Gas‐Phase Mechanism of O.−/Ni2+‐Mediated Methane Conversion to Formaldehyde

Abstract The gas‐phase reaction of NiAl2O4 + with CH4 is studied by mass spectrometry in combination with vibrational action spectroscopy and density functional theory (DFT). Two product ions, NiAl2O4H+ and NiAl2O3H2 +, are identified in the mass spectra. The DFT calculations predict that the global minimum‐energy isomer of NiAl2O4 + contains Ni in the +II oxidation state and features a terminal Al−O.− oxygen radical site. They show that methane can react along two competing pathways leading to formation of either a methyl radical (CH3⋅) or formaldehyde (CH2O). Both reactions are initiated by hydrogen atom transfer from methane to the terminal O.− site, followed by either CH3⋅ loss or CH3⋅ migration to an O2− site next to the Ni2+ center. The CH3⋅ attaches as CH3 + to O2− and its unpaired electron is transferred to the Ni‐center reducing it to Ni+. The proposed mechanism is experimentally confirmed by vibrational spectroscopy of the reactant and two different product ions.

The infrared photodissociation (IRPD) experiments are performed on a cryogenic ion trap tandem mass spectrometer [1] using the widely tunable, intense IR radiation from the Fritz−Haber−Institute Free−Electron Laser (FHI FEL). [2] In brief, NiAl2O4 + ions are produced in a pulsed laser vaporization source by focusing a frequency−doubled Nd:YAG laser (50 Hz, 5−10 mJ) onto a rotating Ni/Al (50/50 at %) metal rod. The resulting plasma is quenched with a gas pulse of 1% O2 seeded in He. Cluster ions are formed during expansion through a clustering channel downstream from the rod and pass through a 4 mm diameter skimmer and are collimated in a radio frequency (RF) decapole ion guide. The desired cations are mass−selected using a quadrupole mass filter, deflected 90° in an electrostatic quadrupole deflector, and focused into a cryogenic RF ring−electrode ion trap. The trap is continuously filled with pure He gas or a reactant gas/buffer gas mix of 0.01 % CH4 in He gas at an ion−trap temperature of 10 K or 100K and 300K, respectively. Many collisions of the trapped ions with the mixture gas provide gentle cooling of the internal degrees of freedom close to the ambient temperature. Under these conditions, the He−tagged NiAl2O4 + He1−2 or the reactions between NiAl2O4 + and CH4 are formed.
For the IRPD experiments of the NiAl2O4 + ·He complex we used the He atoms as a messenger tag at 10 K ( Figure S1). For the IPRD experiments of NiAl2O4H + ·CH4 and NiAl2O3H2 + ·CH4, we used the CH4 molecule as a messenger tag at 100K ( Figure S2). All ions are extracted from the ion trap at 5 Hz and focused both temporally and spatially into the center of the extraction region of an orthogonally mounted reflection time−of−flight (TOF) tandem photofragmentation mass−spectrometer. Here, the ions are irradiated with a counter−propagating IR laser pulse produced by the FHI FEL (within 500−1250 cm −1 , bandwidth: ~0.5 % fwhm, pulse energy: 1−25 mJ). All parent and photofragment ions are then accelerated toward an MCP detector and monitored simultaneously. IRPD scans are recorded by averaging about 100 TOF mass spectra per wavelength step (4 cm −1 or 5 cm −1 ) and scanning the wavelength. Typically, at least three scans are summed to obtain the final IRPD spectrum. The photodissociation cross section σIRPD is determined as described previously. [3] The conversion of the TOF mass spectrum from time-of-flight (μs) to mass-to-charge ratio (u) units is achieved by fitting a second order polynomial function to at least three calibration points obtained with only He in the trap.
Note that the mass spectrometric study requires the use of very low concentration CH4 in He mixtures (~0.01%) in order to minimize formation of larger complexes with methane under our experimental conditions. These mixtures are obtained by successive dilution, which is not a very accurate method. The absolute error of the CH4 concentrations used was S4 estimated to be around ±300%. Here we are predominantly interested in a qualitative analysis of the mass spectra (peak positions of dominant peaks) in order to identify the massto-charge ratio of the main product ions formed. The isotopic reaction with CD4 was mainly performed to confirm the assignment of the mass peaks P1 and P2 based on the observed isotope-dependent mass shift. This does not require exactly the same number densities.

Theoretical methods
Density functional theory (DFT) calculations using Gaussian 16 [4] were carried out to investigate the structures of NiAl2O4 + and the mechanisms of reaction with CH4. The B3P86 [5] functional and the TZVP basis sets [6] were used throughout.
The reaction mechanism calculations involved geometry optimization of reaction intermediates (IMs) and transition states (TSs). The initial guess structures of the TS species were obtained through relaxed potential energy surface scans using single or multiple internal coordinates. [7] Vibrational frequency calculations were performed to check that the IMs or TSs have zero and only one imaginary frequency, respectively. The intrinsic reaction coordinate calculations [8] were carried out to make sure that a TS connects two appropriate minima. The obtained reaction energies were corrected with zero−point vibrational energies to give reaction enthalpies at zero Kelvin (H0). The NBO analysis was performed with NBO 3.1. [9] CCSD(T) [10] single-point energies at the B3P86 optimized structures 2 R and 4 R were also calculated.
To obtain a quantitative measure for the agreement of experimental and theoretical spectra, the cosine similarity score is used. [11] The score S expresses the similarity between two spectra, where the intensity of the experimental and predicted absorptions is represented by vectors A and B in eq. 1. The score can vary from zero to unity, with a value closer to 1 indicating greater similarity. (1) The Rice−Ramsperger−Kassel−Marcus (RRKM) theory [12] and RRKM-based variational transition state theory (VTST) [12] were used to calculate the rate constants of (kc) transition state 2 1/ 2 2 conversion and (kd) CH3• radical desorption from intermediates 2 1, respectively.
The values are shown in Table S4 in Section 4.5.  Figure S4. DFT calculated isomers of NiAl2O4 + . The symmetries, electronic states, zero−point vibration corrected energies (kJ mol -1 ) with respect to the most stable isomer, and bond lengths (pm) are given. Note that the spin distributions are different in IS01 and IS03: IS01 features a local d 8 high spin configuration at Ni and an antiferromagnetically coupled radical electron at the terminal O, while in IS03 Ni(d 8 ) is diamagnetic (local low spin). IS07 has ferromagnetic coupling between high spin Ni(d 8 ) and the terminal O centered radical electron. In IS13 Ni is formally in an excited d 7 s 1 quintet configuration. Figure S5. Experimental IRPD spectra (dark red) of R·He at 10 K and the harmonic B3P86/TZVP IR spectra (green, Gaussian line function convolution FWHM=15 cm −1 ) of lowenergy doublet and quartet structures of NiAl2O4 + (R) (relative energies given in kJ mol -1 ).

Structures
The assignment for peaks a-e is shown in Table S1. The cosine similarity score S is given in parentheses. Figure S5b shows the best S value obtained with a scaling factor of 0.998 for Figure S5c.
We compare calculated harmonic wave numbers with observed (anharmonic) fundamentals. Scaling accounts for both neglected anharmonicities and systematic errors of the calculated harmonic force constants. Depending on the method employed, these may partially compensate each other.
In the present case the effect of using a scaling factor is negligible. The S value for R is 0.91 without a scaling, while the maximum S value (0.93) is obtained for a scaling factor of 0.998, which is very close to unity. Figure S6. DFT calculated isomers of product ions (P1) NiAl2O4H + and (P2) NiAl2O3H2 + . The symmetries, electronic states, zero−point vibration corrected energies (kJ mol -1 ) with respect to the most stable isomer, and bond lengths (pm) are given. The assignment for peaks a-e are shown in Table S1. S11 Figure S7. Experimental IRPD spectra (dark red) of methane tagged P1·CH4 ions at 100 K and the harmonic B3P86/TZVP IR spectra (green, Gaussian line function convolution FWHM=15 cm −1 ) of 3 P1-Ni-CH4 and the isomers shown in Figure S6 (blue, Ni; pink, Al; red, O; grey, C; white, H). The energies relative to the reactants (in kJ mol -1 ) are shown in brackets.
The assignment for peaks a-e is shown in Table S1. S12 Figure S8. Experimental IRPD spectra (dark red) of a) methane tagged P1·CH4 ions at 100 K and the harmonic B3P86/TZVP IR spectra (green, Gaussian line function convolution FWHM=15 cm −1 ) of isomers b) 3 P1-Ni-CH4, c) 3 P1-Al(O3)-CH4, and d) 3 P1-Al(O2-OH)-CH4 with different methane adsorption sites (blue, Ni; pink, Al; red, O; grey, C; white, H). The energies relative to the reactants (in kJ mol -1 ) are shown in brackets. S13 Figure S9. Experimental IRPD spectra (dark red) of methane tagged P2·CH4 ions at 100 K and the harmonic B3P86/TZVP IR spectra (green, Gaussian line function convolution FWHM=15 cm −1 ) of 2 P2-Ni-CH4 and the isomers shown in Figure S6 (blue, Ni; pink, Al; red, O; grey, C; white, H). The energies relative to the reactants (in kJ mol -1 ) are shown in brackets. S14 Figure S10. Experimental IRPD spectra (dark red) of a) methane tagged P2·CH4 ions at 100 K and the harmonic B3P86/TZVP IR spectra (green, Gaussian line function convolution  Ni + is in different electron configurations, d 9 and d 9 s 1 , respectively. This means that starting from 4 the system is in an electronically excited state which explains the much higher energy. (0.30) 4 R Figure S13: Additional DFT doublet PES for methane adsorption and initial activation. The zero−point vibration corrected energies with respect to the separated reactants are given in kJ mol -1 . Bond lengths are given in pm. Note that the methyl radical is located above the NiAl2O4H + surface in 2 2c, while the methyl radical is located below the NiAl2O4H + surface in 2 2.

Ni oxidation state in structures 2 3 and 2 4
Both 2 3 and 2 4 have the same CH4NiAl2O4 + composition, and in both 2 3 and 2 4 the 4 O and 2 Al atoms are in their usual oxidation states -2 and +3, see Table S2. In both species one H atom forms an OH bond and, hence, is in the +1 oxidation state. In 2 3, the CH3 species is a methyl radical (see spin density in Figure 5 of the main manuscript) which is weakly attached to Al (bond distance of 221 pm) and, hence, has a total oxidation state of 0. As the total charge is +1 this leaves a +2 oxidation state for Ni in 2 3.
In contrast, in 2 4, there is no spin-density on the CH3 species. It has formed a bond with an O atom (distance 144 pm) resulting in a methoxy species with oxidation states of -2 and +1 for O and CH3, respectively.  Figure S16 shows the NPA charges obtained with the NBO analysis [9] for the different structures along the reactions path. The sudden change when passing from 2 3 to 2 4 also reflects the change of the Ni oxidation state from +2 to +1.  For these calculations, the energy (E) of intermediate 2 1 and the energy barrier (E ≠ ) for 2 1 → 2 1/ 2 2 and 2 1 → 3 P1 were needed. The reaction intermediate 2 1 possesses the vibrational energies (Evib) of NiAl2O4 + and CH4, the center of mass kinetic energy (Ek), and the binding energy (Eb) which is the energy difference between the separated reactants (NiAl2O4 + + CH4) and the reaction complex 2 1. The values of Evib and Eb were taken from the DFT calculations and Ek = μv 2 /2, in which μ is the reduced mass of 2 1 and v is the velocity (~660 m/s).
( 1 2 ) = vib (NiAl 2 O 4 + ) + vib (CH 4 ) + k + b The rate constant (k) value was calculated by the eq. 3: in which g is the symmetry factor (g is taken as 1), ρ(E) denotes the density of states of the reaction intermediates at the energy E, N ≠ (E-E ≠ ) is the total number of the states of the transition state with a barrier E ≠ (E ≠ was zero-point-vibration corrected energy), and h is the Planck constant. The ρ(E) and N ≠ (E-E ≠ ) were obtained by the direct count method [13] with the DFT calculated vibrational frequencies under the approximation of harmonic vibrations.
For desorption of neutral products CH3• from 2 1, the VTST calculations were performed through partial geometry optimizations of NiAl2O4HCH3 + by fixing the distance between