A Thermodynamic Landscape of Hydrogen Cyanide-Derived Molecules and Polymers

.


INTRODUCTION
https://doi.org/10.26434/chemrxiv-2024-ln735ORCID: https://orcid.org/0000-0001-7645-5923Content not peer-reviewed by ChemRxiv.License: CC BY 4.0 Polymers such as DNA, RNA and polypeptides are essential for information storage, replication, and catalysis, and fundamental to life as we know it.We can assume that earlier, or other, forms of life also require some form of polymers to perform these vital functions.Two of several unknowns in prebiotic chemistry are how 1) information-storing polymers can develop through abiotic chemical processes, and 2) under which chemical conditions (i.e., where in the Universe) such processes may occur.The first biomolecular building blocks may have originated through chemical processes native to the early Earth, or they may have been exogenously delivered, e.g., via asteroids and comets. 1 Both scenarios imply that precursor molecules or polymers are subsequently able to transform into biologically relevant structures.In this work, we use quantum chemistry to map the thermodynamics of one such family of proposed precursors: hydrogen cyanide (HCN) and HCN-derived molecules and polymers.
HCN is a common molecule in the Universe, having been identified on various planets, 2 dwarf planets, 3 Saturn's moon Titan, 4 comets 5 and in the interstellar medium. 6HCN was likely present on the early Earth. 7The molecule is also quite reactive.In experiments, biologically relevant molecules such as amino acids, nucleobases and pterins 8 have all been extracted from the products of HCN polymerization experiments (see ref. 9 for a review).
The prevalence of HCN in many astrochemical environments, and its reactive nature, places the molecule, and its possible reaction products, center stage of prebiotic chemistry and astrobiology. 10,11 owever, a clear picture of HCN reactivity, both in laboratory and in astrochemical environments, remains elusive.HCN-derived polymers are complex materials that can form under a variety of laboratory conditions. 12These product mixtures are typically heterogeneous and insoluble in most common solvents. 13Various forms of characterization have been attempted to elucidate which chemical https://doi.org/10.26434/chemrxiv-2024-ln735ORCID: https://orcid.org/0000-0001-7645-5923Content not peer-reviewed by ChemRxiv.License: CC BY 4.0 structures can form from HCN.For example, mass spectrometry, infrared and nuclear magnetic resonance (NMR) spectroscopy have been used to infer a wide variety of functional groups in polymerization product mixtures. 14-17A plethora of different polymerization pathways have been proposed to explain this complexity (see ref. 12 for a review).Due to their diverse nature, some HCN-derived polymers are functional materials with proposed uses in catalysis, 11,18 as adhesives and as coatings. 19e complex space of HCN-derived chemistry.For this analysis, we have collected HCN-based materials that appear as suggestions, hypotheses, or confirmed detections, in literature.
The limitations to our selection are motivated by practicality.The full structural space of possible HCN-derived polymers and molecules is immense.For example, one automated search for reactions that result in HCN tetramers identified 678 compounds. 20Several other structures have also been computationally predicted. 21We consider here consider a selection of pure HCN-based materials, i.e., structures where the stoichiometry of H, C and N are 1:1:1 (and no additional elements).Other HCN-based materials can incorporate oxygen, 12 additional nitrogen and hydrogen 22 or form through condensation reactions, e.g., through the formation of NH3. 12,18,23,24 Sumaterials, which may also be important, are beyond the scope of this work.In what follows, we will first introduce the materials we study, and then proceed to evaluate their relative thermodynamic stability.
HCN-derived molecules.All HCN-derived molecules that we investigate are shown in Figure 1.In addition to HCN (1), several of these molecules have been proposed to act as monomers in polymerization: 12,14,16,[25][26][27][28][29][30][31][32][33] the HCN dimers iminoacetonitrile (2) and aminocyanocarbene (3), the trimer aminomalononitrile (4) and the tetramer diaminomaleonitrile (5) (Fig. 1).Out of these molecules only 5 has been directly observed during polymerization of https://doi.org/10.26434/chemrxiv-2024-ln735ORCID: https://orcid.org/0000-0001-7645-5923Content not peer-reviewed by ChemRxiv.License: CC BY 4.0 HCN. 31,34 peculations that 2 and 4 might form are based on indirect evidence. 34The proposed formation of 3 is controversial, as we will return to discuss.Aminoimidazole carbonitrile (6) and adenine (7) (Fig. 1) are less likely to take part in polymerization but are included in our study because of their relevance to prebiotic chemistry. 12,25  what follows, we outline a collection of pathways, which connect some of the molecules in Figure 1 to different proposed polymer structures.Sometimes, these pathways will be mentioned in the context of mechanistic details (e.g., base-or radical catalyzed).However, we mostly use pathways to refer to the casual connections between reactant, intermediates, and products.Suggested products of HCN polymerization.Two of the simplest HCN-derived polymers are polyimine (8) (Fig. 2, pathway 1) and the head-to-tail polymer (9) (Fig. 2, pathway 2).Structures 8 and 9 have been suggested to form through different mechanisms.He et al., 16 have suggested that the formation of 8 is base-catalyzed, proceeding through the successive additions of cyanide anions.Mozhaev et al., 32 who studied radiation-induced HCN polymerization, and Mamajanov and Herzfeld, who studied polymerization in the presence of radical-initiators 31 have both suggested 9 as a plausible product.Mamajanov and Herzfeld have further proposed that 9 can subsequently transform into two-dimensional polytriazine sheets (10, Fig. 2 8). 16Bottom: radical-catalyzed 31,32,35 and/or pressure-induced 41 formation of one-and two-dimensional materials.
Figure 3 shows 11, the only three-dimensionally connected polymer in this study.This material can be viewed as an NN↔HCN substituted analogue of cubic gauche nitrogen -a metastable allotrope of nitrogen synthesized above 42 GPa. 36Structure 11 has been predicted to be dynamically stable (a minimum on the potential energy surface).(11). 36Left: color representations: carbonbrown, hydrogen -pink and nitrogen -grey.

Polymerization of diaminomaleonitrile
Interest in polyaminomalononitrile ( 23) is motivated by a suggestion by Matthews and Moser: that 23 may be a precursor to polypeptides. 29This proposal has been criticized for lack of experimental evidence. 40,41

RESULTS & DISCUSSION
In this work, we compute the free energy of all the above-mentioned structures, as well as a few additional ones.Our study makes use of a sampling algorithm to identify candidates to the lowest energy ground states in the vast configurational space of the HCN-derived molecules and polymers (see Methods for details). 43To limit computational costs, polymers have been represented as oligomers of approximately 60 atoms.Figure 7 exemplifies predicted stable conformers for three such structures evaluated with implicit consideration of water solvation.Most experimental literature studies have been performed in aqueous solution (see ref. 12 for a review) or in neat liquid HCN. 16,31,32 HN and water are both polar and hydrogen bonding solvents and can be expected to cause comparable trends in relative solvation energies.
https://doi.org/10.26434/chemrxiv-2024-ln735ORCID: https://orcid.org/0000-0001-7645-5923Content not peer-reviewed by ChemRxiv.License: CC BY 4.0     The energy content per HCN in the studied structures varies between +7.5 and -16.1 kcal/mol (Fig. 8).In other words, note that to arrive at a reaction energy, the values shown in Figure 8 needs to be multiplied with the number of HCN in each structure.For example, for adenine, this multiplication factor is 5, whilst for a polymer it is n.Most investigated structures are clearly thermodynamically downhill from HCN in aqueous solution at 298 K.The overall thermodynamic favorability of HCN-self reactions is thus one part of the explanation for the commonly observed chemical complexity of reaction mixtures.The only materials predicted to be unstable relative to HCN are 3, 9, 12 and 14, effectively ruling these out as plausible reaction products under the studied conditions.
Our calculations infer new insight into the viability of Völker's suggestion, that 2 is the monomer unit of 12 and 13 (Fig. 4, pathway 3a).Our data predicts that formation of 13 from 2 is thermodynamically favored.At the same time, we can rule out 12 as a major product since it is unstable relative to 2, as well as 8 + 1 (and most other structures).We can also rule out Umemoto's single ladder model (14) (Fig. 4, pathway 3b) as a plausible polymerization product on the grounds of unfavorable thermodynamics.
Figure 8 shows that 5 is more stable than most considered structures.This prediction has several important consequences.For example, structures 12, 13, 14 are unlikely to be the products of polymerization of 5, because such transformations are predicted to be thermodynamically unfavored.Other similar examples include structures 23 and 20, predicted to lie ~1.7 and 5.8 kcal/mol HCN above 5, respectively.Establishing that formation of 23 from 5 is not thermodynamically spontaneous is important as the former is a proposed precursor to heteropolypeptides. 27,40 owever, we note that our predictions do not exclude the possibility of https://doi.org/10.26434/chemrxiv-2024-ln735ORCID: https://orcid.org/0000-0001-7645-5923Content not peer-reviewed by ChemRxiv.License: CC BY 4.0 23 forming through other higher energy intermediates, such as the HCN trimer 4 (Δ '() * + = -1.7 kcal/mol HCN).
We have found only a limited number of HCN-derived polymers and molecules to be thermodynamically downhill relative to 5. For example, and in agreement with previous theoretical studies, 46 the formation of 7 from 5 is thermodynamically allowed.The linear polymer 21 is another example that could feasibly form from 5. Structures 19 and 33 are predicted to be the most stable polymers out of those considered, with only the molecule 7 being more stable.Formation of 19 and 33 from 5 is predicted to be spontaneous by -6.0 and -6.3 kcal/mol HCN, respectively.

The corresponding polymerization enthalpy (Δ𝐻 '() * +
) calculates as -9.9 and -9.7 kcal/mol HCN (Supporting Information, Table S3).These energies are in fair agreement with estimates derived from differential scanning calorimetry thermograms of solid-state and melt-polymerization of 5. 18 That study, by Ruiz-Bermejo and colleagues, estimated heat releases of 3-5 kcal/mol HCN at 423-463 K. 18 We furthermore predict that the HCN dimer 3 have an energy content of +7.5 kcal/mol HCN, i.e., its formation from HCN is uphill by 15 kcal/mol.This value is 8.5 kcal/mol lower than the corresponding value in gas phase (Supporting Information, Table S1), in turn comparable to other computational results. 44,47 e note that 3 has a similar energy content as hydrogen isocyanide in solution. 48Nevertheless, 3 is high in energy, and can be ruled out as a major component of reaction mixtures.
The energy of two-and three-dimensional materials.Our methodology for calculating the data shown in Figure 8 is limited to molecules and one-dimensional polymers.For polymers with higher dimensional connectivity, we have relied on DFT calculations with periodic boundary conditions (see Methods).Figure 9 shows our stability estimates for the 2D-and 3D polymers 10 https://doi.org/10.26434/chemrxiv-2024-ln735ORCID: https://orcid.org/0000-0001-7645-5923Content not peer-reviewed by ChemRxiv.License: CC BY 4.0 and 11.Both systems are composed by tetrahedrally coordinated C and N atoms in a graphanelike configuration (Fig. 9).Phonon band structures of 10 (including the isomers 10A and 10B) and 11, provided in the Supporting Information, confirm that these materials are dynamically stable.In other words, these structures all constitute local minima on the potential energy surface, which allows us to account for temperature effects in our relative stability estimates.
Whereas structures 10A, 10B calculates as only slightly thermodynamically favored (-1.9--0.4)relative to our reference of an infinite chain of HCN molecules at ambient conditions, 11 is instead predicted to be unstable by +0.5 kcal/mol.8 can be considered combinations of simpler monomer units.For example, structure 23 can be viewed as a combination of 8 and 15 (Fig. 8). Figure 10 illustrates how our calculated energies of smaller polymer units can be used to estimate the relative energies of more complex HCN-based structures through a weighted averaging approach (see the Methods for details).Such linear extrapolation is approximate and can be expected to fail e.g., in the presence of extensive conjugation.Nonetheless this approach constitutes a rapid route to exploring the thermodynamics of a larger structural space of HCN-derived materials.

CONCLUSIONS
Our study shows that several hypotheses regarding HCN's reactions to molecules and polymers can be ruled out on the grounds of thermodynamics.For example, diaminomaleonitrile (5), a prominently suggested reaction intermediate in HCN-based prebiotic chemistry, is predicted to be lower in energy compared to many proposed polymer products.Our study also infers a new perspective on adenine (7), a nucleobase, present in all life as we currently know it (Fig. 8).
Formation of 7 is predicted to be thermodynamically downhill from all herein considered structures at ambient conditions.The low experimental yields (<0.01 % 9 ) of 7 from HCN in typical condensed phase experiments therefore means such reactions must be kinetically controlled.
The presented thermodynamic landscape of HCN-derived materials has several consequences for interpreting HCN's reactivity in various astrochemical environments, in and beyond the solar system.Most (but not all) previously proposed HCN-derived polymers and molecules can form spontaneously (ΔGr<0) at close to Earth ambient conditions.In low-temperature environments, like those on Titan, the entropic penalty for making larger molecules and polymers (-TΔS) naturally decreases.In other words, the chances for thermodynamic spontaneity of macromolecular formation increases in cold environments.
At the same time as more structures can become thermodynamically viable at lower temperature, such chemistry will naturally be more limited by reaction kinetics. 49Enhanced kinetic control of https://doi.org/10.26434/chemrxiv-2024-ln735ORCID: https://orcid.org/0000-0001-7645-5923Content not peer-reviewed by ChemRxiv.License: CC BY 4.0 HCN-based prebiotic chemistry means a greater ability of colder environments to generate specific metastable products out of an increased pool of thermodynamically allowed options.We can therefore speculate on the potential of colder worlds, such as Titan, in generating kinetically selected products that may otherwise not form at higher temperatures.Some such materials could, hypothetically, be crucial templates for the origin of life. 11

METHODS
Conformational search.The Conformer-Rotamer Ensemble Sampling Tool (CREST) 43 was used in automated searches of lowest lying conformers of molecules and oligomers.The energy evaluations in CREST make use of the semi-empirical xtb program. 50Conformational structure searches in aqueous solution were performed with the analytical linearized Poisson-Boltzmann (ALPB) model. 51Structural differences between predicted larger and smaller oligomers risk influencing the computed energy content, e.g., through different end-effects.We therefore additionally relied on visual inspection to ensure models of oligomers of different length were similar in appearance/folding.

Electronic Structure Calculations.
With the exception for two and three-dimensional networks, all structures were optimized using the B3LYP 52 functional, as implemented in Gaussian 16, revision B.01. 53 Missing treatment of dispersion effects in B3LYP was corrected for using Grimme's method combined with Becke-Johnson damping (D3BJ). 54The standard polarizable continuum (PCM) model of Gaussian was used to model interactions with water solvent. 55Our best estimate to total Gibbs free energies,  , , were calculated as https://doi.org/10.26434/chemrxiv-2024-ln735ORCID: https://orcid.org/0000-0001-7645-5923Content not peer-reviewed by ChemRxiv.License: CC BY 4.0 where  -.// denote thermal corrections obtained following optimization and frequency analyses using the cc-pVDZ basis set.Final electronic energies,  , in Eq. ( 1) were calculated as single point calculations at the B3LYP-D3BJ/aug-cc-pVTZ level of theory.Method validation were performed against the M06-2X 56 meta-GGA functional, and close agreement was found (Supporting Information, Table S4).The average absolute deviation between B3LYP-D3 and M06-2X results are 0.65 kcal/mol, with a maximum of 3.2 kcal/mol for compound 9.The corresponding average deviation is -0.01 ± 0.85 kcal/mol.

Calculations of Extended
where  ,,>.?@ and  ,,AB./9 are the total free energies of the ()-long and ( − )-short polymer models, respectively.In Eq. ( 3)  is the number of HCN in the long oligomer model, and  is the number of HCN in a monomer unit.The sizes of our oligomer models were chosen to have at least 4 repeating polymer units, and  is always near 20.Each polymer model was capped by a cyanide group in one end and a hydrogen atom in the other end.
Computing the energy of 10 and 11.The energies of HCN in 10A, 10B and 11 were calculated by dividing the total energy of the polymeric material by the number of HCN in the unit cell.To obtain relative energies we then compared to the average energy of HCN in infinite HCN chain.
Our molecular and periodic calculations are of comparable levels of theory, also evidenced by the hydrogen bond distances between HCN differing by less than 0.025 Å.

Figure 2 .
Figure 2. Examples of HCN polymerization pathways catalyzed in different ways.Top: base-

Figure 8
Figure 8 summarizes our best estimates for the relative Gibbs free energy of all considered

Figure 8 .
Figure 8.The thermodynamic landscape of HCN-derived structures.Gibbs free energy content