Quantum electronic control on chemical activation of methane by collision with spin–orbit state selected vanadium cation

Abstract

By coupling a newly developed quantum-electronic-state-selected supersonically cooled vanadium cation (V⁺) beam source with a double quadrupole-double octopole (DQDO) ion–molecule reaction apparatus, we have investigated detailed absolute integral cross sections (σ's) for the reactions, V⁺[a⁵D_J (J = 0, 2), a⁵F_J (J = 1, 2), and a³F_J (J = 2, 3)] + CH₄, covering the center-of-mass collision energy range of E_cm = 0.1–10.0 eV. Three product channels, VH⁺ + CH₃, VCH₂⁺ + H₂, and VCH₃⁺ + H, are unambiguously identified based on E_cm-threshold measurements. No J-dependences for the σ curves (σ versus E_cm plots) of individual electronic states are discernible, which may indicate that the spin–orbit coupling is weak and has little effect on chemical reactivity. For all three product channels, the maximum σ values for the triplet a³F_J state [σ(a³F_J)] are found to be more than ten times larger than those for the quintet σ(a⁵D_J) and σ(a⁵F_J) states, showing that a reaction mechanism favoring the conservation of total electron spin. Without performing a detailed theoretical study, we have tentatively interpreted that a weak quintet-to-triplet spin crossing is operative for the activation reaction. The σ(a⁵D₀, a⁵F₁, and a³F₂₎ measurements for the VH⁺, VCH₂⁺, and VCH₃⁺ product ion channels along with accounting of the kinetic energy distribution due to the thermal broadening effect for CH₄ have allowed the determination of the 0 K bond dissociation energies: D₀(V⁺–H) = 2.02 (0.05) eV, D₀(V⁺–CH₂) = 3.40 (0.07) eV, and D₀(V⁺–CH₃) = 2.07 (0.09) eV. Detailed branching ratios of product ion channels for the titled reaction have also been reported. Excellent simulations of the σ curves obtained previously for V⁺ generated by surface ionization at 1800–2200 K can be achieved by the linear combination of the σ(a⁵D_J, a⁵F_J, and a³F_J) curves weighted by the corresponding Boltzmann populations of the electronic states. In addition to serving as a strong validation of the thermal equilibrium assumption for the populations of the V⁺ electronic states in the hot filament ionization source, the agreement between these results also confirmed that the V⁺(a⁵D_J, a⁵F_J, and a³F_J) states prepared in this experiment are in single spin–orbit states with 100% purity.

---

I. Introduction

Methane (CH₄) is the simplest and most widespread alkane on earth. As the main component of natural gas that has been used as a combustion fuel, CH₄ is also one of the main non-CO₂ green-house gases, which is reported to be about 30 times more potent than CO₂ in the measure of global warming potential.¹ In addition, CH₄ is found on other planets and satellites in the solar system,^2,3 such as Mars and Titan; and CH₄ clathrates are one of the important carbon-containing ices in comets, interstellar space, and outer solar systems.^4,5

As one of the four main C1 molecules on earth,⁶ CH₄ has been proposed as a useful chemical feedstock to produce more-valued chemical species and intermediates, including methylene radical (CH₂) and methanol molecule (CH₃OH). Nevertheless, the activation and oxygenation of the C–H bond of CH₄ have been categorized as one of the “Holy Grails” in chemistry,⁷ Due to its notorious thermodynamic stability and chemical inertness, the understanding of detailed mechanisms for chemical activation and functionalization of CH₄ remains far from completion.^8,9 Currently, large scale applications of CH₄ in industry have mainly been concerned with the conversion of CH₄ to H₂, which can then be used for the synthesis of straight-chain hydrocarbons via the Fischer–Tropsch process,^10,11 However, this method is highly energy intensive and thus expensive, making the development of new pathways for CH₄ activation with lower costs extremely desirable.

For decades, transition metal (TM) cations have been shown to exhibit very promising unique effects on activation of hydrocarbons including CH₄.^12–15 As early as in 1979, TM cations were reported to efficiently cleave alkanes by breaking the C–C and C–H bonds.¹⁶ Since then, a great wealth of both experimental and theoretical works on CH₄ activation have been published; and some summaries of these studies can be found in ref. 13, 15 and 17 The research of CH₄ activation has attracted good attention because it is a prototypical system for alkane activation as well as being abundant on earth.¹⁸

In 1987, the Armentrout group reported a heroic experiment concerning chemical reactivity dependences upon translational and electronic energy for the V⁺ + CH₄ reaction using a guided ion beam (GIB) tandem mass spectrometer.¹⁹ The effects of electronic energy were probed by varying the ion source conditions, such as the temperature (T) of the hot surface ionization (SI) filament and the electron ionization energy of the electron ionizer. However, due to the lack of energy resolution and the state-specific detection method, quantitative absolute integral cross section (σ) measurements for individual V⁺ spin–orbit electronic states were not achieved, although approximate state-specific σ determinations were made. Nevertheless, based on observations of the GIB experiment, it was suggested that the mechanism for the activation of CH₄ by V⁺ preferentially proceeds through a triplet spin V⁺ inserted [H–V⁺–CH₃] intermediate, favoring the conservation of total electron spin.

In 1997, the Brucat group reported a photodissociation study of V⁺CH₄ ion–molecule complexes formed in a laser-driven-plasma supersonic beam source.²⁰ The majority of complexes thus formed was believed to have the structure of the charge-induced dipole ion–molecule complex [V⁺–CH₄]. However, the authors could not preclude the existence of a minor amount with the structure of the V⁺ inserted [H–V⁺–CH₃] intermediate.

A density functional (DFT) theoretical study was later performed for the V⁺ + CH₄ reaction system by Sicilia and Russo in 2002, which has provided some valuable insights into the activation mechanism,²¹ and agreed with the qualitative potential energy surface originally suggested by Aristov and Armentrout.¹⁹ The DFT calculation suggested that three reaction intermediates may be formed along the reaction coordinates: the first one is the ion-induced-dipole complex [V⁺–CH₄], which may evolve to the inserted intermediate [H–V⁺–CH₃]. This second intermediate, in which the C–H bond of CH₄ has been activated, was expected to lead to the formation of VH⁺ and VCH₃⁺. The last intermediate may be the [H₂–V⁺–CH₂] structure formed via rearrangement of the other two intermediates, leading to the formation of the VCH₂⁺ + H₂ product channel. The mechanism, invoking the conservation of total electron spins, is also revealed in the DFT theoretical study.

In 2009, the Bohme group reported a systematic kinetic study on the reactions between CH₄ and 59 atomic metal cations, which included the V⁺ ion at room temperature prepared by using a plasma selected ion flow tube tandem mass spectrometer.¹⁷ In these reactions, internal excitations of the reactant TM cations were supposed to be quenched down to the ground state by collisions with the carrier gas, such as helium. However, the authors admitted that the exact electronic states and the relative populations of the reactant TM ions after the collisions are uncertain. This may due to different relaxation mechanisms involved for different long-lived electronically excited TM ions.^22–24 To the best of our knowledge, no σ measurements with reactant V⁺ ions prepared in single electronic states, especially in excited V⁺ states, have been reported previously for the V⁺ + CH₄ reaction. The successful search of quantum electronic state controls of chemical reactivity of V⁺ ion in its excited electronic states is expected to promote new reaction pathways of catalytic relevance.

Recently, we have developed a two-color visible-ultraviolet (VIS-UV) laser pulsed field ionization-photoion (PFI-PI) detection method, which can be used to prepare V⁺ ions in 13 different spin–orbit coupled electronic states, a⁵D_J (J = 0–4), a⁵F_J (J = 1–5), and a³F_J (J = 2–4), with high laboratory kinetic energy (E_lab) resolution or narrow ΔE_lab spread for V⁺ ion. This development has made possible systematic chemical reactivity measurements of quantum state-selected V⁺ ions with simple atmospheric gases.²⁵ Combining the VIS-UV laser PFI-PI ion source with the double quadrupole-double octopole (DQDO) ion–molecule reaction apparatus, we have previously investigated detailed chemical reactivity of V⁺ ion by activating CO₂, D₂ and O₂ as a function of electronic state and kinetic energy of V⁺ ion.^24,26,27 The main observation of these latter experiments is that the triplet electronic states (a³F_2–4) are much more reactive in activating CO₂ and D₂ than the other two quintet electronic states, in agreement with the more qualitative determinations of the Armentrout group on the same systems.^23,28 No J dependences are observed for the σ values of individual V⁺[a⁵D_J (J = 0, 2), a⁵F_J (J = 1, 2), and a³F_J (J = 2, 3)] electronic states to CO₂ and D₂ activation reaction, while the J-state effect for the V⁺(a³F_2,3) + O₂ reactions are unambiguously identified,²⁹ where J is the total angular momentum quantum number of the spin–orbit state of V⁺ ion. Furthermore, the σ curves (σ versus E_cm plots) observed show that both electronic and E_cm energies of the reaction can effectively couple with the reaction coordinates, allowing the E_cm-threshold measurements to yield reliable thermochemical properties, such as 0 K bond dissociation energies (D₀'s) and heats of formation (Δ_fH₀'s) for TM containing molecular species, many of which are still unavailable in the literature. To examine whether the dominant reaction mechanism observed in the V⁺ + D₂(CO₂) reaction systems is also valid for the V⁺ + CH₄ reaction is a major motivation of the present quantum electronic state selected study.

Here, we present the σ values for the V⁺ + CH₄ reaction when V⁺ ions are prepared into single spin–orbit electronic states, covering the E_cm range from 0.1 to 10.0 eV. Detailed dependences of the spin–orbit electronic states and the E_cm on σ values and product branching ratios (BR's) have also been investigated in the present study for the first time. Since the two-color VIS-UV laser PFI-PI method is readily applicable to other TM cation species, this work can also be considered as a demonstration experiment, illustrating that chemical reactivity of TM ions toward hydrocarbons can be readily examined experimentally with TM ions prepared in single, pure electronic states, one spin–orbit state at a time. Thus, the results of this study would serve as a guiding experiment for future state-selected ion–molecule reaction studies involving other TM cations.

II. Experimental considerations

Since the detailed arrangement of the two-color VIS-UV laser PFI-PI ion source and procedures used for σ measurements employing the DQDO ion–molecule reaction apparatus have been reported previously,^24,25,30,31 only a brief description is given below.

(a) Two-color VIS-UV laser PFI-PI ion source

The VIS-UV laser PFI-PI detection scheme has been recently developed in our group to prepare gaseous V⁺ ions in one of the thirteen quantum spin–orbit electronic states: a⁵D_J (J = 0–4), a⁵F_J (J = 1–5), and a³F_J (J = 2–4) in the form of a pulsed supersonic beam, achieving E_cm values down to thermal energies. The precursor neutral V atom sample, in the form of a pulsed (30 Hz) supersonically cooled atomic beam, is generated by a Smalley-type pulsed laser ablation TM beam source. The laser system used for photo-exciting the neutral V atoms consists of two independently tunable dye lasers pumped by one pulsed Nd:YAG laser operated at 30 Hz. The first dye laser is pumped by the third harmonics of the Nd:YAG laser to generate the VIS output (ω₁). The second dye laser is pumped by the second or third harmonics of the same Nd:YAG laser to provide the UV output (ω₂) after passing through a frequency doubling crystal. The VIS ω₁ and UV ω₂ laser beams are then merged into the photoexcitation (PEX) region by using a dichroic mirror. The VIS and UV laser beams perpendicularly intersect the neutral V atom sample in the form of a supersonically cooled V/He seeded beam. The VIS ω₁ is fixed to excite the neutral V atoms from the ground state to a selected neutral intermediate state, and the UV ω₂ is tunable such that the total photoexcitation frequency of (ω₁ + ω₂) covers the photoexcitation transition frequencies needed for photoionization from the ground state to the spin–orbit electronic states of interest. High-n (n > 60) Rydberg states of V [V*(n)] converging to the ionic states of interest are ionized by PFI to produce PFI-PIs in one of the V⁺ [a⁵D_J (J = 0–4), a⁵F_J (J = 1–5), and a³F_J (J = 2–4)] spin–orbit J-states.

Because prompt ions without pure state selection can also be produced along with PFI-PI formation, the most important issue is to reject prompt ions from the PFI-PI beam, and this is achieved as described in detail elsewhere.^{24–26,30,31} Readers are referred to the two-color laser PFI-PI spectra for V⁺[a⁵D_J (J = 0–4)], V⁺[a⁵F_J (J = 1–5)], and V⁺[a³F_J (J = 2–4)] shown in Fig. 8(a), (b), and (c) of ref. 25, respectively. The fully J-resolved PFI-PI spectra observed indicate that the preparation of V⁺ ion in single quantum spin–orbit electronic states is well achieved.

(b) DQDO ion–molecule reaction apparatus and σ measurements

The DQDO ion–molecule reaction apparatus consists of, in sequential order, a supersonically cooled V atom source produced by pulsed laser ablation of a rotating and translating V-rod, a reactant quadrupole mass filter (QMF), a reaction gas cell situated between two radio frequency (rf)-octopole ion guides, a product QMF, and a Daly-type ion detector.³² The second harmonic output of an Nd:YAG laser operated at 2 mJ and 30 Hz is employed as the ablation laser. The V gaseous plumes formed by ablation are merged into a He gas flow, forming a V/He seeded beam. Cooling of the V atom sample occurs as the V/He seeded gas undergoes supersonic expansion. Charged species, which are also formed by laser ablation, are deflected away from the V/He beam path by a pair of ion repeller plates biased at a sufficiently high DC electric field. In this experiment, the reactant QMF is only used as an ion lens. The dual set of rf-octopoles can be used to extract slow product ions formed inside the gas cell and maintain high ion transmission through the gas cell by applying a small dc field between the two rf-octopoles. The gas cell is connected with an electromagnetic valve for gas filing; and the gas cell pressure is monitored by an MKS Baratron. In this study, the pressure of CH₄ in the gas cell is maintained at (1.0 or 2.0) × 10⁻⁴ torr, which is low enough to satisfy the thin target conditions.^33,34 The product QMF and the modified Daly-type detector form the detection system for reactant and product ions.

The σ measurement involves the determination of intensities of the reactant and products ions. Based on the thin target ion-neutral scattering scheme, the σ value can be deduced as [(kT)/(Pl)][ln((I + i)/I)], where k, T, P, l, I, and i represent the Boltzmann constant, the temperature and the pressure of the neutral reactant in the reactant gas cell, the effective length of the gas cell, the intensity of the unreacted reactant V⁺ ions, and the intensity of the product ions, respectively. Under the thin target conditions, product ions formed by secondary reactions are negligible. All σ curves shown in this work are the averaged results of at least three independent measurements. The run-to-run uncertainties are found in the range of 5–10% and the absolute uncertainties of σ's determined in this work are estimated to be ≤30%.

The E_cm is converted from the laboratory kinetic energy (E_lab) by using the formula E_cm = E_lab [M/(m⁺ + M)], where m⁺ and M represent the masses of V⁺ ion and CH₄ molecule, respectively. As pointed out previously, the thermal motion of neutral CH₄ molecules inside the gas cell can give rise to the kinetic energy distribution, which is referred to here as the “thermal broadening” effect. This distribution can significantly affect the E_cm spread or ΔE_cm resolution.³⁵ Thus, for energetic measurements, such as bond dissociation energies (D₀'s) deduced in the studies of the V⁺ + D₂ (CO₂, CH₄) reactions, we have taken into account the kinetic energy distribution as described below.

III. Results and discussions

(a) Mass spectra

The mass spectra for the quantum spin–orbit electronic state-selected V⁺(a³F₂) ion source and the V⁺(a³F₂) + CH₄ reaction are shown as the black curves in Fig. 1(a) and (b), respectively. For both mass spectra, E_cm was set at 2.0 eV. To better view the weak mass peaks with low intensities, the original mass spectra in black are magnified by a factor of 15. The magnified mass spectra thus obtained are shown in red. As shown in Fig. 1(a), the three ion peaks observed at the mass to charge ratios of m/z = 50, 51, and 67 can readily be assigned as ⁵⁰V⁺, ⁵¹V⁺, and VO⁺, respectively. We note that the intensity ratio of the mass peaks for ⁵⁰V⁺ and ⁵¹V⁺ are found to be consistent with the known natural abundances of the V⁺ isotopes.³⁶ Since this mass spectrum for the V⁺(a³F₂) ion source was recorded without CH₄ in the reaction gas cell, all the ion peaks, except the one for ⁵¹V⁺, can be considered as background ions.

Fig. 1 Comparison of mass spectra recorded with and without reactant CH₄ gas in the reaction gas cell. (a) Mass spectrum of the V⁺(a³F₂) state-selected PFI-PI ion source recorded without CH₄ in the gas cell. (b) Mass spectrum of the V⁺(a³F₂) + CH₄ state-selected reaction with CH₄ in the gas cell. For both spectra, the E_cm is set to 2.0 eV.

Different from the spectrum of Fig. 1(a), the mass spectrum in Fig. 1(b) exhibits six ion peaks at m/z = 50, 51, 52, 65, 66, and 67, which are marked in Fig. 1(b) as ⁵⁰V⁺, ⁵¹V⁺, VH⁺, VCH₂⁺, VCH₃⁺, and VO⁺, respectively. We find that the intensity of the m/z = 67 (assigned as VO⁺) peak of Fig. 1(b) is very similar to that of Fig. 1(a), consistent with its formation from reactions of V⁺ with trace amounts of O₂ or H₂O, where the reactions occur with near unit efficiency.²⁹ Since the m/z values for VO⁺ and VCH₄⁺ are identical, this observation can be taken as evidence that negligible VCH₄⁺ ion–molecule complexes are formed by multiple collision events in the reaction gas cell. The mass spectrum of Fig. 1(b) also shows no evidence for the formation of VCH⁺ ion. Similar observations were also obtained from the mass spectra recorded with V⁺ ion prepared in different electronic states at different E_cm values. Therefore, we can conclude that VH⁺, VCH₂⁺, and VCH₃⁺ ions are identified as the major primary product ions in the present experiment. However, this observation cannot exclude the formation of VCH⁺ ion. Based on σ measurements presented below, if VCH⁺ is formed, we estimate its σ value to be about ≤0.001 Ų.

The reaction product channels or states associated with the formation of product ions are listed in reactions (1)–(3), along with the corresponding apparent threshold energies of reaction (E_T) observed here at the reactant sample temperature T, which is mostly determined by the thermal energy of neutral methane in this case but also includes the minor ion kinetic energy distribution.

V⁺(a⁵D₀) + CH₄(X¹A₁) → VH⁺(X⁴Δ) + CH₃(X²A₂′′) E_T = 1.9 ± 0.1 eV (1)

V⁺(a⁵D₀) + CH₄(X¹A₁) → VCH₂⁺(X³A₁) + H₂(X¹Σ_g⁺) E_T = 1.2 ± 0.1 eV (2)

V⁺(a⁵D₀) + CH₄(X¹A₁) → VCH₃⁺(X⁴B₁) + H(²S_1/2) E_T = 1.8 ± 0.1 eV (3)

The E_T values for these reactions given above are obtained directly or indirectly by the E_cm-threshold measurements, in which the T is not zero. We note that the E_cm-thresholds marked in Fig. 2(a)–(f) are identical with their corresponding E_T values. Reactions (1)–(3) are all endothermic with positive E_T values. Since the V⁺(a⁵D₀) + CH₄(X¹A₁) reactant state is the ground electronic state, it is convenient to use it as the reference state of this reaction system. The E_T's for these reaction product channels with V⁺ ions prepared in the excited electronic states, i.e., V⁺(a⁵F₁) or V⁺(a³F₂), can be obtained readily by subtracting the known electronic energy of the excited reactant V⁺ ion^25,37 from the E_T's for reactions (1)–(3) with V⁺ ion prepared in the a⁵D₀ ground electronic state. Here, the σ values for reactions (1), (2), and (3) are designated as σ(a⁵D₀: VH⁺), σ(a⁵D₀: VCH₂⁺), and σ(a⁵D₀: VCH₃⁺), respectively.

Fig. 2 Comparison of the σ(VH⁺), σ(VCH₂⁺), and σ(VCH₃⁺) for the reaction system of V⁺(a³F₂, a⁵F₁, and a⁵D₀) + CH₄. (a) shows the σ(a³F₂: VH⁺), σ(a⁵F₁: VH⁺), and σ(a⁵D₀: VH⁺) in blue triangles, red squares, and black circles, respectively. (b) and (c) Depict the magnified view of the σ(a⁵F₁: VH⁺) and σ(a⁵D₀: VH⁺), respectively. Similarly, the σ(VCH₂⁺) and σ(VCH₃⁺) are shown in (d)–(f) and (g), (h), respectively. In order to better examine the E_cm-threshold positions, the σ(a³F₂: VH⁺) is amplified by a factor of 20 in (a), and the σ(a⁵D₀: VH⁺) is amplified by a factor of 10 in (c).

Because of the very low σ(a⁵D₀: VCH₃⁺) and σ(a⁵F₁: VCH₃⁺) values, the E_cm-thresholds for these σ curves cannot be determined with high precision. However, a more precise E_cm-threshold for σ(a⁵D₀: VCH₃⁺) can be determined by adding the electronic energy of 1.1 eV for σ(a³F₂: VCH₃⁺) to the measured E_cm-threshold of 0.7 ± 0.1 eV for σ(a³F₂: VCH₃⁺), yielding a E_cm-threshold value of 1.8 ± 0.1 eV for the σ(a⁵D₀: VCH₃⁺). This value thus obtained is in marginal agreement with the directly measured E_cm-threshold of 3.0 ± 1.0 eV for the σ(a⁵D₀: VCH₃⁺), after taking into account of the experimental uncertainties. We note that the large E_cm step size (1 eV) used for recording the latter spectrum makes it undesirable for use of precise energetic deductions.

On the basis of the σ(a⁵F₁: VCH₂⁺) measurements of Fig. 2(e), the detection sensitivity of the instrument for σ measurements used is estimated to be 0.001 Ų for σ(VCH⁺). Although this experiment cannot exclude VCH⁺ as a primary product ion, if it is formed, σ(VCH⁺) is expected to be ≤0.001 Ų. As mentioned above, the pressure of CH₄ in the gas cell used in this work was controlled to sufficiently low values in order to minimize multiple-collision events.

(b) Quantum electronic state effects

The σ(VH⁺), σ(VCH₂⁺) and σ(VCH₃⁺) curves are depicted in Fig. 2(a)–(c), Fig. 2(d)–(f), and Fig. 2(g)–(h), respectively. The σ's for the V⁺(a⁵D₀, a⁵F₁, and a³F₂) states are depicted with black circles, red squares, and blue triangles in Fig. 2(a)–(h). For σ(VH⁺), Fig. 2(a) shows the direct contrast when V⁺ is prepared in the a⁵D₀, a⁵F₁, and a³F₂ spin–orbit states, and Fig. 2(b) and (c) provide a magnified view for σ(a⁵F₁: VH⁺) and σ(a⁵D₀: VH⁺), respectively. Similar comparisons for σ(VCH₂⁺) are made in Fig. 2(d) and (f), as well as for σ(VCH₃⁺) in Fig. 2(g) and (h). Since σ(a⁵F₁: VCH₃⁺) was below the detection limit of ≈0.001 Ų in the E_cm range of interest, no σ(a⁵F₁: VCH₃⁺) curve was recorded.

One of the major observations for quantum electronic state effects on chemical reactivity of the V⁺(a³F₂, a⁵F₁, and a⁵D₀) + CH₄ reaction system [as shown in Fig. 2(a)–(h)] is that the triplet reactant ion, V⁺(a³F₂), is much more reactive than the quintet reactant ions, V⁺(a⁵D₀) and V⁺(a⁵F₁). Specifically, as depicted in Fig. 2(a), σ(a³F₂: VH⁺) is dominantly higher than σ(a⁵D₀: VH⁺) by 1000, 120, and 25 times at E_cm = 2.0, 5.0, and 10.0 eV, respectively. Similarly, in Fig. 2(d), σ(a³F₂: VCH₂⁺) is higher than σ(a⁵D₀: VCH₂⁺) by 65 and 12 times at E_cm = 2.0, and 5.0 eV, respectively; and in Fig. 2(g), the peak value of σ(a³F₂: VCH₃⁺) is about 10 times higher than that of σ(a⁵D₀: VCH₃⁺).

Chemical reactivity enhancement observed for the V⁺(a³F₂) + CH₄ reaction can be rationalized by the conservation rule of total electron spins.^19,21,24,26 The surmised reaction mechanisms are depicted in the schematic energy level diagram of Fig. 3. On the left side of Fig. 3, we show the three reactant states, V⁺(a³F₂) + CH₄(X¹A₁) in red, and V⁺(a⁵F₁) + CH₄(X¹A₁) and V⁺(a⁵D₀) + CH₄(X¹A₁) states in black. The three product states, VH⁺(X⁴Δ) + CH₃(X²A₂′′), VCH₃⁺(X⁴B₁) + H(²S_1/2), and VCH₂⁺(X³A₁) + H₂(X¹Σ_g⁺), identified in this experiment are shown on the right side of Fig. 3 according to their energy order. At higher energies, we also include in Fig. 3 the possible dissociative product channels, V⁺(a⁵D₀) + CH₃(X²A₂′′) + H(²S_1/2) and VCH₂⁺(X³A₁) + H(²S_1/2) + H(²S_1/2). The lack of precise energetics has limited the inclusion of other possible product states in the energy level diagram. With the exception of the VCH₂⁺(X³A₁) + H₂(X¹Σ_g⁺) product state, which can only correlate adiabatically to triplet reactant states, the other product states of Fig. 3 are shown in blue, indicating that they can correlate to both triplet and quintet reactant states.

Fig. 3 Schematic energy level diagram of the surmised reaction mechanism for the V⁺ + CH₄ reaction system, where the zero energy is set by the energy of the V⁺(a⁵D₀) ground state. The colors of each component are based upon the total coupled electron spins or multiplicity: red for the triplet, black for the quintet, and purple for both the triplet and quintet. On the left side are the three reactant states, in the middle are the proposed reaction intermediates, and on the right side are the selected product channels. The main reaction mechanism of the V⁺ + CH₄ reaction is interpreted here to favor the conservation of the total electron spins with a “weak quintet-to-triplet spin crossing”, which is marked nominally by the purpled dashed arrow near the middle bottom of the figure. We note that the a⁵F_J state does not correlate with the [V⁺CH₄](X⁵) ground state, but rather with another excited state of this species still having quintet spin. This is shown in the potential energy surface in ref. 19. The purple arrow points to the crossing between the triplet and quintet dashed lines.

As suggested by the previous experimental results¹⁹ and DFT calculations,²¹ two kinds of reaction intermediates, [V⁺CH₄] and [HVCH₃⁺], are involved, and each intermediate can be formed in the triplet as well as quintet states. These intermediates are shown in the middle of the energy level diagram of Fig. 3 according to the DFT predictions and are highlighted in colors based on their multiplicities: red for triplet states and black for quintet states. Since the bond dissociation energy of V⁺–H is much weaker than that of H–CH₃, the formation of the [V⁺CH₄] intermediate is not expected to lead to the cleavage of the C–H bond of CH₄. Thus, as depicted in Fig. 3, the ion–molecule complex [V⁺CH₄] may proceed to rearrange forming the inserted [HVCH₃⁺] structure.

The key reaction intermediate proposed by the previous DFT calculation²¹ has an inserted triplet [HV⁺CH₃](X³) structure^19,21 at an energy lower than that of the V⁺(a³F₂) + CH₄(X¹A₁) reactant state. Therefore, the V⁺(a³F₂) + CH₄(X¹A₁) reactant state can form the inserted [HV⁺CH₃](X³) intermediate via the [V⁺CH₄](a³) ion–molecule complex without flipping electron spins because both of them are in reaction surfaces with the same multiplicity. Meanwhile, reactant states, V⁺(a⁵D₀) + CH₄(X¹A₁) and V⁺(a⁵F₁) + CH₄(X¹A₁), may form a quintet inserted intermediate [HV⁺CH₃](a⁵) by conserving the total electron spins. Based on the previous experimental and theoretical work,^19,21 the [HV⁺CH₃](X³) and [HV⁺CH₃](a⁵) intermediates are estimated to be 0.6 and 1.6 eV, respectively, higher than the V⁺(a⁵D₀) + CH₄(X¹A₁) ground reactant state. Meanwhile, V⁺(a³F₂) is known to be about 1.1 eV higher than V⁺(a⁵D₀). Thus, V⁺(a³F₂) + CH₄(X¹A₁) is both exothermic (by 0.5 eV) and spin-allowed when forming the [HV⁺CH₃](X³) intermediate. In contrast, both reactant states, V⁺(a⁵D₀) + CH₄(X¹A₁) and V⁺(a⁵F₁) + CH₄(X¹A₁), are endothermic and spin-forbidden when forming the [HV⁺CH₃](X³) intermediate, which may lead to very low reactivity of V⁺(a⁵D₀) and V⁺(a⁵F₁) compared with V⁺(a³F₂) towards the activation of CH₄ leading to VCH₂⁺ + H₂. The “weak quintet-to-triplet spin crossing” region is marked nominally by the purple dashed arrow in the schematic energy level diagram of Fig. 3. The observation of the product state, VCH₂⁺(X³A₁) + H₂(X¹Σ_g⁺), of reaction (2) is a strong manifestation of the “weak electron spin crossing” mechanism. If the reaction of V⁺ + CH₄ strictly follows a “no spin-crossing” reaction mechanism, the triplet product state, VCH₂⁺(X³A₁) + H₂(X¹Σ_g⁺), could not have been formed from the quintet reactant states, V⁺(a⁵D₀) + CH₄(X¹A₁) and V⁺(a⁵F₁) + CH₄(X¹A₁). We are grateful to a reviewer who has pointed out that the observed product distribution could be explained by a statistical analysis of the lifetime of the V⁺(CH₄) collision complex and the barriers involved for the relevant reaction steps. Because this theoretical analysis is beyond the scope of the present work, we hope that the results of this experiment will interest in such future theoretical studies. We note that at sufficiently high E_cm values, the collision complex dissociation model is likely to be invalid.

The observed E_cm-thresholds of 0.1 ± 0.1 eV for σ(a³F₂: VCH₂⁺), 0.8 ± 0.1 eV for σ(a⁵F₁: VCH₂⁺), and 1.2 ± 0.1 eV for σ(a⁵D₀: VCH₂⁺) as shown in Fig. 2(d)–(f) are consistent with the electronic energies of 0.3 eV for V⁺(a⁵F₁) and 1.1 eV for V⁺(a³F₂) measured with respect to that for V⁺(a⁵D₀).³⁸ The operation of a “weak quintet-to-triplet spin crossing” allows a very minor fraction of the quintet reactant states, V⁺(a⁵D₀) + CH₄(X¹A₁) and V⁺(a⁵F₁) + CH₄(X¹A₁), to “switch” to form the triplet [HV⁺CH₃](X³) intermediate. Thus, the operation of this “weak quintet-to-triplet spin crossing” mechanism is consistent with the fact that both the σ(a⁵D₀: VCH₂⁺) and σ(a⁵F₁: VCH₂⁺) values are very small compared with the σ(a³F₂: VCH₂⁺).

As shown in Fig. 2(a)–(f), the ground state V⁺(a⁵D₀) ion is mildly more reactive with CH₄ than the first excited state V⁺(a⁵F₁) ion, even though the latter has a 0.3 eV higher energy level. Similar reactivity behaviors have been observed in other reaction systems, such as the V⁺ + CO₂ and V⁺ + D₂ reactions.^24,26 As discussed previously, the high-spin coupled 4s electron of the V⁺(a⁵F₁) ion is believed to adversely affect the bonding and chemical reactivity.^12,23 The 4s electron is speculated to generate larger repulsive interactions between the V⁺ ion and CH₄ molecule than the 4d electrons when the two moieties approach each other; and the larger repulsive interaction leads to lower reaction probabilities. Notably, even though the V⁺(a⁵F₁) with CH₄ reaction is less efficient than the other states, the E_cm-thresholds for endothermic reactions observed in the present study are consistent among all states. As shown in Fig. 2(b), (c), (e), and (f), the threshold positions for the reactant state of V⁺(a⁵F₁) + CH₄(X¹A₁) is between 0.2 and 0.4 eV lower than that of V⁺(a⁵D₀) + CH₄(X¹A₁), which is in accord with the relative energies of the two V⁺ electronic states. This observation indicates that both the electronic energy of V⁺ and the kinetic energy E_cm of the V⁺ + CH₄ reaction can couple with the reaction coordinates to facilitate product ion formation. Furthermore, this observation also supports the conclusion that the reactant V⁺ ions prepared in this experiment are in pure, single electronic states.

(c) Kinetic energy effects

Besides the quantum electronic state effects, the kinetic energy effects for the reaction system of V⁺ + CH₄ can also be observed in Fig. 2(a)–(h). As shown in these figures, all the reaction product channels or states observed for this reaction system are endothermic, which is in agreement with the thermochemistry analysis as the electronic energies of V⁺ are changed. For the σ(VH⁺) shown in Fig. 2(a)–(c), in order to display the threshold regions more clearly, the σ(a³F₂: VH⁺) and σ(a⁵D₀: VH⁺) curves are amplified by a factor of 20 and 10, respectively. As shown in Fig. 2(a)–(c), the σ(a³F₂: VH⁺), σ(a⁵F₁: VH⁺), and σ(a⁵D₀: VH⁺) curves exhibit distinct behaviors, indicating that the electronic states of V⁺ ions play an important role in the formation of this reaction channel. Specifically, σ(a³F₂: VH⁺) has a threshold near E_cm = 0.6 eV and then increases almost exponentially above the threshold. At E_cm = 2.5 eV, σ(a³F₂: VH⁺) reaches the peak value of ≈11.5 Ų. This σ value is quite high for an endothermic reaction, Above 2.5 eV, σ(a³F₂: VH⁺) decreases almost exponentially until E_cm = 8.0 eV. At E_cm = 8.0–10.0 eV, the decreasing trend versus E_cm ends and even starts to increase mildly. Different from σ(a³F₂: VH⁺), σ(a⁵F₁: VH⁺) has a threshold at E_cm = 1.7 eV and then reaches a peak value of ≈0.02 Ų near E_cm = 3.0 eV. Above 3.0 eV, σ(a⁵F₁: VH⁺) is almost flat. The σ(a⁵D₀: VH⁺) shows similar profiles as that of σ(a⁵F₁: VH⁺) when E_cm ≤ 3.0 eV except the threshold position is 1.9 eV. However, σ(a⁵D₀: VH⁺) keeps increasing as E_cm further increases above 3.0 eV. As shown in Fig. 3, when E_cm is high enough to form the quintet [HV⁺CH₃](a⁵) intermediate, it can lead to the formation of VH⁺ and VCH₃⁺ without “weak quintet-to-triplet spin crossing”. Thus, σ(VH⁺) and σ(VCH₃⁺) are expected to be observed at high E_cm values. The trends of σ(a³F₂: VH⁺), σ(a⁵F₁: VH⁺), and σ(a⁵D₀: VH⁺) curves shown in Fig. 2(a)–(c), suggest that these curves may consist of a higher and a lower E_cm overlapping components. As the electronic energy is decreased, the lower E_cm component is found to diminish, resulting in the domination of the higher E_cm component of σ(a⁵D₀: VH⁺) curve as depicted in Fig. 2(c), To understand the dynamics features observed for the σ(VH⁺) as a function of E_cm and electronic state of V⁺, rigorous theoretical dynamics calculations based on accurate reaction potential energy surfaces are required.

One different feature for σ(VH⁺) in Fig. 2(a)–(c) compared to σ(VCH₂⁺) in Fig. 2(d)–(f), and σ(VCH₃⁺) in Fig. 2(h) and (g) is that σ(VH⁺) remains high at E_cm (≥4.0 eV) values. This observation could be the result of different reaction dynamics involved in the formation of different reaction product channels. At sufficiently high E_cm values (≥4.482 eV), the collision-induced dissociation (CID) product channels, such as reaction (4), are expected to occur.

V⁺(a⁵D₀) + CH₄(X¹A₁) → V⁺(a⁵D₀) + CH₃(X²A₂′′) + H(²S_1/2) E₀ = 4.482 ± 0.001 eV (4)

The formation of the CID product channel in reaction (4) can also be considered as generated from the further dissociation of the excited VH⁺ and/or VCH₃⁺ ions initially produced in the collision of V⁺(a⁵D₀) + CH₄(X¹A₁).

The E_cm dependences of σ(VCH₂⁺) are shown in Fig. 2(d)–(f). Similar to the σ(VH⁺), all three σ(VCH₂⁺) reaction channels are found to be endothermic. The E_cm-thresholds are observed at E_cm = 0.1 ± 0.1, 0.8 ± 0.1, and 1.2 ± 0.1 eV for σ(a³F₂: VCH₂⁺), σ(a⁵F₁: VCH₂⁺), and σ(a⁵D₀: VCH₂⁺), respectively. The differences of these E_cm-thresholds observed are consistent with the electronic energies of the corresponding V⁺ ions. The σ(a³F₂: VCH₂⁺), σ(a⁵F₁: VCH₂⁺), and σ(a⁵D₀: VCH₂⁺) curves are found to have similar profiles exhibiting a single peak. The σ(a³F₂: VCH₂⁺) starts to rise at its E_cm-threshold of 0.1 ± 0.1 eV, and reaches the peak value of 2.7 Ų at E_cm ≈ 0.8 eV. Above 0.8 eV, σ(a³F₂: VCH₂⁺) decreases rapidly down to zero at E_cm ≈ 5.0 eV. Similarly, σ(a⁵F₁: VCH₂⁺) [σ(a⁵D₀: VCH₂⁺)] reaches the peak value of 0.01 Ų at E_cm ≈ 2.0 eV [0.02 Ų at E_cm ≈ 2.5 eV], and decreases quickly down to zero at E_cm ≈ 5.0 eV. The decrease down to zero at high E_cm values could be attributed to the dissociation of excited VCH₂⁺ ions, as well as the CID of CH₄, as shown in reaction (4), but these processes occur at higher energies. Rather, as previously described,¹⁹ it can be seen that the peaks in the VCH₂⁺ cross sections match the onsets of VH⁺ + CH₃ formation. As the latter channel can be formed by simple bond cleavage from an H–V⁺–CH₃ intermediate, whereas dehydrogenation is entropically more difficult, competition between these channels explains the decline in the VCH₂⁺ + H₂ cross sections. Another reaction involving the formation of VCH₂⁺ at high E_cm values is shown in reaction (5). However, because of the high endothermicity of 5.7 eV, the occurrence of this reaction channel is expected to have very low probability.

V⁺(a⁵D₀) + CH₄(X¹A₁) → VCH₂⁺(X³A₁) + H(²S_1/2) + H(²S_1/2) E₀ = 5.7 ± 0.1 eV (5)

The σ(VCH₃⁺) reaction channels are also endothermic, as shown in Fig. 2(g) and (h). Due to the very low reactivity for this reaction channel, only σ(a³F₂: VCH₃⁺) and σ(a⁵D₀: VCH₃⁺) have been detected. Attempts were made to measure σ(a⁵F₁: VCH₃⁺) in the E_cm range 0.1 to 10.0 eV, but it was observed that the product VCH₃⁺ ion signal was below the detection limit when the reactant V⁺ ions were prepared in the a⁵F₁ state. In addition, for the same reason, the σ(a⁵D₀: VCH₃⁺) curve was only measured with very crude E_cm step size of 1.0 eV; and the peak value is observed as ≈0.007 Ų at E_cm = 5.0 eV. As the highest cross section among the three, σ(a³F₂: VCH₃⁺) has an E_cm-threshold of E_cm = 0.7 ± 0.1 eV and reaches a peak value of 0.08 Ų near E_cm = 2.7 eV. A flat profile for σ(a³F₂: VCH₃⁺) is observed at E_cm = 0.7 to 1.3 eV. Above 1.3 eV, σ(a³F₂: VCH₃⁺) starts to increase exponentially, which may indicate the formation of a new reaction channel involving VCH₃⁺ populated in an excited state. After reaching the peak value, σ(a³F₂: VCH₃⁺) decreases rapidly to zero near E_cm = 4.0 eV. Similar to σ(VCH₂⁺), the decay of σ(VCH₃⁺) can be related to the further dissociation of primary excited VCH₃⁺ product ions.

(d) Spin–orbit J-state effects

To our best knowledge, no experimental σ measurements for this reaction system with V⁺ ion prepared in single J states have previously been reported. The main reason for this challenge can be attributed to the lack of general experimental schemes for the preparation of TM cations in the selected J states. From the point of view of fundamental research, unravelling the J-state effects in chemical reactions involving TM cations is closely related to understanding the roles played by different kinds of angular momenta: spin (S), orbital angular momentum (L), and the total angular momentum (J) arising from the spin–orbit coupling.

In this work, by preparing reactant V⁺ ions in single J states, the J-state effects have been examined for the V⁺ + CH₄ reaction. The comparisons of σ(a³F_J: VH⁺, J = 2 versus 3), σ(a⁵F_J: VH⁺, J = 1 versus 2), σ(a⁵D_J: VH⁺, J = 0 versus 2), σ(a³F_J: VCH₂⁺, J = 2 versus 3), σ(a⁵F_J: VCH₂⁺, J = 1 versus 2), σ(a⁵D_J: VCH₂⁺, J = 0 versus 2), σ(a³F_J: VCH₃⁺, J = 2 versus 3), and σ(a⁵D_J: VCH₃⁺, J = 0 versus 2) are shown in Fig. 4(a)–(h), respectively. There it can be seen that the two corresponding J states exhibit essentially identical σ curves as shown in the figures. These results clearly show that no discernible J-state effects are observed for this V⁺ + CH₄ reaction system. This conclusion is in agreement with that observed in the recent study of other reaction systems, i.e., V⁺ + CO₂, and V⁺ + D₂,^24,26 indicating that the spin–orbit coupling of V⁺ is weak in the chemical reaction system of V⁺ + CH₄.

Fig. 4 The spin–orbit J-state effects on σ(VH⁺), σ(VCH₂⁺), and σ(VCH₃⁺) of the reaction system of V⁺(a³F_2–3, a⁵F_1–2, and a⁵D_0,2) + CH₄. The comparisons of σ(a³F_J: VH⁺, J = 2 vs. 3), σ(a⁵F_J: VH⁺, J = 1 vs. 2), σ(a⁵D_J: VH⁺, J = 0 vs. 2), σ(a³F_J: VCH₂⁺, J = 2 vs. 3), σ(a⁵F_J: VCH₂⁺, J = 1 vs. 2), σ(a⁵D_J: VCH₂⁺, J = 0 vs. 2), σ(a³F_J: VCH₃⁺, J = 2 vs. 3), σ(a⁵F_J: VCH₃⁺, J = 1 vs. 2), and σ(a⁵D_J: VCH₃⁺, J = 0 vs. 2) are shown in (a), (b), (c), (d), (e), (f), (g), and (h), respectively. These σ curves (arbitrarily selected) for two different J values of individual electronic states are found to be in excellent agreement. This finding clearly indicates negligible J effects for the titled reaction system.

This observation of Fig. 4(a)–(h) is also consistent with the “weak quintet-to-triplet spin crossing” mechanism. The spin–orbit coupling is known to facilitate the mixing among electronic states of TM cations with different multiplicities.^39,40 Thus, if the spin–orbit coupling is strong enough to mix reaction surfaces with different multiplicities, similar chemical reactivity would be observed for TM cations in electronic states with different multiplicities. However, distinct chemical reactivity is observed in this work when the V⁺ ion is prepared in single electronic states with different spins. Therefore, this observation is in accordance with weak spin–orbit interaction, suggesting that electron spin S, not J, of the reactant V⁺ ion is the constraining factor in determining the chemical reactivity of the V⁺ + CH₄ reaction.

It is interesting to note that spin–orbit coupling might have been expected to conserve the total electronic angular momentum J. If this were the case, then the ⁵D₀ level should not couple efficiently with a³F_1,2,3, whereas the a⁵D_1,2 levels could. The observation that a⁵D₀ and a⁵D₂ have essentially identical reactivities suggests that molecular angular momentum allows coupling of surfaces of different J.

(e) Branching ratios

The branching ratios (BR's) of the product channels, VH⁺ + CH₃, VCH₂⁺ + H₂, and VCH₃⁺ + H, of the reaction system V⁺(a⁵D₀, a⁵F₁, or a³F₂) + CH₄(X¹A₁) in the E_cm range from 0.1 to 10.0 eV are summarized in Table 1 by comparing the relative product VH⁺, VCH₂⁺, and VCH₃⁺ ion intensities. This comparison reveals that as the E_cm is increased, BR(VH⁺) increases monotonically from 0% to 100%, while BR(VCH₂⁺) shows the opposite trend. Furthermore, the BR(VCH₃⁺) values are found to have very small values, which are less than 10%.

Table 1 The branching ratios (BR's) of VH⁺ + CH₃, VCH₂⁺ + H₂, and VCH₃⁺ + H reaction product channels for the reaction system of V⁺ + CH₄ with V⁺ prepared in three of its spin–orbit coupled electronic states, a⁵D₀, a⁵F₁, and a³F₂ in the E_cm range 0.1–10.0 eV. The error limits of ±0.01 represent uncertainties from run-to-run independent measurements^a

E cm (eV)	V^+(a^5D0) + CH4			V^+(a^5F1) + CH4			V^+(a^3F2) + CH4
	VH^+	VCH2^+	VCH3^+	VH^+	VCH2^+	VCH3^+	VH^+	VCH2^+	VCH3^+
a The BRs are listed as zero if they are less than 0.01 and as “—” when all three product channels (or states) have zero σ values.
0.1	—	—	—	—	—	—	0.00	1.00	0.00
0.5	—	—	—	—	—	—	0.00	1.00	0.00
1.0	—	—	—	0.00	1.00	0.00	0.10	0.89	0.01
1.5	0.00	1.00	0.00	0.00	1.00	0.00	0.65	0.34	0.01
2.0	0.05	0.95	0.00	0.41	0.59	0.00	0.88	0.11	0.01
2.5	0.33	0.67	0.00	0.68	0.32	0.00	0.93	0.06	0.01
3.0	0.70	0.30	0.00	0.79	0.21	0.00	0.97	0.02	0.01
4.0	0.85	0.07	0.08	0.87	0.13	0.00	0.98	0.01	0.01
5.0	0.90	0.01	0.09	1.00	0.00	0.00	1.00	0.00	0.00
6.0	0.94	0.00	0.06	1.00	0.00	0.00	1.00	0.00	0.00
7.0	1.00	0.00	0.00	1.00	0.00	0.00	1.00	0.00	0.00
8.0	1.00	0.00	0.00	1.00	0.00	0.00	1.00	0.00	0.00
9.0	1.00	0.00	0.00	1.00	0.00	0.00	1.00	0.00	0.00
10.0	1.00	0.00	0.00	1.00	0.00	0.00	1.00	0.00	0.00

---

(f) Simulation of literature σ(SI) curves by using state-selected σ(a⁵D_J, a⁵F_J, and a³F_J) curves

The previous GIB mass spectrometric experiment was conducted about 33 years ago by the Armentrout group using a hot filament SI ion source at T = 1850–2200 K. The populations of the V⁺(a⁵D_J, a⁵F_J, and a³F_J) states thus generated were assumed to be governed by the Boltzmann distribution.¹⁹ In order to shed light into this assumption, we have performed a simulation of the experimental σ(SI-1850 K) and σ(SI-2200 K) curves. Here, we use the state-selected σ(a⁵D_J, a⁵F_J, and a³F_J) curves obtained in the present study. This simulation also aims to illustrate that hot-band excitations arising from impurity states in σ(SI) measurements can easily prevent the observation of the E_cm-thresholds or the E_T values.

As shown below, by taking the linear combination of state-selected σ(a⁵D_J, a⁵F_J, and a³F_J) curves determined in the present PFI-PI measurements, along with weighted Boltzmann populations of these electronic states,¹⁹ we show in Fig. 5(a) and (b) that excellent simulations of the respective experimental σ(SI-1850 K: VH⁺) and σ(SI-2200 K: VCH₂⁺) curves can be achieved. Fig. 5(a) compares the σ(a⁵D₀: VH⁺) curve with the experimental and simulated σ(SI-1850 K: VH⁺) and σ(SI-2200 K: VH⁺) curves. The V⁺ ions produced by thermal SI at 1850–2200 K cannot be in single quantum states. They are expected to populate mostly in the ground a⁵D_J cationic state, along with minor populations in the excited a⁵F_J and a³F_J states, which are governed by the Boltzmann distribution. By setting the SI source at 1850 K (2200 K), previous studies assumed that the relative populations of the V⁺(a⁵D_J), V⁺(a⁵F_J), and V⁺(a³F_J) states were 0.854, 0.145, and 0.00083 (0.800, 0.191, and 0.0023), respectively.

Fig. 5 (a) The red solid circle curve is the σ(a⁵D₀: VH⁺) curve obtained in the present study, which has been rescaled by a factor of 0.80. The blue open triangle and green open square curves are the respective experimental σ(SI-1850 K: VH⁺) and σ(SI-2200 K: VH⁺) curves. The orange solid circle and green solid circle curves are the respective simulated curves for σ(SI-1850 K: VH⁺) and σ(SI-2200 K: VH⁺) curves obtained based on the thermal Boltzmann populations of V⁺(a³F₂, a⁵F₁, and a⁵D₀) states. (b) The red solid circle curve is the σ(a⁵D₀: VCH₂⁺) curve obtained in this work, which has been rescaled by factor of 0.8. The blue open triangle curve is the experimental σ(SI-1850K: VCH₂⁺) curve; and the orange solid circle and green solid circle curves are the simulated curves for σ(SI-1850 K: VCH₂⁺) and σ(SI-2200 K: VCH₂⁺) curves obtained based on the thermal Boltzmann populations of V⁺(a³F₂, a⁵F₁, and a⁵D₀) states.

Since we have obtained detailed quantum state-selected cross section measurements: σ(a⁵D₀: VH⁺), σ(a⁵F₁: VH⁺), σ(a³F₂: VH⁺), σ(a⁵D₀: VCH₂⁺), σ(a⁵F₁: VCH₂⁺), and σ(a³F₂: VCH₂⁺) curves, we should be able to obtain the simulated σ(SI-1850 K) and σ(SI-2200 K) curves by using these state-selected σ curves and their assumed Boltzmann thermal populations.

In Fig. 5(a), the red solid circle curve represents the σ(a⁵D₀: VH⁺) curve obtained from this work, which has been rescaled by a factor of 0.80 in order to emphasize the similarity in the energy dependence. The blue open triangles and green open squares mark the experimental σ(SI-1850 K: VH⁺) and σ(SI-2200 K: VH⁺) curves, respectively. The orange solid circle curve shows the simulated curve obtained according to the thermal Boltzmann populations at 1850 K calculated as: σ(SI-1850 K: VH⁺) = [0.854 × σ(a⁵D₀: VH⁺) + 0.145 × σ(a⁵F₁: VH⁺) + 0.00083 × σ(a³F₂: VH⁺)] × 0.8. The green solid circle curve shows the simulated σ(SI-2200 K: VH⁺) curve, calculated based on the weighted Boltzmann populations as: [0.800 × σ(a⁵D₀: VH⁺) + 0.191 × σ(a⁵F₁: VH⁺) + 0.0023 × σ(a³F₂: VH⁺)] × 0.8. These simulations thus calculated reveal that V⁺(a³F_J) ions make a significant contribution of broadening of the σ curve involved and to the hot-band tailing structure observed around and below the reaction onset, even though the population of the a³F_J state is only 0.00083 and 0.0023 at 1850 and 2200 K, respectively. This is because the hot-band contribution of the σ(a³F_J: VH⁺) curve is hugely amplified by the much higher reactivity of the triplet a³F_J state compared to that of the quintet states. Thus, hot-band excitations, as in this case, can prevent observation of the true reaction onset.

By comparing the σ(SI-1850 K: VH⁺) and σ(SI-2200 K: VH⁺) curves with the σ(a⁵D₀: VH⁺) curve obtained in this study, we can conclude that the hot-band excitation of the σ(a⁵D₀: VH⁺) curve is much reduced; showing that the true 0 K E_T onset, i.e., E₀, is located at a higher E_cm still. As shown in Fig. 5(a), the σ(SI) curves observed at 1850 and 2200 K are in excellent agreement with the simulated σ(SI) curves at E_cm ≤ 4 eV, where the simulation of the σ(SI) curves can be obtained by the linear combination of the σ(a⁵D₀: VH⁺), σ(a⁵F₁: VH⁺), and σ(a³F₂: VH⁺) curves. The fact that the experimental σ(SI-1850 K: VH⁺) and σ(SI-2200 K: VH⁺) curves can be well simulated based on the weighted Boltzmann populations is a strong support of the thermal equilibrium assumption. However, the comparison of Fig. 5(a) reveals deviation between the experimental σ(SI) and the simulated curves at E_cm ≥ 4 eV; and the nature of this deviation is not known.

By using similar procedures, we have also obtained excellent simulations for the σ(SI-1850 K: VCH₂⁺) and σ(SI-2200 K: VCH₂⁺) curves as depicted in Fig. 5(b). Here, the red solid circle curve is the σ(a⁵D₀: VCH₂⁺) curve obtained from this work, whereas the blue open triangle curve is the experimental σ(SI-1850 K: VCH₂⁺) curve obtained previously by the Armentrout group. The orange solid circle and green solid circle curves are the simulated curves obtained as the linear combination of the σ(a⁵D₀: VCH₂⁺), σ(a⁵F₁: VCH₂⁺), and σ(a³F₂: VCH₂⁺) curves with weighted populations in accordance with the Boltzmann thermal populations observed at T = 1850–2200 K. The simulations of Fig. 5(b) indicate that the hot-tail appearing in the low E_cm region is overwhelmingly contributed by the excited triplet V⁺(a³F_J) electronic state in the σ(SI-1850–2200 K: VCH₂⁺) measurements.

In addition to validating the thermal equilibrium assumption for the populations of the V⁺ electronic states generated by thermal excitations, the excellent simulation observed can also be taken as strong confirmation that the σ(a⁵D₀), σ(a⁵F₁), and σ(a³F₂) curves produced in the present PFI-PI study are in single quantum electronic states with 100% purity.

(g) Comparison of present spin–orbit state-selected cross sections with previous results

The fact that the present state-specific results can be used to reproduce the previous data obtained using a surface ionization source also suggests that the assumptions made in this previous work regarding the distribution of electronic states was reasonable. This hypothesis can be further checked by comparing the approximate state-specific cross sections provided by Aristov and Armentrout¹⁹ with the robust determinations obtained here. Fig. 6 compares the present results for σ(a⁵D₀: VH⁺) and σ(a³F₂: VH⁺) with those from ref. 19 (taken from Fig. 2 and scaled by the inverse populations: 1/0.854 for the quintet states and 1/0.00083 for the triplets). Clearly, both the shapes and the magnitudes agree well, further validating the accuracy of the present results. A similar comparison of the σ(a⁵D₀: VCH₂⁺) and σ(a³F₂: VCH₂⁺)s with those from ref. 19 (taken from Fig. 8 directly) find similar agreement in shapes and magnitudes for the quintet states, but the previous data for triplet states is about two times larger in magnitude than the present results, a discrepancy that can be attributed to the extrapolation needed in the previous work. Notably, no reasonable information regarding the a⁵F state was obtained in the previous work, which the present study clearly shows is primarily because it is so much less reactive.

Fig. 6 State-selected σ(a⁵D₂: VH⁺) curve in black circles and σ(a³F₂: VH⁺) curve in solid red circles for the reaction channels of V⁺ + CH₄. The solid lines show the extrapolated state-specific results from ref. 19 for triplet (red) and quintet (black) states. Both data sets for the quintet states have been multiplied by a factor of 100.

(h) Bond dissociation energies of V⁺–H, V⁺–CH₂, and V⁺–CH₃

The D₀ values of V–H⁺, V–CH₂⁺, and V–CH₃⁺ can be derived from E_cm-threshold energies or threshold energies of reaction (E_T's) determined in the present experiment. Similar to the derived procedures used in the study of the reaction systems of V⁺ + D₂ (CO₂),^24,26 we can show that the D₀ values are related to E_T at T = 0 (or E₀) of reactions (1)–(3), given as E₀(1), E₀(2), and E₀(3), in eqn (6)–(8), respectively.

D₀(V⁺–H) = D₀(H–CH₃) – E₀(1) (6)

D₀(V⁺–CH₂) = D₀(H–CH₃) + D₀(H–CH₂) − 2Δ_fH₀(H) − E₀(2) (7)

D₀(V⁺–CH₃) = D₀(H–CH₃) − E₀(3) (8)

Here, D₀(H–CH₃), D₀(H–CH₂), and Δ_fH₀(H) are the 0 K bond dissociation energies of H–CH₃, H–CH₂, and the 0 K heat of formation of H atom [Δ_fH₀(H)], respectively. From available ref. 41 and 42, the values of D₀(H–CH₃), D₀(H–CH₂), and 2Δ_fH₀(H) = D₀(H₂) are known to be 4.482 ± 0.001, 4.739 ± 0.001, and 4.478 ± 0.001 eV, respectively.

As shown in Fig. 2(a)–(c), the E_cm-thresholds or E_T values observed for σ(a³F₂: VH⁺), σ(a⁵F₁: VH⁺), and σ(a⁵D₀: VH⁺) are 0.6 ± 0.1, 1.7 ± 0.1, and 1.9 ± 0.1 eV, which give the values of bond dissociation energy of VH⁺ (D₀(V⁺–H)) as 2.8 ± 0.1, 2.5 ± 0.1, and 2.6 ± 0.1 eV, respectively. Thus, the averaged value of D₀(V⁺–H) can be determined as 2.6 ± 0.2 eV, which is in good agreement with the D₀(V⁺–D) value of 2.5 ± 0.2 eV that has been deduced recently in the study of another reaction system of V⁺ + D₂.²⁶ Similarly, the D₀(V⁺–CH₂) can be derived as 3.6 ± 0.1, 3.7 ± 0.1, and 3.6 ± 0.1 eV, corresponding to the E_T's of 0.1 ± 0.1, 0.8 ± 0.1, and 1.2 ± 0.1 eV for σ(a³F₂: VCH₂⁺), σ(a⁵F₁: VCH₂⁺), and σ(a⁵D₀: VCH₂⁺) in Fig. 2(d)–(f), respectively. Thus, the averaged D₀(V⁺–CH₂) is 3.6 ± 0.2 eV. For σ(VCH₃⁺) shown in Fig. 2(g) and (h), due to the very low reactivity, only the E_T for σ(a³F₂: VCH₃⁺) has been determined with sufficiently high quality for reliable bond energy determination. Based on the latter E_T value of 0.7 ± 0.1 eV for σ(a³F₂: VCH₃⁺), the D₀(V⁺–CH₃) is deduced as 2.7 ± 0.2 eV.

We emphasize that the direct D₀ determination as shown in eqn (6)–(8) requires the E₀ instead of the E_T measurement. The most important thermal energy correction for the conversion of E_T to E₀ measurement is expected to be the thermal energy of reactant CH₄ molecule, in this case. Since the thermal energy for CH₄ has not been properly accounted and corrected for in the above thermochemical analyses and derivation, all the D₀ values deduced above associated with the reaction systems of V⁺ + D₂ (CO₂, CH₄) are upper bound values, which are found to be higher than the accepted corresponding literature values by ≈0.3–0.5 eV. That is, following the data analysis as given above, we have: D₀(V⁺–H) ≤ 2.6 ± 0.2 eV, D₀(V⁺–CH₂) ≤ 3.6 ± 0.2 eV, and D₀(V⁺–CH₃) ≤ 2.7 ± 0.2 eV.

As pointed out earlier, the shifting of the E_cm-threshold positions of σ(VH⁺), σ(VCH₂⁺), and σ(VCH₃⁺) observed, due to the change of the quantum electronic states of the reactant V⁺ ions, indicates that the quantum electronic energy can couple with the reaction coordinates in promoting accessible chemical reaction channels, similar to the E_cm.

(i) Modelling of kinetic energy distribution due to thermal broadening

Previous studies have shown that, in order to obtain reliable 0 K bond dissociation energies for simple TM-ligated molecules, such as D₀(V⁺–H), D₀(V⁺–CH₂), and D₀(V⁺–CH₃), it is necessary to account for the proper correction of thermal energies involved, particularly on the thermal energy associated with the neutral reactant CH₄ molecule in this case. On the basis of the theoretical analysis of Chantry³⁵ and Lifshitz et al.,⁴³ the Armentrout group has developed a simulation program for the determination of the threshold energy of reaction E₀ and the kinetic energy distribution by fitting the experimental σ curves based on the semi-empirical modified line-of-centers (MLOC) model as shown in eqn (9).^44,45

σ₀(E_cm) = ∑g_i(E_cm + E_el + E_i − E₀)ⁿ/E_cm (9)

Here σ₀ is an empirical scaling parameter, E_el is the electronic energy of the specific spin–orbit level of V⁺, E_i is the internal energy of the methane having rovibrational states i with population g_i, ∑g_i = 1, at the reaction cell temperature of 298 K, and n is an empirical fitting parameter. Before comparison with the experimental data, this model was convoluted over the kinetic energy distributions of the reactants.^35,43,46 In the present study, the value of n was fixed and the σ₀ and E₀ parameters were optimized by a nonlinear least-square method for best reproduction of the experimental reaction cross sections. As an example, we show in Fig. 6 typical fits achieved to the state-selected σ(a⁵D₂ and a³F₂: VH⁺) curves; and in Fig. 7 state-selected σ(a⁵D₂: VCH₂⁺) curve in black circles, σ(a⁵F₁: VCH₂⁺) curve in solid blue circles, and σ(a³F₂: VCH₂⁺) curve in solid red circles based on the semi-empirical MLOC model. Uncertainties in the modeling parameters were obtained via analyses using a range of acceptable n values and include the absolute uncertainty in the center-of-mass energy scale. At higher energies, the σ curve can decline because the product ion can dissociate or because of competition with other channels. This behavior was reproduced using a model detailed elsewhere that includes conservation of angular momentum along with an empirical parameter (p) that controls how fast the decline occurs.⁴⁷Eqn (9) is multiplied by P_D, the probability of product ion dissociation (competition), which is controlled by two parameters, p, similar to n but limited to integral values, and E_D, the energy where the product ion begins to dissociate (or competition ensues). These two parameters were optimized for best reproduction of the experimental data without affecting the threshold determinations.

Fig. 7 State-selected σ(a⁵D₂: VCH₂⁺) curve in black circles, σ(a⁵F₁: VCH₂⁺) curve in solid blue circles, and σ(a³F₂: VCH₂⁺) curve in solid red circles for the reaction channels of V⁺ + CH₄. The solid (dashed) lines show the fits based on the empirical modified line-of-centers (MLOC) models for each data set including (excluding) convolution with the kinetic and internal energy distributions of the reactants. The data and models for the two quintet states have been multiplied by a factor of 10.

Threshold energies of reaction can be converted to thermochemical parameters and properties using eqn (6)–(8). This assumes that the thresholds correspond to the asymptotic product energies, such that there are no reverse activation barriers. This result is expected in the present system for all reactions. As reported above, relevant literature thermochemistry includes the active thermochemical table (aTcT) values of D₀(CH₂–H₂) = 4.743 eV and D₀(CH₃–H) = 4.482 eV.^41,42

To extract meaningful thermochemistry from the kinetic energy dependent cross sections, they were modeled using eqn (9), which explicitly includes all sources of energy after convolution with the kinetic energy distributions of both reactants. Because the density of data points is relatively low, it is not possible to allow all parameters in this equation to vary freely, hence the modeling results from Aristov and Armentrout¹⁷ were used as a guide for selecting the value of n coupled with whether the cross section was adequately reproduced. In all cases, the simple line-of-centers (LOC) model where n = 1 reproduces the data well. The optimized parameters used are listed in Table 2. For the formation of VCH₂⁺ + H₂, the thresholds for the a⁵F₁ and a³F₂ excited levels are smaller than that for the a⁵D₀ ground level by 0.46 ± 0.09 and 1.11 ± 0.09 eV, in reasonable agreement with the excitation energies of 0.32 and 1.07 eV.³⁸ Likewise, for the VH⁺ + CH₃ channel, the thresholds shift by 0.24 ± 0.12 and 1.06 ± 0.12 eV, respectively. In both cases, the thresholds obtained provide weighted average bond dissociation energies of D₀(V⁺–CH₂) = 3.40 ± 0.14 eV and D₀(V⁺–H) = 2.02 ± 0.09 eV (where the uncertainties are two standard deviations of the mean). The former value can be compared to that obtained by Aristov and Armentrout of 3.30 ± 0.06 eV (from reactions of V⁺ with C₂H_2p)⁴⁸ and by Aristov and Armentrout of 3.47 ± 0.13 eV (from reaction of V⁺ with CH₄),¹⁹ both at 298 K. The latter result was later adjusted to a 0 K value of 3.37 ± 0.06 eV by Armentrout and Kickel.⁴⁹ Likewise, the value for D₀(V⁺–H) obtained here agrees nicely with that obtained by Elkind and Armentrout, 2.05 ± 0.06 eV (reaction of V⁺ + H₂ and D₂),²³ and with that obtained by combining these earlier results with state-selected experiments on the reaction V⁺ + D₂ similar to the present study, 2.07 ± 0.09 eV.²⁷

Table 2 Modified line-of-centers models eqn (9) of state-selected data for reaction of V⁺ with methane^a

Product	State	σ 0	N	E 0 (eV)	D 0(V^+–X)
a Uncertainties (one standard deviation) in parentheses.
VCH2^+	V^+(a^5D0)	0.075 (0.005)	1.0 (0.1)	1.41 (0.08)	3.33 (0.08)
	V^+(a^5F1)	0.025 (0.004)	1.0 (0.1)	0.95 (0.06)	3.47 (0.06)
	V^+(a^3F2)	3.9 (0.2)	1.0 (0.1)	0.30 (0.06)	3.37 (0.06)
VH^+	V^+(a^5D0)	0.14 (0.03)	0.9 (0.2)	2.42 (0.10)	2.06 (0.10)
	V^+(a^5F1)	0.22 (0.02)	1.0 (0.1)	2.18 (0.06)	1.98 (0.06)
	V^+(a^3F2)	28.5 (0.5)	1.0 (0.1)	1.36 (0.06)	2.05 (0.06)
VCH3^+	V^+(a^3F2)	0.15 (0.1)	1.0 (0.1)	1.34 (0.09)	2.07 (0.09)

---

In contrast to the results for VCH₂⁺ and VH⁺ products, only the thresholds obtained using the LOC model for VCH₃⁺ + H reaction from the a³F₂ state yields a reliable threshold that corresponds to D₀(V⁺-CH₃) = 2.07 ± 0.09 eV. This value agrees with that previously obtained by Aristov and Armentrout⁴⁸ after being adjusted to 0 K by Armentrout and Kickel, 2.00 ± 0.07 eV.⁴⁹ Furthermore, it is similar to the value obtained here for D₀(V⁺–H). As discussed by Armentrout and Kickel,⁴⁹ this similarity, which holds for all first-row transition metal cations, is expected because both molecules involve single covalent bonds to V⁺.

(j) E _T-threshold energy of reaction approach for bond energy measurements

As pointed out above, the effect of the thermal motion of neutral gaseous molecules in the reaction cell contributes significant uncertainty of collision energy. Chantry³⁵ has shown that the kinetic energy distribution at E_cm has the full-width-at-half-maximum of

W_1/2 = √[11.1 × γkT × E_cm]. (10)

Here, T = 298 K of neutral CH₄ gas, k is the Boltzmann constant, and γ = [m⁺/(M + m⁺)], where m⁺ and M are the masses of reactant ion and reactant neutral, respectively. For the reaction of V⁺ + CH₄, m⁺ = 51 amu, M = 16 amu, and γ = 51/67. Because of the broadening effect from the thermal kinetic motion of CH₄, the E_T value should be down-shifted from the true onset of reaction E₀. At E_cm = E₀ (the true reaction onset), the kinetic energy spread is W_1/2 = 2ΔE = √[11.1 × γkT × E₀] = √[0.217 × E₀]. Assuming the E_T onset is observed when CH₄ moves against V⁺ with a kinetic energy lower by the half maximum of the distribution, then E₀ = E_T + ΔE. This yields eqn (11) and (12), which allow the calculation of ΔE from E_T.

W_1/2 = √[0.217 × E₀] = √[0.217 × (E_T + ΔE)] = 2ΔE (11)

4ΔE² − 0.217 ΔE − (0.217E_T) = 0 (12)

By taking into account the ΔE term, which can be deduced from eqn (10)–(12) based on the thermal broadening effect, we have deduced the D₀ values of V⁺–H, V⁺–CH₂, and V⁺–CH₃ using eqn (6)–(8). The D₀ and E₀ values obtained based on E_T-threshold energy measurements are compared in Table 3 with the results obtained based on the simulation approach. As shown in the table, excellent agreement is observed between the results of the two experimental approaches for VCH₂⁺, whereas the values for VH⁺ and VCH₃⁺ are outside the combined uncertainties. Considering that the simulation approach is a more precise treatment and includes the entire distributions of energies available, the simulation approach should be the method of choice. Nevertheless, the E_T-threshold approach has the advantage of being straightforward with clearly tractable physical insight. When combined with high level ab initio calculations, both the E_T-threshold and the simulation approaches can be profitable for the study of energetics and bonding properties of TM-ligated chemical species, many of which are still unavailable in the literatures.

Table 3 Comparison of E₀ and D₀ values obtained based on the simulation of state-selected σ(VH⁺), σ(VCH₂⁺), and σ(VCH₃⁺) curves with those observed by E_T-threshold measurements for the reaction system of V⁺(a³F₂, a⁵F₁, and a⁵D₀) + CH₄^a

Product	State	Simulation approach		E T-threshold approach
		E 0 (eV)	D 0(V^+–X) (eV)	E 0 (eV)	D 0(V^+–X) (eV)
a Uncertainties (one standard deviation) in parentheses. b Weighted averages of D0(V^+–X), X = H and CH2. c Ref. 23. d Ref. 49. e Ref. 27.
VH^+	V^+(a^5D0)	2.42 (0.10)	2.06 (0.10)	2.25 (0.17)	2.23 (0.17)
	V^+(a^5F1)	2.18 (0.06)	1.98 (0.06)	2.03 (0.17)	2.13 (0.17)
	V^+(a^3F2)	1.36 (0.06)	2.05 (0.06)	0.81 (0.10)	2.60 (0.10)
			2.02 (0.05)^b		2.43 (0.26)^b
			2.05 (0.06)^c^d
			2.07 (0.09)^e
VCH2^+	V^+(a^5D0)	1.41 (0.08)	3.33 (0.08)	1.48 (0.14)	3.26 (0.14)
	V^+(a^5F1)	0.95 (0.06)	3.47 (0.06)	1.01 (0.12)	3.41 (0.14)
	V^+(a^3F2)	0.30 (0.06)	3.37 (0.06)	0.21 (0.10)	3.47 (0.10)
			3.40 (0.07)^b		3.40 (0.11)^b
			3.37 (0.06)^d
VCH3^+	V^+(a^3F2)	1.34 (0.09)	2.07 (0.09)	0.92 (0.10)	2.48 (0.10)
			2.00 (0.07)^d

---

IV. Conclusions

In this work, the σ(VH⁺), σ(VCH₂⁺), and σ(VCH₃⁺) of the reaction system V⁺(a⁵D₀, a⁵F₁, and a³F₂) + CH₄(X¹A₁) have been measured in the E_cm range from 0.1 to 10.0 eV, by coupling a novel two-color VIS-UV laser PFI-PI V⁺ ion source with a DQDO ion–molecule reaction apparatus. Both quantum spin–orbit electronic state and E_cm effects on chemical reactivity for this reaction system have been examined in detail. The triplet V⁺(a³F_J) ion is found to exhibit much higher chemical reactivity than that of the two quintet ions, V⁺(a⁵D_J) and V⁺(a⁵F_J), confirming the more qualitative conclusions of previous studies.¹⁹ Without a detailed theoretical examination of the reaction dynamics of the titled reaction system, this observation is tentatively interpreted by a weak quintet-to-triplet spin crossing mechanism, favoring dominantly the conservation of total electron spin. The preference for the conservation of total electron spin may promote the formation of an inserted intermediate, [HV⁺CH₃], which can thus enhance the reactivity of the triplet V⁺(a³F_J) ion. Although the electronic energy of V⁺(a⁵F_J) ion is 0.3 eV higher than that of the V⁺(a⁵D_J) ion, the reactivity of the V⁺(a⁵F_J) ion is found to be lower than that of the V⁺(a⁵D_J) ion, indicating that chemical reactivity of V⁺ ions is governed by quantum state effects rather than energy effects.

The E_cm-thresholds of σ(VH⁺), σ(VCH₂⁺), and σ(VCH₃⁺) for V⁺ prepared in the a⁵D₀, a⁵F₁, or a³F₂ states have been determined except that for σ(a⁵F_J: VCH₃⁺). From the E_T-threshold energies of reaction measurements, the upper limits for D₀(V⁺–H), D₀(V⁺–CH₂), and D₀(V⁺–CH₃) values have been deduced. By properly accounting for the thermal kinetic energy distribution primarily resulting from the thermal broadening effects of the neutral reactant CH₄ molecule, we have obtained reliable D₀ values for these V⁺-ligated molecular ions. The differences of E_cm-thresholds observed are consistent with the electronic state energy levels of reactant V⁺ ions, indicating that quantum electronic energies of V⁺ ions similar to E_cm, can couple effectively with the reaction coordinates of the V⁺ + CH₄ reaction system. No J effect has been observed, which may mean that the spin–orbit coupling of V⁺(a⁵D₀, a⁵F₁, or a³F₂) of V⁺ ion is weak and J is not a constraining factor to this reaction system. The weak spin–orbit coupling is expected to lower the mixing of electronic states with different multiplicities (or spins), which is in accordance with the distinct differences of observed chemical reactivity for V⁺ ions prepared in electronics states with different spins. Detailed BR's have also been obtained as a function of E_cm and electronic states of V⁺ ion, together with quantum state-selected σ's, can serve as experimental benchmarks for state-of-the-art theoretical calculations of model reaction systems. The much higher reactivity and product selectivity of the V⁺(a³F_J) + CH₄ reaction leading to H₂ formation observed in this work may provide valuable insight into designing more effective catalytic pathways for CH₄ activation. This and the recent V⁺ state-selected ion–molecule reaction experiments have shown that the E_T-threshold energy and σ curve measurements represent a fruitful experimental and theoretical research area for the study of chemical bonding between TM cations and ligands.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work is supported by the National Science Foundation, Grant CHE-1763319 (CYN) and CHE-1664618 (PBA). CYN is also grateful to Dr Huie Tarng Liou for his generous donation of research support for the Ng Laboratory.

References

1. S. A. Montzka, E. J. Dlugokencky and J. H. Butler, Nature, 2011, 476, 43–50.
2. C. R. Webster, P. R. Mahaffy, S. K. Atreya, G. J. Flesch, M. A. Mischna, P. Y. Meslin, K. A. Farley, P. G. Conrad, L. E. Christensen, A. A. Pavlov, J. Martín-Torres, M. P. Zorzano, T. H. McConnochie, T. Owen, J. L. Eigenbrode, D. P. Glavin, A. Steele, C. A. Malespin, P. D. Archer, Jr., B. Sutter, P. Coll, C. Freissinet, C. P. McKay, J. E. Moores, S. P. Schwenzer, J. C. Bridges, R. Navarro-Gonzalez, R. Gellert and M. T. Lemmon, Science, 2015, 347, 415–417.
3. S. K. Atreya, E. Y. Adams, H. B. Niemann, J. E. Demick-Montelara, T. C. Owen, M. Fulchignoni, F. Ferri and E. H. Wilson, Planet. Space Sci., 2006, 54, 1177–1187.
4. C. J. Bennett, C. S. Jamieson, Y. Osamura and R. I. Kaiser, Astrophys. J., 2006, 653, 792–811.
5. O. Mousis, E. Chassefiere, N. G. Holm, A. Bouquet, J. H. Waite, W. D. Geppert, S. Picaud, Y. Aikawa, M. Ali-Dib, J.-L. Charlou and P. Rousselot, Astrobiology, 2015, 15, 308–326.
6. C. Mesters, Annu. Rev. Chem. Biomol. Eng., 2016, 7, 223–238.
7. A. Bard, G. M. Whitesides, R. N. Zare and F. W. McLafferty, Acc. Chem. Res., 1995, 28, 91.
8. H. Schwarz, Angew. Chem., Int. Ed., 2011, 50, 10096–10115.
9. L. Barelli, G. Bidini, F. Gallorini and S. Servili, Energy, 2008, 33, 554–570.
10. M. E. Dry, Catal. Today, 2002, 71, 227–241.
11. H. Jahangiri, J. Bennett, P. Mahjoubi, K. Wilson and S. Gu, Catal. Sci. Technol., 2014, 4, 2210–2229.
12. J. C. Weisshaar, Acc. Chem. Res., 1993, 26, 213–219.
13. J. Roithová and D. Schröder, Chem. Rev., 2010, 110, 1170–1211.
14. P. B. Armentrout and J. L. Beauchamp, J. Am. Chem. Soc., 1981, 103, 784–791.
15. P. B. Armentrout and J. L. Beauchamp, Acc. Chem. Res., 1989, 22, 315–321.
16. J. Allison, R. B. Freas and D. P. Ridge, J. Am. Chem. Soc., 1979, 101, 1332–1333.
17. A. Shayesteh, V. V. Lavrov, G. K. Koyanagi and D. K. Bohme, J. Phys. Chem. A, 2009, 113, 5602–5611.
18. D. Schröder and H. Schwarz, Proc. Natl. Acad. Sci. U. S. A., 2008, 105, 18114–18119.
19. N. Aristov and P. B. Armentrout, J. Phys. Chem., 1987, 91, 6178–6188.
20. T. Hayes, D. Bellert, T. Buthelezi and P. J. Brucat, Chem. Phys. Lett., 1997, 264, 220–224.
21. E. Sicilia and N. Russo, J. Am. Chem. Soc., 2002, 124, 1471–1480.
22. E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra, Cambridge University Press, 1951.
23. J. L. Elkind and P. B. Armentrout, J. Phys. Chem., 1985, 89, 5626–5636.
24. Y. C. Chang, Y. Xu and C.-Y. Ng, Phys. Chem. Chem. Phys., 2019, 21, 6868–6877.
25. Y. C. Chang, B. Xiong, Y. Xu and C.-Y. Ng, J. Phys. Chem. A, 2019, 123, 2310–2319.
26. Y. Xu, Y.-C. Chang and C.-Y. Ng, J. Phys. Chem. A, 2019, 123, 5937–5944.
27. P. B. Armentrout, Y.-C. Chang and C.-Y. Ng, J. Phys. Chem. A, 2020, 124(26), 5306–5313.
28. M. R. Sievers and P. B. Armentrout, J. Chem. Phys., 1995, 102, 754–762.
29. Y. C. Chang, Y. Xu, B. Xiong and C.-Y. Ng, Mol. Phys., 2020, 1–11.
30. Y. C. Chang, H. Xu, Y. Xu, Z. Lu, Y.-H. Chiu, D. J. Levandier and C. Y. Ng, J. Chem. Phys., 2011, 134, 201105.
31. Y. C. Chang, Y. Xu, Z. Lu, H. Xu and C. Y. Ng, J. Chem. Phys., 2012, 137, 104202.
32. N. R. Daly, Rev. Sci. Instrum., 1960, 31, 264–267.
33. Y. Xu, B. Xiong, Y. C. Chang and C.-Y. Ng, Astrophys. J., 2018, 861, 17.
34. Y. Xu, B. Xiong, Y. C. Chang and C.-Y. Ng, J. Phys. Chem. A, 2018, 122, 6491–6499.
35. P. J. Chantry, J. Chem. Phys., 1971, 55, 2746–2759.
36. G. Friedlander, J. W. Kennedy and E. S. Macias, Nuclear and radiochemistry, John Wiley & Sons, 1981.
37. J. E. Sansonetti and W. C. Martin, J. Phys. Chem. Ref. Data, 2005, 34, 1559–2259.
38. A. Kramida, Y. Ralchenko, J. Reader and N. A. Team, National Institute of Standards and Technology, Gaithersburg, MD, 2012.
39. H. Schwarz, Int. J. Mass Spectrom., 2004, 237, 75–105.
40. J. N. Harvey, Phys. Chem. Chem. Phys., 2007, 9, 331–343.
41. B. Ruscic, R. E. Pinzon, M. L. Morton, G. von Laszevski, S. J. Bittner, S. G. Nijsure, K. A. Amin, M. Minkoff and A. F. Wagner, J. Phys. Chem. A, 2004, 108, 9979–9997.
42. B. Ruscic and D. H. Bross, Active Thermochemical Tables (ATcT) values based on ver. 1.122g of the Thermochemical Network, available at ATcT.anl.gov, accessed 4/29/20.
43. C. Lifshitz, R. L. C. Wu, T. O. Tiernan and D. T. Terwilliger, J. Chem. Phys., 1978, 68, 247–260.
44. R. H. Schultz, K. C. Crellin and P. Armentrout, J. Am. Chem. Soc., 1991, 113, 8590–8601.
45. N. Dalleska, K. Honma, L. Sunderlin and P. Armentrout, J. Am. Chem. Soc., 1994, 116, 3519–3528.
46. K. M. Ervin and P. B. Armentrout, J. Chem. Phys., 1985, 83, 166–189.
47. M. E. Weber, J. L. Elkind and P. B. Armentrout, J. Chem. Phys., 1986, 84, 1521–1529.
48. N. Aristov and P. B. Armentrout, J. Am. Chem. Soc., 1986, 108, 1806–1819.
49. P. B. Armentrout and B. L. Kickel, in Organometallic Ion Chemistry, ed. B. S. Freiser, Kluwer, Dordrecht, 1996, pp. 1–45.

---