies that the respective photofragment emission occurs in the same direction as CHF₂⁺ (CH₃⁺) from the oriented, selectively ionized molecules.

There are two possibilities for the dissociation pathway producing C⁺ and CH⁺ from the CHF₂ side or the CH₃ side,

The phase dependency of C⁺ and CH⁺ is CH₃⁺-like behavior. This result shows that C⁺ and the CH⁺ are produced from the CH₃⁺ side [dissociation pathway (2)], which is consistent with the fact that C–H bonds are more likely to dissociate than C–F bonds for neutral molecules (see supplementary material S2). It is energetically favorable to produce the molecular products F₂ and H₂. However, we could not detect molecular products.

There are three possibilities for the dissociation pathway producing CHF⁺,

The phase dependency of CHF⁺ is CHF₂⁺-like behavior, and it is out of phase with both C₂H₄F⁺ and C₂H₃F₂⁺. This result shows that CHF⁺ is produced via dissociation pathway (3), which is consistent with the amount of bond dissociation energy (see supplementary material S2).

Similarly, there are two possibilities for the dissociation pathway producing C₂H₃F₂⁺ by emission of H from the CHF₂ side or the CH₃ side,

The phase dependency of C₂H₃F₂⁺ is CH₃⁺-like behavior. This result shows that C₂H₃F₂⁺ is produced by emitting H from the CHF₂⁺ side [dissociation pathway (6)] and that the C–H bond on the CHF₂ side is easier to dissociate than that on the CH₃ side. To confirm consistency, the C–H bond dissociation energies were evaluated by quantum chemical calculations. Figure 5(a) shows the calculated PECs for the C–H bond for the CHF₂ and CH₃ sides. The distance between C and trans-position H was scanned in the calculations. From the calculated PECs, the C–H bond dissociation energies were 3.23 eV for the CH₃ side and 2.19 eV for the CHF₂ side. We found that the C–H bond on the CH₃ side is more stable than that on the CHF₂ side. This result agrees with the experimental result in which the H atom is more likely dissociated from the CHF₂ side.

C₂H₄F⁺ is produced via C₂H₄F₂⁺ → C₂H₄F⁺ + F, and its phase dependence is CH₃⁺-like behavior. This result can be explained by considering the selected molecular orientation where F atoms are emitted opposite to the CH₃ side.

We did not observe phase-dependent behavior for H⁺. Possible explanations are (1) the dissociation process is slow, which causes H⁺ to be produced on a time scale longer than the rotational period, allowing orientation averaging, and (2) H⁺ is produced from both the CHF₂⁺ and CH₃⁺ sides, canceling any directional photofragment emission. Since prompt laser-induced deprotonation of hydrocarbons has been reported,⁴² the latter explanation is probable.

We note that how electronic excitation and dissociation take place for producing each photofragment ion and discuss what the degree of the ion yield asymmetry A_yield reflects. The ladder-switching mechanism is frequently used to explain dissociative ionization induced by nanosecond intense laser pulses.⁴³ According to this mechanism, nanosecond laser excitation causes the molecular parent cations to further absorb laser energy to energy levels above the fragmentation limit and produce photofragments either promptly or delayed, and the generated fragment ions proceed stepwise. This mechanism allows us to provide some information about what the degree of the ion yield asymmetries reflects. Basically, the large contrasts observed in the main photofragment ions (CHF₂⁺ and CH₃⁺) reflect high orientation selectivity. However, as the experimental results show, the contrasts of A_yield in other photofragment ions depend on the photofragments. The photofragment ions produced by stepwise dissociation (CHF⁺, CH⁺, and C⁺) from the main photofragment ions (ladder-switching mechanism) could inherit the direction and kinetic energy of the main photofragments ions, with a tendency to show large contrasts in A_yield. However, other photofragments consisting of many constituent atoms have a tendency to show small contrasts in A_yield because of unclear forward–backward splitting owing to the small kinetic energy and broad energy distribution. Statistical energy redistribution could take place in which the excess energy that molecular cations obtain during the ionization process is divided between the translational and internal (vibrational and rotational) energies of the photofragments. Because the number of internal degrees of freedom increases, the translational energy of the photofragments decreases with the increasing number of constituent atoms.

The molecular structure and isocontour of the HOMO of the HFC-134a molecule are shown in Fig. 1(b). The number of nodes structures originating from the p orbital of F atoms increase owing to the increase in the number of F atoms. Like HFC-152a, it is not apparent from which side the OSM-TI is likely to remove an electron.

The TOF spectra of singly charged ions generated by dissociative ionization of HFC-134a from irradiation by phase-controlled ω+2ω pulses are shown in Fig. 3(a). Various singly charged photofragment ions are discernable. In particular, CF₃⁺ and the counterpart CH₂F⁺ photofragment exhibited a pair of forward–backward peaks.

Figures 3(b) and 3(c) show expanded views of TOF spectra of CH₂F⁺ and the counterpart cation CF₃⁺ with relative phase differences ϕ = 0, π/2, and π. The forward–backward asymmetry was clearly observed in the TOF spectra with ϕ = 0 or π. The backward peak of CH₂F⁺ predominated, and the forward peak of the counterpart CF₃⁺ predominated at ϕ = 0. This forward–backward asymmetry was reversed at ϕ = π. (We discuss the high kinetic energy component seen in CHF₂⁺ and CF₃⁺ later.) We defined the positive orientation of a molecule as the configuration in which the CF₃⁺ side of the molecule points toward the ion detector. Since other photofragment ions were not split into forward–backward peaks because of their small kinetic energy release and broad energy distribution, phase-dependent behavior was not clearly discernible in the TOF spectra.

Clear sinusoidal patterns of A_yield were observed in CF₃⁺ and its counterpart CH₂F⁺, and the A_yield values of the CF₃⁺ and CH₃F⁺ ions were completely out of phase with each other [Fig. 4(b)]. Like HFC-152a, these results show that OSM-TI was induced by the phase-controlled ω+2ω laser fields and that the orientation was inverted between ϕ = 0 and ±π. The calibration of ϕ using the gas mixture of target molecules and reference OCS molecules showed that CH₂F⁺ and S⁺ (large-amplitude side in the wavefunction) were in phase with each other (not shown). We can qualitatively say that the shape of the HOMO plays important roles in the OSM-TI where the liberation of an electron by the TI process occurs on the CH₂F side by the shrinkage and nodal structures of the HOMO on the F-rich CF₃ side.^10,11 However, further theoretical investigation is needed to understand why orientation selectivity (contrast in A_yield) observed for HFC-134a was less pronounced than that for HFC-152a.

We note the origin of the high kinetic energy component seen in the photofragments CHF₂⁺ and CF₃⁺ produced from the HFC-134a molecules. The experiment was performed with a laser intensity (<10¹³ W/cm²) below the regime where doubly charged cations are observed. In addition, we did not observe clear phase-dependent behavior of A_yield in the high kinetic energy component. If the high kinetic energy wing is due to Coulomb explosion with prompt dissociation, the A_yield results should have shown clear phase-dependent behavior. At present, although the origin of the high kinetic energy component is unknown, it seems reasonable to conclude that it is not due to the Coulomb explosion process.

We discuss the dissociation pathway from the phase dependencies of the respective photofragment ions by comparing the phase dependencies between the main photofragment ions (CH₂F⁺ and CF₃⁺) and other ones. Because of the lower orientation selectivity (smaller contrast in A_yield) compared to HFC-152a, photofragment ions that showed phase-dependent behavior were fewer than for HFC-152a. Slight sinusoidal patterns of A_yield were observed in CF⁺ and C₂H₂F₃⁺, and both had CH₂F⁺-like behavior. CH₂F⁺-like behavior implies that the respective photofragment emission occurs in the same direction as CH₂F⁺.

Two dissociation pathways producing C₂H₂F₃⁺ by emission of F from the CF₃ side or the CH₂F side are possible,

The phase dependency of C₂H₂F₃⁺ is CH₂F⁺-like behavior. This result shows that C₂H₂F₃⁺ is produced by emitting F from the CF₃⁺ side [dissociation pathway (8)] and that the C–F bond on the CF₃ side is easier to dissociate than that on the CH₂F side. Quantum chemical calculations were also conducted to confirm consistency, similar to those for HFC-152a. From the calculated PECs for the C–F bonds on the CF₃ and CH₂F sides [Fig. 5(b)], the C–F bond dissociation energies were 3.32 eV for the CH₂F side and 2.76 eV for the CF₃ side. The C–F bond on the CH₂F side was found to be more stable than that on the CF₃ side. This result agreed with the experimental result in which the F atom is more likely dissociated from the CF₃ side.

Two dissociation pathways producing CF⁺ from the CF₃ side or the CH₂F side are possible,

The phase dependency of CF⁺ is also CH₂F⁺-like behavior. This result showed that CF⁺ was produced by emission of H from the CH₂F⁺ side [dissociation pathway (11)], which is consistent with the fact that C–H bonds are more likely to dissociate than C–F bonds (see supplementary material S2).

We did not observe phase-dependent behavior in CF₂⁺, CH⁺, C⁺, and H⁺. These results are mainly owing to lower orientation selectivity than that of HFC-152a, allowing orientation averaging.

The OSM-TI of two HFC molecules has been investigated by using intense nanosecond phase-controlled ω+2ω laser fields. From the phase-dependent behavior of photofragment emission from selectively ionized molecules, dissociation pathways were elucidated experimentally. We showed that OSM-TI is a powerful method to elucidate dissociative photoionization pathways while eliminating loss of information due to orientational averaging, even for dissociative ionization pathways that produce neutral photofragments that cannot be detected by an ion detector. The bond dissociation energies obtained by quantum chemical calculations supported our experimental results.

We observed large orientation selectivity (large contrast in A_yield), particularly in HFC-152a. Although we qualitatively concluded that the geometric structure of the HOMO dominates the OSM-TI, the large orientation selectivity (large contrast in A_yield) observed for HFC-152a cannot be explained solely by the geometric nature of its HOMO because the HOMO of HFC-152a is not so prominently asymmetric. Advanced theories that consider the Stark effect,^14,15 orbital distortion in the presence of intense laser fields,^16,17 and the multi-electron effect^18–20 have been developed. These contributions have been shown to entangle with and depend on the molecule and cannot be determined by just looking at the shape of the HOMOs. The observed large orientation selectivity for HFC-152a with its less asymmetric HOMO structure will be a benchmark in the development of the theory of molecular TI and helpful for a deep understanding of molecular TI.

See the supplementary material for (S1) the Cartesian coordinate of the optimized structure by Møller–Plesset perturbation theory using the GAUSSIAN 09 package with the MP2/aug-cc-pVTZ level. Spin multiplicity is singlet. (S2) The bond dissociation energy of neutral and cation of methane and fluoro-substituted methane calculated with the M06-2X/aug-cc-pVTZ level.

This work was partially supported by the Japan Society for the Promotion of Science (KAKENHI) under Grant Nos. 24340097 and 16H04103. K.O. acknowledges the AIST Innovation School.

The data that support the findings of this study are available from the corresponding author upon reasonable request.