# Laboratory detection of the methoxymethyl radical, CH<sub>3</sub>OCH<sub>2</sub>, using Faraday rotation and chirped-pulse techniques in the (sub-)millimeter wave range

ROSEMONDE CHAHBAZIAN,¹ MARIE-ALINE MARTIN-DRUMEL,¹ AND OLIVIER PIRALI¹

¹Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay, 91400 Orsay, France

## ABSTRACT

Modeling the abundance of interstellar Complex Organic Molecules (iCOMs) in space is a major challenge for astrophysicists. The relative roles of gas-phase and grain-surface processes in the formation and destruction of such large molecules remain unclear. Methyl formate (CH<sub>3</sub>OCHO, MF) and dimethyl ether (CH<sub>3</sub>OCH<sub>3</sub>, DME) species have been detected at relatively high abundances in both warm and cold objects of the interstellar medium (ISM), challenging an initial hypothesis favoring grain-surface processes for their formation. In this context, the methoxymethyl radical (CH<sub>3</sub>OCH<sub>2</sub>, RDME) has been proposed as a key species linking the abundances of MF and DME in the gas-phase. Its detection may provide crucial information to disentangle and quantify the different processes involved in the formation and destruction of MF and DME. To support the search for RDME in space, we present the laboratory detection of its pure rotational spectrum in the vibronic ground state. Special care was taken to measure the frequencies of transitions expected intense under cold interstellar conditions. In total, we assigned and fitted 1007 transitions of the RDME with N' and K'<sub>a</sub> values up to 34 and 5, respectively. A reliable spectral catalog has been generated using the spectroscopic parameters derived from the fit and can be used confidently for future searches of the RDME radical in the ISM.

## 1. INTRODUCTION

Radical species play a critical role in interstellar chemistry (Balucani et al. 2015; Herbst 2017). Among the numerous radicals involved in chemical networks, the methoxymethyl radical (CH<sub>3</sub>OCH<sub>2</sub>, hereafter noted RDME for Radical of DME), is proposed to be an important intermediate for the formation of many abundant interstellar Complex Organic Molecules (iCOMs) observed in the interstellar medium (ISM), in particular dimethyl ether (CH<sub>3</sub>OCH<sub>3</sub>, DME in the following; Balucani et al. 2015), methyl formate (CH<sub>3</sub>OCHO, MF; Herbst 2017), and C<sub>3</sub>O<sub>3</sub>H<sub>6</sub> structural isomers such as methoxy acetic acid (CH<sub>3</sub>OCH<sub>2</sub>COOH; Gámez & Senent 2021). RDME is also a constituent group of other recently detected iCOMs: ethyl methyl ether (CH<sub>3</sub>CH<sub>2</sub>OCH<sub>3</sub>; Tercero et al. 2015), methoxy methanol (CH<sub>3</sub>OCH<sub>2</sub>OH; McGuire et al. 2017), and 2-methoxy ethanol (CH<sub>3</sub>OCH<sub>2</sub>CH<sub>2</sub>OH; Fried et al. 2024). The formation and destruction processes of iCOMs are still unclear, and several chemical pathways are discussed in the literature. According to Jaber et al. (2014), the linear correlation between the abundances of DME and MF may reflect that their formation processes must be the same in cold and warm environments, favoring the gas-phase formation process. In this scenario, Balucani et al. (2015) proposed a new model for the synthesis of DME and MF in cold environments, adding new gas-phase reactions where DME is the precursor of MF through oxidation of RDME. As an alternative to gas-phase routes, grain-surface and grain-gas chemistry has also been shown to play a central role in the formation of iCOMs such as MF (Laas et al. 2011), DME (Garrod et al. 2008), and dehydrogenated iCOMs such as RDME (Garrod et al. 2022). Garrod et al. (2022) proposed that the main mechanism for DME production is the recombination of H and CH<sub>3</sub>OCH<sub>2</sub> radicals on grain surfaces, followed by chemical desorption in the gas-phase. In their model, DME and MF can be modeled considering only grain surface reactions, and RDME itself could be produced by the reaction of CH<sub>2</sub> and CH<sub>3</sub>O on grain surfaces. However, the predominance of grain-surface chemistry compared to gas-phase chemistry in cold environments of the ISM has been questioned by several groups since the detection of MF and DME in the prestellar core of L1544 (T ≤ 30 K; Bacmann et al. 2012; Vastel et al. 2014). The search for gaseous RDME in the ISM would provide new insights into the chemical mechanisms at play in the ISM and would constrain astrochemical models. Such searches require to perform high-resolution (rotationally resolved) spectroscopy in the laboratory to provide an accurate set of transitions relevant to ISM conditions. However, the synthesis and spectroscopic characterization of such a large
and fragile radical demand well-adapted techniques, and thus, to date, there is no experimental data on the rotational structure of RDME.

From a more general point of view, the literature on the spectroscopic properties of RDME remains quite scarce. Vibronic transitions (rotationally unresolved) were reported in the gas-phase by Langer et al. (1995) and Maricq et al. (1997), showing intense absorptions centered around 204 and 295 nm. Four vibrational bands at 1468.1, 1253.9, 1226.6, and 944.4 cm⁻¹ were observed and assigned to the vibronic ground state (GS) of RDME, synthesized from photodissociation of DME trapped in Ar matrix (Gong & Andrews 2011). From the theoretical side, ab initio calculations have been carried out by Yazidi et al. (2019), providing equilibrium structure, GS rotational constants, projections of the permanent dipole moments along the *a*, *b*, and *c* axis, and internal barriers for the three large-amplitude motions of RDME (see Section 2.1). In this work, we present the first rotationally resolved spectrum of RDME. In Section 2, we present the methodology used to produce the radical and to record and analyze its spectrum. The results of the spectral analysis are presented and discussed in Section 3. The frequencies of the transitions predicted intense under cold astrophysical conditions, which can thus be used for interstellar searches of the radical, are also reported in that section.

## 2. LABORATORY METHODS

For the acquisition of the rotationally resolved spectrum of RDME, we used two experimental setups recently developed in our group: 1) a Faraday rotation spectrometer (Chahbazian et al. 2024a) was used to record the room temperature spectrum in the 140–600 GHz range and, once the spectral analysis was sufficiently robust, 2) a chirped pulse (CP) jet discharge apparatus was used to record transitions under jet-cooled conditions in the 75–110 GHz range. The spectral analysis was performed using a combination of freely available software and the results of quantum calculations.

### 2.1. *Quantum chemical calculations*

High-level quantum chemical calculations were performed by Yazidi et al. (2019) at the RCCSD(T)-F12/aug-cc-pVTZ level of theory. They found that the RDME is an asymmetric top molecule belonging to the C₁ point group with an X²A electronic ground state, and they provided precious information to predict the pure rotational spectrum of the radical, notably the rotational constants, the dipole moments projections along the three axes of inertia ($\mu_a$=0.695 Debye, $\mu_b$=1.215 Debye, and $\mu_c$=0.302 Debye), and the barrier heights for the large amplitude motions. There are three large amplitude motions, represented in Fig. 1: –CH₂ torsion, –CH₂ wagging, and –CH₃ torsion, with calculated barrier energies respectively equal to about 2000 cm⁻¹, 109 cm⁻¹, and 500 cm⁻¹.

However, the calculations performed by Yazidi et al. (2019) lacked the spin-rotation coupling parameters (coupling between the electronic spin and the overall rotation of RDME), which are also important pieces of information for rotational spectroscopy. We thus performed a geometry optimization using density functional theory at the ωB97X-D/cc-pVQZ level of theory (Dunning 1989; Woon & Dunning 1993; Chai & Head-Gordon 2008) using the Gaussian 16 suite of electronic structure programs (Frisch et al. 2016). Anharmonic frequencies, rotational constants, and fine structure parameters have been derived. Spectroscopic parameters derived from both Yazidi et al. (2019) and our calculations have been used here as a starting point for the assignment process of the spectrum of this radical.

<figure><img src="image_1.png" /><figcaption>**Figure 1.** Molecular structure and representation of the large amplitude motions in RDME: rotation of the –CH₃ (angle $\theta$), inversion of the CH₂ (angle $\alpha$), and rotation of the –CH₂ (angle $\beta$).</figcaption></figure>

### 2.2. *Room-temperature Faraday-rotation spectroscopy at sub-millimeter wavelengths*

The CH₃OCH₂ radical was produced by H-abstraction from DME precursor using F atoms, as previously developed by several groups (in particular by Sears et al. 1982). In our setup, already used to investigate several radical species in the past few years (Chitarra et al. 2020, 2022; Chahbazian et al. 2024a,b; Martin-Drumel et al. 2024), F atoms are synthesized from a mixture of F₂ diluted in He (~5% dilution) passing through a 2450 MHz microwave discharge (50 W), and then injected into the reaction cell through 3 injections inlets. In the cell, F atoms collide with the
precursor to produce the sought radical, here RDME. Partial pressures of 5 µbar of CH₃OCH₃ and 14 µbar of F₂/He were found to maximize the signal of the RDME radical. The pressure was measured above the throat of the roots blower when the discharge was operating.

To record the RDME spectrum in the 140–650 GHz range, we exploited a methodology published in Chahbazian et al. (2024a). The (sub-)millimeter wave spectrometer (Chitarra et al. 2022) used to measure the transitions of the CH₃OCH₂ radical at room temperature is composed of a frequency multiplication chain (from Virginia Diode Inc., WR10) fed by a radio frequency synthesizer (Rhode & Schwarz) for which a 10 MHz reference signal is provided by the REFIMEVE infrastructure (Cantin et al. 2019). This ensemble allows for continuous coverage of the 75–900 GHz spectral range. To maximize the signal-to-noise ratio (SNR) in each portion of the frequency range, we used either a Schottky diode detector (for frequencies ranging from 140 to 330 GHz) or a 4 K mechanically cooled indium antimonide (InSb) bolometer (from 330 to 900 GHz). The Faraday rotation (FR) technique that we recently implemented, was used to record the spectrum and has proven again to be particularly advantageous to study new radical species. The details of this technique and the comparison with alternative methods (Zeeman modulation or frequency modulation) are given in Chahbazian et al. (2024a). In short, FR spectroscopy is based on the rotation of the plane of polarization of the (sub-)millimeter wave (mmW) radiation, occurring under an external magnetic field and when the radiation frequency is in resonance with a transition of a paramagnetic species. The modulation of the polarization plane is converted into an amplitude modulation through an analyzer grid at the output of the cell. As the FR is only observed for paramagnetic species, this technique allows most of the lines carried by diamagnetic species, such as the DME precursor in this experiment, to be filtered out. Another interesting aspect of the FR modulation is the discrimination between the two spin-rotation components, having opposite phases. This can be observed in Fig. 2 where a small portion of the spectrum is plotted showing two pairs of spin-rotation transitions belonging to A and E components of RDME, arising from the coupling between the –CH₃ torsion and the overall molecular rotation. This property is beneficial when dealing with dense spectra. Indeed, considering that we expect similar amplitude for the spin-rotation splitting of both the A and E series, the FR detection technique allows a rapid identification of the spin-rotation doublets. In the present work, this spin-rotation discrimination was highly beneficial as the different series of A and E components can sometimes overlap and intertwine with each other. In extreme but rare cases, however, the perfect overlap of spin-rotation doublets can lead to the cancellation of the molecular signal rendering the Faraday rotation inefficient (see Figure 6 in Appendix A).

<figure><img src="image_2.png" /><figcaption>**Figure 2.** Illustration of the spin-rotation phase discrimination of the FR technique. In the upper panel, the experimental trace is plotted and four lines of the RDME are visible. Among these lines, the two lines with positive relative intensities correspond to the *J* = *N* + 1/2 spin rotation components of the A and E components, and the two lines with relative negative intensities correspond to the *J* = *N* − 1/2 spin rotation components. The lower panel shows the predicted spectrum of RDME calculated with SPCAT (Pickett 1991, using the final set of parameters), together with the line assignment.</figcaption></figure>

## 2.3. Jet-cooled chirped-pulse millimeter-wave spectroscopy

To complete the dataset obtained at room temperature, we recorded several lines expected intense under cold interstellar conditions using a recently developed apparatus allowing for chirped-pulse millimeter-wave spectroscopy in combination with a supersonic expansion equipped with electrodes for electrical discharge.
To produce RDME, a mixture of DME diluted in Argon (with dilution varying from 0.5 to 2 %) at a backing pressure of 4 bars was introduced inside the experimental chamber using a pulsed nozzle source (Parker, series 9) operating at 5 Hz. RDME was generated by a 1.75 kV electrical discharge between two cylindrical copper electrodes in a discharge stack located right after the pulse nozzle source. Pumping off the chamber was ensured by a diffusion pump (8000 L/s) backed up by a roughing pump. The content of the supersonic expansion was probed perpendicularly using a CP spectrometer (BrightSpec, Inc.) that covers the 75–110 GHz spectral region. Typically, 10 FIDs were collected per gas pulse. Such experimental conditions usually lead to rotational temperatures of the order of 10 K.

For the measurement performed here, we used the Target mode of the Edgar acquisition software (developed by BrightSpec). This mode allows to probe narrow spectral regions (typically 1–4 MHz here) with more power than in the broadband mode of operation, resulting in enhanced SNR. The lines were recorded with 10,000 to 100,000 averages and each FID was post-processed for 2 to 6 µs to maximize the SNR of the transitions while maintaining high resolution (see Martin-Drumel et al. 2024, for more detailed explanations). The uncertainty for each frequency was set to the half-width of the experimental lines.

Since the radical lines are weak, we carried out two tests to ensure that the lines visible in the spectra were from paramagnetic species. The observed transitions were first checked under the influence of a permanent magnet (which causes the paramagnetic lines to disappear) and by shifting the local oscillator frequency to identify electronic spurious features.

### 3. RESULTS AND DISCUSSION

#### 3.1. Methodology used for the lines assignment

To start the analysis, the values of the *A*, *B*, and *C* rotational constants in the GS and the other molecular parameters calculated by Yazidi et al. (2019) were used together with the spin-rotation constants from our DFT calculations to simulate the spectrum of the radical using a Watson A-reduced Hamiltonian and the SPCAT program (Pickett 1991). The standard *N*, *K*<sub>a</sub>, and *K*<sub>c</sub> quantum numbers are used to label the rotational levels. Each level is split into two *J* sub-levels because of the electronic spin-rotation interaction, with **J** = **N** + **S** (*S*=1/2). The Hamiltonian is constructed as follows: $\hat{H} = \hat{H}_{rot} + \hat{H}_{sr}$, where $\hat{H}_{rot}$ is the rotational Hamiltonian and $\hat{H}_{sr}$ accounts for the spin-rotation coupling.

Thanks to the broadband coverage allowed by FR acquisition, we graphically searched for series of lines in the experimental spectrum using the LLWP software developed by Bonah et al. (2022). Such a Loomis-Wood (LW) graphic is shown in Fig. 3, where chunks of 160 MHz of the experimental spectrum are plotted around the predicted frequencies of the *a*-type and *K*<sub>a</sub>=0 transitions for the A components. Increasing values of *N* are plotted from top to bottom, and we can see several series of lines corresponding to *a*− and *b*-type transitions for two different values of *K*<sub>a</sub>. Each of them is split into two series of lines belonging to the A and E components (represented respectively by orange and green dashed lines in Fig. 3) resulting from the splitting of the energy levels due to the torsion of the –CH<sub>3</sub> group. In addition, each A and E series is further split due to spin-rotation interaction, observed with positive and negative signals. We note that the splitting due to the –CH<sub>2</sub> torsion (barrier height about 2000 cm<sup>-1</sup>) is not resolved. This is in agreement with our recent analysis of the acetonyl radical (Chahbazian et al. 2024a) showing an equivalent barrier height for the –CH<sub>2</sub> torsion (El Hadki et al. 2022). Concerning the inversion of the –CH<sub>2</sub> group, it has a negligible effect on the spectrum as the corresponding barrier height stands below the zero point vibrational energy. We also note that the hyperfine structure, due to the interaction between the electron spin and the nuclear spin of the hydrogens, is not resolved either.

At this stage of the analysis, we were not able to unambiguously assign the series to the components of A and E symmetry. To solve this, we used the XIAM software (Hartwig & Dreizler 1996) neglecting the spin-rotation coupling by averaging the frequencies of the two spin-rotation components. We ran two different fits inverting the A and E series assignments. The comparison of both the RMS obtained and the calculated energy levels enabled us to assign unambiguously the A and the E components. Moreover, the fit allowed us to derive an experimental value of the barrier height of the –CH<sub>3</sub> torsion, *V*<sub>3</sub> ≃ 513 cm<sup>-1</sup>, that is in excellent agreement with the value of 510 cm<sup>-1</sup> calculated by Yazidi et al. (2019). Further details of the XIAM fit are given in the Appendix B.1.

#### 3.2. Fit of the lines using SPFIT

In the following, to fit the RDME lines at their experimental accuracy, the A and E components were fitted separately using the semi-rigid Hamiltonian described above, which allows to describe the rotation and the spin-rotation structure. The fit was performed using the SPFIT/SPCAT programs (Pickett 1991).
<figure><img src="image_3.png" /></figure>

**Figure 3.** LLWP plot of RDME. Portions of 160 MHz are plotted for $N'=25$ to $N'=34$, centered around the a-type and $K_a=0$ transitions for the A components. We see eight different series of lines corresponding to four different selection rules and $K_a$ values. Each of them is divided into two series of lines belonging to the A and E components resulting from the splitting of the energy levels because of the torsion of the -CH₃ group. To ease the observation of the several branches, series are indicated by dashed lines (A and E series are respectively indicated by green and orange dashed lines). For each series identified in the figure, we observe a small spin-rotation splitting (one component up, one down).

Using the room-temperature spectrum, we assigned 475 A components (361 a-type and 114 b-type) and 469 E components (349 a-type and 120 b-type) to RDME, with $N'$ and $K'_a$ values up to 34 and 5, respectively. This early-stage analysis was used to derive a first set of parameters and to simulate the spectrum at 40 K, a temperature relevant to ISM searches. The simulation at 40 K shows that the most intense lines are expected around 400 GHz (see Fig. 5). Then, we performed line-by-line measurements of 24 A and 15 E components, predicted intense at 40 K, with $N'$ and $K'_a$ values up to 9 and 5, respectively. Including these lines in the fit led to a more constrained set of parameters allowing us to extend our laboratory detection in the 75-110 GHz range, under jet-cooled conditions. Finally, using the CP jet discharge, we measured 10 A components and 14 E components, with $J'$ and $K'_a$ values up to 5 and 1. The final dataset contains all lines involving $N'$ and $K'_a$ up to 34 and 5, respectively. The extent of the data sets is shown in Fig. 4, where the distribution plot of the $N'$ values as a function of $K'_a$ is given for all the A and E components assigned here. More details on the different steps of the assignment and fit are given in Appendix B.2 and B.3.

The final sets of parameters including all the lines measured at 300 K with the FR setup, and all the lines measured under jet-cooled conditions with the CP-jet-discharge setup, are summarized in Table 1. These fits were performed using the A-reduction of the Hamiltonian which we have found to significantly better reproduce our data than the S-reduction (standard deviation increasing from 1.3 to 1.9 for the A components). The uncertainty of each line has been chosen according to the half-width of the lines and ranges from 100 kHz to 350 kHz (except for the b-type lines measured with the CP that have 500 kHz uncertainty). All the lines are included in the fit with a rejection factor $\sigma=8$. We remind the reader that such rigid Hamiltonians are not suited for fitting a molecule presenting a CH₃ torsion but that no models adapted to these are readily available for open-shell species. It is thus not surprising that our final standard deviation deviates from 1 (here 1.3 and 1.5 for the A and E components, respectively). Nevertheless, we obtain two effective sets of rotational parameters, allowing to derive the structural rotational constants as $A = \frac{1}{3}(A_A+2A_E) = 46671.78(13)$ MHz, $B = \frac{1}{3}(B_A + 2B_E) = 10758.4986(33)$ MHz, and $C = \frac{1}{3}(C_A + 2C_E) = 9280.4254(25)$ MHz (see Kraśnicki et al. 2010). These constants can be compared with the calculated values of Yazidi et al. (2019) and are in excellent agreement with relative differences within 0.1%. Coriolis terms have been added in the model to fit effectively the E components, more affected by internal rotation than the A components. However, it seems that the internal
<figure><img src="image_4.png" /><figcaption>**Figure 4.** Distribution plot of $N'$ as a function of $K'_a$ for the A (left panel) and E (right panel) components of RDME.</figcaption></figure>

rotation is not fully treated by the additional Coriolis parameters as terms depending on the quantum number *K* (for instance $\Delta_K$ and $\Phi_K$) greatly differ from the calculations. Concerning the spin rotation terms, we have a good agreement between the fitted and calculated values for $\epsilon_{aa}$ and $\epsilon_{bb}$ terms. The fitted $\epsilon_{cc}$ term is of opposite sign and 4 times smaller in magnitude than our calculated value with Gaussian.

### 3.3. Astrophysical implications

In this work, we report the first set of parameters allowing accurate predictions of the rotational spectrum of RDME from 75 to 650 GHz. As it can be seen in Fig. 5, the RDME spectrum extends to high frequencies both at 10 K (strongest transitions around 200 GHz) and 40 K (strongest transitions around 400 GHz). As our model is constrained by the addition of lines with low *N* values, our parameters should enable searches for RDME in warm to cold environments.

To facilitate the search for this radical in the ISM, we provide a catalog of frequencies for the A and E transitions at 300 K using SPCAT, containing all the measured frequencies with their experimental uncertainties (see the electronic supporting information). An excerpt is given in Table 2, reporting transitions expected to be among the most intense at about 40 K that we measured using our room temperature setup. In this table, the experimental uncertainty and the difference between the observed and calculated frequencies are reported. The catalogs provided in SI have been derived using the appropriate partition function and projections of the dipole moment. For further calculations at different temperatures, the partition function as a function of the temperature is provided in Appendix C.
<table><caption>**Table 1.** GS rotational constants of the A and E components of RDME derived from a fit of the transitions with $K_a$ up to 5 using two sets of parameters with a semi-rigid A-reduced Hamiltonian, and compared with GS calculated values from this work and from Yazidi et al. (2019). Other calculated parameters are given at equilibrium. Errors ($1\sigma$) on the experimentally derived parameters are reported in parenthesis in the unit of the last significant digit. Relevant fit parameters are reported at the bottom of the table.</caption><thead><tr><th></th><th>units</th><th>Calc. Yazidi et al. (2019) <sup>a</sup></th><th>Calc. this study <sup>b</sup></th><th>A components</th><th>E components</th></tr></thead><tbody><tr><td>A<sub>0</sub></td><td>/MHz</td><td>46718.67</td><td>47342.97</td><td>46714.515(81)</td><td>46650.492(80)</td></tr><tr><td>B<sub>0</sub></td><td>/MHz</td><td>10748.42</td><td>10665.27</td><td>10759.1485(22)</td><td>10758.1742(20)</td></tr><tr><td>C<sub>0</sub></td><td>/MHz</td><td>9272.51</td><td>9252.05</td><td>9280.3337(16)</td><td>9280.4701(16)</td></tr><tr><td>Δ<sub>N</sub></td><td>/kHz</td><td></td><td>9.30</td><td>9.5507(15)</td><td>9.4198(15)</td></tr><tr><td>Δ<sub>NK</sub></td><td>/kHz</td><td></td><td>-33.01</td><td>13.59(13)</td><td>-46.26(13)</td></tr><tr><td>Δ<sub>K</sub></td><td>/kHz</td><td></td><td>615.13</td><td>1626.8(59)</td><td>211.3(63)</td></tr><tr><td>δ<sub>N</sub></td><td>/kHz</td><td></td><td>1.96</td><td>2.0840(10)</td><td>2.0133(10)</td></tr><tr><td>δ<sub>K</sub></td><td>/kHz</td><td></td><td>-45.07</td><td>-34.45(22)</td><td>-77.55(22)</td></tr><tr><td>Φ<sub>N</sub></td><td>/Hz</td><td></td><td>0.01</td><td></td><td></td></tr><tr><td>Φ<sub>NK</sub></td><td>/Hz</td><td></td><td>-0.62</td><td>8.96(37)</td><td>-6.65(37)</td></tr><tr><td>Φ<sub>KN</sub></td><td>/Hz</td><td></td><td>-6.07</td><td>678.7(56)</td><td>-389.3(85)</td></tr><tr><td>Φ<sub>K</sub></td><td>/Hz</td><td></td><td>32.20</td><td>7665.(135)</td><td>2707.(184)</td></tr><tr><td>φ<sub>N</sub></td><td>/Hz</td><td></td><td>0.01</td><td></td><td></td></tr><tr><td>φ<sub>NK</sub></td><td>/Hz</td><td></td><td>0.77</td><td>5.66(14)</td><td>-2.13(14)</td></tr><tr><td>φ<sub>K</sub></td><td>/Hz</td><td></td><td>-10.11</td><td>530.(11)</td><td>-213.(12)</td></tr><tr><td>ε<sub>aa</sub></td><td>/MHz</td><td></td><td>-186.10</td><td>-170.54(21)</td><td>-171.10(19)</td></tr><tr><td>ε<sub>bb</sub></td><td>/MHz</td><td></td><td>-32.46</td><td>-30.737(32)</td><td>-30.840(31)</td></tr><tr><td>ε<sub>cc</sub></td><td>/MHz</td><td></td><td>3.26</td><td>-0.783(22)</td><td>-0.664(22)</td></tr><tr><td>(ε<sub>ab</sub> + ε<sub>ba</sub>)/2</td><td>/MHz</td><td></td><td>-23.94</td><td>17.41(26)</td><td>-16.41(31)</td></tr><tr><td>D<sub>a</sub></td><td>/MHz</td><td></td><td></td><td></td><td>135.02(19)</td></tr><tr><td>D<sub>aN</sub></td><td>/MHz</td><td></td><td></td><td></td><td>-0.05178(61)</td></tr><tr><td>D<sub>aK</sub></td><td>/MHz</td><td></td><td></td><td></td><td>-7.298(22)</td></tr><tr><td>D<sub>aKK</sub></td><td>/MHz</td><td></td><td></td><td></td><td>0.11126(83)</td></tr><tr><td>#/n<sup>c</sup> at 300 K</td><td></td><td></td><td></td><td>475/471</td><td>469/466</td></tr><tr><td>#/n<sup>c</sup> at 300 K, predicted intense at ~ 40 K</td><td></td><td></td><td></td><td>24/20</td><td>15/15</td></tr><tr><td>#/n<sup>c</sup> CP-jet</td><td></td><td></td><td></td><td>10/10</td><td>14/13</td></tr><tr><td>N'<sub>max</sub>, K'<sub>a max</sub></td><td></td><td></td><td></td><td>34,5</td><td>34,5</td></tr><tr><td>RMS<sup>d</sup></td><td>/MHz</td><td></td><td></td><td>0.282</td><td>0.326</td></tr><tr><td>σ<sup>e</sup></td><td></td><td></td><td></td><td>1.3</td><td>1.5</td></tr></tbody></table>

## 4. CONCLUSION

In this study, we report the first rotationally resolved investigation of the CH<sub>3</sub>OCH<sub>2</sub> radical in its vibrational ground state. The transitions have been measured at room temperature in the 140–650 GHz range (using the FR acquisition technique) and under jet-cooled conditions in the 75–110 GHz range (using CP spectroscopy).

As no available model accounts for both the spin-rotation and the rotation-torsion couplings to date, we performed two different fits to model our experimental spectrum. The first one used the XIAM software to fit the internal rotation and get a value of the torsion barrier of the –CH<sub>3</sub> group, fitted to 513.0(6) cm<sup>-1</sup> and in excellent agreement with the value calculated by Yazidi et al. (2019) (see Appendix B.1). The second fit was made using the SPFIT program to fit the spin-rotation splitting resulting from the interaction of the electronic spin and the rotation of the

<footnote><sup>a</sup> This study also provides all the quartic and sextic constants in the S-reduction. They are thus not reported in this table. We refer the reader to the article for the exact values.</footnote>

<footnote><sup>b</sup> The calculated rotational constants have been Bayesian corrected by a 0.9866 factor (see Lee & McCarthy 2020), the rest of the calculated constants are equilibrium values.</footnote>

<footnote><sup>c</sup> Number of lines (#) and number of lines with different frequencies (n)</footnote>

<footnote><sup>d</sup> Root mean square of the pure rotation data, in MHz</footnote>

<footnote><sup>e</sup> Weighted standard deviation, unitless</footnote>
<figure><img src="image_5.png" /><figcaption>**Figure 5.** Upper panel - Simulated spectrum of RDME plotted from 0 to 800 GHz at 300 K, 40 K, and 10 K.</figcaption></figure>

**Bottom left panel** - Example of A and E components measured at room temperature but predicted intense at 40 K, for the $5_{5,0}/1 \leftarrow 4_{4,1}/0$ A components and for the $5_{5,1} \leftarrow 4_{4,1}$ E components (allowed because of the Coriolis terms added to take into account the effect of internal rotation on the E symmetry lines, see Hernandez-Castillo et al. 2017). As two selection rules are superimposed for the A components, the lines are twice as intense as for the E components. The transitions are weak at room temperature, about 40 min acquisition time was necessary to record the 190 MHz plotted here.

**Bottom right-hand panel** - Experimental traces of the $5_{1,4} \leftarrow 4_{1,3}$ transitions for A and E components of RDME recorded with the CP jet-discharge apparatus. They have been recorded with 50000 to 80000 averages and post-analyzed with an FID length of 2 µs. The experimental lines of RDME are larger than expected (from 250 kHz to 1.3 MHz), possibly due to the splitting of the magnetic sub-levels by the Earth's magnetic field, since the apparatus was not placed inside Helmholtz coils. The simulation is also plotted and shows a good agreement with the experimental lines.

molecule. In this approach, two sets of parameters of a semi-rigid Hamiltonian were used to fit the A and E torsional components independently. To fit the E components, Coriolis terms have been added to effectively account for the internal rotation. The fits reported here allow the reproduction of the experimental data but, since this effective model is not suited for an open-shell molecule with internal rotation, predictions for transitions not observed experimentally can not be guaranteed at an accuracy better than a few MHz. For this reason, we took care of measuring lines that are intense at low temperatures. The catalog files are merged files in which experimental frequencies are provided. These experimental frequencies should be used to search for the $CH_3OCH_2$ radical in many different environments of the ISM. Its detection could provide crucial information for understanding the process of formation and destruction of several iCOMs in space.
<table><caption>**Table 2.** Frequencies (in MHz) and intensities (in log units) of the most intense lines of RDME at 37.5 K measured in this work. The residuals from our fit (O-C in MHz) are also reported. Intensities are reported here for 37.5 K.</caption><thead><tr><th>S.<sup>a</sup></th><th>Transition<sup>b,c</sup></th><th>Exp. freq.</th><th>O-C</th><th>log(I<sub>calc</sub>)</th></tr></thead><tbody><tr><td>A</td><td>4<sub>4,−</sub>(4.5) ← 3<sub>3,−</sub>(3.5)</td><td>336684.67(50)</td><td>-0.77</td><td>-1.86</td></tr><tr><td>A</td><td>4<sub>4,−</sub>(3.5) ← 3<sub>3,−</sub>(2.5)</td><td>336852.95(50)</td><td>0.80</td><td>-1.97</td></tr><tr><td>E</td><td>4<sub>4,1</sub>(4.5) ← 3<sub>3,1</sub>(3.5)</td><td>336527.00(30)</td><td>0.73</td><td>-1.86</td></tr><tr><td>E</td><td>4<sub>4,1</sub>(3.5) ← 3<sub>3,1</sub>(2.5)</td><td>336696.10(50)</td><td>2.21</td><td>-1.97</td></tr><tr><td>E</td><td>4<sub>4,0</sub>(3.5) ← 3<sub>3,0</sub>(2.5)</td><td>336592.18(30)</td><td>0.73</td><td>-1.97</td></tr><tr><td>A</td><td>5<sub>5,−</sub>(5.5) ← 4<sub>4,−</sub>(4.5)</td><td>429861.28(30)</td><td>-0.49</td><td>-1.76</td></tr><tr><td>A</td><td>5<sub>5,−</sub>(4.5) ← 4<sub>4,−</sub>(3.5)</td><td>430030.29(30)</td><td>0.53</td><td>-1.84</td></tr><tr><td>E</td><td>5<sub>5,1</sub>(5.5) ← 4<sub>4,1</sub>(4.5)</td><td>429840.50(30)</td><td>-0.23</td><td>-1.76</td></tr><tr><td>E</td><td>5<sub>5,1</sub>(4.5) ← 4<sub>4,1</sub>(3.5)</td><td>430010.20(30)</td><td>0.55</td><td>-1.84</td></tr><tr><td>A</td><td>6<sub>4,3</sub>(6.5) ← 5<sub>3,2</sub>(5.5)</td><td>376768.20(40)</td><td>0.13</td><td>-1.86</td></tr><tr><td>A</td><td>6<sub>4,2</sub>(6.5) ← 5<sub>3,3</sub>(5.5)</td><td>376792.60(40)</td><td>0.40</td><td>-1.86</td></tr><tr><td>A</td><td>6<sub>4,3</sub>(5.5) ← 5<sub>3,2</sub>(4.5)</td><td>376911.80(40)</td><td>0.18</td><td>-1.94</td></tr><tr><td>A</td><td>6<sub>4,2</sub>(5.5) ← 5<sub>3,3</sub>(4.5)</td><td>376936.83(40)</td><td>0.85</td><td>-1.94</td></tr><tr><td>E</td><td>6<sub>4,3</sub>(6.5) ← 5<sub>3,3</sub>(5.5)</td><td>376627.60(30)</td><td>-0.56</td><td>-1.86</td></tr><tr><td>E</td><td>6<sub>4,2</sub>(6.5) ← 5<sub>3,2</sub>(5.5)</td><td>376523.10(30)</td><td>-0.33</td><td>-1.86</td></tr><tr><td>E</td><td>6<sub>4,3</sub>(5.5) ← 5<sub>3,3</sub>(4.5)</td><td>376772.10(30)</td><td>-0.50</td><td>-1.94</td></tr><tr><td>E</td><td>6<sub>4,2</sub>(5.5) ← 5<sub>3,2</sub>(4.5)</td><td>376667.60(30)</td><td>-0.27</td><td>-1.94</td></tr><tr><td>A</td><td>7<sub>4,3</sub>(7.5) ← 6<sub>3,4</sub>(6.5)</td><td>396832.74(30)</td><td>-0.69</td><td>-1.87</td></tr><tr><td>A</td><td>7<sub>4,4</sub>(7.5) ← 6<sub>3,3</sub>(6.5)</td><td>396760.09(30)</td><td>-0.64</td><td>-1.88</td></tr><tr><td>A</td><td>7<sub>4,3</sub>(6.5) ← 6<sub>3,4</sub>(5.5)</td><td>396965.04(30)</td><td>-0.36</td><td>-1.94</td></tr><tr><td>A</td><td>7<sub>4,4</sub>(6.5) ← 6<sub>3,3</sub>(5.5)</td><td>396892.71(30)</td><td>0.60</td><td>-1.94</td></tr><tr><td>E</td><td>7<sub>4,4</sub>(7.5) ← 6<sub>3,4</sub>(6.5)</td><td>396651.34(30)</td><td>-0.35</td><td>-1.88</td></tr><tr><td>E</td><td>7<sub>4,3</sub>(7.5) ← 6<sub>3,3</sub>(6.5)</td><td>396539.06(30)</td><td>-1.48</td><td>-1.88</td></tr><tr><td>E</td><td>7<sub>4,4</sub>(6.5) ← 6<sub>3,4</sub>(5.5)</td><td>396782.64(30)</td><td>-1.48</td><td>-1.94</td></tr><tr><td>E</td><td>7<sub>4,3</sub>(6.5) ← 6<sub>3,3</sub>(5.5)</td><td>396673.33(30)</td><td>-1.48</td><td>-1.94</td></tr></tbody></table>

a Symmetry of the transition

b $N'_{K'_a, K'_c}(J') \leftarrow N''_{K''_a, K''_c}(J'')$

c When $K_c$ is not reported, the transitions with $K_a + K_c = N, N + 1$ are not resolved under our experimental conditions.

This work was performed thanks to financial support from LabEx PALM (ANR-10-LABX-0039-PALM), from the Région Ile-de-France through DIM-ACAV+, and from the Agence Nationale de la Recherche (ANR-19-CE30-0017-01). We acknowledge support from the Programme National “Physique et Chimie du Milieu Interstellaire” (PCMI) of CNRS/INSU with INC/INP co-funded by CEA and CNES. Quantum chemical calculations were performed using HPC resources from the “Mésocentre” computing center of CentraleSupélec and École Normale Supérieure Paris-Saclay supported by CNRS and Région Île-de-France (http://mesocentre.centralesupelec.fr/). We thank Jean-Christophe Loison for the loan of the F reaction setup. RC is grateful to Anthony Roucou for useful discussions regarding the Pickett fit.

# APPENDIX

## A. SUPPLEMENTARY INFORMATION ON THE EXPERIMENTAL SETUP AND FR

The FR, happening at resonance frequencies of paramagnetic species, is based on the rotation of the polarization of the (sub-)mmW radiation under an external magnetic field. In these conditions, the magnetic components of paramagnetic species are split by the Zeeman effect, causing the radical to behave as a birefringent medium. In our experiment, a field (of about 6.6 Gauss peak-to-peak) was generated in the cell by feeding a surrounding coil (about 750
spirals/m) with a sinusoidal current (700 mA AC) generated by a waveform generator followed by an audio amplifier. The (sub-)mmW emitted radiation is a well-defined vertical linear polarization that we further polarize by placing a polarization grid at the entrance of the cell. To convert the polarization modulation into amplitude modulation, we placed a polarization grid rotated by an angle $\theta=45^\circ$ at the output of the cell. This amplitude modulation is demodulated by a phase-sensitive lock-in amplifier at the AC frequency modulation. Typically, the spectra in this study have been recorded with a frequency step ranging from 0.2 to 0.3 MHz with a time constant ranging from 200 to 460 ms. The frequency of the magnetic field ranges from 2.9 to 3.9 kHz to maximize the SNR in the different ranges. As the Doppler broadening increases with the frequency, a larger magnetic field is required for higher frequencies to split the Zeeman components.

In our previous experience with the acetonyl radical (Chahbazian et al. 2024a), FR acquisition proved to be efficient in filtering out most of the lines of diamagnetic species. However, in the present study, the most intense transitions of the precursor were also detected in the FR spectrum, as they can acquire an induced magnetic moment under an external magnetic field. This magnetic moment depends on the external magnetic field and depends on the magnetic polarizability of the diamagnetic molecule (Demtröder 2010).

In addition to the possibility to perform broadband scans of radical species, the FR technique has the great advantage of differentiating the two spin-rotation components. Similarly to our recent observation concerning the acetonyl radical (Chahbazian et al. 2024a), the opposite signs of the Landé factors for the two spin-rotation components ($S = 1/2$) of a given rotational level ($N$) lead signal having opposite phases. On the right panel of Fig. 6, we can see four series of lines, two belonging to the two spin-rotation transitions of the A components and two belonging to the spin-rotation transitions of the E components. The discrimination of the spin-rotation components is particularly helpful in this situation where the series intersect each other as $N'$ is increasing.

<figure><img src="image_6.png" /></figure>

**Figure 6.** Illustration of the advantage and drawback of the spin-rotation discrimination using FR. On the left panel, we see four series of lines, with two belonging to the spin-rotation components of the A components (in green dashed lines), and the other two to the E components (in orange dashed lines). As the series intersect each other, the phase information of the spin-rotation components is really helpful for the assignment. On the right panel, is the LW plot of the A components with the following selection rule: $N'_{1,(N'-1)} \leftarrow (N' - 1)_{1,(N'-1)-1}$. We can see a crossing of two spin-rotation components, leading to a suppression of the FR signal at $N'=19$, as the two components are too close and cancel each other.

However, this technique showed limitations in the case where the spin rotation splitting is too small to be resolved in our setup. In such conditions, the signals with opposite phases cancel out, leading to an absence of line detection. This situation is illustrated in the left panel of Fig. 6, at $N'=19$. Indeed, we can see a crossing of two spin-rotation components as $N'$ is increasing, but at $N'=19$ we do not have any signal as the two components cancel each other. To bypass this issue, the Zeeman-modulation (ZM) spectrum can be recorded simultaneously with the FR one, by simply using the 2nd channel of the locking amplifier where the signal is demodulated at the 2nd harmonic (see Chahbazian et al. 2024a, for a detailed explanation of the procedure)
## B. ITERATIVE FITTING PROCEDURE

Using FR at room temperature, we assigned 475 A components and 469 E components to the CH₃OCH₂ radical, with N' and K'_a values up to 34 and 5, respectively. To fit these transitions, we used two models: XIAM (section B.1) and SPFIT (section B.2).

### B.1. Fit of the lines using XIAM

To assign the series to the components of A and E symmetry, we used the XIAM software (Hartwig & Dreizler 1996) neglecting the spin-rotation coupling by averaging the frequencies of the two spin-rotation components. In total, 477 transitions (241 A components, 236 E components, both a- and b-types transitions) recorded using FR spectroscopy have been included in the fit using XIAM. All components were equally weighted in the fit.

We ran two different fits inverting the A and E series assignments. The comparison of both the RMS obtained and the calculated energies enabled us to assign unambiguously the A and the E components. The final assignment leads to an RMS of 353 kHz. This fit provided a value of the V₃ barrier of 513.0(6) cm⁻¹, in excellent agreement with the value of 510 cm⁻¹ calculated by Yazidi et al. (2019). The rotational constants B<sub>J</sub> = 10.0194596 (20) MHz, B<sub>K</sub> = 36.652523 (89) MHz, and B<sub>-</sub> = 0.743880 (11) MHz are also in really good agreement with the calculations, with relative differences of 0.09%, 0.15%, and 0.8% respectively. The reduced barrier height noted s is calculated to be equal to 32.9, meaning that RDME can be considered as a pseudo-rigid rotor with a relatively high barrier and large asymmetry splitting, larger than the splittings caused by internal rotation (Lin & Swalen 1959).

The parameters of the fit are presented in Table 3. They can be directly compared with the values derived in the study of Yazidi et al. (2019).

<table><caption>**Table 3.** Rotational constant of RDME fitted using XIAM (Hartwig & Dreizler 1996) averaging the frequencies of the two spin-rotation components, in the S-reduction.</caption><thead><tr><th></th><th>units</th><th>Calc. <sup>a</sup></th><th>Exp.</th></tr></thead><tbody><tr><td>B<sub>J</sub><sup>b</sup></td><td>/GHz</td><td>10.010465</td><td>10.0194596(20)</td></tr><tr><td>B<sub>K</sub><sup>b</sup></td><td>/GHz</td><td>36.708205</td><td>36.652523(89)</td></tr><tr><td>B<sub>-</sub><sup>b</sup></td><td>/GHz</td><td>0.737955</td><td>0.743880(11)</td></tr><tr><td>D<sub>J</sub></td><td>/MHz</td><td>0.0103</td><td>0.0100899(33)</td></tr><tr><td>D<sub>JK</sub></td><td>/MHz</td><td>-0.0357</td><td>-0.028568(93)</td></tr><tr><td>D<sub>K</sub></td><td>/MHz</td><td>0.5832</td><td>0.6063(24)</td></tr><tr><td>d<sub>1</sub></td><td>/MHz</td><td>-0.0021</td><td>-0.0020599(11)</td></tr><tr><td>d<sub>2</sub></td><td>/MHz</td><td>0.0002</td><td>0.00032866(60)</td></tr><tr><td>H<sub>J</sub></td><td>/Hz</td><td>0.0008</td><td>-0.0180(20)</td></tr><tr><td>V<sub>3</sub></td><td>/cm<sup>-1</sup></td><td>510.</td><td>512.72(54)</td></tr><tr><td>D<sub>2-</sub><sup>π</sup></td><td>/MHz</td><td></td><td>-1.55(11)</td></tr><tr><td>ρ</td><td></td><td></td><td>0.27162(31)</td></tr><tr><td>β</td><td></td><td></td><td>3.02677(17)</td></tr><tr><td>s<sup>c</sup></td><td></td><td></td><td>32.9</td></tr><tr><td>F<sup>d</sup></td><td>/GHz</td><td></td><td>207.7</td></tr><tr><td>#/n <sup>e</sup></td><td></td><td></td><td>477/477</td></tr><tr><td>N'<sub>max</sub>, K'<sub>a max</sub></td><td></td><td></td><td>34, 5</td></tr><tr><td>RMS <sup>f</sup></td><td>/MHz</td><td></td><td>0.353</td></tr></tbody></table>

<footnote><sup>a</sup> Yazidi et al. (2019).</footnote>

<footnote><sup>b</sup> B<sub>J</sub> = (B+C)/2, B<sub>K</sub> = A - (B+C)/2, and B<sub>-</sub> = (B-C)/2</footnote>

<footnote><sup>c</sup> Reduced barrier height, s = 4V<sub>3</sub>/9F (Lin & Swalen 1959), calculated from the experimental values.</footnote>

<footnote><sup>d</sup> Reduced rotational constant of the internal rotor (Lin & Swalen 1959), calculated from the experimental values.</footnote>

<footnote><sup>e</sup> Number of lines (#) and number of lines with different frequencies (n)</footnote>

<footnote><sup>f</sup> Root mean square of the pure rotation data, in MHz</footnote>
<figure><img src="image_7.png" /></figure>

**Figure 7.** The upper panel of the figure is a zoom of the experimental RDME spectrum from 403.0 to 403.5 GHz. Below this plot is the simulation of the A and E components in the vibrational GS done with the SPFIT/SPCAT programs (Pickett 1991), which allows to reflect the good agreement between the experiment and the simulation. A few other less intense lines, not in the simulation, are still unidentified.

## B.2. *Fit of the 300 K lines using SPFIT*

To reproduce the full dataset at its experimental accuracy, we fitted the A and E components using the semi-rigid Hamiltonian described in section 3.1, using two distinct sets of parameters. The two effective fits were performed using SPFIT/SPCAT (Pickett 1991) programs.

The uncertainties of each line position were chosen according to the line width and the SNR, ranging from 100 to 350 kHz. The RMS and standard deviation were equal to 260 kHz and 1.3, respectively, for the A and E components. The fit of the A components has been limited to $K'_a=5$, but branches with higher $K'_a$ values up to $K'_a=9$ could be assigned and fitted. To fit the E transitions, Coriolis constants $D_a, D_{aN}, D_{aK}$, and $D_{aKK}$ have been added (following similar fit on pyruvonitrile by Kraśnicki et al. 2010) to effectively account for the effect of the internal rotation affecting the E components. In Fig. 7 a small part of the spectrum is plotted with the lines simulated by the SPFIT/SPCAT program and shows a good agreement between the experimental data and the simulation. However, if this analysis remains valid, another model with more physical sense will be developed in the future to fit transitions with only one Hamiltonian considering both the internal rotation and the spin-rotation couplings.

Using the first set of parameters using the previous transitions, we simulated the spectrum of RDME at 40 K, showing several intense lines around 400 GHz. To constrain the model, we measured at room temperature the lines expected intense at 40 K doing line-by-line acquisitions with a longer acquisition time of 2410 ms per frequency step, as these lines are weak at room temperature. We included 24 A components and 15 E components in the fit, with $N'$ and $K'_a$ values up to 9 and 5, respectively. An example of an experimental trace of lines predicted to be very intense at 40 K is shown in the bottom left-hand panel of Fig. 5.

## B.3. *Inclusion of the lines measured with the CP-jet-discharge setup*

Using the second set of parameters derived by adding the lines predicted to be intense at 40 K, we simulated the spectrum at 10 K using the SPCAT program to search for the most intense lines in the 75–110 GHz range with the CP-jet-discharge setup. We recorded 10 A components and 14 E components (including 5 *b*-type transitions) with $J'$ values of 4 and 5 and $K'_a$ values up to 1. The experimental lines were close to the predicted frequencies, from 100 kHz to 1.4 MHz for *a*-type transitions and up to 2 MHz for the less well-predicted *b*-type transitions. After including all the lines in the fit, it appears that for most of the spin-rotation pairs measured with the CP, one component is better fitted than the other. We believe that the model cannot correctly reproduce the spin-rotation splitting for transitions involving small *N* values because of some other physical effects, such as electron spin-torsion coupling (Coudert et al. 2024), that might appear and are not taken into account in the model used here.

## C. PARTITION FUNCTIONS

The partition functions were determined using Pickett's SPCAT program (Pickett 1991) and were obtained after converging at $N=200$.
<table><caption>**Table 4.** Rotational partition functions of the A and E components of RDME ($v = 0$)</caption><thead><tr><th>Temperature (K)</th><th>Q(SPIN-ROT.) A</th><th>Q(SPIN-ROT.) E</th></tr></thead><tbody><tr><td>300.000</td><td>25578.4592</td><td>25630.5374</td></tr><tr><td>225.000</td><td>16666.1175</td><td>16684.7765</td></tr><tr><td>150.000</td><td>9085.2997</td><td>9088.8455</td></tr><tr><td>75.000</td><td>3215.4757</td><td>3216.1169</td></tr><tr><td>37.500</td><td>1138.7489</td><td>1139.1712</td></tr><tr><td>18.750</td><td>404.1085</td><td>404.3206</td></tr><tr><td>9.375</td><td>143.9897</td><td>144.0788</td></tr></tbody></table>

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