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A theoretical investigation of the reaction between the amidogen, NH, and the ethyl, C2H5, radicals: a possible gas-phase formation route of interstellar and planetary ethanimine

The reaction between the amidogen, NH, radical and the ethyl, C2H5, radical has been investigated by performing electronic structure calculations of the underlying doublet potential energy surface. Rate coefficients and product branching ratios have also been estimated by combining capture and RRKM calculations. According to our results, the reaction is very fast, close to the gas-kinetics limit. However, the main product channel, with a yield of ca. 86-88% in the range of temperatures investigated, is the one leading to methanimine and the methyl radical. The channels leading to the two E-, Z- stereoisomers of ethanimine account only for ca. 5-7% each. The resulting ratio [E-CH3CHNH]/[Z-CH3CHNH] is ca. 1.2, that is a value rather lower than that determined in the Green Bank Telescope PRIMOS radio astronomy survey spectra of Sagittarius B2 North (ca. 3). Considering that ice chemistry would produce essentially only the most stable isomer, a possible conclusion is that the observed [E-CH3CHNH]/[Z-CH3CHNH] ratio is compatible with a combination of gas-phase and grain chemistry. More observational and laboratory data are needed to definitely address this issue.


Introduction
Imines are a family of N-containing organic compounds of great interest in the context of space prebiotic chemistry, because the small members of the family are simple enough to be formed in the extreme conditions of the interstellar medium, but they are very reactive and have the capability to evolve into much more complex species once brought to denser and chemically active environments (Woon, 2002;Balucani, 2009;Balucani, 2012;Loison et al., 2015). The strong propensity to react in dense media is caused by the presence of a carbon-nitrogen double bond which easily opens up providing an excellent addition site Vazart et al. 2015).
Having already an N-atom bound to a C-atom, small imines are believed to be valid precursors of small aminoacids like glycine/alanine or nucleobases (Woon, 2002). In particular, the smallest aldimine, namely methanimine (CH2=NH), has been called into play to account for the formation of glycine by various mechanisms (Woon, 2002;Rimola et al, 2011;Rimola et al., 2012). Considering all these aspects, imines, together with the more familiar class of nitriles, might well represent the link between interstellar matter and the N-rich complex molecules from which life possibly emerged on primitive Earth (Caselli and Ceccarelli, 2012;Ehrenfreund et al., 2000;Chyba et al. 1990).
Until recently, no detection of imines in low mass protostars has been reported and only upper limits have been given (Suzuki et al., 2016;Melosso et al., 2018). Ligterink et al. (2018) have finally identified methanimine towards IRAS 16293-2422B.
Remarkably, Loomis et al. (2013) detected ethanimine in both isomeric forms E-and Z-, with column densities of 7.00×10 13 cm −2 and 2.3×10 13 cm −2 , respectively. Among the possible formation routes of ethanimine (see below for more details), Quan et al. (2016) have suggested the gas-phase reaction NH + C2H5, for which, however, there are no experimental data nor theoretical evaluations of the rate coefficient. Because of the great uncertainty associated to the NH + C2H5 reactive system, we have started a dedicated investigation by means of electronic structure calculations of the stationary points along the minimum energy path. Preliminary data have been reported in Rosi et al. (2018a). In this contribution, we have refined the electronic structure calculations of the transition states associated to all possible reaction channels. We have also performed a kinetic analysis and, given the complexity of this multichannel reaction, we have provided the product branching ratio at the temperatures of relevance for interstellar objects. In particular, we have carefully analyzed the formation routes of the two E-,Z-stereoisomers of ethanimine in an attempt to verify whether this gas-phase route is able to account for the observed Z-to-E isomer abundance ratio. Before presenting the results of our work, a brief summary of what has been suggested to account for the formation of ethanimine and other imines in the interstellar medium is presented to motivate the need of a reliable estimation of rate coefficients and product branching ratio for the title reaction.

Previous work on the formation of ethanimine and other related imines in the interstellar medium
While the formation of nitriles in extraterrestrial environments has been widely explored and their formation routes are well-established (see, for instance, Kaiser and Balucani, 2001;Balucani et al., 2000), more uncertain is the mechanism of formation of imines. Quan and Herbst (2007) suggested that ketenimine is likely formed by the dissociative recombination of protonated acetonitrile, CH3CNH + . Vazart et al. (2015) identified an easy gas-phase formation route for cyanomethanimine. A recent paper by Suzuki et al. (2016) reported the first comprehensive attempt to model methanimine abundance in hot cores. According to their rather complete gas-grain chemical simulations, hot core CH2NH is mostly formed in the gas phase by neutral-neutral reactions, rather than being the product of thermal evaporation from the surface of dust grains.
Finally, Quan et al. (2016) recently attempted to model the abundance of ethanimine in Sgr B2 (N) and concluded that CH3CHNH is mainly formed on grain surfaces by hydrogenation of CH3CN, as previously suggested by Loomis et al. (2016) according to the scheme However, the gas-grain network of reactions employed by Quan et al. is affected by incomplete information on the included reactions. First of all, even though hydrogenation of CH3CN on the icy mantles of interstellar grains appears to be a reasonable process, the formation of ethanimine, that is, the species resulting from the partial hydrogenation of acetonitrile, can be questioned if one considers the work by Theule et al. (2011), who have characterized a similar process involving HCN in laboratory experiments. In that work, methanimine, possibly resulting from partial hydrogenation of HCN, was never observed. Theule et al. (2011) explained the failure to observe CH2NH by suggesting that hydrogenation of methanimine is so favorable that it leads all the way to the fully hydrogenated counterpart, that is, methylamine (CH3NH2), even on small exposure to H atoms. In the same vein, it appears improbable that hydrogenation of CH3CN stops at the formation of ethanimine, rather than proceeding efficiently all the way to ethylamine according to Incidentally, while methylamine has been observed in interstellar objects (see Sleiman et al., 2018, and references therein), to the best of our knowledge there has been no detection of ethylamine.
Another process occurring on ice has been considered by Quan et al. (2016), that is, the radicalradical recombination reaction Being a radical-radical recombination, the reaction has been included in the model by Quan et al. (2016) as a barrierless process. However, if one carefully considers the spin density of the H2CN radical (the unpaired electron is mostly localized on the N-atom), it appears quite obvious that the barrierless recombination process can only lead to the isomer H2C=N-CH3 (N-methyl methanimine), rather than to ethanimine (CH3-CH=NH). H2C=N-CH3 is a stable closed-shell molecule, with an enthalpy of formation of only 39 kJ/mol higher than that of ethanimine, which is the most stable C2H5N isomer. Therefore, only a severe rearrangement of the pre-existing chemical bonds can bring to ethanimine formation in reaction (R2) and this process requires surmounting a high energy barrier. For instance, according to the calculations by Balucani et al. (2010), the isomerization of the related radical species is characterized by a transition state located at +246.3 kJ/mol (see also below). And, as has been well illustrated by several works (Woon 2002; Rimola et al. 2014;Enrique-Romero et al., 2016, Rimola et al., 2018 the presence of ice molecules can only reduce a similar barrier height by a minimal part. In conclusion, if reaction (R2) is operative in interstellar ice, the final product will not be ethanimine, but its isomer N-methyl methanimine.
As already mentioned, both the E-and Z-isomers have been detected by Loomis et al. (2013).
The Z-isomer is less stable than the E-isomer by 4.60 kJ/mol according to the calculations by Quan et al. (2016). This value has been refined to 2.77 kJ/mol in higher level calculations by Melli et al. (2018). The isomerization barrier is instead very high (115.8 kJ/mol according to the high level calculations of Melli et al.) because it is necessary to break the double bond of C=N to move from the Z-to E-isomers and vice versa. In this situation, it is not clear how ice-assisted chemistry can actually reproduce the observed difference, as tunneling through the high isomerization barrier can only favor the more stable isomer independently from the original amount formed of the two isomeric species. Were the grains involved in the ethanimine formation, only the E-isomer should be observed because the thermal population at the temperature of interstellar ice (10 K) favors the E-isomer by 14 orders of magnitude.
Among the gas-phase reactions considered by Quan et al. (2016), the reaction NH+C2H5 is certainly the best candidate, because the analogous reaction NH+CH3 was seen to be the dominant formation route of methanimine in the model by Suzuki et al. (2016). In the absence of any information about the NH+C2H5 reaction, Quan et al. (2016)  In conclusion, a reliable estimate of the rate coefficient and product branching ratio for the title reaction is highly desirable. Given that an experimental determination is difficult to pursue because of the involvement of two radical species, we have applied a combination of electronic structure and kinetics calculations based on capture and statistical theories that are able to provide a realistic estimate, as already proved for reactions where experimental rate coefficients and/or product branching ratios are available (see, e.g., Sleiman et al., 2018;Leonori et al., 2009).

Computational Methodology for Electronic Structure and Kinetics Calculations
The whole reaction is assumed to take place exclusively in the lowest doublet electronic state of the [C2H6N] system. The global potential energy surface (PES) is a subset of the PES of the reaction N( 2 D)+C2H6 that we have already characterized to assist the interpretation of the crossed molecular beam experiments of Balucani et al. (2010). However, since the total available energy is lower by ca. 140 kJ/mol, the system explores only specific regions of the global PES. In addition, the discrimination between the two E-.Z-isomers was not considered in previous calculations because it was not relevant for the results of the crossed molecular beam experiments.
Subsequently, all stationary points (minima and saddle points) were subjected to energy refinement at the coupled cluster level, employing both single and double excitations and using a perturbative estimate of the effect of triple excitations (the CCSD(T) level, (Olsen et al., 1996;Raghavachari et al., 1989;Bartlett, 1981)). The correlation consistent aug-cc-pVTZ basis set has been used for both methods (Dunning, 1989). Saddle points (transition states) were located on the PES by making use of the synchronous transit-guided quasi-Newton method of Schlegel and coworkers (Peng et al., 1996;Peng and Schlegel, 1993). Vibrational frequencies were determined at the optimized geometries using the B3LYP/aug-cc-pVTZ method so that the nature of the stationary point was established (minimum if all frequencies are real and saddle point if exactly one frequency is imaginary). Transition states were connected with the corresponding reactant and product species through performing intrinsic reaction coordinate (IRC) calculations (Gonzalez and Schlegel, 1990;Gonzalez and Schlegel, 1989). The zero-point energy corrections, as calculated at the B3LYP/aug-cc-pVTZ level, were added to both B3LYP and CCSD(T) energies. The Gaussian 09 program suite (Frisch et al., 2009) was exclusively used for all calculations, while the vibrational frequencies were analyzed using Molekel (Portmann and Lüthi, 2000;Flükiger et al., 2000). Finally, some parts of the PES were computed also at the more accurate W1 level of theory (Martin & de Oliveira, 1999;Parthiban & Martin, 2001). We remind that in the W1 method the geometry optimization and the evaluation of the frequencies are performed at the B3LYP/VTZ + d level while the energies are computed at the CCSD(T)/AVDZ + 2d, CCSD(T)/AVTZ + 2d1f, CCSD/AVQZ + 2d1f level of theory (AVnZ is for aug-cc-pVnZ with n = D, T, Q). This method reproduced very nicely the experimental heat of formation of CH2NH and is expected to perform well for the system under study in this work (de Oliveira et al., 2001).
Subsequently, kinetics calculations were performed on the calculated PES, as previously done in Skouteris et al. (2018) and Skouteris et al. (2017) for similar reactive systems. Initially, the capture (Langevin) model is used to calculate the rate coefficient for the initial association of NH and CH3CH2. The long-range interaction potential (determined as a series of points through quantum calculations) was fitted to a V(r) = -C/r 6 equation (the typical interaction equation for two neutral species). Having obtained an association rate constant, we have calculated the corresponding dissociation rate coefficient through the detailed balance principle where kass(E) is the association rate coefficient (as a function of energy), ρreac(E) is the density of states per unit volume of the associating reactants at energy E and ρcomp(E) is the density of states of the initial complex at energy E. Through this scheme, we have seen that the dissociation rate coefficient is essentially negligible (the large depth of the potential energy well raises the density of states of the complex). From this, we can deduce that the initial association rate coefficient equals the sum of all rate coefficients leading to specific products, i.e. the total reaction rate constant.
The microcanonical reaction rate coefficient for each subsequent unimolecular step is calculated using the Rice-Ramsperger-Kassel-Marcus (RRKM) scheme, whereby the rate coefficient is given by the expression where N(E) is the sum of states of the transition state, ρ(E) is the reactant density of states at energy E and h is Planck's constant. All densities of states are calculated through the convolution of the classical rotational density of states (and translational, in the case of the reactant channel) with the vibrational density of states. The vibrational density of states is taken to be the one deriving from the harmonic oscillator model and thus the Bayer-Swinehart algorithm is used for the convolution.
The sum of states N(E) for each transition state is calculated through a convolution of the density of states and the energy-dependent tunneling probability (what would be a threshold function if tunneling were not included). Tunnelling is taken care of for each step by simulating each transition state with an Eckart barrier whose height is given by the relevant energy difference and its width calculated from the corresponding imaginary frequency.
Once all microcanonical rate coefficients have been calculated, a master equation is solved in order to determine rate coefficients for all product channels. After all microcanonical rate coefficients have been calculated, the master equation is solved for the particular energy in order to take account of the possibility of interconversion between intermediates. We set up a matrix k of the rate constants such that the off-diagonal element kij represents the rate constant from species j to species i and the diagonal elements are such that the sum of each column is 0. Moreover, we set up a concentration vector c such that the element cj corresponds to the concentration of channel j. Then, all kinetics expressions can be written as a vector differential equation This is a linear differential equation and thus can be solved using standard methods. In order to determine the behavior of c in the infinite future we diagonalise the matrix k and determine its eigenvectors. These eigenvectors will either correspond to eigenvalues with a negative real part (vanishing in the infinite future) or 0 (stable eigenvectors). The initial concentration vector is written as a linear combination of all eigenvectors and, subsequently, those with a negative eigenvalue are discarded. What remains is the concentration vector in the infinite future, yielding the branching ratios of all channels. Finally, Boltzmann averaging is carried out over a range of temperatures to determine canonical (temperature-dependent) rate constants.
Finally, a comment on electron spin statistics is in order. The two reactants CH3CH2 and NH are in a spin-doublet and a spin-triplet state respectively, which implies a total of six spin substates.
As a chemical bond must be formed between the reactants, the relevant two electrons (one from each species) to participate in the bond must be found in a singlet state. Among the six total spin states, two correspond to an overall doublet state and are reactive, while four correspond to an overall quartet state and are non-reactive. As a result, a statistical factor of 1/3 was applied to the total reaction rate constant in order to account for the non-reactive spin states of the reactants.

Electronic structure calculations of minima along the minimum energy path
According to the present electronic structure calculations, there are eleven open channels for the title reaction:  Table 2).

The E, Z-CH3CHNH formation pathways
Since the reaction scheme is quite congested, we will first describe only the portion of the PES including the pathways leading to the two isomers E, Z-CH3CHNH (see Figures 1 and 2) and to CH2NH.
The initial association adduct CH3CH2NH is formed by the interaction of NH in the electronic . We, therefore, expect that the channel (R4a) leading to methanimine + CH3 will prevail over the channels (R4c)/(R4d).

The CH3CHNH2 intermediate can also produce E-,Z-CH3CHNH by undergoing a N-H bond
fission. In addition, it can also form CH2CHNH2 + H in a slightly less exothermic channel (-185.7 kJ/mol, at the CCSD(T) level) or CHNH2 + CH3 and CH3CNH2 + H in significantly less exothermic channels (-82.7 kJ/mol and -58.9 kJ/mol, respectively, at the CCSD(T) level). Starting from this intermediate, therefore, formation of E-,Z-CH3CHNH + H would be by far the dominant reaction channels.
Finally, according to the present CCSD(T)/aug-cc-pVTZ level) calculations, the energy gap between E-,Z-CH3CHNH is 2.9 kJ/mol, a value which compares very well with that determined by Therefore, we can confirm that the significant deviation in the enthalpies of reactions is mostly due to the poor characterization of the NH reactant in the CCSD(T) calculations.

Rate coefficients and product branching ratio
The RRKM analysis of the complete PES calculated at the CCSD(T) level revealed that only 3 out of the 11 possible channels actually contribute to the global rate coefficients. The channels are, in order of decreasing importance, those leading to methanimine (R4a), E-ethanimine (R4c), and Zethanimine (R4d). The contribution of all other channels is negligible, either because those channels are characterized by the presence of much higher transition states or because too many rearrangements are necessary to reach the final configuration (this is, for instance, the case of the channel leading to C2H4 + NH2).
After having established than only channels (R4a), (R4b) and (R4c) have a significant yield when considering the entire PES, we have repeated the kinetics calculations using the W1 energies for the reduced PES. In Fig. 3 are shown the rate coefficients as a function of the temperature for the three dominant reaction channels. Since the entrance channel is barrierless, the global rate coefficient is very high at the gas kinetics limit; once partitioned according to the branching ratio, however, only the dominant channel remains in the 10 -10 range, while the rate coefficients of the two channels leading to the E-,Z-ethanimine isomers do not exceed the 10 -11 range. Moreover, it can be seen from Fig. 2 that, as expected from a capture-like rate coefficient, at low temperatures they rise steeply and afterwards they reach a plateau at higher temperatures. The rate constant has been fitted to a modified Arrhenius law k=α × (Tgas/300 K) β × exp[ − γ/Tgas] (E4) which essentially implies a linear variation of the activation energy with the temperature The best-fit resulting coefficients valid in the T range between 10 and 300 K are reported in Table 2, while the branching ratios at selected temperatures representative of interstellar objects are shown in Table 3. As visible, at all the temperatures considered the channel leading to methanimine + CH3 is by far the dominant one accounting for more than 85% of the global yield at all temperatures considered. Also, the branching ratio between the E-and Z-isomers of ethanimine are comparable, being ca. 1.1 in the entire analyzed range. Even though the E-isomer is slightly more abundant, the branching ratio is far from the factor of ca. 3 derived from the observation of Loomis et al. (2013).
The fact that the rate coefficients resulting from the W1 calculations (where the energies of the relevant intermediates and TS differ from the CCSD(T) ones typically by 3-5 kJ/mol) are essentially identical to the ones resulting from CCSD(T) confirms that the rate coefficients are reasonably robust with respect to quantum chemistry errors.

Discussion and astrophysical implications
A first comment we would like to make is that the NH + C2H5 reaction appears to be generally more difference between k(R4c) and k(R4d), as instead assumed by Quan et al. (2016). In addition, Quan et al. (2016) totally omitted in their model to consider the main channel (R4a) that will consume a large fraction of the reactants, thus reducing the total production rate of ethanimine.
A more general comment concerns the comparison between the E-,Z-isomers branching ratio that we have determined here and the relative abundance observed in Sgr B2(N). The NH+C2H5 reaction is certainly the best candidate to explain ethanimine formation in the gas phase. We can affirm this by considering the related work on methanimine formation by Suzuki et al. (2016). In their model, methanimine is formed in the gas-phase essentially via NH+CH3, because during the cold collapsing phase methanimine formed in the ice is completely hydrogenated to methylamine.
Also, in their model the saturated complex molecules like NH3, CH4, CH3OH, and CH3NH2 formed on the dust sublimate during the warm-up phase and then generate the precursor NH and CH3 radicals through gas-phase processes. Notably, methanimine does not have stereoisomers like ethanimine.
Therefore, provided that some ethane is also sublimated from dust together with methane and the other saturated compounds, the distribution of the two isomers of ethanimine can give additional general information on aldimine formation routes in interstellar objects, as it is a very sensitive test for astrochemical models. We have already commented on the fact that, were ethanimine formed on the ice in the cold phase, irrespectively from the detailed mechanism of formation, tunneling through the very high isomerization barrier would inevitably favor the most stable isomer E-CH3CHNH if only thermal sublimation is considered. The thermal population at possible ice temperatures provides a ratio [E-CH3CHNH]/[Z-CH3CHNH] of 6x10 14 at 10 K or 8x10 4 at 30 K.
However, were the gas-phase reaction NH+C2H5 the only formation mechanism of ethanimine, the [E-CH3CHNH]/[Z-CH3CHNH] ratio would be close to unity, namely approximately consistent with the one determined by Loomis et al. (2013). To be noted that, because of the very high isomerization barrier, once released in the gas-phase only chemical reactions could alter the E-/Z-ratio.
Unfortunately, Quan et al. (2016) did not explain how they quantified the amount of the two isomers produced in their model. In all cases, a possible conclusion is that, if no other, yet unexplored, formation routes of ethanimine are actually contributing, the observed ethanimine is mostly produced in the gas-phase (where the process is controlled by kinetics and provides almost identical populations of the two isomers), with a much smaller contribution from the grain-surface k=6.0×10 -11 (T/300) 0.17 cm 3 s -1 . Therefore, the main channel (R4a) is missing, k(R4b) is largely overestimated (according to our determination its value is in the 10 -14 cm 3 s -1 range for the temperatures of interest for the upper atmosphere of Titan) while the value of rate coefficient leading to both isomers of ethanimine is not far (within a factor 2) from the present determination.
In the light of the present work, the importance of the title reaction in the NH3 budget of Titan needs to be reconsidered.

Acknowledgments
This work has been supported by MIUR "PRIN 2015" funds, project "STARS in the CAOS (Simulation     For simplicity, only the CCSD(T) relative energies (kJ/mol) are reported. B3LYP values are reported in Table   1. Only the channel leading to the E-isomer of CH3CHNH is shown (see text).