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Home All issues Volume 672 (April 2023) A&A, 672 (2023) A49 Full HTML
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A&A
Volume 672, April 2023
Article Number A49
Number of page(s) 21
Section Atomic, molecular, and nuclear data
DOI https://doi.org/10.1051/0004-6361/202245811
Published online 29 March 2023

© The Authors 2023

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1 Introduction

Cyanamide (NH2CN) and its tautomer carbodiimide (NHCNH) are recognized as key molecules in prebiotic chemistry and chemical evolution, dating back to the first experiments addressing the problem of the origin of life (Steinman et al. 1964; Schimpl et al. 1965). Cyanamide is a versatile precursor thanks to the duality of its nucleophilic amino and electrophilic nitrile moiety. This capacity of cyanamide has long been known to produce abiotic urea (CH4 N2O) and guanidine (CH5N3; Fenton 1894; Kilpatrick 1947; Tordini et al. 2003). Cyanoacetylene (C3HN) is another important product formed in prebiotic model reactions involving electric discharges in nitrogen and methane (CH4) bearing atmospheres (Kaur et al. 2019). In combination with cyanamide or its derivatives urea and guanidine, these species are precursors of pyrimidines, including canonical cytosine (C4H5N3O) and uracil (C4H4N2O2; Orgel 2004) as well as relevant noncanonical nucleosides (Kaur & Sharma 2019). In the presence of ribose (C5H10O5), cyanamide forms aminooxazoline (C3H6N2O), which leads to ribocytidine (C18 H28N6 O16P2) and arabinocytidine (C9 H13 N3 O5) after reacting with cyanoacetylene (C3HN) through anhydro nucleosides (Sanchez & Orgel 1970). The reaction between ribose and cyanamide has been proposed to be a primordial separation system that has led to the selection of ribose derivatives for further chemical evolution (Shannahoff & Sanchez 1973; Robertson & Joyce 2010). The formation of oxazoline intermediates from cyanamide to nucleosides has also garnered great interest lately given that the reaction between cyanamide and glycolaldehyde (C2H4O2) yielding 2-aminooxazole (C3H4N2O) could bypass the necessity for free sugars to form nucleosides (Powner et al. 2009; Powner & Sutherland 2011). The combination between these two possible molecules formed in the interstellar medium (ISM) led to the search for the presence of 2-aminooxazole in molecular clouds (Sanchez & Orgel 1970; Tapiero & Nagyvary 1971; Jiménez-Serra et al. 2020). From a purines perspective, and according to Oró & Kimball (1961), cyanamides might be involved in the production of 4-aminoimidazole-5-carboxamidine by reacting with the condensed product of glycinamidine (C3H7N3O2) and formamidine (CH4N2). Cyanamide is a condensing agent that could play a role in prebiotic phosphorylation and peptide formation (Ferris & Hagan 1984; Schwartz 2006). In addition, cyanamides formed jointly with their dimer dicyandiamide (C2H4N4) are able to generate pyrophosphate (O7P2) from the orthophosphate (O4P), glucose-6-phosphate (C6H13O9P) via glucose (C6H12O6), and orthophosphoric acid (H3PO4; Schimpl et al. 1965) as well as adenosine-5’-phosphate (C10H12N5O7P) from adenosine (C10H13N5O4) and H3PO4 (Steinman et al. 1964). Figure 1 shows a schematic representation of the main processes described above.

Therefore, cyanamide and carbodiimide have commonly been accepted as key precursors of nitrogenous bases, and subsequently of nucleosides, assuming a relevant role in chemical evolution schema on primitive Earth. However, and despite all evidence, their terrestrial formation mechanisms are not entirely clear, remaining an open topic of debate.

In the 1970s, the discussion of such chemical evolution turned into astrobiology after the detection of hetero-cyclic compounds (Folsome et al. 1971), purines and triazines (Hayatsu et al. 1975), purines and pyrimidines (van der Velden & Schwartz 1977), and, more recently, extraterrestrial nucleobases (Martins et al. 2008) in the Murchison meteorite. Even so, the detection of significant blocks of chemicals needed for life from outside Earth is not exclusive to this controversial meteorite. A decade later, nitrogen-hetero-cyclic compounds such as adenine (C5H5N5), guanine (C5H5N5O), xanthine (C5H4N4O2), and hypoxanthine (C5H4N4O) were identified in remains belonging to the Murray and Orgueil meteorites (Stoks & Schwartz 1981), and in 2011 the pyrimidine adenine was reported to be present in 11 out of 12 different carbonaceous chondrites (Callahan et al. 2011). In cometary media, adenine and guanine were also observed to be present in comet Halley (Kissel & Krueger 1987) as well as the simplest amino acid, glycine (NH2CH2COOH), in samples from the comet 81P/Wild 2 (Elsila et al. 2009). All of these detections suggest the chemistry in the Solar System, and by extension in the ISM, is rich and capable of producing such molecular complexes that can be transported and delivered across similar planetary systems throughout the galaxy. Nevertheless, so far, neither purines nor pyrimidines have been detected in the ISM, despite the successful observation of some molecular substitutes and potential synthetic precursors, such as interstellar cyanamide and carbodiimide.

Interstellar cyanamide (NH2CN) was detected for the first time by Turner et al. (1975) in the microwave region of the electromagnetic spectrum close to the center of the Milky Way (within ~100pc) in a region known as Sagittarius B2 (hereafter Sgr B2). In 1986, Cummins et al. confirmed its presence in Sgr B2 but this time at the millimeter spectrum bands. Nummelin et al. (1998, 2000), further refined the detection of NH2CN in Sgr B2, specifying the emitting regions inside the molecular cloud (M for “Middle” and N for “North”), which was confirmed by Belloche et al. (2014). In 2003, the presence of NH2CN in the central area of the Orion molecular complex (Orion KL) was reported by White et al. (2003), expanding the known presence of this molecule in our galaxy. Closer to Earth, the detection of NH2CN in comets (Crovisier et al. 2004) might well justify the presence of cyanamide on primitive Earth, as this may be linked to the late heavy bombardment period (LHB; e.g., Gomes et al. 2005). Furthermore, the presence of cyanamide is not exclusive to our galaxy; in 2006, it was detected in the nuclear region of a Seyfert-type galaxy cataloged as NGC253 (Martin et al. 2006) and more recently in 2015 in a Seyfert-type 2 galaxy (Costagliola et al. 2015). Despite these findings, the origin of cyanamide itself in the galactic or extra-galactic ISM is not well understood (Duvernay et al. 2005). The latest detection was reported by Coutens et al. (2018) within the envelopes of two low-mass protostars, classified as IRAS16293-2422 and NGC1333-IRAS2, signifying that the scientific interest in cyanamide continues. While cyanamide has been detected inside and outside the Milky Way, the spatial detection of its ephemeral tautomer carbodiimide (HNCNH) waited decades. Finally, in 2012 McGuire et al. were able to determine its presence in the molecular cloud Sgr B2(N). Although undetectable with rotational spectroscopy, these latter authors were able to detect the emission features of HNCNH in amplified maser transitions at centimeter wavelengths. These emission lines show energy levels of around 170 K, suggesting that this molecule likely resides in relatively hot gas typical of denser regions.

The most massive star-forming region of our galaxy is known to be in the vicinity of the center of the Milky Way at a distance (R0) from the Earth of ~8 kpc (Reid et al. 2009, 2014; Abuter et al. 2018). Sgr B2 is a giant molecular complex of ~45 pc in diameter and is composed of a mass of 7 × 106 M⊙ (Lis & Goldsmith 1990; Schmiedeke et al. 2016) constituted from different cores that are chemically diverse and have different structures. The gas temperature in the cloud is reasonably constant, at ~20 K (Scoville & Solomon 1975), with an average pressure of Pgas = 6 × 10−3 mbar (5.92 × 10−6 atm; Ordu et al. 2012) governed by conditions very close to local thermodynamic equilibrium (LTE; Scoville & Solomon 1975). The dominant form of the hydrogen therein is molecular, with an average density n(H2) of ~103 cm−3, two orders of magnitude lower than the central region. Due to its proximity to the Galactic center (~107 pc; Reid et al. 2009), this molecular cloud is subjected to the gravitational action of the super-massive black hole cataloged as Sgr A*. Sgr B2(N) is located to the galactic north of the cloud where NH2CN and HNCNH have been detected, and is composed of a filamentous structure with an estimated mass of 3–10 × 104 M⊙, a particle density of 105 cm−3 (Lis & Goldsmith 1990), and an average H2 column density of ~1025 cm−2 s−1 (Nummelin et al. 2000). A column density of 2–6 × 1016 cm−2 is predicted for cyanamide, assuming a Tгot = 150 K. However, for a Tгot = 20 K, the column density drops to ~2.5 × 1013 cm−2 as determined by Belloche et al. (2014) and Neill et al. (2014).

The unique carbodiimide detection in space was in this region and reveals a column density of 2.0 × 1013 cm−2 at Trot =170 K (McGuire et al. 2012). Inside the cloud, four differentiated hot cores were recently detected, identified as N2, N3, N4, and N5, with estimated luminosities of 2.6 × 105 L⊙, 4.5 × 104 L⊙, 3.9 × 105 L⊙, and 3.9 × 105 L⊙, respectively, and high variability in the abundances of detected interstellar complex organic molecules (iCOMs; Bonfand et al. 2019). Multiple molecular species have been detected in Sgr B2(N) in addition to cyanamide and carbodiimide. Among them, probably the most relevant because of its relationship with the presence of cyanamide and carbodiimide and the related astrobiological implications is interstellar urea (CH4N2O; Belloche et al. 2014). This detection shows a column density of 2.3 × 1015 cm−2 with a Trot = 180 K for urea in Sgr B2(N). This makes it one order of magnitude less abundant than cyanamide and two orders of magnitude more than carbodiimide for a temperature environment of between 150 and 170 K. The chemistry of this region is obviously rich, and reactions involving the above species are likely influenced by the presence of other known molecules in this rich environment, including cyanic acid (HOCN; Brünken et al. 2010), methylene-amidogen (H2CN; Ohishi et al. 1994), hydrogen isocyanide (HNC; Neill et al. 2014), cyano radical (·CN; Neill et al. 2014), methylene (CH2; Polehampton et al. 2005), hydrogen cyanide (HCN; Neill et al. 2014), amino radical (3NH; Neill et al. 2014), imidogen (NH; Neill et al. 2014), fulminic acid (HCNO; Brünken et al. 2010), formaldehyde (H2CO; Nummelin et al. 2000), nitrous oxide (N2O; Nummelin et al. 2000), methylamine (CH3NH2; Halfen et al. 2013), nitric oxide (·NO; Nummelin et al. 2000), molecular nitrogen (N2; Knauth et al. 2004), ammonia (NH3; Huettemeister et al. 1993), methanimine (H2CNH; Halfen et al. 2013), and formamide (NH2CHO; Neill et al. 2014; Nummelin et al. 2000). These may have an influence on the chemistry of carbodiimide and cyanamide, but this has yet to be determined, which is the major motivation behind the present work.

thumbnail Fig. 1

Contextualization of the prebiotic roles of cyanamide and carbodiimide. Panel A: processes in the ISM, including the formation of cyanamide and carbodiimide explored in this work. Panel B: fate of cyanamide in planetary conditions. Cyanamide directly formed in planetary atmospheres, or in the ISM and delivered to a planet after accretion, could lead to a rich diversity of organic compounds or intervene as condensing agents in the formation of organophosphates. Panel C: processes that may take place in both the ISM and in planetary environments.

2 Known reaction mechanisms

Radiative and thermal isomerization (tautomerization) of carbodiimide (HNCNH) into cyanamide (NH2CN) ((a → b); Duvernay et al. 2005) is a well-known exothermic and exergonic reaction, with cyanamide being ~4.0 kcal mol−1 for a temperature range close to room conditions (273-383 K; Birk et al. 1989; Jabs et al. 1999; Tordini et al. 2003; Duvernay et al. 2004). Therefore, in principle, this reaction might be cataloged as a viable channel to synthesize cyanamide in the gas phase in the cold conditions of space. However, this reaction requires an energy of at least ~80 kcal mol−1 if tunneling and catalysis are not considered (Tordini et al. 2003; Duvernay et al. 2004). This aspect suggests that its kinetics are not the most favorable, even at room conditions. On the other hand, it has been experimentally demonstrated that in the presence of water (hydrolysis), the energy barrier is drastically reduced (Tordini et al. 2003), and its thermodynamic values can even be reversed. Thus, the reaction becomes exothermic and exergonic in the direction (b → a) due to the catalytic effect of water. However, this process where three or more molecules interact at the same time in cold space is very unlikely to occur in the gas phase, and consequently, the reverse process (b→ a) should be considered as nonviable in cold, gas-phase reactions. Even so, Duvernay et al. (2005) demonstrated in the laboratory that cyanamide trapped on water-ice dust grains can tautomerize, forming carbodiimide at temperatures of ~70 K. HNCNH desorbs from grain mantles in the range of 70–170 K, yielding ~10% with respect to H2CN abundance (Duvernay et al. 2004). This agrees with the abundances and temperature (170 K) found by McGuire et al. (2012) for carbodiimide. Regardless, given the low dust-gas density typical of cold molecular clouds (1–100 ratio; Hildebrand 1983), low temperatures, and the energy from molecular shocks as the only source of energy for desorption, this process cannot be considered as the only one responsible for carbodiimide production in Sgr B2(N).

Some of the most-cited databases, including KIDA (Wakelam et al. 2012), UMIST (McElroy et al. 2013), and NIST (Linstrom 1997), contain possible gas-phase formation pathways with NH2CN as a product, but none for carbodiimide. The reaction between the cyano radical and ammonia (·CN + NH3 → NH2CN +·H) was studied computationally by Talbi & Smith (2009). These authors conclude that there is no low-energy pathway to produce cyanamide and hydrogen with the reaction flowing to HCN+·NH2 as end products. Thus, the production of cyanamide by this route seems to be entirely negligible, a hypothesis that was confirmed experimentally by Blitz et al. (2009) the same year. The formation of cyanamide through the decomposition of 5-aminotetrazole (CH3N5) → NH2CN+HN3 was also reported (Zhang et al. 2008; Paul et al. 2009; Kiselev & Gritsan 2009), but unfortunately the existence of this compound or any of its isomers has not yet been reported in astrophysical environments. Electronic recombination of protonated cyanamide (NH2CNH+ + e− → NH2CN +·H) was proposed to produce neutral cyanamide (Wakelam et al. 2012). However, the only way to form this product is through preceding protonation, which is not a robustly useful result. Fulminic acid and the amino radical reaction (·NH2 +HCNO → NH2CN +·OH) were analyzed by Nguyen et al. (2018) for a temperature range of 700 to 2000 K at 1 atm. This reaction under the produced temperature and pressure (P&T) profiles is normally applicable in combustion studies. The results show low yields of cyanamide under the mentioned conditions with only a 5% contribution to the total measured yield. These conditions do not improve when P&T profiles decrease to astrophysical levels. Sleiman et al. (2018) proposed the reaction CH3NH2 +·CN → NH2CN +·CH3 as a probable route to cyanamide in cold space (23–297 K). The final products of this reaction have yielded a branching ratio of 0.88 in favor of cyanamide, and this was confirmed experimentally and computationally. Undoubtedly, because of the detection of methylamine (CH3NH2) in two molecular clouds (Sgr B2(N) and Ori A; Kaifu et al. 1974; Neill et al. 2014) and the known ubiquity of the cyano radical (·CN), this reaction, in principle, is one the most propitious to consider for the synthesis of NH2CN under cold astrophysical conditions.

With regards to carbodiimide, Shakhova et al. (2018) proposed the formation of cyanamide via thermal decomposition of 1,5-diaminotetrazole (CH4N6) and its tautomer (2,5). It should be noted that although these previous authors mention cyanamide as a product, they refers to its tautomer carbodiimide (Fig. 4 therein; P6 + HN3 route). Unfortunately, as diaminotetrazole or any of its variants have not yet been detected in astronomical environments of any sort, its inclusion will not be considered in this work, either. Yadav et al. (2019) computationally studied two possible reactions to synthesize carbodiimide in the ISM: (a) HNC + NH → HNCNH and (b) NH+ + CN− → HNCN; HNCN + H → HNCNH. These two routes will be taken into consideration in the present study. The recent detection of the cyanoamidogen radical (·HNCN; Rivilla et al. 2021) and aminomethylidyne (·H2NC; Cabezas et al. 2021) in the ISM opens up possibilities for the formation of cyanamide and carbodiimide through these two pathways as well, avenues that are explored and duly considered below.

After examining the available information, it was found that there is no definitive explanation for how cyanamides form. This is especially true for mechanisms that require reagents with densities greater than what is observed for H2CNN and HNCNH in the gas phase. Identification of the possible formation mechanisms would clearly allow us to determine and understand how they are formed under Sgr B2(N) astrophysical conditions. Therefore, the main objective of this work is to determine the relative abundances of species that can act as reagents in Sgr B2(N) (detected or not) and to propose molecular reaction mechanisms based on these that can justify the detected abundances of both cyanamides in this astrophysical medium. In addition, we estimate the rate coefficients of the most favored reactions in order to propose the most favored ones kinetically. State-of-the-art computational methods are employed for this purpose, as explained in the following section.

3 Method and computational details

As stated above, the first condition to determine how cyanamide and carbodiimide can be formed is to conduct an assessment of the detected species in outer space that could synthesize cyanamide and carbodiimide in the ISM. Once these species have been identified, (1) we proceed to propose the base reactions that in principle may form the above products. In order to determine which of these could proceed under the astro-physical conditions of Sgr B2(N), (2) a thorough and detailed thermodynamic study of reagents and products is required. Once these reactions are known, as well as their exothermicity and exergonicity, the next condition is to (3) differentiate the reactions that have reactants detected in Sgr B2(N) from those that have not been detected in this region yet. Of the resulting reaction mechanisms (4), those that have at least one reactant with an unambiguous detected lower density than cyanamide and carbodiimide in Sgr B2(N) can be eliminated from further consideration. Thus, all the obtained mechanisms have favorable thermodynamics in Sgr B2(N) and are split into two groups: (A) those composed of reactants with a detected density higher than the products in Sgr B2(N) (5), and (B) those with species not yet found in Sgr B2(N), but in the ISM (6). This is a generous consideration, where we allow for the possibility that the main compounds responsible of forming cyanamides in Sgr B2(N) have not yet been detected in the aforementioned medium. This way, type A and B reaction mechanisms are subjected to a molecular dynamics study (7) that combines quantum and molecular mechanics with quantum statistical thermodynamics. This enables us to identify all of the possible routes on the potential energy surface (PES) that lead from the starting materials to the final products. Once these reactions have been determined, a kinetic study (8) is carried out on those that present a submerged energy in all their elementary pathways with respect to the asymptotic energy of their respective reactants, or nearby profiles to them.

3.1 Electronic structure calculations

Molecular energies of reagents and products are computationally calculated at two different levels of theory. We use explicitly correlated coupled-cluster theory at the singles and doubles level with perturbative triple corrections, CCSD(T)-F12b (Adler et al. 2007; Knizia et al. 2009), and second-order Møller–Plesset perturbation theory (MP2; Möller & Plesset 1934; Pople et al. 2009). The basis set for CCSD(T)-F12b is the correlation-consistent triple-zeta basis set (cc-pVTZ-F12; Dunning Jr. 1989; Peterson et al. 2008; Hill & Peterson 2010), while for MP2 calculations, the augmented double-zeta basis set (aug-cc-pVDZ; Dunning Jr. 1989; Kendall et al. 1992) is selected. The combination of both levels of theory with the selected basis sets provides an excellent description of the form of the wave function (Ramal-Olmedo et al. 2021) for the atoms of the molecular species detected in Sgr B2(N) and their molecular correlation effects. Furthermore, this union represents an outstanding compromise between accuracy and computational cost (Kaminsky et al. 2008; Knizia et al. 2009). Version 2020.01 of the Molpro quantum chemistry package (Werner et al. 2020) is employed for the CCSD(T)-F12/cc-pVTZ-F12 calculations, while Revision B.01 of Gaussian 16 (Frisch et al. 2016) is used for MP2/aug-cc-pVDZ. Restricted references are used for closed-shell species, while restricted open-shell reference states are employed for nonspin-paired molecules. With respect to the calculations of the thermodynamic function values and their corresponding partition functions, Maxwell-Boltzmann statistical mechanics theory (Muncaster 1979; Rowlinson 2005, and ref. therein) has been applied, considering the initially proposed P&T profiles. Unless otherwise mentioned, all energies presented in the results section of this paper have been corrected for their corresponding harmonic zero-point vibrational energy (ZPVE). These preliminary quantum chemical calculations present adequate values of exothermicity and exergonicity at the mentioned P&T profiles for the initially proposed reactions. However, depending on the results obtained, it is possible to determine whether formation routes with a low entrance barrier are included or not.Once identified the reactions from the initial proposals that have the potential to produce cyanamide and carbodiimide, the possible chemical compounds that compose such reactions containing molecules detected in Sgr B2(N) are reviewed in addition to their respective abundances with respect to H2 (n(X) = N(x)/N(H2)) published in the literature. We therefore present a computational analysis of these reactions, and determine the favorability of the molecular PESs. To this end, with the previously optimized reactants at the CCSD(T)-F12/cc-pVTZ-F12 level of theory, the program Automekin-2021 (Martínez-Núñez 2015a,b; Stewart 2016; Martínez-Núñez et al. 2021) is used with the aim of finding possible structures and molecular routes. Before going to high-level calculations, the identified transition states (TSs) and intermediates are optimized with density functional theory, utilizing the hybrid GGA B3LYP (Becke 1988; Lee et al. 1988) with the aug-cc-pVTZ (Dunning Jr. 1989) basis set in Gaussian 16 (Frisch et al. 2016). A TS from the semi-empirical quantum mechanics (SQM) level must be confirmed as a real stationary point (first-order saddle point) by the Berny algorithm (Schlegel 1982) via the DFT functional mentioned, B3LYP, in combination with the aug-cc-pVTZ (Dunning Jr. 1989; Kendall et al. 1992) basis set. If the geometry found shows insurmountable hurdles in convergence, we use the synchronous transit-guided quasi-Newton method (Peng & Schlegel 1993, STQN;) among two confirmed and optimized minimum structures by CCSD(T)-F12/cc-pVTZ-F12. All definitive TS structures presented in this paper are confirmed by intrinsic reaction coordinate (IRC) analysis (Fukui 1981; Hratchian & Schlegel 2005) in order to assure that all existing saddle points are stationary and really connect reagents to minima, minima to minima, and/or minima to products.

3.2 Kinetic calculations

As suggested in Sect. 3.1, the reactions that are most likely to occur and are therefore selected for kinetic analysis are those that (i) have no initial energy barrier, and (ii) have all their stationary structures located at lower energy levels than the asymptotic energy of the reactants. Reactions with energetically submerged intermediates but with TSs close to the equilibrium could also be considered. Therefore, we are faced with barrierless reactions that directly form an initial adduct or intermediate stationary structure. In this way, the reaction can continue toward the products through one or several potential wells. In this regard, it should be noted that direct (radiative) gas-phase reactions are likely faster than initially would be expected under cold space conditions (e.g., Barker 1992; Smith 1995; Fukuzawa et al. 1998; Smith et al. 2004). The approach used to determine the bimolecular rate constant is tailored to the characteristics of the reaction profiles that will be encountered. The rate coefficients for barrierless entrance channels have been obtained by performing a series of calculations across the reaction coordinates. After defining the entrance channel, the cascade has been subjected to the canonical variational transition state theory (VTST) evaluated via interpolation. The bimolecular rate constants for reactions with a TS in the reaction entrance are calculated using TST theory (Laidler & King 1983; Truhlar et al. 1996) with an Eckart one-dimensional tunneling correction (Eckart 1930). Both VTST and TST are calculated with revision 2022.01.20m1 of the Gpop software (Miyoshi 2010a). Branching rates (fractions) from unimolecular decomposition, recombination, or complex-forming reactions with one or multiple wells and multiple channels are considered once the steady-state master-equation is solved. The Rice-Ramsperger-Kassel-Marcus (RRKM) theory (Marcus 1952) is used for this purpose, and is implemented in revision 2018.06.14m5 of the Ssumes software (Miyoshi 2010b). The selected buffer gas for the RRKM simulations is N2. We note that the resultant rate coefficients obtained in initial calculations at the two indicated pressures (5.92 × 10−6 and 5.92 × 10−4 atm) did not return any difference. This means that the reactions under study do not show a complex pressure dependence, and consequently the Chebyshev polynomial (Venkatesh et al. 1997; Venkatesh 1999) or equivalent fits are not required for the purpose of this work. Therefore, the presented results are obtained at 5.92 × 10−4 atm (0.45 mmHg) for a temperature range of 20–300 K in intervals of 10 K. The method used in the kinetic calculations, in terms of electronic energy + ZPE is CCSD(T)-F12/cc-pVTZ-F12//B3LYP/aug-cc-pVTZ. Finally, the LennardJones parameters for RRKM calculation pair species, such as the collision diameter (σ − Å) and the potential depth (ε/kB − K), are calculated by arithmetic mean [αpaiг = (αmolec + αbuffer)−2] for the first, and by geometrical mean [εpair = (εmolec × εbuffer)1/2] for the second.

4 Results and discussions

4.1 Initial reaction mechanisms

After a detailed literature review, Table 1 shows the initially considered reaction mechanisms that could potentially lead to synthesis of cyanamide (NH2CN) and carbodiimide (HNCNH). The reactants involved are formed by chemical species that have been unambiguously detected in astrophysical environments. Although the ammonia cation has not yet been detected in such environments, we include it because of the spatial ubiquity of ammonia (NH3) in Sgr B2(N) (Neill et al. 2014), which may be formed in hotter (HII) regions.

Furthermore, neutral reagents are assumed to be in their electronic ground states, as are the two ionized species (N2H+, and HCNH+) included in this investigation and present in Sgr B2(N). Now that we have identified the individual reactants, we compute their molecular energies and respective thermodynamic functions. The temperature and pressure profiles associated with the environments in Sgr B2(N) where NH2CN and HNCNH are observed have been identified in this procedure. Consequently, 20 K and 5.92 × 10−6 atm, and 170 K and 5.92 × 10−4 atm are applied in the respective calculations. The molecular species identified serve as a basis for the determination of those reactions that in principle may synthesize cyanamide and carbodiimide in the gas phase. The 120 initial reactions presented in Table 1 are then used to produce the thermodynamic function values, enthalpy (∆H°), entropy (∆S°), and Gibbs free energy (∆G°), which are shown in Table 2 for cyanamide, and in Table 3 for carbodiimide. From the obtained thermodynamic function values for the reactions initially proposed in the two regions of Sgr B2(N), the ones that proceed thermodynamically to synthesize the targeted products are readily identifiable. The number determined to be endothermic and exergonic for NH2CN is reduced to 28, while for HNCNH, this drops to 24. At this point, of the 14 initially proposed reactions based on the cyanomidyl radical (HNCN), the only reactions that show favorable initial thermodynamics are those involving atomic hydrogen (·H), imidogen (3NH) and amino-radical (·NH2). Neutral compounds, such as ammonia (NH3) and water (H2O), along with radicals, such as the methyl-radical (·CH3) and more complex compounds, as in iso/cyanic acids (HOCN, and HNCO), fulminic acid (HCNO), and even·HNCN, are relegated to scenarios based on different chemistry. This same selective effect also occurs with compounds such as formamide (NH2CHO), which initially reacts favorably with three out of the proposed 12 chemical species: atomic nitrogen (·N(2D)), imidogen (3NH), and the cyano radical (·CN). The complete reaction details are given in Table 2 and Table 3 as mentioned above. Therefore, as this selective process determines the reactions that are favorable at both proposed P&T profiles, which of the reagents are present in Sgr B2(N) remains to be determined, as does their relative density compared to products. Thus, the total number of molecular species to be considered that is, those which originate from the viable reactions shown in Tables 2 and 3 is 25 (excluding cyanamide itself, carbodiimide, and urea, which is mentioned only for reference). As a result, and after a detailed literature review on the radio detection of molecules in Sgr B2(N), 19 of them could initially act as reagents given that they are undoubtedly present in the cited cloud. As the abundances of the detected species are sensitive to the kinetic temperature of the gas and in this study reactions are assumed to be under cold LTE conditions, the rotational levels of these molecules may be excited primarily by collisions. Hence, we utilize the Trot of the aforementioned species as a reference to contrast the detected abundances in the corresponding region. Figure 2 presents the density number (cm−3) of the reactants detected in Sgr B2(N) at their respective rotational temperatures (Tгot) in K. In this figure, only methylene-amidogen (·H2CN) has a lower density than cyanamide at very low temperature (<50 K). This will generate a limiting effect on the possible reactions that may occur based on this molecule, and therefore·H2CN cannot be considered as the main precursor in the production of NH2CN in this environment and in this temperature range. Additionally, the case of carbodiimide is clearly different, because the densities of all the reagents detected at temperatures above 100 K exceed the detected density of carbodiimide itself. Table 4 lists the previously defined species ordered from lower to higher molecular mass (amu) along with the electronic state, the electronic total energy (Etot), the detection status in Sgr B2(N), the rotational temperature in K (Ttot) when available, the density number (n in cm−3), and the respective publication(s). Closer examination of the sixth column shows that five compounds, namely methylene (3CH2), aminomethylidyne (·H2NC), cyanomidylradical (·HNCN), fulminic acid (HCNO), and isocyanogen (CNCN), as well as·, have not been detected in Sgr B2(N) so far, even though they have been observed elsewhere in the ISM (except for the ammoniumyl). Based on the consideration of this latter information, we can propose a large group of reactions that could, in principle, be responsible for the synthesis of NH2CN and HNCNH under the described astrophysical conditions of Sgr B2(N).

Table 1

Initial set of reactions proposed in this research.

Table 2

Thermodynamic function values for reactions to synthesize NH2CN at Tgas = 20 K and Pgas = 5.92 × 10−6 atm.

Table 3

Thermodynamic function values for reactions to synthesize HNCNH at Tgas = 170 K and Pgas = 5.92 × 10−4 atm.

4.2 Cyanamide (NH2CN)

4.2.1 Class A reactions

Table 5 presents the 14 favored “Class A” molecular formation mechanisms for cyanamide. All of the reactions that compose this group proceed to form cyanamides, with the exception of Ra22. For the reaction between methylene-amidogen (·H2CN) and nitrous oxide (1N2O), no entrance channel could be computationally determined, and so this reaction is not considered any further.

The proceeding reactions flow as follows:

Ra1 (HNCNH → NH2 CN) and Ra5 (·CN +·NH2 → NH2 CN). Ra1 is an isomerization (tautomerization) reaction of carbodiimide that, in principle, might produce the more stable cyanamide tautomer (−2.65 kcal mol−1, relative to starting materials at 20 K). When there is enough energy, one of the hydrogens (·H) is transferred between both nitrogen atoms through the central carbon. In order for the reaction to proceed, a free energy of at least 76.58 kcal mol−1 is required, as represented in pathway Ra1 of Fig. 3A. The computations imply that this barrier remains almost constant from 20 K up to 170 K (76.51 kcal mol−1), suggesting that this reaction is not going to proceed at LTE conditions in cold regions. Ra5 presents the reaction between the two radicals (·CN+·NH2); see Fig. 3A. The routes will mostly depend on the orientations and kinetic energy of the two species. The first pathway (Ra5-1) is a result of the hydrogen abstraction of the amino radical (·NH2) in favor of the nitrogen atom of the cyano radical (·CN), forming HNC and 3NH. The transition state (ts2), although with a moderated barrier (+7.74 kcal mol−1), excludes Ra5-1 from being the favored channel in this reaction. Ra5-2 and Ra5-3 take place when the cyanide and the amine group approach one another. Albeit energetically possible, if atom (N) of the ·CN radical reaches the nitrogen (N) of the·NH2, the formation of isocyanamide (NH2NC) would take place at a very low rate, and so we do not consider this reaction any further. However, the computations insistently returned an entrance channel between the carbon atom (C) of the ·CN radical and the nitrogen (N) of the ·NH2, from distances (R) of ~8 Å. As mentioned, Ra5(2-3) is initiated between the NC–NH2 nitrogen without barriers, following two possible formation routes. Ra5-2 goes through triplet PES to initially bond with an angle of 110.51° at a distance of RC−N = 1.65 Å, forming triplet cyanamide as an intermediate.3NH2CN is submerged by ~26.88 kcal mol−1 with respect to the energy of the reagents. The reaction continues through a unimolecular recombination process, passing a tiny internal transition state of only ~1 kcal mol−1. During this process, a spin-flip transition from triplet cyanamide to a more stable singlet cyanamide is produced. The direct formation of singlet cyanamide is also possible via singlet PES (Ra5-3), which is submerged −114.34 kcal mol−1 at 20 K with respect to the asymptotic free energy of the reagents. In this case, the intersystem triplet-to-singlet crossover (ISC) does not occur, as the reaction only takes place through singlet PES. The pathways belonging to the four reactions (R1, R5-1, Ra5-2, and Ra5-3) are represented in Fig. 3A.

Ra6 (·CN+NH3 → NH2CN+ ·H). The reaction between the cyano radical (·CN) and ammonia (NH3) modeled here agrees well with the findings of Talbi & Smith (2009). However, the PES profiles for Tgas = 20 K and Pgas = 5.92 × 10−6 differ from the chemistry at room conditions. As shown in Fig. 2B, four different routes (Ra6-1, Ra6-2, Ra6-3, and Ra6-4) are presented to produce NH2CN + ·H from the combination of ·CN and NH3. Routes Ra6(1-2-3) are initiated through a preassociation complex (min1), which constitutes a more energetic stationary point by −8.88 kcal mol−1 with respect to the energy of the reagents on the PES. In contrast, Ra6-4 flows through the stationary point, min4, which is energetically 5.38 kcal mol−1 above the energy of the free reactants. This higher energy rules it out as a viable route to produce NH2CN at 20 K. The entrance channel for min1 initiates when the carbon (C) of the ·CN radical approaches the nitrogen (N) of the ammonia (NH3) at a distance of 2.04 Å, conforming an N−C−N(H3) angle of 128.33°. The reaction could flow through two possible transitions states (ts4 and ts1). In the Ra6-1 pathway involving ts4, cyanamide can be formed via this transition state when one of the three hydrogens begins detaching from the ammonia. For this process to continue, a barrier of 13.24 kcal mol−1 over the reactants’ energy must be surpassed, limiting the cyanamide production. However, as established by Talbi & Smith (2009), the reaction may take a different channel if ·CN turns slightly and abstracts a hydrogen atom from NH3 to form hydrogen cyanide (HCN) and the amino radical (·NH2) as main products. The required energy for this step is lower than in the previous path (only +7.46 kcal mol−1 from the (min1) preassociation complex) forming an inner ts2, which is submerged at −1.42 kcal mol−1 (see Ra6 (2-3) in Fig. 2) below the energy of the reactants. Although the successive routes described can be reinitiated from these products from a kinetic point of view, as can be seen in Fig. 2C, both pathways are endothermic Ra6(2-3), indicating that they will not flow kinetically under the cold conditions of Sgr B2(N).

Ra7 (1HNC+3NH → NH2CN), Ra8 (1HNC + NH2 → NH2CN +·H), & Ra9 (1 HNC + NH3 → NH2CN + H2). The combination of hydrogen isocyanide (HNC) in its singlet ground state with three hydrogenated nitrogen compounds, such as imidogen (3NH; Ra7), amino-radical (·NH2; Ra8), and ammonia (NH3; Ra9), represent three possible routes studied for the production of NH2CN as depicted in Fig. 2C. The entrance channels in Ra7 and Ra8 are initially formed through two transition states (ts1 and ts3). In both cases, the nitrogen of the HNC, the carbon of the imidogen, and amine are the key atomic reactants. This is not the case for Ra9, where the entrance is direct and without barriers to form a prereactive complex (min3). Ra7 falls into a potential well to form min1 (−18.40 kcal mol−1) through the triplet channel. However, 44.87 kcal mol−1 is needed to break through the barrier separating it from cyanamide, of which 26.47 kcal mol−1 are above the initial energy of the reactants. This excludes Ra7 as a candidate. Meanwhile, Rb8, with a low initial barrier (ts3; 4.77 kcal mol−1), can form a hydrogenated doublet cyanamide (min2; −23.73 kcal mol−1), which to produce cyanamide +·H only needs to surpass a small barrier of only 2.50 kcal mol−1. Ra8 will be considered for a deeper kinetic study. Finally, Ra9 has to face two consecutive barriers: a first of 48.64 kcal mol−1 to reach min4, and a second of 70.07 kcal mol−1 from min4 (through ts6) to get the products. This energy constraint automatically excludes Ra9 as a reaction worthy of further investigation.

Ra10 (HCN + 3NH→ NH2CN). Figure 4A presents the possible reaction between hydrogen cyanide (HCN) and imidogen (3NH) at 20 K. After the formation of an initial prereactive complex, the input channel (min1) is established through the formation of a transition state (ts1) in the triplet electronic state, which requires an energy of 10.42 kcal mol−1 to be overcome, with a split crossing that produces two possible routes (confirmed by IRC analysis). Both minima generated (triplet min2 and singlet min3) are submerged −15.19 kcal mol−1 and −19.01 kcal mol−1 with respect to the reactants. The two next transition states for Ra10-1 and Ra10-3 have a barrier of ~40 kcal mol−1 above that of the reactants, removing them from the possible reactions at 20 K. The Ra10-2 route, although more moderate in terms of energy requirements (21.63 kcal mol−1), is discarded as well. Therefore, to conclude this association, the reaction between hydrogen cyanide (HCN) and imidogen (3NH) at 20 K is not going to produce significant amounts of cyanamide in the gas phase under LTE conditions.

Ra26 (HOCN+NH3 → NH2 CN+H2O), Ra52 (NH2 CHO + ·CN→ NH2CN+·HCO), & Ra60 (CH3NH2 +·CN→NH2CN + ·CH3). Of these three proposed reactions, the first two are composed of cyanic acid (HOCN) + ammonia (NH3) and formamide (NH2CHO) + cyano radical (·CN), respectively; the reaction paths are illustrated in Fig. 4B. While Ra26 is initiated through an unfeasible transition state (ts1), with an energy of at least 51.00 kcal mol−1 being required to overcome it, Ra52 is initiated via a prereactive complex with a slightly lower energy than its reactants (−1.07 kcal mol−1). Unfortunately, ~20 kcal mol−1 is required to overcome the transition state of the Ra52 pathway, ruling it out as a cyanamide-producing reaction in this environment. However, the reaction between methylamine (CH3NH2) and the cyano radical (·CN) shown in Fig. 4B (Ra60) remains energetically submerged with respect to the energy of the reagents in its three reaction steps. In principle, the reaction starts after the formation of a prereactive complex (min1) where the carbon atom of the ·CN radical faces the nitrogen (N) belonging to methylamine at a distance of 1.99 Å, with an N−C−N angle of 124.53 degrees (CCSD(T)-F12/cc-pVTZ-F12). This orientation indicates the presence of a weak bond between them. This adduct has a submerged energy of −25.37 kcal mol−1. Upon breaking the N-C bond linking the amide and methyl group of methylamine, cyanamide and ·CH3 are formed. The barrier belonging to the transition state (ts1) to be overcome for this step is 21.27 kcal mol−1 from the min2, and is submerged at −4.10 kcal mol−1 below the free energy of the reactants. Subsequently, Ra60 may be able to produce cyanamide under the conditions investigated here, and is studied below from a kinetic view point.

Ra48 (NH2CHO + ·N → NH2CN+ ·OH). We determined four possible routes on PES for the reaction between singlet formamide (NH2CHO) and atomic nitrogen (N) in its quartet ground state (; see Fig. 5A). The entrance channel is initiated through the formation of a prereactive complex that is defined when nitrogen approaches formamide carbon at 3.5 Å. From here, the quartet nitrogen might bond to the carbon of the formamide through an initial quartet transition state (ts1), which will consume a free energy of 30.76 kcal mol−1. From the top of the saddle point and according to IRC calculations, the reaction might flow either to a quartet minimum (min2) or to a more energetic (~ 15 kcal mol−1) doublet minima (min4). While the reaction would flow through the four described routes to produce cyanamide and a hydroxyl radical, none of the studied routes presents a fully submerged free energy with respect to the free energy of the reactants over all reaction paths. Consequently, and in spite of the computational effort, Ra48 is discarded as well.

Ra30 (H2CNH1 + ·NO → NH2CN + ·OH) and Ra50 (CH3 H2+·C → NH2CN +H2O). As in the previous case, the reactions between methamimine (H2CNH) and nitric oxide (·NO) and between methylamine (CH3NH2) and the CN radical given in Fig. 5B do not show favorable routes to produce cyanamide formed in this environment.

thumbnail Fig. 2

Density of the reagents detected in Sgr B2(N), as well as that of cyanamide (NH2CN), carbodiimide (HNCNH), and urea (CH4N2O). The density number in cm−3 is represented on the vertical axis, and the molecular rotational temperature (Trot) in K is on the horizontal axis. The bibliography related to each of the species is available in Col. (9) of Table 4.
Table 4

Molecular and atomic species that are part of the viable reactions to produce cyanamide (NH2CN) and caгbodiimide (HNCNH) in Sgr B2(N).

Table 5

NH2CN – Class A reactions.

4.2.2 Class B reactions

The following reactions under study are composed of at least one reagent not detected to date in Sgr B2(N). As this does not conclusively rule out the existence of these reagents in Sgr B2(N), reactions involving them could still be possible. Except for the case of Ra24 (HCNO + NH3), no entrance channel has been found, but the rest of the initially plausible reactions appear to exhibit different routes for the formation of cyanamide, as listed in Table 6.

Ra2 (3CH2 +N2 → NH2CN), Ra23 (HCNO+ NH2 → NH2CN+ ·2OH), & Ra27 (CNCN + H2O → NH2CN +1CO). After computationally exploring the reactions between methylene (·CH2) + molecular nitrogen (N2), fulminic acid (HCNO) + imidogen (3NH), and isocyanogen (CNCN) + water (H2O), as depicted in Fig. 6A, the reactions drawn in gray on the Markus diagram will not proceed to form cyanamides under the defined astrophysical conditions. The energetic demands of these reactions to yield cyanamide are better suited to hotter environments with supplementary sources of energy, rather than to the cold expanse of space.

Ra36 ( HNCN+3NH → NH2 CN + •N) and Ra37 (•HNCN+ •NH2 → NH2CN+3NH). When the cyanomidyl radical (•HNCN) is combined with imidogen (3NH) or with the amino radical (•NH2), it can react following the indicated pathways in Fig. 6B. The amine radical can follow two distinct routes to form cyanamide. However, the energy required, although relatively low for both reactions, does not enable them to form the desired products spontaneously and rapidly.

Ra4 (), Ra16 (•H2NC+ •N → NH2 CN, and Ra34 (•HNCN+ •H → NH2 CN). Ra4 represents the only reaction of all those under study for the formation of cyanamide that has an ionized reagent (). If the cation encounters the cyano-radical (•CN) in Sgr B2(N), according to the present computations, it would proceed to form ionized cyanamide in a favorable reaction with respect to the energies of the reactants (see Ra4 in Fig. 7A). The entrance channel is activated when the carbon of ·CN engages the nitrogen of the ammonia ion to form a cation of hydrogen cyanamide intermediate (H3NCN+). From there, losing one of the hydrogens attached to the nitrogen will produce ionized cyanamide (NH2CN+). From this reaction step, an energy of ~30 kcal mol−1 is required to produce ionized cyanamide. As the energy difference between that of NH2CN+ and its1 A’ ground state is only 0.38 kcal mol−1 (calculated with CCSD(T)-F12/cc-pVTZ-F12), and as electron rate coefficients in the ISM are some orders of magnitude greater than cyanamide abundances (~10−6 cm3 s−1; Desrousseaux et al. 2020), an e− could be gained to form neutral cyanamide. On the other hand, Ra16 is composed of aminomethylidyne (·H2NC) and a nitrogen atom in its doublet state •H2NC, producing the cyanamide triplet (as in the case of Ra5) as an intermediate. At the same time, the computations did not return any viable interaction when •H2NC joins the quartet N (4S03/2) ground state. From triplet cyanamide to the singlet ground state, a transition state (ts1) is found with an energy of only 1 kcal mol−1 in the route to its singlet ground state, indicating that the lifetime of the triplet cyanamide should be very short. In Ra34, the cyanomidyl radical (•HNCN) and atomic hydrogen could lead to the formation of cyanamide through a transition state (ts1) of 17.32 kcal mol−1. Even though all three reactions are based on at least one undetected reactant in Sgr B2(N), all indicate that under the cited conditions, and if and ·H2NC are present, Ra4 and Ra16 could lead to the production of some quantity of cyanamide. The chemical kinetic study below provides more details.

Ra17 (•H2 NC +3 NH → NH2 CN + •H), & Ra18 (•H2NC + •NH2 → NH2CN + H2). The reactions involving aminomethylidyne (•H2NC) together with the triplet imidogen (3NH; Ra17) and the amino radical (•NH2; Ra18) are a viable source of cyanamides from a thermodynamic point of view. Both reactions have an energetically submerged PESs with respect to the energy of the reagents. In Ra17, we find two channels. While Ra17-1 conforms as a direct reaction where the entrance channel is barrierless toward min2, the reagents of Ra17-2 have to pass a quartet transition state (ts1) of only 0.88 kcal mol−1 (confirmed by an IRC test) to fall directly in a doublet well of 113.06 kcal mol−1. From min2 to cyanamide, a dehydration of the ·H attached to the extreme N is required. The resultant barrier is submerged at ~−80 kcal mol−1 with respect to the energy of the reagents and will fall into the cyanamide PES well ~7 kcal mol−1 deeper. For its part, Ra18 advances through two submerged energy wells, falling to −38.94 kcal mol−1 (min3) in the first. From here to reach the cyanamide minimum, the reaction has to overcome two transitions states of ~20 kcal mol−1 and ~13 kcal mol−1, respectively. The second well is −93.90 kcal mol−1, and that of cyanamide is ~5 kcal mol−1 more submerged, at −99.06 kcal mol−1, which will undoubtedly act in favor of its kinetics.

Ra19 (•H2NC + •N2O → NH2CN+ •NO), & Ra21 (•H2NC+•HOCN → NH2CN+•COH). Ra19 and Ra21 also include aminomethylidyne (•H2NC), but this time react it with nitrous oxide (N2O) and cyanic acid (HOCN), respectively. In both cases, the reaction is initiated by the formation of submerged prereactive complexes (see Fig. 7C). In the case of Ra19, when the nitrous oxide (N2O) approaches ·H2NC, it stops at a N-C distance of 3.22 Å, forming a dihedral angle (ONN-C) of 83.18° and presenting a submerged energy of −1.20 kcal mol−1 with respect to the energy of the reagents. From here and through a transition state (ts1; 16.13 kcal mol−1), the formation of min4 is possible, where the ·NO group can be easily detached (<1 kcal mol−1) through ts2 to form cyanamide and nitric oxide (•NO). Similarly, in Ra21, the initial prereactive compound (min3) is produced by facing both initial compounds. The distance between the hydrogen of the cyanic acid and the carbon belonging to aminomethylidyne (H–C) is 1.88 Å and the distance between the carbons (C–C) is 2.91 Å. In principle, it would seem reasonable that the next step of the reaction to form cyanamide is initiated through this carbon-carbon bond. However, this bonding would lead to the formation of a triangular compound (C-C-N), which given its stability would not form cyanamide (not in cold regions). If, on the other hand, the entrance were to occur through the nitrogen of the cyanic acid and the carbon of aminomethylidyne (N-C; Fig. 7C –pathway Ra21), it would proceed through the transition state ts3 (24.13 kcal mol−1) to form min2. From this minimum, hydroxymethylidyne (•COH) would detach from the aforementioned intermediate but not before consuming another 16.13 kcal mol−1 to form cyanamide. These barriers make the synthesis of cyanamide unlikely from aminomethylidyne (•H2NC) combined with nitrous oxide (N2O) and cyanic acid (HOCN) in the cold regions of Sgr B2(N).

thumbnail Fig. 3

Cyanamide – Class A reactions (1). (A) Ra1 & Ra5; (B) Ra6; (C) Ra7, Ra8, & Ra9. Free energy profiles computed at Tgas = 20 K, and Pgas = 5.92 × 10−6 atm. Values calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected; min = minimum (adduct-intermediate), ts = transition state, prod = products; in parenthesis (charge and spin multiplicity). The energy units are given in kcal mol−1. Lines and bars related to stationary points are black when the next stationary point is submerged with respect to the energy of the reactants. Atoms: H = gray, C = lightblue, and N = blue.
thumbnail Fig. 4

Cyanamide – Class A reactions (2). (A) Ra10; (B) Ra26, Ra52, & Ra60. Gibbs free energy profiles computed at Tgas = 20 K, and Pgas = 5.92× 10−6 atm. for reactions. The ΔG° values are calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected. min = minimum (intermediate), ts = transition state, pw = pathway, prod = products; between parenthesis (charge and spin multiplicity). The energy units are given in kcal mol−1. PES surfaces (lines and horizontal bars related to stationary points) are black when the energy of the next stationary point is submerged with respect to the energy of the reactants, and gray when this energy is lower. Atoms: H = gray, C = lightblue, N = blue, and O = red.
Table 6

NH2CN – Class B reactions.

thumbnail Fig. 5

Cyanamide – Class A reactions (3). (A) Ra48. (B) Ra30 and Ra50. Gibbs free-energy profiles computed at Tgas = 20 K and Pgas = 5.92 × 10−6 atm.. The ΔG° values are calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected. Here, min = minimum (intermediate), ts = transition state, pw = pathway, prod = products; and charge and spin multiplicity are shown in parentheses. The energy units are given in kcal mol−1. PES surfaces (lines and horizontal bars related to stationary points) are black when the energy of the next stationary point is submerged with respect to the energy of the reactants. Atoms: gray = H, light blue = C, blue = N, red = O.
thumbnail Fig. 6

Cyanamide – Class B reactions (1). (A) Ra2, Ra23, and Ra 27. (B) Ra36 and Ra37. Gibbs free-energy profiles computed at Tgas = 20 K and Pgas = 5.92 × 10−6 atm. The ΔG° values are calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected. Here, min = minimum (intermediate), ts = transition state, pw = pathway, prod = products; and charge and spin multiplicity are given in parentheses. The energy units are given in kcal mol−1. PES surfaces (lines and horizontal bars related to stationary points) are black when the energy of the next stationary point is submerged with respect to the energy of the reactants, and gray when this energy is lower. Atoms: H = gray, C = light blue, N = blue, and O = red.
thumbnail Fig. 7

Cyanamide – Class B reactions (2). (A) Ra4, Ra16, and Ra34. (B) Ra17 and Ra18. (C) Ra19 and Ra21. Gibbs free-energy profiles computed at Tgas = 20 K and Pgas = 5.92 × 10−6 atm. The ΔG° values are calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected. Here, min = minimum (intermediate), ts = transition state, in = intermediate, pw = pathway, prod = products; between parenthesis (charge and spin multiplicity). The energy units are given in kcal mol−1. PES surfaces (lines and horizontal bars related to stationary points) are black when the energy of the next stationary point is submerged with respect to the energy of the reactants, and gray when this energy is lower. Atoms: gray = H, light blue = C, blue = N, red = O.

4.3 Carbodiimide (HNCNH)

4.3.1 Class A reactions

Regarding the formation of carbodiimide based on reagents present in Sgr B2(N), 11 reactions initially return favorable thermodynamics at 170 K and 5.92 × 10−4 atm. Their values are presented in Table 7. Four of them (Rb5 •CN + •NH2 → HNCNH, Rb26 HOCN + NH3 → HNCNH+ H2O, Rb52 NH2CHO + •CN → HNCNH+ •HCO, and Rb60 CH3NH2 + •CN → HNCNH + •CH3) are disregarded because the present electronic structure calculations do not find consistent pathways for the desired final structure. Additionally, Rb22 (•H2CN + 1N2O → HNCNH + •NO) does not exhibit any realistic entrance channel, which makes it an unvaluable reaction in this environment, as well. The PES profiles belonging to the remaining six reactions are presented in Figs. 8 and 9, and are analyzed in the following sections.

Rb6 (•CN + NH3 → HNCNH + •H). As ascertained computationally, the bonding between cyano radical (•CN) and ammonia (NH3) can, in principle, follow at least three different routes to form carbodiimide (HNCNH), as depicted in Fig. 8A. Two are the possible entrance channels similar to those already explained for cyanamide (Ra6). In all cases, the reactions form doublet electronic structures on PES. In the case of Rb6(1–2), the main abduct structure (N–C–N) is formed at min3, passing through a TS (ts1) of 12.74 kcal mol−1 in Rb6-3. Although Fig. 8A shows how the three reactions could continue, as explained in Ra6, both routes will stop in prod1 (Rb6-3) and in prod2 (Rb6(1-2)), which means they are of no value from these products onward.

Rb7 (1HNC + 3NH → HNCNH), & Rb10 (HCN+3NH → HNCNH). Rb7 and Rb10 share imidogen (3NH) in its triplet ground state as a reactant, which in the first case binds to singlet hydrogen isocyanide (HNC) and in the second to its isomer, hydrogen cyanide (HCN). In both cases, the entrance channels occur through the interaction between the carbon of the (iso)cyanide and the nitrogen of the amine. In Rb7, a triplet carbodiimide is formed, but not without first passing through a ~14 kcal mol−1 barrier (ts1). Once through, triplet carbodiimide can isomerize, consuming almost ~9 kcal mol−1 (−4.26 kcal mol−1 from reactants) in order to stabilize in its singlet ground state. If HNC as the second reactant is replaced with HCN (Rb10), a prereactive complex is formed (min2) 4.61 kcal mol−1 up to the transition state (ts3) 15.72 kcal mol−1 above the initial species. From this point on PES, there is a crossing effect between the spin–split electron levels in the energy spectrum, where triplet (min4) and singlet (min5) minima can be formed. Therefore, and unfortunately for both channels, the energies required to produce the products are ~38 kcal mol−1 (ts4) and ~46 kcal mol−1 (ts5) above that of the reagents. This unfavorable energetic route likely will not produce any significant amount of carbodiimide in this medium.

Rb8 (1 HNC + •NH2 + → HNCNH + •H), & Rb12 (HCN + •NH2 + → HNCNH + •H). In the following two reactions, the PES energy profiles of cyanide and isocyanide hydrogen are paired with the amino radical (•NH2) in its ground state (see Fig. 8C) to synthesize carbodiimide and atomic hydrogen. In Rb8, one potential well is submerged by -17.68 kcal mol−1 (min2) delimited at both ends by two TSs (ts1 and ts2) of 10.40 and 13.84 kcal mol−1 respectively, in the pathway from reactants to products. Rb8 is exergonic by a small value, whereas Rb12 is endergonic with barriers of higher than 30 kcal mol−1 and two energy wells. The latter of these two will not produce any of the products sought in this medium.

Rb48 (NH2CHO+ •N → HNCNH+ •OH). Formamide (NH2CHO) is also present in Sgr B2(N), and when it encounters a nitrogen atom, it reacts to form carbodiimide, as can be seen in Fig. 9A. However, there are some additional considerations. First, a prereactive complex is formed where the N atom lies in front of the formamide’s carbon at 3.40 Å. This minimum, under the conditions of Sgr B2(N), acquires a slightly positive free energy of 4.57 kcal mol−1 above the energy of the reactants, which will initially limit the production of any final compound. From here, the reaction aimed at synthesizing carbodiimide can flow through four different reaction paths; the most notable must surpass an energy barrier above 50 kcal mol−1, which will undoubtedly hinder carbodiimide production.

Rb50 (NH2CHO + 3NH → HNCNH + H2O). When for-mamide (NH2CHO) collides with imidogen (3NH), the process is similar to Rb48; see Fig. 9B. In this case, the initial prereactive complex also has a slightly lower energy than the reactants, which will not favor its development. However, even the two paths presented to produce carbodiimide show lower energy requirements than Rb48. The Rb50-1 route can be discarded as it needs ~50 kcal mol−1 (ts6), leaving Rb50-1 likely more favorable as it does not exceed its energy consumption of 37.33 kcal mol−1. Nevertheless, this also represents too high a barrier for further consideration.

thumbnail Fig. 8

Carbodiimide – Class A reactions (1). (A) Rb6. (B) Rb7 and Rb10. (C) Rb8 and Rb12. Gibbs free-energy profiles computed at Tgas = 170 K and Pgas = 5.92 × 10−4 atm. The ΔG° values are calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected; min = minimum (intermediate), ts = transition state, pw = pathway, prod = products; with charge and spin multiplicity given in parentheses. The energy units are given in kcal mol−1. PES surfaces (lines and horizontal bars related to stationary points) are black when the energy of the next stationary point is submerged with respect to the energy of the reactants, and gray when this energy is lower. Atoms: gray = H, light blue = C, blue = N, red = O.
thumbnail Fig. 9

Carbodiimide – Class A reactions (2). (A) Rb48. (B) Rb50. Gibbs free-energy profiles computed at Tgas = 170 K and Pgas = 5.92 × 10−4 atm. The ΔG° values are calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected. Here, min = minimum (intermediate), ts = transition state, pw = pathway, prod = products; and charge and spin multiplicity are shown in parentheses. The energy units are given in kcal mol−1. PES surfaces (lines and horizontal bars related to stationary points) are black when the energy of the next stationary point is submerged with respect to the energy of the reactants, and gray when this energy is lower. Atoms: gray = H, light blue = C, blue = N, red = O.
Table 7

HNCNH – Class A reactions.

thumbnail Fig. 10

Carbodiimide – Class B reactions. (A) Rb4 and Rb36. (B) Rb2, Rb23, and Rb27. (C) Rb17, Rb18, and Rb19. Gibbs free-energy profiles computed at Tgas = 170 K and Pgas = 5.92 × 10−4 atm. The ΔG° values are calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected. Here, min = minimum (adduct-intermediate), ts = transition state, pw = pathway, prod = products; between parenthesis (charge and spin multiplicity). The energy units are given in kcal mol−1. PES surfaces (lines and horizontal bars related to stationary points) are black when the energy of the next stationary point is submerged with respect to the energy of the reactants, and gray when this energy is lower. Atoms: H = gray, C = light blue, N = blue, and O = red.

4.3.2 Class B reactions

With respect to the 11 Class B reactions presented in Table 8 to produce carbodiimide in this environment, as in the previous case, not all of them follow routes to produce carbodiimide, despite having favorable thermodynamics. Related to the unsuitable ones, Rb16 is excluded because the nitrogen atom will bond to the carbon belonging to aminomethylidyne creating cyanamide, which is similar to the case of Rb34. According to the computational optimization, the hydrogen atom mainly flows in favor of cyanamide formation. In Rb20, no routes to carbodi-imide have been found, showing the same result as for Rb24, where no entrance channels are determined. Rb37 is endergonic at 170 K, but this is not the case for other physical conditions.

Rb4 (), & Rb36 (•NHCN + 3NH). According to the computations, and as in the case of Ra4 (), Rb4 might form ionized carbodiimide, having -CN and ammoniumyl () as reactants. The difference is that instead of losing a hydrogen from the initial intermediate (min2; Fig. 10 A), the nitrogen attached to the carbon could capture a hydrogen from the ammonia group of the molecule, generating a new intermediate (min3). This new minimum can again lose another hydrogen (H), forming ionized carbodiimide. All the steps of this reaction are submerged below the free energy of the reactants, as in Ra4. In this reaction, the hydrogen given off may possibly be ionized. However, the calculations appear to indicate that the ionized product is carbodiimide. As a result, we consider this reaction in kinetic calculations below. In Rb36, the formation of an intermediate (min1) and a transition state (ts1) with energies above those of the reactants (at least 20 kcal mol−1) is predicted here. This, as in previous reactions, means that this reaction has unfeasible kinetics that would not justify the detected density of carbodiimide in this environment.

Rb2 (3CH2CHO + N2 → HNCNH), Rb23 (HCNO+ •NH2 → HNCNH + •OH), Rb27 (CNCN+H2 → HNCNH+1 CO). Here, three reactions are presented that are very different from the point of view of the reagents. From Fig. 10B we see that the three reactions do not develop energetically below the energies of their respective reactants. In Rb2 and Rb27, the reaction entrance channel is generated through an initial TS that requires 25.75 kcal mol−1 (ts5) and 53.04 kcal mol−1 (ts1), respectively. Rb2 evolves through four TSs and three intermediates on its PES before forming carbodiimide. A free energy of 88.57 kcal mol−1 is required to overcome its most energetic transition state (ts7), which energetically rules it out as a reasonable option. The hydration of isocyanogen (CNCN) in Rb27 is energetically more favorable than in Rb2, requiring lower energy input. This reaction pathway is not promising either, because its reaction steps are above the energies of the reactants (shown in gray in Fig. 10B). The case of Rb23 is also not optimal but is quite different. The entrance occurs through a prereaction complex (min7) with similar energy to the reactants. Although the three wells are energetically submerged, the first three transition states are not, with an initial barrier of 7.74 kcal mol−1 (ts9) and a maximum ramp to overcome of 24.57 kcal mol−1 (ts10). This makes the combination between fulminic acid (HCNO) and the amino radical (•NH2) more feasible in relation to the production of carbodiimide when compared with Rb2 and Rb27. Unfortunately, this would still lead to low amounts of carbodiimide, if any.

Rb17(•H2NC + 3NH → HNCNH + •H), Rb18(•H2NC + •NH2 → HNCNH+H2), Rb19 (•H2NC+ 1N2O → HNCNH+ •NO), Rb21 (•H2NC + HOCN → HNCNH + •COH). The last set of reactions has aminomethylidyne (•H2NC) as one of the reactants. When •H2NC encounters triplet imidogen (3NH; Rb17), amino radical (•NH2; Rb18), and nitrous oxide (1 N2O; Rb19), Ra17-1 and Rb18 have all the pathways over their respective PES submerged with respect to the reactants we find, as can be seen in Fig. 10C. In Rb18, the first well is submerged -32.30 kcal mol−1 while the second is −86.86 kcal mol−1. Between them, there is an inner TS of −12.42 kcal mol−1 relative to the •H2CN and NH2, with the products being ~8 kcal mol−1 more submerged with respect to the previous well. The second inner TS is also submerged −34.35 kcal mol−1 with respect to the energy of the asymptotic reactants. This energy profile will undoubtedly work in favor of its chemical kinetics. In addition, Rb18 is also the most exothermic of all proposed reactions for carbodiimide (−94.43 kcal mol−1). Rb17 (as in Ra17 case) poses two entry routes. Rb17-1 channel flows directly to doublet min2. In Rb17-2, the entrance occurs through a first-order saddle point, and an energy of 6.50 kcal mol−1 is required to energetically fall toward min2 (−106.64 kcal mol−1). From min2 on the pathway to the products, a second TS (ts2) is present, this time submerged -68.55 kcal mol−1 with respect to the reagents. Finally, in Rb19, the energy required to be activated is 22.54 kcal mol−1 and an additional energy of 50.72 kcal mol−1 (ts3) is needed to go from min6 to min7. In view of these energies, we can undoubtedly exclude Ra19 from any further consideration. In conclusion, Rb17-1 and Rb18 are in principle firm candidates for HNCNH production under the aforementioned conditions and wherever the reagents are available.

Table 8

HNCNH – Class B reactions.

4.4 Kinetics

From the energy profiles analyzed and described in the previous sections, we find the most thermodynamically favored reactions to produce the synthesis of cyanamide and carbodiimide under the dominant astrophysical conditions of Sgr B2(N) where both species have been detected are as follows:

  • Cyanamide (NH2 CN)

    Class A reactions

    Ra5-2 and Ra 5-3: •CN + •NH2 → NH2CN

    Ra6-1: •CN + NH3 → NH2CN + •H

    Ra8: 1HNC + •NH2 → NH2CN + •H

    Ra60: •CN + CH3NH2 → NH2CN + •CH3

    Class B reactions

    Ra4:

    Ra16-1 and Ra16-2: •H2NC + •N → NH2CN

    Ra17-1 and Ra17-2: •H2NC + 3NH → NH2CN + •H

    Ra18: •H2NC + •NH2 → NH2CN + H2

    Ra37-2: •HNCN + •NH2 → NH2CN + 3NH

  • Carbodiimide (HNCNH)

    Class A reactions

    Rb7: 1HNC + 3NH → HNCNH

    Class B reactions

    Rb4:

    Rb17-1 and Rb17-2: •H2NC + 3NH → HNCNH + •H

    Rb18: •H2NC + •NH2 → HNCNH + H2

Figures 11 and 12 illustrate the evolution of the bimolecular rate coefficients (cm3 molecule−1 s−1) for NH2CN, while Fig. 13 reflects the evolution of HNCNH rates, all over a temperature range of 20–300 K and at a constant pressure of 5.92 × 10−4 atm. The rate coefficients shown here and in Table 9 are the result of multiplying the high-pressure limiting rate constant by the branching fraction(s) obtained from RRKM simulations. Figure 11 shows that the reaction with the most favored rate at low temperatures (<60 K) is Ra60 (CH3 NH2 + •CN → NH2 CN + •CH3) with a clear nonAr-rhenius behavior. The modified Arrhenius fit obtained for this reaction is . From 60 to 300 K, the reaction probably responsible for maintaining the production of H2NCN is Ra5 (•CN + •NH2 → NH2CN), which is divided into two channels, Ra5-2 and Ra5-3. Both channels exhibit a nearly constant rate evolution as temperature changes, with Ra5-2 exhibiting a magnitude of order higher than the other channel. The modified Arrhenius fit calculated for Ra5-2 is , while we find for Ra5-3. Of the two missing reactions, neither Ra8 nor Ra6-1 can produce any considerable fraction of the NH2CN observed below 200 K. With respect to reactions with undetected reactants in Sgr B2(N), in Fig. 12 the reaction that contributes most to cyanamide synthesis above 80 K is Ra37-2 (•HNCN + •NH2 → NH2CN + 3NH). The modified Arrhenius fit for this reaction is , which exhibits a remarkable positive behavior with respect to temperature. Below 80 K, Ra18 (•H2NC+ •NH2 → NH2CN+ H2) is the reaction most worthy of consideration. The best fit with respect to the modified Arrhenius equation is .

The case for carbodiimide is different. With only one candidate reaction in Class A (Rb7), its rate constant is relatively far from what would be an appropriate coefficient to reach the density found by McGuire et al. (2012) (6.6 × 10−12 at 170 K; see Fig. 13). For the reactions and channels belonging to Class B (Rb4, Rb18 and Rb17(1-2)), Rb17-1, Rb7, and Rb4 should be disregarded because their rate coefficients are not sufficiently productive (see Fig. 13 and Table 9). Finally, according to the calculations obtained, the only reaction that would explain the formation of carbodiimide in the gas phase in the amounts detected in Sgr B2(N) is Rb18 (•H2NC + •NH2 → HNCNH + H2).

Table 9

Computed bimolecular rate coefficients (cm3 mol−1 s−1) for a range of temperatures of 20–300 K at a constant pressure of 5.92 × 10−4 atm.

thumbnail Fig. 11

Cyanamide: Class A reactions. Evolution of the bimolecular rate coefficients (cm3 molecule−1 s−1) of thermodynamically favored reactions for a temperature range of 20–300 K, at a constant pressure of 5.92 × 10−4 atm.
thumbnail Fig. 12

Cyanamide: Class B reactions. Evolution of the bimolecular rate coefficients (cm3 molecule−1 s−1) of thermodynamically favored reactions for a temperature range of 20–300 K, at a constant pressure of 5.92 × 10−4 atm.
thumbnail Fig. 13

Carbodiimide: Class A + B reactions. Evolution of the bimolec-ular rate coefficients (cm3 molecule−1 s−1) of Class A (Rb7) + B reactions for a range of temperatures between 20 and 300 K at a constant pressure of 5.92 × 10−4 atm.

5 Conclusions

The abundance of cyanamide (NH2CN) in cold regions (~20 K) of Sgr B2(N) has been determined to be 3.6 × 10−11 cm−3 (Belloche et al. 2014). According to the calculations we present here, the detected cyanamide density could be explained by Ra60 (•CN + •CH3NH2 → NH2CN + •CH3). This reaction is supported by the detected abundances of both reagents in these regions (9.9 × 10−10 cm−3 for cyano radical at 20 K and 5.7 × 10−9 for methylamine at 40 K (Table 4). As the gas temperature increases above ~60 K, Ra5-2 (•CN + •NH2 → NH2CN) with nearly constant production capacity could enhance the production of cyanamide according to the vibrational cascade obtained for the association. However, this is not sufficient to justify the NH2CN densities found at ~120 K and above. Figure 14 provides the evolution of the total rate coefficient for the different families of reactions. Cyanamide (A+B) does have a sufficient rate constant to justify the observed density in the whole range from 20 to 300 K. In this way, the cyanamide production in Sgr B2(N) could correspond to a combined process: from ~20 K to ~120 K, the reactions based on detected reagents (Ra60 and Ra5) dominate the production, whereas Class B reactions dominate above that temperature. This points to Ra37-2 as the most productive reaction that can produce the complementary cyanamide. Consequently, the molecular species cyanomidil radical (•HNCN) should be present in Sgr B2(N). The predicted column density is on the order of 1016 cm2 s−1 at 150 K or higher. On the other hand, the chemistry of the detected reagents in Sgr B2(N) alone is not sufficient to explain the formation of carbodiimide (HNCNH). According to the present computations, HNCNH can be formed in enough quantities in the gas phase through Rb18 (•H2NC + •NH2 → HNCNH + H2; see Table 9). The amino radical (•NH2) is a compound unambiguously detected in cold (20 K) and slightly warmer regions (100 K) of Sgr B2(N) with densities above HNCNH (on the order of 10−9 cm−3). However, the second required ingredient, amino methylidine (•H2NC), albeit recently detected in L483 and B1-b, has not yet been detected in Sgr B2(N). Therefore, considering our calculations and given that •H2NC is an essential ingredient for the gas-phase formation of carbodiimide (HNCNH) in Sgr B2(N), we suggest its presence there is likely. The minimum column density is hypothesized to be on the order of 1013 cm2 s−1 at 100 K. As such, radio-astronomical searches for •H2NC and •HNCN in this region are warranted.

thumbnail Fig. 14

Evolution of the total bimolecular rate coefficients (cm3 mol−1 s−1) for cyanamide (A+B) and carbodiimide (A+B). The range of temperatures is 20–300 K at a constant pressure of 5.92 × 10−4 atm.

Acknowledgements

JCRO wishes to thank all the staff of the Mississippi Center for Supercomputing Research (MCSR) at the University of Mississippi (Ole Miss), in Oxford, MS, USA. RCF also acknowledges funding from NASA grants NNX17AH15G & NNH22ZHA004C and start-up funds provided by the University of Mississippi. MCSR funding has been provided in part by NSF grant OIA-1757220.

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All Tables

Table 1

Initial set of reactions proposed in this research.

In the text
Table 2

Thermodynamic function values for reactions to synthesize NH2CN at Tgas = 20 K and Pgas = 5.92 × 10−6 atm.

In the text
Table 3

Thermodynamic function values for reactions to synthesize HNCNH at Tgas = 170 K and Pgas = 5.92 × 10−4 atm.

In the text
Table 4

Molecular and atomic species that are part of the viable reactions to produce cyanamide (NH2CN) and caгbodiimide (HNCNH) in Sgr B2(N).

In the text
Table 5

NH2CN – Class A reactions.

In the text
Table 6

NH2CN – Class B reactions.

In the text
Table 7

HNCNH – Class A reactions.

In the text
Table 8

HNCNH – Class B reactions.

In the text
Table 9

Computed bimolecular rate coefficients (cm3 mol−1 s−1) for a range of temperatures of 20–300 K at a constant pressure of 5.92 × 10−4 atm.

In the text

All Figures

thumbnail Fig. 1

Contextualization of the prebiotic roles of cyanamide and carbodiimide. Panel A: processes in the ISM, including the formation of cyanamide and carbodiimide explored in this work. Panel B: fate of cyanamide in planetary conditions. Cyanamide directly formed in planetary atmospheres, or in the ISM and delivered to a planet after accretion, could lead to a rich diversity of organic compounds or intervene as condensing agents in the formation of organophosphates. Panel C: processes that may take place in both the ISM and in planetary environments.
In the text
thumbnail Fig. 2

Density of the reagents detected in Sgr B2(N), as well as that of cyanamide (NH2CN), carbodiimide (HNCNH), and urea (CH4N2O). The density number in cm−3 is represented on the vertical axis, and the molecular rotational temperature (Trot) in K is on the horizontal axis. The bibliography related to each of the species is available in Col. (9) of Table 4.
In the text
thumbnail Fig. 3

Cyanamide – Class A reactions (1). (A) Ra1 & Ra5; (B) Ra6; (C) Ra7, Ra8, & Ra9. Free energy profiles computed at Tgas = 20 K, and Pgas = 5.92 × 10−6 atm. Values calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected; min = minimum (adduct-intermediate), ts = transition state, prod = products; in parenthesis (charge and spin multiplicity). The energy units are given in kcal mol−1. Lines and bars related to stationary points are black when the next stationary point is submerged with respect to the energy of the reactants. Atoms: H = gray, C = lightblue, and N = blue.
In the text
thumbnail Fig. 4

Cyanamide – Class A reactions (2). (A) Ra10; (B) Ra26, Ra52, & Ra60. Gibbs free energy profiles computed at Tgas = 20 K, and Pgas = 5.92× 10−6 atm. for reactions. The ΔG° values are calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected. min = minimum (intermediate), ts = transition state, pw = pathway, prod = products; between parenthesis (charge and spin multiplicity). The energy units are given in kcal mol−1. PES surfaces (lines and horizontal bars related to stationary points) are black when the energy of the next stationary point is submerged with respect to the energy of the reactants, and gray when this energy is lower. Atoms: H = gray, C = lightblue, N = blue, and O = red.
In the text
thumbnail Fig. 5

Cyanamide – Class A reactions (3). (A) Ra48. (B) Ra30 and Ra50. Gibbs free-energy profiles computed at Tgas = 20 K and Pgas = 5.92 × 10−6 atm.. The ΔG° values are calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected. Here, min = minimum (intermediate), ts = transition state, pw = pathway, prod = products; and charge and spin multiplicity are shown in parentheses. The energy units are given in kcal mol−1. PES surfaces (lines and horizontal bars related to stationary points) are black when the energy of the next stationary point is submerged with respect to the energy of the reactants. Atoms: gray = H, light blue = C, blue = N, red = O.
In the text
thumbnail Fig. 6

Cyanamide – Class B reactions (1). (A) Ra2, Ra23, and Ra 27. (B) Ra36 and Ra37. Gibbs free-energy profiles computed at Tgas = 20 K and Pgas = 5.92 × 10−6 atm. The ΔG° values are calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected. Here, min = minimum (intermediate), ts = transition state, pw = pathway, prod = products; and charge and spin multiplicity are given in parentheses. The energy units are given in kcal mol−1. PES surfaces (lines and horizontal bars related to stationary points) are black when the energy of the next stationary point is submerged with respect to the energy of the reactants, and gray when this energy is lower. Atoms: H = gray, C = light blue, N = blue, and O = red.
In the text
thumbnail Fig. 7

Cyanamide – Class B reactions (2). (A) Ra4, Ra16, and Ra34. (B) Ra17 and Ra18. (C) Ra19 and Ra21. Gibbs free-energy profiles computed at Tgas = 20 K and Pgas = 5.92 × 10−6 atm. The ΔG° values are calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected. Here, min = minimum (intermediate), ts = transition state, in = intermediate, pw = pathway, prod = products; between parenthesis (charge and spin multiplicity). The energy units are given in kcal mol−1. PES surfaces (lines and horizontal bars related to stationary points) are black when the energy of the next stationary point is submerged with respect to the energy of the reactants, and gray when this energy is lower. Atoms: gray = H, light blue = C, blue = N, red = O.
In the text
thumbnail Fig. 8

Carbodiimide – Class A reactions (1). (A) Rb6. (B) Rb7 and Rb10. (C) Rb8 and Rb12. Gibbs free-energy profiles computed at Tgas = 170 K and Pgas = 5.92 × 10−4 atm. The ΔG° values are calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected; min = minimum (intermediate), ts = transition state, pw = pathway, prod = products; with charge and spin multiplicity given in parentheses. The energy units are given in kcal mol−1. PES surfaces (lines and horizontal bars related to stationary points) are black when the energy of the next stationary point is submerged with respect to the energy of the reactants, and gray when this energy is lower. Atoms: gray = H, light blue = C, blue = N, red = O.
In the text
thumbnail Fig. 9

Carbodiimide – Class A reactions (2). (A) Rb48. (B) Rb50. Gibbs free-energy profiles computed at Tgas = 170 K and Pgas = 5.92 × 10−4 atm. The ΔG° values are calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected. Here, min = minimum (intermediate), ts = transition state, pw = pathway, prod = products; and charge and spin multiplicity are shown in parentheses. The energy units are given in kcal mol−1. PES surfaces (lines and horizontal bars related to stationary points) are black when the energy of the next stationary point is submerged with respect to the energy of the reactants, and gray when this energy is lower. Atoms: gray = H, light blue = C, blue = N, red = O.
In the text
thumbnail Fig. 10

Carbodiimide – Class B reactions. (A) Rb4 and Rb36. (B) Rb2, Rb23, and Rb27. (C) Rb17, Rb18, and Rb19. Gibbs free-energy profiles computed at Tgas = 170 K and Pgas = 5.92 × 10−4 atm. The ΔG° values are calculated at CCSD(T)-F12/cc-pVTZ-F12, with their respective ZPVE corrected. Here, min = minimum (adduct-intermediate), ts = transition state, pw = pathway, prod = products; between parenthesis (charge and spin multiplicity). The energy units are given in kcal mol−1. PES surfaces (lines and horizontal bars related to stationary points) are black when the energy of the next stationary point is submerged with respect to the energy of the reactants, and gray when this energy is lower. Atoms: H = gray, C = light blue, N = blue, and O = red.
In the text
thumbnail Fig. 11

Cyanamide: Class A reactions. Evolution of the bimolecular rate coefficients (cm3 molecule−1 s−1) of thermodynamically favored reactions for a temperature range of 20–300 K, at a constant pressure of 5.92 × 10−4 atm.
In the text
thumbnail Fig. 12

Cyanamide: Class B reactions. Evolution of the bimolecular rate coefficients (cm3 molecule−1 s−1) of thermodynamically favored reactions for a temperature range of 20–300 K, at a constant pressure of 5.92 × 10−4 atm.
In the text
thumbnail Fig. 13

Carbodiimide: Class A + B reactions. Evolution of the bimolec-ular rate coefficients (cm3 molecule−1 s−1) of Class A (Rb7) + B reactions for a range of temperatures between 20 and 300 K at a constant pressure of 5.92 × 10−4 atm.
In the text
thumbnail Fig. 14

Evolution of the total bimolecular rate coefficients (cm3 mol−1 s−1) for cyanamide (A+B) and carbodiimide (A+B). The range of temperatures is 20–300 K at a constant pressure of 5.92 × 10−4 atm.
In the text

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