Peptide Bonds in the Interstellar Medium: Facile Autocatalytic Formation from Nitriles on Water-Ice Grains

A recent suggestion that acetamide, \ce{CH3C(O)NH2}, could be readily formed on water-ice grains by the acid induced addition of water across the \ce{CN} bond is now shown to be valid. Computational modelling of the reaction between \ce{R-CN} (R = H, \ce{CH3}) and a cluster of 32 molecules of water and one \ce{H3O+} proceeds auto-catalytically to form firstly a hydroxy imine \ce{R-C(OH)=NH} and secondly an amide \ce{R-C(O)NH2}. Quantum mechanical tunnelling, computed from small-curvature estimates, plays a key role in the rates of these reactions. This work represents the first credible effort to show how amides can be formed from abundant substrates, namely nitriles and water, reacting on a water-ice cluster containing catalytic amounts of hydrons in the interstellar medium with consequential implications towards the origins of life.


Introduction
The peptide bond, -C(O)NH -, found in amides connects amino acids to peptides -of paramount importance to present day life on Earth. Unsurprisingly, how, when and where peptide bond formation arose is of immediate interest in prebiotic astrochemistry, tackling that challenging question: the origins of life [1,2].
The simplest amides, formamide HC(O)NH 2 , and acetamide, CH 3 C(O)NH 2 , are common constituents of star-forming regions in our galaxy [3,4] but apparently propionamide, CH 3 CH 2 C(O)NH 2 , is not [5]. Adande et al. [3] have shown, based on their observations of formamide towards starforming regions of dense molecular clouds, that the compound could have been brought to Earth by exogenous delivery in substantial amounts of ∼ 0.18 mmol m −2 in a single impact.
The formation routes to formamide are still unclear; some have suggested gas-phase pathways via formaldehyde and amidogen [6,7]: • −−→ HCONH 2 + H • but disputed by Song and Kästner [8] and convincingly refuted by Douglas et al. [9] or surface reactions [10] by the hydrogenation of isocyanic acid, HNCO, and on carbon monoxide-ammonia ices [11]: and more recently by metal-ion mediated substitution reactions [12]: where M = Na + , K + , Mg + , Mg ++ , Al + and X = H, OH, CH 2 OH but the evidence for all these is underwhelming. A comprehensive summary has been given recently by Chuang et al. [13] during the course of their laboratory work on the formation of formamide in water-and carbon monoxide-rich water ices with ammonia as the substrate. VUV irradiation of water-rich and CO-rich ammonia ices at 10 K with compositions H 2 O:CO:NH 3 =10:5:1, CO:NH 3 =4:1 and CO:NH 3 =0.6:1 have shown that formamide is preferentially formed, although mechanistically the situation is complicated with no clear indication as to actual formation routes [13]. Indirect evidence for the formation routes of formamide based on the stratified distribution of the molecules HNCO and H 2 CO, putative parents of HCONH 2 , in the atmosphere of the HH 212 protostellar disk appear to rule out HNCO as a parent [14]. Studies of comets have indicated that the early Solar Nebula had nitriles (cyanides) such as HCN and CH 3 CN in abundance [15,16]. It is currently assumed that reactions in the bulk or on the surface of water-ice grains are the most likely formation routes for complex organic molecules which are then liberated into the gas-phase by UV irradiation, electron and cosmic ray bombardment, via thermal shocks or grain-grain collisions [17,18,19].
In a computational study of the direct reaction HC ---N + H 2 O −−→ HC(OH) --NH neither the presence of a second H 2 O as a catalyst, or as a spectator or as a reactant was sufficient to reduce the high barriers encountered which thereby rule out the possibility of it occurring in cold molecular clouds [20]. The most pertinent previous work simulated a 33 H 2 O molecule cluster and showed that HC ---N cannot react to HC(O)NH 2 under interstellar ice conditions because of large energy barriers. Any reactivity that was feasible proceeded through the CN • radical [21].
UV photolysis of water methyl cyanide ices at 20 K (H 2 O:CH 3 CN = 20:1) does give rise to the formation of CH 3 C(O)NH 2 , and its isomer N-methyl formamide CH 3 NHCHO, but many other products as well [22].
A consideration of the various suggested reactions in the literature led one of us to suggest that H 3 O + induced water addition to nitriles on waterice grains was likely to provide the most probable route [23]. It is known that H 3 O + exists in the ISM and even in other galaxies, that it reacts in water-ices and that it has the potential to drive subsequent reaction [24,25,26,27]. Woon has very recently reviewed what is known about cation-ice reactions from quantum chemical cluster studies, highlighting the novel and more efficient pathways, vis-à-vis the gas-phase, that HCO + , CH 3 + and C + (but not H 3 O + ) undergo and appealed for experimental confirmation [28]. Laboratory experiments have shown that bombardment of water ice samples on a copper substrate at 10 K yields a number of secondary ions including (H 2 O) n · H + with n = 1 → 8, although these ions are perhaps more accurately denoted as (H 2 O) n−1 · H 3 O + [29]. The production efficiency is much lower when crystalline ice is bombarded in comparison to amorphous ice.
The first step in the proposed addition of water is the protonation at nitrogen of the nitrile to form RC ---NH + , and in the case of HCN to form imino methylium, HC ---NH + ; this species has been widely detected in star-forming regions [30,31,32] and in Titan's atmosphere [33]. Although it had been characterised as a precursor of HC ---N in the most recent observations Fontani et al. show that it is formed from HC ---N or HC ---N + [34]. Fundamental laboratory work to characterise the spectroscopic parameters for CH 3 C ---NH + have been carried out but interstellar searches have not so far been successful [35].
A primary consideration for suggesting acidified amorphous water-ice is the high mobility of the proton through the lattice; the transfer mechanism, via Grotthus hops, takes place on a sub-picosecond time scale and with barriers of ≈ 1 kJ mol −1 -these effectively increase the "collision rate" or encounter between reactant and H 3 O + [27,36].
The hydronium induced addition of water was seen as a two-step process with the first forming hydroxy imines or imidic acids RC(OH) --NH and the second converting these to amides RC(O)NH 2 ; the latter reaction can occur either by intramolecular hydrogen-transfer via quantum-mechanical tunnelling or by the further protonation of the nitrogen-atom followed by deprotonation from the O-atom.
The actual formation of peptides as a by-product was observed [37] after the deposition of C atoms onto a CO + NH 3 ice at 10 K and subsequent warming to 300 K. The authors argue that the initial reaction product is aminoketene, H 2 NCH --C --O, which polymerises on warming yielding ( -CH 2 -C(O) -NH -) n chains. While the experiments are compelling the conditions are somewhat artificial since they consider pure CO + NH 3 ices with substantial quantities of carbon atoms. The initial step H 3 N + C( 3 P 0 ) −−→ H 3 N ---C is highly exothermic, ∆ r H = −103 kJ mol −1 , this is followed by a 1,2-H-transfer to H 2 N -CH and finally reaction with CO to H 2 N -CH --C --O.
Interestingly Canepa [38] in considering the survival rates of glycine, NH 2 CH 2 C(O)OH, embedded in micrometeorites undergoing atmospheric reentry has shown that aminoketene, the product of dehydration, would also survive.
In this paper we focus on a solid-state chemistry formation mechanism of R -C(OH) --NH and subsequently R -C(O)NH 2 . We perform electronic structure investigations of the energetics and also thermal rate constants calculations of this reaction mechanism. This information can then be used in astrochemical modelling and may prompt experimental laboratory confirmation.

Methods
Calculations were performed with the application Gaussian [39] and used the long-range dispersion corrected hybrid meta-GGA density functional ωB97X-D together with the triple ζ basis set with added polarization and diffuse functions 6-311++G(d,p) [40] with a factor of 0.96 was applied to scale the zero-point energy.
A system with thirty-two water molecules and one hydronium ion, H 3 O + , with a total 'volume' of ≈ 2, 600Å 3 , was chosen together with one reactant, either HCN or CH 3 CN. This choice represents a compromise between realistic ISM concentrations and computational effort Fig. 1.
All structures were fully optimized and the harmonic frequencies computed using DFT. Frequency calculations were performed in order to verify that all intermediates are true minima on the potential energy surface, and that all transition states exhibit a single imaginary frequency. We study all species in the reaction mechanism with the unrestricted ωB97XD/6-311++G(d,p) model chemistry. Gaussian 16 automatically includes an ultrafine integration grid in the DFT calculations in order to improve the accuracy of the results. The grid greatly enhances the accuracy at reasonable additional cost.
The reaction paths are computed using the intrinsic reaction coordinate (IRC) methodology [41,42] to confirm the identities of the reactants and products for every transition state. IRC calculations require initial force constants of the transition state. Then, the first and second order energy derivatives are obtained to calculate the projected harmonic vibrational frequencies along each reaction path. The minimum energy paths (MEPs) were computed using the Page-McIver integrator with a gradient step size of 0.1 a 0 [43].
Small curvature quantum mechanical and quantised-reactant-states tunnelling calculations [44,45] employed the PILGRIM application [46] for the computation of rate constants via transition state theory (TST) and variational TST (VTST) necessitating calculations along the minimum energy path.

Results
Prior to the first reaction steps we begin by considering a previously published [47]

First step: imidic acid formation
As originally envisaged the hydrolysis of HC ---N proceeded in three distinct phases: Overall reaction (4) is exothermic by −80 kJ mol −1 which is considerably different to the gas-phase ∆ r H − • (0K) = −22.2 kJ mol −1 reflecting the tighter binding of the hydrolysed product in comparison to the reactant.
The barrier to reaction (1), that is protonation at the N-atom, in the case of HCN is 78.5 kJ mol −1 and is even lower at 51.9 kJ mol −1 for acetonitrile.
Although Fig. 1 shows the actual reaction structure, an oversimplified version, Fig. 2, shows the parts played by four key water molecules; the first is the proton donor H 3 O + , the second is the "reactant" which will attack the Catom and also transfer a H + to the "acceptor" water, whilst the "companion" H 2 O is less involved but nevertheless stabilises the system through H···OH 2 hydrogen-bonding; snapshots along the IRC path are shown in Fig. 3 to the final product, methanimidic acid in its (E,Z ) conformation with respect to the dihedrals ∠ OCNH and HOCN, respectively.
In Fig. 4 we plot the potential energy along the minimum energy path for the imidic acid formation given by reaction (4).

Second step: amide formation
We can distinguish between two different routes from the hydroxy imines to the corresponding amides which can proceed intra-molecularly or intermolecularly.

Intramolecular route
Once the hydroxy imines, methanimidic and ethanimidic acids, are formed then an intra-molecular 1,3-H-transfer leads to formamide, Fig. 5, or acetamide; however, the barriers are considerable ranging from 136 or 128 kJ mol −1 in the gas-phase to 169 and 142 kJ mol −1 in this water-cluster; clearly, surmounting such barriers is unfeasible at temperatures much less than 300 K except by tunnelling. Fig. 2: Key elements of the reaction scheme for the first step Note that the presence of additional water molecules makes very little difference to the energetics of the process in comparison to the gas-phase. Exactly the same conclusion can be drawn from the gas-phase work of Darla et al. which showed in ωB97xD/aug-cc-pVTZ calculations that even in the presence of a "catalytic" water molecule the 1,3[H]-transfer faces a barrier of 131 kJ mol −1 or 132 kJ mol −1 with the additional water present as a "spectator" [20].
The additional water molecules and H 3 O + in our system only marginally affect the 1,3[H]-transfer reaction; this is seen in the energetics, as discussed above, and also from the values of the imaginary frequencies which are gas-phase: 2,002 and 1,988 cm −1 and cluster: 1,953 and 1,916 cm −1 for HC(OH)NH ↔ HC(O)NH 2 and CH 3 C(OH)NH ↔ CH 3 C(O)NH 2 respectively.
In the case of the gas-phase RC(OH)NH ↔ RC(O)NH 2 isomerisation reaction, PILGRIM [49] calculations at B3LYP/cc-pVTZ incorporating smallcurvature tunnelling yields rate constants, k, and half-lives, τ , as shown in Table 1; the ice-cluster values are probably not dis-similar. At the lowest temperatures, here ≤ 150 K, quantised reactant states tunnelling is included. The barrier to reaction is higher at 131.5 kJ mol −1 for HC(OH)NH 2 than the 123.9 kJ mol −1 for CH 3 C(OH)NH 2 consequently the rate of isomerisation to the appropriate amide is faster for ethanimidic acid. These are substantially faster rates of isomerisation than our previous Multiwell values, Fig. 6, which were based on Eckart tunnelling [23]; this renders the intermolecular route, discussed below, essentially redundant.
A not dis-similar situation is considered by Concepción et al [50] in their work on the origin of the (E /Z ) isomer ratio of imines in the ISM; thus   The detection of isotopically labelled compounds can be useful for tracing formation routes; specifically, deuteration has been used in this regard by Bianchi et al. [51] in their study of CH 3 C ---N in the SVS13-A Class I hot corino. Unfortunately, such a tool is unavailable here since the hydrogen transferred has been sourced from the water-ice; however were CH 3 C(OD)NH or CH 3 C(OH)ND to be detected then that might prompt other avenues of investigation. In Fig. 7 we plot the potential energy, the zero point energy (ZPE), and vibrationally adiabatic ground state energy V G a along the minimum energy path for the gas phase 1,3-H-transfer.

Intermolecular route
The same outcome, that is RC(OH)NH → RC(O)NH 2 , can come about by the attack of hydronium at the N-atom leading similarly to R -C(OH) --NH 2 + + H 2 O and attack by a further water molecule at the O-atom leading to deprotonation, resulting in the final products R -C(O) -NH 2 + H 3 O + .
So this reaction follows the same course mechanistically as the first; firstly, protonation at the nitrogen atom, which has a tiny barrier of 1.6 kcal/mol (disappears when adding ZPE), is followed by H-abstraction from the OH group and transfer of H to a neighbouring water and transfer of H to a second water, Fig. 8, which just shows the active site. The reaction can be summarised as: [HC(OH)NH 2 and the barrier for this is low at 5.8 kJ mol −1 . The results are summarised in Table 2 where E † is the zero-point corrected electronic energy and ∆ r H is the reaction enthalpy, with both expressed in units of kJ mol −1 .

Discussion
There are of course other nitriles present in the ISM and one would anticipate that a similar fate would befall them; Manna and Pal [52]    Auto-catalytic addition of water on ice-grains, as per this work, would lead to the formation of carbonyl diamide, OC(NH 2 ) 2 , better known as urea, which has been detected previously [53].
In an extensive computational study by Slate et al. [54] into urea formation in the ISM they concluded that closed shell reactions had prohibitive barriers but that a route involving charged species was feasible except that their starting point involved iso-cyanic acid HN --C --O with protonation at the O-atom followed by addition of ammonia and subsequent deprotonation; a somewhat more complex sequence than that envisaged here but nevertheless comparable. Previously Brigiano et al. had considered ion-molecule, neutral-neutral and radical reactions leading to the formation of urea but only in the gas-phase [55].

Conclusion
The auto-catalytic addition of water to RC ---N triple bonds is shown to be a credible process on water clusters which are impacted by hydrons H + . The high mobility of the hydron through the cluster leads to the initial reactive step, protonation at the N-atom in a facile manner. This effectively transforms a bimolecular reaction into a unimolecular process -thus removing the 'collisional handicap' which hampers all gas-phase reactions in the interstellar medium.
Subsequent attack by water at carbon and abstraction of H + yields the hydroxy imine RC(OH)NH which can then undergo a 1,3[H]-transfer reaction either intra-molecularly or inter-molecularly to the amide RC(O)NH 2 . Quantum-mechanical tunnelling plays a key role in these processes.
The recent review by Woon with its stress on the need to pay more attention to cation-ice reactions is shown to be prescient and his call for experimental confirmation timely. [28] ORCID Boutheïna Kerkeni: 0000-0002-5762-5058 John M. Simmie: 0000-0003-0714-7956