First Detection in Space of the High-energy Isomer of Cyanomethanimine: H₂CNCN

N-cyanomethanimine (H₂CNCN) is a planar asymmetric-top molecule with a large total dipole moment of 4.84D (Bak et al. 1978; Bak & Svanholt 1980). To perform its search toward G+0.693, we used the spectroscopic entry 054514 (2014 February) from the CDMS catalog, which incorporates the rotational spectroscopy from the Bak & Svanholt (1980), Winnewisser et al. (1984), and Stolze et al. (1989) experimental works. We have identified a plethora of distinct a-type rotational transitions belonging to this species, which cover an energy level range between J_up = 3 and J_up = 11 and correspond to different K_a = 0, 1, 2 ladders. This delineates nearly the entirety of the most prominent rotational spectroscopic features attributed to the R-branch a-type lines, rendering this detection exceptionally robust. Figure 1 shows all of the transitions we have selected to perform the LTE fit for H₂CNCN, which are all those among those targeted that are either unblended or present certain blending with other molecular species but in which case the combined profiles closely match the observed spectrum. The rest of the H₂CNCN lines covered by the observations are too faint to be detected or exhibit more significant blending with the emission from other molecular species (either unidentified or already modeled toward G+0.693), being the predicted emission for all these other lines also consistent with the observed spectrum (see Figure 8 of Appendix A). The spectroscopic information of the transitions displayed in Figure 1 is given in Table 2. All of them have been identified within a signal-to-noise ratio (S/N) in integrated intensity larger than 6 (see Table 2).

Table 2. List of H₂CNCN Rotational Transitions Detected toward G+0.693 and Selected for This Molecule LTE Fit

Frequency	Transition a	$\mathrm{log}I$	Eup	rms	$\int {T}_{{\rm{A}}}^{* }{\rm{d}}v$	S/N b	Blending c
(GHz)	(${J}_{{K}_{{\rm{a}}},{K}_{{\rm{c}}}}$'$-{J}_{{K}_{{\rm{a}}},{K}_{{\rm{c}}}}$'')	(nm2 MHz)	(K)	(mK)	(mK km s−1)
31.3664834(10)	30,3 − 20,2	−5.469	3.0	0.5	179(15)	53(5)	Blended with U
32.0353082(10)	31,2 − 21,1	−5.505	5.9	0.5	113(13)	34(4)	Unblended
40.9516386(13)	41,4 − 31,3	−5.183	7.7	0.5	165(15)	56(5)	Unblended
41.8100713(12)	40,4 − 30,3	−5.133	5.0	0.5	253(19)	87(7)	Unblended
41.8372354(12)	42,3 − 32,2	−5.444	16.2	0.5	46(11)	16(4)	Unblended
42.7104885(13)	41,3 − 31,2	−5.147	7.9	0.5	168(15)	58(6)	Blended: N-CH3NHCHO and U
74.7161692(19)	71,6 − 61,5	−4.468	17.1	2.4	180(60)	10(3)	Blended: s-C2H5CHO and C2H3NH2
81.8614891(21)	81,8 − 71,7	−4.344	20.5	2.4	151(60)	9(3)	Blended: CH3COCH3
83.4576038(20)	80,8 − 70,7	−4.317	18.0	1.6	213(40)	19(4)	Blended with U
85.3755815(21)	81,7 − 71,6	−4.309	21.2	1.6	144(40)	13(3)	Unblended⋆
92.0779012(21)	91,9 − 81,8	−4.204	24.9	0.9	112(22)	19(4)	Blended with U
96.0290895(21)	91,8 − 81,7	−4.169	25.8	1.5	104(35)	11(4)	Blended: ${aGg}^{\prime}$-(CH2OH)2 and CH3COCH3
104.171562(10)	100,10 − 90,9	−4.057	27.5	1.8	104(42)	9(4)	Slightly blended: Z-HNCHCN
106.675828(10)	101,9 − 91,8	−4.045	31.0	1.8	69(41)	6(3)	Blended: g-C2H5OH

Notes. For each transition, we provide its rest frequency in units of GHz, its associated quantum numbers, the base 10 logarithm of its integrated intensity at a fixed temperature of 300 K in units of nm² MHz ($\mathrm{log}I$), the energy in K of the upper level involved in the transition (E_up), the noise measured in mK within line-free spectral ranges close to it (rms), the integrated intensity over the line width as derived from the fit in mK km s⁻¹ ($\int {T}_{{\rm{A}}}^{* }{\rm{d}}v$), and the detection level (in terms of the S/N). The numbers in parentheses represent the uncertainty associated with the last digits. The last column accounts for the possible contamination of other molecular species.

^a Rotational transitions are labeled following the common notation for asymmetric tops: ${J}_{{K}_{{\rm{a}}},{K}_{{\rm{c}}}}$, where J refers to the total angular momentum of the molecule, while K_a,c points to its projections along the a and c principal axes. ^b The S/N is calculated from the integrated intensity over the line width ($\int {T}_{{\rm{A}}}^{* }{\rm{d}}v$) and noise level $\sigma =\mathrm{rms}\times \sqrt{\delta v\times \mathrm{FWHM}}$, where δ v is the spectral resolution of the spectra in velocity units and the FWHM is estimated from the LTE line fitting. ^c The term "unblended" alludes to those transitions that exhibit no contamination of other molecular species, while an asterisk is added when scarce line blending accounting for less than 5% of the targeted line total integrated intensity is present. "U" refers to blending with an unknown (not yet identified) species.

Download table as:  ASCIITypeset image

To achieve the best LTE modeling for H₂CNCN, we followed a two-step methodology. First, we fitted only the most unblended transitions (depicted in panels (b), (d), (e), and (j) of Figure 1), which provided the most accurate estimate for the FWHM. To do so, we ran AUTOFIT leaving the four parameters free and obtained an FWHM of 21.9 ± 1.4 km s⁻¹, which we subsequently kept fixed in the second step. Then, we fitted all of the transitions shown in Figure 1 and ran AUTOFIT again but now leaving only the other three parameters free. We obtained v_LSR = 68.1 ± 0.5 km s⁻¹, T_ex = 7.9 ± 0.3 K, and N = (2.9 ± 0.1) × 10¹² cm⁻² (see Table 1). The derived H₂CNCN column density translates into a total molecular abundance with respect to H₂ of (2.1 ± 0.3) × 10⁻¹¹, assuming ${N}_{{{\rm{H}}}_{2}}\,=1.35\times {10}^{23}\,{\mathrm{cm}}^{-2}$ (Martín et al. 2008) with an associated uncertainty of 15% of its value.

We have also performed a complementary rotational diagram analysis (Goldsmith & Langer 1999) for H₂CNCN, which is implemented in MADCUBA and incorporates two distinctive functionalities that provide greater versatility in contrast with the method conventionally used. On one hand, the MADCUBA rotational diagram accounts for opacity effects. Moreover, a very recent update allows one to consider the predicted emission from all of the molecular species previously detected in the source. This is done by subtracting the predicted line profiles of the blending species from the observed data to generate an "unblended" spectral data set, from which the rotational diagram for the species of interest can be derived following the same procedure that would apply for unblended lines. Figure 2 shows the rotational diagram we obtained for H₂CNCN. To compute it, we used all of the transitions shown in Figure 1 but excluded those that exhibit blending with yet-unidentified species (see Table 2) and employed their associated velocity integrated intensity over the line width as calculated by MADCUBA. This analysis yields N = (2.4 ± 0.9) × 10¹² cm⁻² and T_ex = 6.9 ± 0.8 K, which are in perfect agreement with SLIM-AUTOFIT estimates.

Zoom In Zoom Out Reset image size

Both the E- and Z-isomers of the C-cyanomethanimine species (HNCHCN) were previously detected toward G+0.693 by Rivilla et al. (2019), albeit on the basis of a less sensitive IRAM 30 m spectral survey with narrower spectral coverage (85–109 GHz). In this regard, the presence of new high-sensitivity Yebes 40 m observations at frequencies of ∼30–50 GHz, along with the significant enhancement of the spectral sensitivity at also higher frequencies, has prompted us to revisit the detection of these isomers toward G+0.693.

To perform the new analysis of these two species, we employed the same spectroscopic entries from the CDMS catalog that Rivilla et al. (2019) also used: 054512 for Z-HNCHCN and 054513 for E-HNCHCN (both dated 2018 November), which contain the rotational transitions measured by Takano et al. (1990), Zaleski et al. (2013), and Melosso et al. (2018). We have almost tripled the number of Z- and E-HNCHCN unblended or partially blended lines detected toward G+0.693 with an S/N in integrated intensity above 6, which are shown in Figures 3 and 4, respectively. For both isomers, these lines correspond to different K_a = 0, 1, 2 ladders of a-type rotational transitions sweeping a wider range of energy levels (∼5–50 K) than those previously covered by Rivilla et al. (2019; ∼21–34 K) and starting from J_up = 4 up to J_up = 14. Moreover, we have also targeted for the first time some b-type transitions belonging to E-HNCHCN (see panels (g), (j), (m), (q), (t), and (u) in Figure 4), facilitated by the relatively high μ_b dipole moment component, albeit smaller compared to its μ_a counterpart (2.51D versus 3.25D, respectively; Takano et al. 1990). The spectroscopic information of all these transitions is gathered in Table 3 within Appendix B, which highlights how some of the lines that Rivilla et al. (2019) targeted as "unblended" actually exhibit slight blending from other species. Furthermore, we have now detected all of them with a nearly 3 times greater S/N in integrated intensity.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

We have carried out the LTE line fitting for the Z- and E-HNCHCN isomers by using all of the transitions depicted in Figures 3 and 4, respectively. As already explained for H₂CNCN (see Section 3.1), we followed a similar two-step approach in both cases, whose results are summarized in Table 1. In the case of Z-HNCHCN, we first constrained its FWHM by fitting the unblended lines shown in panels (e), (g), (p), and (z) of Figure 3 while leaving the four parameters unfixed, obtaining an FWHM of 22.3 ± 0.8 km s⁻¹. As for E-HNCHCN, we derived a similar FWHM of 22.1 ± 0.6 km s⁻¹ by fitting the seven unblended transitions displayed in panels (b)–(d), (j), (l), (o), and (s) in Figure 4. In the second step, we repeated the fit but including the rest of the transitions shown in Figure 3 for Z-HNCHCN and Figure 4 for the E-isomer while keeping the FWHM fixed to the former values, respectively. We obtained N = (7.5 ± 0.3) × 10¹³ cm⁻², T_ex = 14.1 ± 0.8 K, and v_LSR = 67.0 ± 0.5 km s⁻¹ for Z-HNCHCN and N = (1.68 ± 0.03) × 10¹³ cm⁻², T_ex = 15.5 ± 0.5 K, and v_LSR = 67.8 ± 0.2 km s⁻¹ for E-HNCHCN. The column density derived for each isomer results in a molecular abundance with respect to H₂ of (5.5 ± 0.9) × 10⁻¹⁰ for Z-HNCHCN and (1.2 ± 0.2) × 10⁻¹⁰ for E-HNCHCN, which were calculated following the same approach as explained in Section 3.1.

As for N-cyanomethanimine, we have also performed a rotational diagram analysis for both C-cyanomethanimine isomers, which we show in Figure 5. In line with the methodology we followed for H₂CNCN (see Section 3.1), we constructed this diagram by using all of the unblended and partially blended rotational transitions, which are shown in Figures 3 and 4 for Z- and E-HNCHCN, respectively, while incorporating their associated velocity integrated intensity. As done for H₂CNCN, we did not include those transitions that are blended with species that have not yet been identified (see Table 3 within Appendix B). The results derived from this complementary analysis are N = (5.9 ± 1.3) × 10¹³ cm⁻² and T_ex = 14.4 ± 1.3 K for Z-HNCHCN and N = (1.3 ± 0.3) × 10¹³ cm⁻² and T_ex = 16.5 ± 1.9 K for E-HNCHCN, being in both cases consistent with SLIM-AUTOFIT outcomes.

Zoom In Zoom Out Reset image size

The substantial increase in the number of detected lines, along with their improved S/N and broader energy distribution, has resulted into a more accurate characterization of the physical parameters describing the emission from these two isomers. Our enhanced fit now sets a higher but consistently similar T_ex for both isomers of almost twice the value derived by Rivilla et al. (2019) for Z-HNCHCN (8 ± 2 K), which was the only one they could explicitly obtain from the lower-sensitivity data. The notable difference in the T_ex, linked to the more precise scrutiny of the molecular line blending from other species, leaves its imprint in the column density estimates as well, which are now set to be ∼2–3 times lower in comparison with Rivilla et al.'s (2019) findings. Similarly, we have also computed a rather lower Z/E-HNCHCN abundance ratio toward G+0.693 of 4.5 ± 0.2, which remains consistent within the uncertainty with the former estimate (6.1 ± 2.4). Nonetheless, we emphasize the comparably refined accuracy concerning this new result, which highlights the direct impact that full spectroscopic coverage exerts on determining the physical parameters.

Based on the new column density estimates derived for both the Z- and E-HNCHCN isomers (see Table 1), we have computed a total column density for C-cyanomethanimine toward G+0.693 of (9.2 ± 0.3) × 10¹³ cm⁻², which results in a total molecular abundance with respect to H₂ of (6.8 ± 1.0) × 10⁻¹⁰. This value, although ∼3 times lower than that previously derived by Rivilla et al. (2019), is of the same order as the abundances of other complex nitriles detected toward this cloud, such as CH₃CN, C₂H₃CN, or C₂H₅CN (Zeng et al. 2018). This indicates that C-cyanomethanimine might indeed be a relatively abundant species in the ISM, which could favor its detection toward other astronomical sources.

Nevertheless, this scenario significantly shifts for the N-cyanomethanimine species (H₂CNCN), which exhibits a remarkably lower molecular abundance with respect to H₂ of (2.1 ± 0.3) × 10⁻¹¹. In fact, H₂CNCN emerges as one of the least abundant species detected thus far toward G+0.693, being ∼2–3 times lower in abundance in comparison to other even more complex nitrogen-bearing species already identified in this cloud (Rivilla et al. 2022c). This disparity becomes even sharper with respect to both C-cyanomethanimine isomers, for which we have computed Z, E-HNCHCN/H₂CNCN isomeric ratios of 25.9 ± 1.6 and 5.8 ± 0.3, respectively. Consequently, we have derived a C/N-cyanomethanimine abundance ratio of 31.8 ± 1.8 toward G+0.693.

At this point, it is worth mentioning that while the Z- and E-HNCHCN isomers exhibit quite similar T_ex of ∼14 K, we have derived a much lower value of ∼8 K for H₂CNCN (see Table 1). Although we have already demonstrated the reliability of our results regarding the LTE fitting of these species, we have also evaluated the possibility of a T_ex of ∼14 K for H₂CNCN. In this scenario, we have obtained a poorer fit and a reduction of ∼25% in its estimated column density, which results into an even lower molecular abundance and hence a greater C/N-cyanomethanimine ratio. In any case, our observational results set the N-isomer as over 1 order of magnitude less abundant compared to the more stable C-cyanomethanimine species, which suggests that its detection toward other sources could become a much more challenging task.

In astrochemistry, there is still a prevalent belief that the search for high-energy isomers in the ISM is bound to fail, since these isomers are expected to exhibit molecular abundances that could be several orders of magnitude lower than their most stable analogs. This idea is rooted in the so-called minimum energy principle (MEP), which states a strong correlation between the observed abundances of the different members that compose a given isomeric family and their relative energies, with the most stable member expected to exhibit the highest abundance (Lattelais et al. 2009). In this respect, the cyanomethanimine family analyzed in this work would seem to adhere to this principle. However, the detection of N-cyanomethanimine toward G+0.693 cast doubts on the reliability of the MEP as a predictive tool for assessing high-energy isomer traceability in the ISM, as discussed below.

According to the original formulation of the MEP by Lattelais et al. (2009), the abundance ratios between structural isomers (denoting those molecular species sharing the same generic formula but whose constituent atoms are arranged differently) must be governed by thermodynamic equilibrium, scaling with $\exp (-{\rm{\Delta }}E/{T}_{\mathrm{kin}})$, ¹¹ where ΔE is their electronic energy difference and T_kin indicates the kinetic temperature of the gas. This points to their relative abundances being determined by isomerization mechanisms, which would prevail over other processes. Nevertheless, this is far from being the case of N-cyanomethanimine. With an estimated ΔE of 3570 ± 130 K (Puzzarini 2015) with respect to the most stable Z-HNCHCN isomer, its abundance based on thermodynamical considerations is predicted to be more than 10 orders of magnitude lower in comparison to C-cyanomethanimine at the T_kin of G+0.693 (∼70–140; Zeng et al. 2018), nearly 9 orders of magnitude below what has actually been observed. Therefore, it ought to be explained in terms of kinetics instead. The most plausible explanation for the C/N-cyanomethanimne ratio markedly deviating from the thermodynamic equilibrium prediction is probably related to the very distinct molecular structures of the N- and C-cyanomethanimine species, which makes their unimolecular isomerization impossible under ISM conditions since it must involve a reaction intermediate far superior in energy to both species.

On top of that, the N- and C-cyanomethanimine isomers do not emerge as the unique exception to the MEP, since recent detections in the ISM of many other isomeric families have also raised serious doubts about its general applicability regarding structural isomers. Some of these findings have demonstrated that high-energy structural isomers can share similar abundances to their more stable counterparts, as is the case for the H₂CN and H₂NC isomers (Cabezas et al. 2021; Agúndez et al. 2023a; San Andrés et al. 2023) and the two most stable isomers within the C₃H₄O family (trans-propenal, CH₂CHCHO, and methyl ketene, CH₃CHCO; Bermúdez et al. 2018; Fuentetaja et al. 2023), or even higher, as noted for the C₃H₂O, C₂H₄O₂, and C₂H₅N₂O isomeric families (see, e.g., Loomis et al. 2015 and Shingledecker et al. 2019; Mininni et al. 2020; Rivilla et al. 2023, respectively). Therefore, it is clear that the MEP cannot be taken as a strict rule to argue about the actual detectability of high-energy structural isomers in the ISM.

In this regard, the MEP only appears to primarily apply for some stereoisomers (also referred as spatial isomers, i.e., those species that possess identical constitutions but differ in the three-dimensional orientation of their bonding atoms), where the Z- and E-HNCHCN isomeric pair of C-cyanomethanimine emerges as the nearest example. In fact, the energy difference of these two isomers is 309 ± 72 K (Takano et al. 1990), which, based on the gas kinetic temperatures of the G+0.693 cloud of ∼70–140 K (Zeng et al. 2018), results in an abundance ratio fairly consistent with that observed by Rivilla et al. (2019) and reported in this work. Although the energy barrier associated with their isomerization is huge (∼15.95 kK; Takano et al. 1990), García de la Concepción et al. (2021) demonstrated that this process can take place, even at the low temperatures of G+0.693, when quantum tunneling is considered using a small curvature approximation (Skodje et al. 1981) and predicted a Z/E-HNCHCN abundance ratio at 150 K that mimicked Rivilla et al.'s (2019) observational value (6.1 ± 2.4). Our revised estimate for this ratio of 4.5 ± 0.2 would correspond to a T_kin of ∼180 K (see Figure 6), slightly higher than those typically associated with this source but still in good agreement with the thermodynamic equilibrium prediction. Furthermore, as Figure 6 shows, this mechanism emerges as the only plausible explanation for this ratio, as none of the formerly suggested chemical pathways are capable of describing the observations (Vazart et al. 2015; Shingledecker et al. 2020; Barone & Puzzarini 2022).

Zoom In Zoom Out Reset image size

Besides both C-cyanomethanimine isomers, the list of stereoisomers that also support the MEP rule is rather scarce, where the Ga and Aa conformers of n-propanol (n-C₃H₇OH; Jiménez-Serra et al. 2020), the anti and gauche conformers of ethyl formate (CH₃CH₂(O)CHO; Rivilla et al. 2017), and the cis and trans conformers of thioformic acid (HC(O)SH; García de la Concepción et al. 2022) are some of the clearest examples. However, there is also growing evidence that thermodynamics cannot account for the observed abundance ratios of many other stereoisomers, such as the cis-cis and cis-trans conformers of carbonic acid (HOCOOH; Sanz-Novo et al. 2023), the cis and trans conformers of methyl formate (CH₃OCHO; Neill et al. 2012), and the cis and trans conformers of formic acid (HCOOH; García de la Concepción et al. 2022). We note that all of the stereoisomers so far detected in the ISM whose abundance ratios match the thermodynamic prediction exhibit energy differences ≲500 K, which appears to be a doable energetic boundary for quantum tunneling to efficiently enable their isomerization reactions at the low temperatures of the ISM, as García de la Concepción et al. (2021) demonstrated for several imines. On the other hand, the stereoisomers mentioned above that do not follow the thermodynamic ratio exhibit much higher energy differences, which surely prevents their direct isomerization and hence causes their abundance ratios to be shaped by chemical kinetics instead.

All in all, observational evidence increasingly indicates that the MEP lacks predictive capability regarding which species within a specific isomeric family are more readily detectable and, consequently, cannot be generally used as a reliable indicator of isomeric abundances. In this regard, the detection of N-cyanomethanimine toward G+0.693 provides robust evidence that high-energy isomers can also be found in the ISM. Therefore, although it is possible that in some cases the detection of such species would deserve deeper integrations, we note that it is equally important and necessary to obtaining their spectroscopy to enable their interstellar identification, significantly contributing to providing a full inventory of the molecular complexity of the ISM.

The aforementioned results have also continued to support the prominent role of chemical kinetics, rather than thermodynamics, in establishing the observed abundance ratios between structural isomers. For this reason, we discuss in the following section the possible chemical pathways leading to H₂CNCN.

Over the last decade, several authors have investigated the chemistry of cyanomethanimines under interstellar conditions (Vazart et al. 2015; Shivani & Tandon 2017; Shingledecker et al. 2020; Zhang et al. 2020). However, biased by the exclusive detection in the ISM of the Z- and E-HNCHCN isomers (Zaleski et al. 2013; Rivilla et al. 2019), many of these works mainly focused on the chemical processes involving these two species. Consequently, the potential chemical pathways yielding to H₂CNCN have often been overlooked, resulting in a limited characterization of the chemistry linked to this isomer.

To date, there is just one formation mechanism leading to H₂CNCN that has been specifically studied. This route occurs through the gas-phase reaction between the cyanogen radical (CN) and methanimine (CH₂NH), which Vazart et al. (2015) initially examined by performing quantum chemical calculations using a composite CBS-QB3 methodology. This reaction leads to the three cyanomethanimine isomers as the main products,

$$\begin{eqnarray}\mathrm{CN}+{\mathrm{CH}}_{2}\mathrm{NH} & \to & Z,E-\mathrm{HNCHCN}+{\rm{H}}\end{eqnarray} \tag{ 1.1 }$$

$$\begin{eqnarray} & \to & {{\rm{H}}}_{2}\mathrm{CNCN}+{\rm{H}}\end{eqnarray} \tag{ 1.2 }$$

being the C-cyanomethanimine isomers formed when the CN radical attacks the carbon atom of methanimine (route 1.1), while N-cyanomethanimine is produced from the attack on its N-side (route 1.2). All these processes are exothermic and proceed without an entrance barrier, making this reaction a feasible mechanism forming cyanomethanimines under interstellar conditions. Among the two possible pathways, the one leading to the Z, E-HNCHCN isomers is much more thermodynamically favored, hence arising as the predominant route. Although the kinetic calculations performed by these authors establish a rather low Z/E-HNCHCN abundance ratio of ∼1.5 from this reaction (which is far below the 4.5 ± 0.2 ratio we observed; see Figure 6), the prediction for the C/N-cyanomethanimine ratio fits extremely well to the observational value (see Figure 7). Given that this ratio ought to be described in terms of chemical kinetics (see Section 4.1), this result would point to the CN + CH₂NH reaction being mainly responsible for C- and N-cyanomethanimine chemistry in G+0.693. Moreover, its viability is also supported by the high abundance of the parent species (CH₂NH and CN) found in this region (see Zeng et al. 2018 and Rivilla et al. 2019, respectively). On top of that, this reaction can also proceed at a very fast pace. With associated rate constants at 150 K of ∼10⁻¹¹–10⁻¹⁰ cm⁻³ s⁻¹ as derived by Vazart et al. (2015), the observed abundances of the cyanomethanimines would be reproduced through this reaction at timescales smaller than those related to depletion on dust grains due to the cooling of the gas (≳10⁵ yr; Requena-Torres et al. 2006), even in spite of the low H₂ densities of this cloud (∼10⁴–10⁵ cm⁻³; Zeng et al. 2020).

Zoom In Zoom Out Reset image size

Nonetheless, a new theoretical study recently carried out by Puzzarini & Barone (2020) has revealed that the energy of the transition states along the reaction profile calculated by Vazart et al. (2015) could be slightly underestimated, causing their computed branching ratios not to be entirely accurate. In a subsequent study, Barone & Puzzarini (2022) performed improved kinetic calculations using both the CBS-QB3 model as well as the more optimized and recently developed jun-Cheap scheme, outlining a slightly divergent C/N-cyanomethanimine abundance ratio as a function of the temperature with respect to the Vazart et al. (2015) results, as shown in Figure 7. The prediction for the Z/E-HNCHCN ratio remains unchanged (see Figure 6). Nevertheless, the differences encountered in the predicted C/N-cyanomethanimine ratio are merely within a factor of ∼2 with respect to our observations, so that the gas-phase CN + CH₂NH reaction is still considered as the main mechanism likely producing cyanomethanimines in G+0.693. Moreover, its rate constant peaks at ∼150 K as derived by Barone & Puzzarini (2022), in line with the kinetic temperature of this cloud (∼70–140 K; Zeng et al. 2018). Nonetheless, a more refined study of this process is needed to clarify the small discrepancies detected between the quantum chemical calculations and the astronomical observations.

Besides gas-phase processes, chemical reactions occurring on the icy mantles of interstellar dust grains could also be an important source producing H₂CNCN in G+0.693, where grain surface chemistry is believed to play a key role (Rivilla et al. 2020a, 2021b, 2022b, 2023; Molpeceres 2021; San Andrés et al. 2023). However, little research has been done on these process for cyanomethanimine isomers, especially for H₂CNCN. According to recent astrochemical models run by Zhang et al. (2020), the surface analog of the already-characterized gas-phase CN + CH₂NH reaction could be a second relevant route forming the three cyanomethanimine isomers. However, while it is well established that methanimine (CH₂NH) is mainly produced on grains, making this reaction feasible (Theule et al. 2011; Suzuki et al. 2016), the hinted extraordinary reactivity that the CN radical exhibits upon contact with H₂O molecules (Rimola et al. 2018), one of the major constituents of dust grain ices, would pose a significant barrier to its occurrence. Indeed, as is also shown in the models of Zhang et al. (2020), the contribution from this reaction to the total abundances of cyanomethanimines seems not to be as significant as that of its gas-phase counterpart, which can easily proceed once CH₂NH is desorbed into the gas. Furthermore, the observed abundances for the three cyanomethanimine isomers are reproduced within their models at timescales of <10⁵ yr attending to the CN + CH₂NH gas-phase reaction, which strongly supports it as the primary and most efficient formation mechanism. However, the C/N-cyanomethanimine abundance ratio is not consistently explained according to their chemical network, indicating that other chemical processes might also need to be invoked. Moreover, the absence of comprehensive theoretical or experimental investigations examining this particular mechanism on grains forces us to assume the same branching ratio toward the formation of the three isomers in chemical models. Nonetheless, in spite of these shortcomings, it appears more likely that the role of the CN + CH₂NH reaction in producing cyanomethanimines is only relevant in the gas phase.

Another possible surface pathway has been proposed by Vasconcelos et al. (2020), whose experiments irradiating a N₂-CH₄ icy mixture with cosmic rays produced the three isomers of cyanomethanimine. However, it remains unclear whether the presence of additional molecules in the ice, such as H₂O, CO, or CO₂, can alter the chemistry observed in these irradiation experiments. Intuitively, and because H₂O, CO, and CO₂ are the main constituents of interstellar ices (see, e.g., Boogert et al. 2015; McClure et al. 2023), the free path of the radicals derived from CH₄ and N₂ radiolysis is likely to encounter reaction partners of this ternary, reducing the amount of cyanomethanimines being produced and hence rendering this specific route probably not dominant.

Shivani & Tandon (2017) also proposed that both the Z- and E-HNCHCN isomers could be formed in the grains through two consecutive hydrogenations of the cyanogen species (NCCN), which is expected to be abundant in G+0.693 (Rivilla et al. 2019). However, the astrochemical model performed later by Shingledecker et al. (2020) showed that this route has a minor impact on the formation of C-cyanomethanimine in G+0.693. By analogy, it could be proposed that the hydrogenation of the high-energy metastable isomer of NCCN, the isocyanogen species (CNCN), could be another possible route remaining to be added in the H₂CNCN solid-phase chemical network. Nonetheless, this alternative route is currently hampered by the poor knowledge of how this precursor could be synthesized through interstellar chemistry, for which the only pathway so far studied (CN + HNC → CNCN + H) has been shown to have high energy barriers when leading to CNCN (Petrie & Osamura 2004). Furthermore, this species exhibits a low abundance in the ISM (<10⁻¹⁰ with respect to H₂), with only one reported detection so far (Agúndez 2018). Indeed, using our spectral survey and assuming a T_ex of 10 K and an FWHM of 22.0 km s⁻¹, we have just derived an upper limit for its molecular abundance toward G+0.693 of ≤2 × 10⁻¹¹, which is lower than the abundance of H₂CNCN itself. Consequently, all evidence points to this route not being a promising alternative for boosting H₂CNCN abundance, as happened for the Z- and E-HNCHCN isomers through the analog reaction triggered by NCCN.

In summary, none of the chemical pathways proposed to date for grain surface chemistry seem capable of substantially increasing the abundance of the three cyanomethanimine isomers to adequately match the observational values. In this context, the gas-phase CN + CH₂NH reaction stands out as the primary formation route for these species, while the role of surface chemistry would primarily point to enhancing the abundance of CH₂NH in the gas after ejection, thereby enabling the occurrence of this reaction.