Methanimine as a key precursor of imines in the interstellar medium: the case of propargylimine
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Methanimine as a key precursor of imines in the interstellar medium: the case of propargylimine
Jacopo Lupi , Cristina Puzzarini , and Vincenzo Barone Scuola Normale Superiore, Piazza dei Cavalieri 7, Pisa, 56126, Italy Department of Chemistry “Giacomo Ciamician”, University of Bologna, Via F. Selmi 2, Bologna, 40126, Italy
Submitted to ApJLABSTRACTA gas-phase formation route is proposed for the recently detected propargylimine molecule. Inanalogy to other imines, such as cyanomethanimine, the addition of a reactive radical (C H in thepresent case) to methanimine (CH NH) leads to reaction channels open also in the harsh conditions ofthe interstellar medium. Three possible isomers can be formed in the CH NH + C H reaction: Z- andE-propargylimine (Z-,E-PGIM) as well as N-ethynyl-methanimine (N-EMIM). For both PGIM species,the computed global rate coefficient is nearly constant in the 20-300 K temperature range, and of theorder of 2-3 × − cm molecule − s − , while that for N-EMIM is about two orders of magnitudesmaller. Assuming equal destruction rates for the two isomers, these results imply an abundance ratiofor PGIM of [Z]/[E] ∼ Keywords:
ISM: abundances – ISM: molecules INTRODUCTIONCurrently, the number of molecules detected in the interstellar medium (ISM) thanks to their rotational signaturesfar exceeds 200 (McGuire 2018). Among them more than 70 species belong to the class of the so-called interstellarcomplex organic molecules (iCOMs), namely molecules containing at least one carbon atom and a total of more than 6atoms (Herbst & van Dishoeck 2009). Nitrogen-bearing iCOMs are particularly interesting because of their prebioticcharacter; indeed, they represent key intermediates toward the main building blocks of biomolecules, like aminoacidsand nucleobases. Within this class of iCOMs, six members of the imine family have been detected so far in the ISM,namely methanimine (CH NH, Godfrey et al. (1973); Dickens et al. (1997)), ethanimine (CH CHNH, Loomis et al.(2013)), ketenimine (CH CNH, Lovas et al. (2006)), 3-imino-1,2-propadienylidene (CCCNH, Kawaguchi et al. (1992)),C-cyanomethanimine (NCCHNH, Zaleski et al. (2013); Rivilla et al. (2018)), and –very recently– Z-propargylimine(2-propyn-1-imine, HC −− C − CH −− NH, Bizzocchi et al. (2020)).The main hypotheses on their formation mechanisms in astrophysical environments involve either tautomerization ofsimple nitriles (Lovas et al. 2006) or their partial hydrogenation on dust-grain surface (Theule et al. 2011; Krim et al.2019). However, for C-cyanomethanimine, a gas-phase formation route has been recently proposed, which involvesaddition of the cyano radical (CN) to methanimine (Vazart et al. 2015). It is thus quite natural to hypothesize thatmethanimine can play a role in the formation of other imines upon addition/elimination of reactive radicals alreadydetected in the ISM, like CH , C H or OH. Indeed, the reaction of the hydroxyl radical with methanimine is provento effectively lead to the formation of formamide in the gas phase (Vazart et al. 2016; Codella et al. 2017).The focus of the present letter is the possible formation pathway of propargylimine (PGIM), whose Z-isomer hasbeen very recently identified in the quiescent G+0.693-0.027 molecular cloud with an estimated column density of0 . × cm − (Bizzocchi et al. 2020). In the same study, an upper limit of 1 . × − was retrieved for the Corresponding author: Vincenzo [email protected] author: Cristina [email protected] a r X i v : . [ a s t r o - ph . GA ] O c t Lupi et al. fractional abundance (w.r.t. H ) of the higher-energy E isomer (which means a column density < NH(Zeng et al. 2018), this has not been taken into consideration, notwithstanding the authors reported, among the others,a large fractional abundance for the ethynyl radical (C H, Σ + ), i.e. 3 . × − .Based on these premises, we decided to perform a state-of-the-art quantum-chemical (QC) characterization of thestationary points on the doublet reactive C H + CH NH potential energy surface (PES) followed by kinetic computa-tions in the framework of a master equation model rooted in generalized transition state estimates of the elementaryreaction rates. From a theoretical point of view, the reactions between the ethynyl radical and several substrates havebeen recently investigated by state-of-the-art QC approaches (Bowman et al. 2020), but addition/elimination reactionswith unsaturated substrates have not yet been explored. COMPUTATIONAL METHODOLOGYThe starting point for the study of the formation pathway of PGIM is the identification of the potential reactantsand the analysis of the corresponding reactive PES, which implies the accurate characterization of all stationary pointsfrom both a structural and energetic point of view. This first step then requires to be completed by kinetic calculations.In the derivation of a feasible reaction mechanism, one has to take into account the extreme conditions of the ISM:low temperatures (10-100 K) and low number density (10-10 cm − ). By translating density in terms of pressure, anumber density of 10 cm − corresponds to a pressure of 3.8 × − Pa ( ∼ × − atm).2.1. Reactive potential energy surface
We have followed the general computational strategy validated in several recent studies (Salta et al. 2020; Baianoet al. 2020; Lupi et al. 2020; Puzzarini et al. 2020; Tonolo et al. 2020), which involves the following steps:i) The stationary points have been located and characterized using the double-hybrid B2PLYP functional (Grimme2006), combined with D3(BJ) corrections (to incorporate dispersion effects; Grimme et al. (2010, 2011)) and inconjunction with the jun-cc-pVTZ “seasonal” basis set (Papajak et al. 2009).ii) Single-point energy calculations, at the B2PLYP-D3(BJ)/jun-cc-pVTZ geometries, have been performed by meansof the so-called “cheap” composite scheme (ChS; Puzzarini & Barone (2011); Puzzarini et al. (2014)), which startsfrom the coupled-cluster theory including single and double excitations augmented by a perturbative estimate oftriples (CCSD(T); Raghavachari et al. (1989)) in conjunction with a triple-zeta basis set (cc-pVTZ; Dunning Jr.(1989)) and within the frozen-core (fc) approximation. To improve this level of theory, the ChS model considersthe extrapolation to the complete basis set (CBS) limit and the effect of core-valence (CV) correlation usingMøller-Plesset theory to second order (MP2; Møller & Plesset (1934)). Concerning the former contribution, thefc-MP2 energy is extrapolated to the CBS limit using the n − expression (Helgaker et al. 1997) in conjunction withthe cc-pVTZ and cc-pVQZ basis sets. The CV correlation correction is, instead, the difference between the MP2energy evaluated correlating all electrons and that computed within the fc approximation, both in conjunctionwith the cc-pCVTZ basis set (Woon & Dunning Jr. 1995).iii) ChS energies have been combined with anharmonic zero-point energy (ZPE) corrections evaluated at the B2PLYP-D3(BJ)/jun-cc-pVTZ level within hybrid degeneracy-corrected second-order vibrational perturbation theory (HD-CPT2; Bloino et al. (2012); Puzzarini et al. (2019)).All calculations have been performed with the Gaussian software (Frisch et al. 2016).2.2. Kinetic models
Global rate constants have been calculated by using a master equation (ME) approach based on ab initio transitionstate theory (AITSTME), thereby employing the MESS software as master equation solver (Georgievskii et al. 2013).For elementary reactions involving a transition state, rate constants have been computed using transition state theory(TST), while for barrier-less elementary reactions, they have been evaluated by means of phase space theory (PST;Pechukas & Light (1965); Chesnavich (1986)). The basic assumption of PST is that the interaction between two reactingfragments is isotropic (following a C R power law) and does not affect the internal fragment motions (Fern´andez-Ramos ormation route of propargylimine C parameter for the PST calculation, we performed a scan of the HCC − CH NHand HCC − NHCH distances for the C- and N-end attack, respectively. Then, the corresponding minimum energypaths have been fitted to a f ( x )= f − C x function, thus obtaining a C value of 131 . a E h for the former attackand of 180 . a E h for the latter. In all cases, tunnelling has been accounted for using the Eckart model (Eckart1930).The rate constants of the overall reactions leading to the C H N imine isomers (namely, the E-,Z-PGIM speciesand N-ethynyl-methanimine, N-EMIM) have been evaluated in the 20-500 K temperature range. To model theirtemperature dependence, the rate constants at different temperatures have been fitted to a three-parameter modifiedArrhenius equation, namely the Arrhenius-Kooij expression (Kooij 1893; Laidler 1996): k ( T ) = A (cid:18) T (cid:19) n exp (cid:18) − ERT (cid:19) (1)where A , n , and E are the fitting parameters, R being the universal gas constant. Figure 1.
Formation route of N-EMIM and the PGIM isomers: ChS energies augmented by anharmonic B2PLYP-D3(BJ) ZPEcorrections. 3.
RESULTS AND DISCUSSION3.1.
Reactivity and energetics
A recent re-investigation of the reaction channel starting from attack of the cyano radical to the C-end of methanimine(Puzzarini & Barone 2020) has shown that, for all stationary points, the ChS model has a maximum absolute deviationof 3 kJ mol − and an average absolute deviation of 1.1 kJ mol − with respect to a reference composite scheme, whichis able to reach sub-kJ accuracy energetics. These errors are much smaller than those issuing from widely employedcomposite schemes (e.g. CBS-QB3, Montgomery et al. (2000), or G4, Curtiss et al. (2007)) and well sufficient for Lupi et al. obtaining quantitative estimates of reaction rates and branching ratios (Salta et al. 2020; Baiano et al. 2020; Lupiet al. 2020; Puzzarini et al. 2020; Tonolo et al. 2020). On these grounds, we have performed a full characterizationof the doublet PES for the addition-elimination reactions of both CN and CCH radicals to methanimine at the ChSlevel.As far as the reaction mechanism is concerned, hydrogen abstraction could be competitive with addition/elimination(Bowman et al. 2020), but test computations showed that the former reaction channel is at least one order of magnitudeslower than the latter one. As a consequence, only the addition/elimination reaction channel is analyzed in detail inthe following. The reaction mechanism proposed in the present paper for the formation of N-EMIM and the PGIMisomers is sketched in Figure 1 and the relative energies of all the stationary points, with respect to reactants, arecollected in Table 1 together with the corresponding results for the CH NH + CN reaction. There are three possibleinitial adducts, corresponding to the attack of the ethynyl radical to the C or N ends and to the π -system of the iminedouble bond. However, the cyclic adduct resulting from the third option (CYCLO-1) is significantly less stable andeasily interconverts to one of the corresponding open-chain minima (1Z or 1N). For both the CN and CCH radicals, theintermediate obtained upon attack to the N moiety is slightly more stable, but the reaction channels originating fromit are ruled by transition states significantly less stable (albeit always submerged) than those ruling the correspondingchannels issuing from 1Z or 1E. Noted is that the PES for the CH NH + CN reaction is, in any detail, analogous tothat of the C H radical.
Table 1.
ChS relative electronic energies (∆ E el ) and corresponding standard enthalpies at 0 K (∆ H ◦ ) for the stationary pointsof the CH NH + X reaction. Values in kJ mol − . X = C H X = CN∆ E el ∆ H ◦ ∆ E el ∆ H ◦ CH NH + X 0.00 0.00 0.00 0.001Z -229.36 -218.72 -203.59 -198.67TS-1E1Z -217.65 -205.90 -192.39 -183.241E -225.75 -213.58 -201.48 -191.95TS-1Z2 -96.36 -93.12 -63.55 -62.81TS-1E2 -88.80 -86.01 -57.47 -57.182 -314.60 -299.69 -284.59 -271.29TS-2PZ -88.09 -94.97 -48.37 -58.27TS-2PE -84.99 -92.15 -46.22 -56.40TS-1ZPZ -77.81 -83.90 -40.62 -49.89TS-1EPE -73.86 -80.46 -37.97 -47.70Z − IM + H (PZ) -99.21 -110.00 -60.89 -74.73E − IM + H (PE) -95.40 -106.61 -58.55 -72.78CYCLO-1 -167.50 -151.41 -108.93 -96.69TS-CY-C -144.35 -133.03 -97.62 -88.32TS-CY-N -122.80 -114.02 -88.77 -80.941N -233.04 -223.67 -208.44 -201.32TS-1N2N -53.16 -53.04 -25.66 -27.152N -272.23 -260.55 -223.19 -211.85TS-2NPN -52.98 -62.22 -22.76 -33.56TS-1NPN -35.54 -44.05 -3.85 -14.67N − IM + H (PN) -59.22 -72.69 -30.64 -45.80 ormation route of propargylimine ∼
135 (or ∼ − . Onthe other hand, considering the presence of the stabilizing C H moiety on the carbon atom, hydrogen migration mightbe observed in order to localize the unpaired electron on this atom. This migration occurs through the submergedtransition state TS-1Z2 (TS-1E2 for the E-PGIM), which lies 125.6 kJ mol − above 1Z (127.6 kJ mol − above 1E forthe E-route), thus forming the most stable intermediate of the whole PES, namely 2, which is nearly 300 kJ mol − below the reactants. Next, loss of hydrogen leads again to the Z (or E) form of PGIM through the submerged transitionstate TS-2PZ (TS-2PE), lying about 95 kJ mol − (92 kJ mol − for the E species) below the reactants (exit barrierof about 205 and 208 kJ mol − , respectively). The comparison with the analogous reaction paths for the gas-phaseproduction of C-cyanomethanimine (Puzzarini & Barone 2020) shows that the formation of PGIM is characterized bygreater exothermicity (-108 vs. -60 kJ mol − for the average of Z and E isomers) and lower exit barriers (126 vs. 140kJ mol − for the average of TS-1Z2 and TS-1E2 and 206 vs. 238 kJ mol − for the average of TS-2PZ and TS-2PE).Furthermore, the stability of the pre-reactive complex 1Z or 1E (ruling the barrier-less entrance channel) and that ofthe intermediate 2 (involved in the two-step mechanism) are greater in the case of the addition of C H than for CN(-218.7 vs. -203.6 kJ mol − for the average of 1Z,1E and -299.7 vs. -284.6 kJ mol − for 2).Moving to the attack to the N-end of methanimine, from the inspection of Figure 1, it is evident that the twopossible paths originating from the 1N pre-reactive complex are similar to those described above for the C-end attack,as already noted for the CH NH + CN reaction (Vazart et al. 2015). With the only exception of 1N, which lies lower inenergy than 1Z and 1E, all intermediates and transition states of these paths are less stable with respect to the C-endcounterparts. The product itself, i.e. N-EMIM + H (PN), lies at higher energy: -72.7 kJ mol − , to be compared with-106.6 kJ mol − for E-PGIM + H (PE) and -110.0 kJ mol − for Z-PGIM + H (PZ).Studies for reactions of radical species with molecules containing a double bond have shown that the reactivitydepends on the type of system. For the C=C bond, addition/elimination is barrierless and strongly favored overhydrogen elimination (e.g. Bouwman et al. (2012)), whereas for C=O bonds, only H elimination is barrierless, whereasboth the C- and O- addition/eliminations involve small barriers (e.g. Dong et al. (2005)). Preliminary computationsfor the addition of other radicals (e.g. CP, OH, and CH ) to methanimine show that the mechanism described in theprevious paragraphs for the reaction with C H or CN represents a quite general route to the formation of compleximines, although in a few cases (e.g. CH ) some transition states are not submerged with respect to reactants.3.2. Rate constants
To definitely confirm the effectiveness of the mechanism proposed, kinetic computations are required. The productspecific rate constants as a function of temperature are shown in Figure 2 for the reaction of methanimine with C Hand in Figure 3 for the reaction with CN, whereas the parameters of the Arrhenius-Kooij fits are given in Table 2.These have been obtained by fitting the global rate constants computed in the 20-500 K range. In more detail, for eachfigure, four panels are provided: those on the left refer to the C-end attack (panels (a) and (c)), while those on theright to the N-end attack (panels (b) and (d)). In both figures, the upper panels show the temperature profiles of rateconstants for the formation of the “C-isomers” (namely, Z-/E-PGIM and Z-/E-C-cyanomethanimine, CMIM), whilethe lower panels refer to the formation of the “N-isomers” (namely, N-EMIM and N-cyanomethanimine, N-CMIM).Focusing on the C-end reaction paths, the prevalence of the Z-product is related to the slightly lower energy ofthe corresponding transition states compared to those leading to the E isomer. Back-dissociation into reactants isnegligible in the whole temperature range considered, whereas the overall rate constant for the PGIM formation raisesby increasing the temperature, also showing progressive deviations from the Arrhenius behavior. The overall rateconstant, which is of the order of 2-3 × − cm molecule − s − , is mainly ruled by the one-step mechanism leadingto products from the 1Z/1E pre-reactive complex through the TS-1ZPZ/TS-1EPE transition state. However, this isalways true for Z-PGIM, while for the E isomer the two-step mechanism seems to be the rate determining one above ∼
350 K. The derived branching ratio is of the order of 1.5, smaller than the observational result ( ≥ Lupi et al. . × − × − . × − × − . × − × − k / c m m o l ec u l e − s − T /K(a) C H attack to the CH NH C-endE-PGIM + HZ-PGIM + H 1 . × − × − . × − × − . × − × − k / c m m o l ec u l e − s − T /K(b) C H attack to the CH NH N-endE-PGIM + HZ-PGIM + H5 × − × − . × − × − . × − k / c m m o l ec u l e − s − T /K(c) C H attack to the CH NH C-endN-EMIM + H 5 × − × − . × − × − . × − k / c m m o l ec u l e − s − T /K(d) C H attack to the CH NH N-endN-EMIM + H
Figure 2.
Temperature dependence plots of the CH NH + C H reaction rate constants. destruction rates (see Shingledecker et al. (2020)). More specifically, Shingledecker et al. (2020) proposed a generalrule-of-thumb for estimating the abundances of isomers based on their dipole moments, which has been denoted as“relative dipole principle”. According to this, for propargylimine, whose isomers have very similar dipole moments( ∼ H and CN additions to methanimine are very similar, thusgiving further support to the plausibility and generality of the proposed mechanism. At 100 K, for PGIM, the overallrate constants for Z and E species (in cm molecule − s − ) are 3 . × − and 2 . × − , respectively, to becompared to 2 . × − and 1 . × − for the two corresponding isomers of C-cyanomethanimine.As far as the formation of the N-species is concerned, it is interesting to note that this process would be a little bitfavored over formation of the C-species if the attacks to the two ends of the imino group would be independent (as ormation route of propargylimine × − . × − × − . × − × − k / c m m o l ec u l e − s − T /K(a) CN attack to the CH NH C-endE-CMIM + HZ-CMIM + H 1 × − . × − × − . × − × − k / c m m o l ec u l e − s − T /K(b) CN attack to the CH NH N-endE-CMIM + HZ-CMIM + H2 × − × − × − × − × − × − k / c m m o l ec u l e − s − T /K(c) CN attack to the CH NH C-endN-CMIM + H 2 × − × − × − × − × − × − k / c m m o l ec u l e − s − T /K(d) CN attack to the CH NH N-endN-CMIM + H
Figure 3.
Temperature dependence plots of the CH NH + CN reaction rate constants. actually is in the case of the CN addition to the CH or NH moiety of methylamine, see Puzzarini et al. (2020)), witha rate constant of 4-5 × − cm molecule − s − ). However, Figure 1 shows that the two channels are connected bya low-lying cyclic intermediate. Under these circumstances (also valid for the attack of the CN radical), the formationof C-products becomes faster by two orders of magnitude with respect to formation of the N-product, with the rateconstant of the latter process slightly increasing with the temperature. To provide a graphical explanation of thebehavior of the global constant with temperature, the contributions of some specific reaction channels are shown inFigure 4. These are the two barrier-less (C- and N-end) entrance channels, the one- and two-step processes leading toZ-/E-PGIM for the C-end attack and the corresponding channel leading to N-EMIM for the attack to the N end ofmethanimine. It is noted that, even if the entrance channel flux for the N-end attack is faster than the C-end attackone, the subsequent high barriers of the N-EMIM formation path slow down the flux, thus resulting in the preferentialformation of the E,Z-PGIM, which presents lower lying barriers. In this picture, an important role is played by theTS-CY-N transition state linking 1N to the cyclic pre-reactive complex, CYCLO-1. In fact, this interconversion is the Lupi et al. elementary step characterized by the lowest barrier for the N-end side of the overall CH NH + C H reaction. Similararguments also apply to the reaction involving CN.
Table 2.
The Arrhenius-Kooij parameters for the CH NH + X reaction.
C-end attack N-end attackX = C H E Z N E Z N A /cm molecule − s − . × − . × − . × − . × − . × − . × − n . × − . × − . × − − . × − − . × − . × − E /kJ mol − . × − . × − − . × − . × − . × − − . × − rms a . × − . × − . × − . × − . × − . × − X = CN E Z N E Z N A /cm molecule − s − . × − . × − . × − . × − . × − . × − n − . × − − . × − . × − − . × − − . × − − . × − E /kJ mol − . × − . × − . × − . × − . × − . × − rms a . × − . × − . × − . × − . × − . × − a rms stands for root-mean-square deviation of the fit. It is noteworthy that the behavior discussed above for both types of radical attack to methanimine is specific of thelow pressure limit (see computational details). In fact, moving to a pressure of 1 atm (of limited astrophysical interest,but of potential relevance in planetary atmospheres), the N-EMIM formation remains unfavorable with respect toE,Z-PGIM and, in general, all formation rate constants become slower. This trend is due to the stabilization of theentrance channel wells (namely 1N and 1Z) by collisions (that occurs at pressure values as high as 1 atm), thus leadingto an increase of the effective reaction barriers with the consequent decrease of the overall rate constant, which showsa monotonic increase with temperature. × − . × − × − . × − × − . × − × − . × − k / c m m o l ec u l e − s − T /K(a) C H + CH NH entrance channels
C-end attack entrance channelN-end attack entrance channel . × − × − . × − × − . × − × − k / c m m o l ec u l e − s − T /K(b) C H attack to the CH NH C-end
One step (PE)One step (PZ)Two step (PE)Two step (PZ) × − × − × − × − × − . × − . × − . × − . × − × − k / c m m o l ec u l e − s − T /K(c) C H attack to the CH NH N-end
One step (PN)Two step (PN)
Figure 4.
Temperature dependence of the rate constants for the elementary steps of the overall CH NH+C H reaction, namelybarrier-less entrance (panel (a)), and one- or two-step paths leading to Z-/E-PGIM (panel (b)) and N-EMIM (panel (c)).
A curved Arrhenius plot is obtained when the activation energy depends on the temperature and this behavior iscaptured by the Arrhenius-Kooij formula (see Equation 1) when this dependence is linear. The root mean squaredeviations reported in Table 2 demonstrate that the data for the C H N imine isomers are indeed well fitted by theArrhenius-Kooij expression. Within this model, E represents the activation energy at 0 K and the activation energyat a generic temperature T is given by E + n (cid:0) RT (cid:1) . In the present case, the activation energy is always positive, withthe exception of N-EMIM, as a result of both the capture rate constant and the subsequent energy barriers for theunimolecular steps. The n parameter (the first derivative of the activation energy with respect to temperature) isalways positive for the C-end attack, while it is negative for the PGIM isomers when the N-end attack takes place.Finally, the values of the pre-exponential factor A are typical for this kind of reactions and rule the branching ratio ormation route of propargylimine A factors is 1.44 and the branching ratio ranges between1.43 and 1.47 in the whole temperature range (20-500 K). CONCLUDING REMARKSIn this letter, we have proposed a gas-phase formation route for the recently detected Z-PGIM molecule. In analogyto the addition of the CN radical to methanimine leading to cyanomethanimine, addition of the isoelectronic ethynylradical easily leads to PGIM through a similar reaction mechanism, which involves the formation of a stable pre-reactive complex and its successive evolution by means of submerged transition states. Since the level of the QC andkinetic computations carried out gives strong supports to the quantitative accuracy of our results, search for PGIMisomers in the other regions of the ISM where methanimine and the ethynyl radical have been both detected could beattempted to further validate the proposed reaction mechanism.In a more general perspective, the results of our state-of-the-art computations provide convincing evidences aboutthe feasibility of a general addition/elimination mechanism for the formation of complex imines. This starts frommethanimine as a precursor and involves reactive radicals abundantly present in the interstellar space.ACKNOWLEDGMENTSThis work has been supported by MIUR (Grant Number 2017A4XRCA) and by the University of Bologna (RFOfunds). The SMART@SNS Laboratory (http://smart.sns.it) is acknowledged for providing high-performance comput-ing facilities. Support by the Italian Space Agency (ASI; ‘Life in Space’ project, N. 2019-3-U.0) is also acknowledged.0
Lupi et al.