Astro-electrochemistry of NH₃ clusters and ice: e⁻ trapping, stability, and electron transfer

ABSTRACT

1 INTRODUCTION

Ammonia (NH₃) shares structural simplicity with water, and exhibits a similarly complex physical chemistry in the liquid state. Specifically, the ability of ammonia to form stable NH|$_4^+$| and NH|$_2^-$| ions in acid-base equilibrium (akin to H₃O⁺ and OH⁻ for water), and when ionized, the formation of ammonia radicals showing a strong electron affinity (EA). Both water and ammonia (and their ions) also share utmost importance within the biosphere as well as in the industrial, technological (Briggs et al. 2018), and agricultural sectors. As a consequence, ammonia attracts research interest to understand many aspects of its physical chemistry from investigations of small clusters (Almeida et al. 2008; Wang et al. 2020), to analysis of the hydrogen bond network (Malloum & Conradie 2021), and studies of liquid phase structure and properties at different temperatures and pressures on both experimental and theoretical levels (Li et al. 2017; Queyroux et al. 2019).

In astrophysical environments, NH₃ is an important probe to understand the physical conditions in star-forming environments (Fehér et al. 2022), molecular clouds (Yan et al. 2022), and interstellar medium (Doherty et al. 2022). Efforts are dedicated to analyse and characterize the infrared spectra of ammonia ice (Hudson, Gerakines & Yarnall 2022) to be used in astronomical observations. NH₃ is a relevant precursor for N-based astrochemistry (Koga & Naraoka 2022; Marks et al. 2022) and is formed by a complex network of reactions occurring at the gas-solid interface (Hashimoto, Takayanagi & Murakami 2023). In the Solar system, the presence of ammonia is observed in the Kuiper Belt Objects (KBOs; Jewitt & Luu 2004) and on the Pluto–Charon system (Ore et al. 2019) in the form of ammonia-hydrate. Since the 1980s, NH₃ was proposed to play an important role in the evolution and physicochemical characteristics of the outer giant planets, due to the formation of ‘hot ice’, an ammonia-water-methane mixture (Hubbard 1981; Sasselov 2008) or ammonia-hydrate (Robinson et al. 2017), stable at high pressures and temperatures. Ammonia plays an important role in the chemistry of cold planetary environments by the formation of ‘cryomixtures’ together with organic molecules such as acetylene (Thakur & Remsing 2023). Similar ammonia-organic mixtures in the presence of low volatile compounds such as CO, N₂, and CH₄ can be an important factor for the cryovolcanism on KBOs (Neveu et al. 2015).

However, one of the distinctive characteristics of liquid ammonia shared with some low molecular weight primary amines like CH₃NH₂ and CH₃CH₂NH₂ (Burrows, Kamo & Koide 2021) is its ability to solvate and stabilize electrons when in the presence of the electropositive s-block metals (Combellas, Kanoufi & Thiébault 2001; Vöhringer 2015; Chaban & Prezhdo 2016; Jackson & Miliordos 2022). In fact, ammonia solutions are able to form ‘ammoniated electrons’ detected by a sharp transition in colour from blue to gold, coupled with an increase of six orders of magnitude in electrical conductivity (Zurek, Edwards & Hoffmann 2009). The electron stabilization process in liquid ammonia is explained by two main models (Shkrob 2006): (i) the electron is shared by 6–9 ammonia molecules or (ii) the electron is a solvent-stabilized multimer radical anion where most of the excess electron density is placed in the frontier orbitals of the ammonia molecules forming the solvation cavity.

To better analyse the ammoniated electron, small ammonia clusters were studied by photoelectron spectroscopy (Sarkas et al. 2002) and computational techniques (Baranyi & Turi 2019; Malloum & Conradie 2021). In small clusters of neat ammonia (NH₃)_n with n = 8–32, 48, the excess electron is highly diffuse and localized on the cluster surface. There is almost no penetration to the nitrogen frontier orbitals setting a difference when compared to liquid ammonia where the excess electron is surrounded by solvent molecules forming a cavity (Baranyi & Turi 2019, 2020). Mixed ammonia-water clusters within and without the presence of Li were analysed by ab initio molecular dynamics (AIMD) showing how water hydrogens or ammonia molecules capture the free electron. The vertical detachment energy as well as the vertical ionization energy change with time along the simulation trajectories, i.e. geometrical rearrangements (Pratihar & Chandra 2011).

Furthermore, there is a consistent corpus of studies analysing the effect of ionizing radiation and particles at different energies on neat ammonia liquid and ice or when in mixtures with other molecules such as CH₄ (Kundu, Prabhudesai & Krishnakumar 2017; Marks et al. 2022), H₂O (Loeffler, Raut & Baragiola 2010), and NH₃-H₂O-CO mixtures (Pilling et al. 2010). In particular, the effect of impinging electrons presenting a wide energy spectra (7 eV ≤ E_kin ≤ 1 keV) on a film of NH₃ has shown the formation of hydrazine (N₂H₄) and diazene (N₂H₂) (Shulenberger et al. 2019). Corresponding to the dissociative electron attachment peaks at 5.5 and 10.5 eV, the formation of highly reactive ^·−NH₂ radical anions was reported (Ram & Krishnakumar 2012). However, depending on the incident energy, different products will be generated according to the differential cross-sections of various physical phenomena such as the electron capture, dissociative electron attachment, neutral dissociation, dissociative ionization, and dipolar dissociation (Böhler, Warneke & Swiderek 2013; Lipton-Duffin & MacLeod 2023).

In this work, by means of computational methods, the ability of NH₃ clusters (A) to capture and trap electrons by the general relation A + e⁻ →A^−·, was hypothesized and analysed. The resulting radical anion, A^−·, is a highly reactive supramolecular system and its stability and chemical reactivity/electron transfer with specific molecules relevant to astrochemistry such as H₂O, CH₃OH, CO, and HCN, was analysed. Finally, the plausible existence of the ammoniated electron in ammonia clusters and ice (crystalline and amorphous state) in astrochemical environments, resulting in ‘astro-electrochemistry’, is discussed.

2 COMPUTATIONAL METHODS

The orca software (version 5.0.4) (Neese 2022) was used for all performed computational analysis. Geometry minimizations, potential energy surface (PES), and vibrational frequency analyses used the global hybrid functional PBE0 (Perdew, Ernzerhof & Burke 1996) with the split valence triple-ζ def2-TZVPPD (Weigend & Ahlrichs 2005; Hellweg & Rappoport 2015) and quadruple-ζ def2-QZVPPD (Weigend & Ahlrichs 2005; Hellweg & Rappoport 2015) basis sets with two sets of polarization and diffuse basis functions. In selected cases, a comparison with the functional BHandLYP (Becke 1993) and the influence of the aug-cc-pVnZ (n = D,T,Q) basis sets (Kendall, Dunning & Harrison 1992) on both DFT functionals was conducted. For the smaller (NH₃)₄ cluster, the doubly augmented d-aug-cc-pV(D,T)Z basis sets (Dunning 1989; Kendall et al. 1992; Woon & Dunning 1994) obtained by the web-based Basis Set Exchange (Feller 1996; Schuchardt et al. 2007; Pritchard et al. 2019) were aplied to determine the effect on the calculated EA (Woon & Dunning 1994). Convergence criteria for both SCF and geometry optimization (internal redundant coordinates) procedures were set to ‘tight’. DFT integration grid setting used the ‘defgrid3’ level. The dispersion correction was evaluated by the atomic-charge dependent London dispersion correction (D4) (Caldeweyher et al. 2019). To speed up calculations, the RI (Resolution of the Identity) (Neese 2003) and RIJCOSX (Neese et al. 2009) algorithms were used coupling the Coulomb-fitting basis sets def2/J (Weigend 2006). Since the d-aug basis sets have no preset/optimized Couloumb-fitting auxiliary functions in orca, these were newly generated (Stoychev, Auer & Neese 2017) by checking/deleting redundant basis functions and linear dependences (see Input files in ESI). To test if the computed structures represent a minimum or a transition state, frequency calculations within the harmonic approximation were performed on all compound models using the quasi-rigid-rotor harmonic oscillator (QRRHO) model for the estimation of the entropic contribution (Grimme 2012). The selected level of theory (PBE0-D4/def2-TZVPPD) was shown to be one of the most robust, reliable and accurate theoretical tools in the estimation of general main group thermochemistry, kinetics, and non-covalent interactions after the double hybrid functionals (Goerigk et al. 2017; Bursch et al. 2022).

The amorphous (NH₃)₂₃ cluster was obtained by performing an AIMD simulation (NVT ensemble, with the Nosé–Hoover thermostat (Nosé 1984; Hoover 1985) using the following simulation parameters: τ_T = 10 fs, T = 210 K, time-step = 0.5 fs, and a 5ps+5ps relaxation + production run using the composite electronic-structure method r2-SCAN3c (Grimme et al. 2021) with the initial configuration based on two NH₃ crystal cells in the neutral state. The final relaxed configuration was used for the (NH₃)₂₃ computational analysis (minimization + single point).

Electron correlation effects with frozen core electrons (Bistoni et al. 2017) were considered by running single point calculations on the DFT optimized geometries using the domain-based local pair-natural orbital (DLPNO) approach coupled with the CCSD(T) method (Riplinger & Neese 2013; Riplinger et al. 2013) in conjunction with the aug-cc-pVnZ (n = D, T, Q) basis sets (Kendall et al. 1992) and the auxiliary basis set aug-cc-pVnZ/C (Weigend, Köhn & Hättig 2002). Convergence criteria for the DLPNO procedure was set to ‘normalPNO’. A wave function stability analysis of DFT or Hartree–Fock calculations was performed before DFT geometry optimization and DLPNO-CCSD(T) single point calculations. To avoid spin-contamination in the open-shell DLPNO-CCSD(T) calculations, quasi-restricted orbitals (QRO) were used, transforming the UHF α-β set to double α and β sets (Neese 2006). To check if the molecules/clusters have multireference character, a T₁ diagnostic analysis (Lee & Taylor 2009) was conducted. For all the analysed systems T₁ ≤ 0.009 was obtained, with the exception of the (NH₃)₂₃ amorphous radical-anion cluster demonstrating a T₁ value of 0.019. All values are thus within the recommended T₁ ≤ 0.02 for main group chemistry (Lee & Taylor 2009), ensuring that the single-reference DLPNO-CCSD(T) approach will reliably describe electron affinities. Spin contamination was evaluated by the relation Err = <S² > _calc-<S² > _nocont where <S² > _nocont is the expectation value of the total spin operator. For all the systems Err = 10^−6/−7 ensuring the near absence of spin contamination. The complete basis set (CBS) extrapolation scheme as implemented in orca, was used. The SCF and correlation extrapolation parts are based on the Petersson (Zhong, Barnes & Petersson 2008) and Noga (Helgaker et al. 1997) schemes, respectively, while exponents for both approaches are derived by Valeev and Neese (Neese & Valeev 2011) (see ESI). For the (NH₃)₄ cluster, CBS schemes with no predetermined fitting parameters were preferred, based on the inverse power of the highest angular momentum (1/n³), (1/n⁴) (Schwartz 1962; Martin 1996) and, for comparison, the exponential form E_CBS + Bexp(-αX) (Halkier et al. 1999). The obtained enthalpies and entropies were used to estimate the free energies (G) at T = 100 and 300 K. The DFT thermal and entropy corrections were added to the single point energies (E_El.) of the corresponding DLPNO-CCSD(T) levels of theory to obtain the reported H and G values.

Input files of the orca program, i.e. DFT optimization/frequency calculations, DLPNO-CCSD(T) procedure, wavefunction stability analysis, AIMD input, Cartesian coordinates and further details on the CBS extrapolation methods can be found in the ESI. Figures were rendered by avogadro (Hanwell et al. 2012) and vmd (Humphrey, Dalke & Schulten 1996; Stone 1998) packages.

2.1 Method validation

The theoretical definitions of adiabatic electron affinity (AEA), vertical attachment energy (VAE), and vertical detachment energy (VDE) are reported in Fig. 1, following the definitions given in Rienstra-Kiracofe et al. (2002).

Figure 1.

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Simplified scheme (Rienstra-Kiracofe et al. 2002) to visualize the AEA, VAE, and VDE. Neutral geometry-relaxed and geometry-unrelaxed state are labelled A⁰ and A^0*. Radical anion geometry-relaxed and geometry-unrelaxed states are labelled A^−· and A^−·*. The assumption of the A^−· lower in energy than the A⁰ one is depicted though not always true.

The EA, VAE, and VDE are calculated only by the DLPNO-CCSD(T) electronic contribution (see ESI for details of the computational procedures) and the abbreviated form ‘EA’ instead of ‘AEA’, will be used. Note that by definition, EA = -(A_gas - A|$_{gas}^{-\cdot }$|⁠), where positive values indicate a stabilized electron.

Quantifying properties of dipole and weakly bound anion clusters are challenging both experimentally and computationally. Many recent efforts are dedicated to solve this problem (Lee, Lee & Zewail 2008; Simons 2023; Ufondu et al. 2023). The use of diffuse basis functions as well as correlated methods such as CCSD(T) are of fundamental importance to obtain results comparable with experimental findings (Skurski, Gutowski & Simons 2000; Fortenberry 2015; Simons 2023).

Unfortunately, EA, VAE, and VDE experimental measurements based on small (NH₃)_n clusters are not currently available due to the proposed stability (n ≥ 32), meta-stability (20 ≤ n ≤ 32) and meta-stability/instability of ammonia clusters with n ≤ 20 (Marchi, Sprik & Klein 1988; Sarkas et al. 2002; Lee et al. 2008; Young & Neumark 2012) at room temperature. Consequently, for the validation of the PBE0/DLPNO-CCSD(T) approach, an experimental data set based on single molecules and water clusters is used.

The adoption of the DLPNO-CCSD(T) procedure is to avoid the known limitations of DFT functionals introduced by the exchange-correlation part which includes a fraction of the electron–electron self-repulsion or self-interaction error (SIE) (Nattino et al. 2019; Ufondu et al. 2023). Furthermore, as observed in other studies, the use of correlated methods is of fundamental importance to analyse anionic systems (Skurski et al. 2000; Fortenberry 2015). Finally, the much less computationally demanding DLPNO-CCSD(T) level of theory allows the analysis of systems with hundreds of atoms introducing only a |$\approx 1~{{\ \rm per\ cent}}$| error compared to conventional CCSD(T) (Riplinger & Neese 2013; Riplinger et al. 2013).

Relevant to this work, EAs of single radical molecules such as ^·NH₂ (DeFrees et al. 1979; Wickham-Jones et al. 1989), HO^· (Goldfarb et al. 2005), CH₃O^· (Ramond et al. 2000), and CH₃CH₂O^· (Ramond et al. 2000) are analysed. In Table 1, the comparison of EAs calculated at different levels of theory are reported. Two important conclusions can be drawn: (i) DFT results underestimate the EA (Amati, Stoia & Baerends 2020), a problem corrected by the use of DLPNO-CCSD(T) single points (SP) on optimized DFT geometries; (ii) the use of the PBE0/def2-TZVPPD instead of the PBE0 / def2-QZVPPD optimized geometries does not affect the DLPNO-CCSD(T) SP results. As such, the PBE0/def2-TZVPPD optimized geometries are used as inputs of the single point DLPNO-CCSD(T)/aug-cc-pVQZ calculations.

A second validation of the adopted computational procedure is performed by comparing the experimental EA of small water clusters (H₂O)_nn = 4–6, to the calculated ones. Water clusters have been particularly well studied, both experimentally and theoretically, to understand the nature of the hydrated electron in the bulk water (Gaiduk et al. 2018; Lan et al. 2021) as well as in clusters (Herbert & Head-Gordon 2006; Mato et al. 2023). However, a word of caution is needed. Experimental EA or VDE measurements of anionic clusters stabilized by weak interactions are strongly dependent on the isomers/hydrogen bond network relaxation (Ehrler & Neumark 2009; Young & Neumark 2012; Zho et al. 2018) resulting in a broad or multipeaked EA/VDE distribution (Kim et al. 1998; Linstrom & Mallard 2001; Ehrler & Neumark 2009) due to the low-energy landscape characterizing such systems. For example, considering the neutral water cluster data sets BEGDB and WATER27 (Manna et al. 2017), where a series of minimum energy conformers for the tetra-, penta-, and hexa-water clusters are listed, the number of conformers increases with the number of water units showing a difference in the adiabatic dissociation energy (ADE) of only fractions of kcal/mol to a few kcal/mol.

While the experimental EA/VDE values are based on a conformational ensemble with the cluster geometries corresponding to the EA/VDE peaks, EA/VDE values estimated by the proposed computational protocol are calculated on single conformers implying a sampling limitation. Estimation of EA/VDE cluster conformational dependence by Previous computational studies on single conformers (Herbert & Head-Gordon 2005) or on AIMD trajectories (Zho et al. 2018) results in considerable fluctuation of EA values. In this study, large VDE fluctuations were found by analysing an AIMD trajectory related to the (NH₃)₂₃ cluster with a ΔVDE_MAX of 6.6 kcal/mol (see ESI). As a consequence, different neutral cluster geometries based on the minima reported in the data sets BEGDB and WATER27 (Manna et al. 2017) are analysed (Table 2).

The agreement between the calculated and experimental EA of the water tetramer is very good. For the pentamer and hexamer isomers, differences from experiment of over 4 kcal/mol are found. Due to the strong sensitivity of computed EAs to the cluster geometry, the aforementioned sampling problem is likely the main cause of the difference. In the following sections, further analysis will be devoted to how to relate AIMD and SP calculations at higher levels of theory.

3 RESULTS AND DISCUSSION

3.1 Electron source considerations

Although the possibility of access to abundant electropositive elements exists (Combellas et al. 2001; Vöhringer 2015; Chaban & Prezhdo 2016), we hypothesize astrochemical scenarios where the electron directly impinges on the ammonia cluster or on an icy surface, producing low-energy secondary electrons. Due to possible electron sources like stellar winds, the energy spectrum is extremely wide. For example, solar electrons display a huge variance in kinetic energy (E_kin) from a few eV to several MeV depending on the distance to the Sun, undergoing different processes of acceleration and deceleration (Halekas et al. 2020; Gómez-Herrero et al. 2021).

In general, high-energy electrons are expected to start a sequence of ionization reactions with a cascade of products. However, low-energy electrons and secondary electrons, the latter also depending on the stopping power of the material (L'Annunziata 2003); i.e. the average energy dissipated by ionizing radiation in a medium per unit path length of travel of the radiation; can be an important source of free electrons without ion formation. For example, the formation of the highly reactive ^·−NH₂ radical anion can be avoided if electron energies do not overlap with the resonance peaks corresponding to the dissociative electron attachment at 5.5 and 10.5 eV (Ram & Krishnakumar 2012). Electrons with an E_kin between 2 and 9 eV can accumulate on the surface of ammonia ice inducing surface charge (Sagi et al. 2021).

The surface reactivity of ammonia ice is affected when strong static electric fields (Youngwook et al. 2019) are produced by electron accumulation, in particular if in presence of hetero-molecules, i.e. H₂O, CH₃OH, CO, and HCN. In the selected computational approach, the electron is by definition characterized by E_kin = 0, at best approximating a low-energy electron. In the following sections, the mechanism by which free electrons can be ammoniated and stabilized on or into ammonia clusters and, by extrapolation, on or into ice and amorphous solid ammonia, is reported.

3.2 (NH₃)_n clusters

To gain insights on the nature of the ammoniated electron in the bulk, ammonia clusters have been used as models by analysing various cluster geometries, mainly linear and branched, with a varying number of NH₃ molecules (Sommerfeld 2008; Baranyi & Turi 2019, 2020; Ufondu et al. 2023). The ammoniated electron was either found diffusely localized externally to the cluster (external state) or internally (internal state) if present in a pocket within the cluster (Baranyi & Turi 2020). A total of six (NH₃)_n clusters was analysed with n = 4, 5, 6, 8, 14, and 23 as depicted in Fig. 2.

Figure 2.

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Optimized neutral clusters A⁰ (left column) and spin density of the optimized A^−· (right column). The n = 5,6 neutral structures were based on the most stable conformer (see ESI). Spin isosurface: 0.0002 a.u.

Starting geometries of the neutral clusters (n = 4, 5, 6, 8) are based on the dihedral D₄, D₅, D₆ and octahedral O_h point groups, while in the case of (NH₃)₁₄ and (NH₃)₂₃, the starting structures were based on one and two unit cells of crystalline NH₃ (Olovsson & Templeton 1959), respectively. The D_x (cyclic) geometries were selected due to the higher stability compared to the linear counterparts as reported in previous studies (Tachikawa 2020). Both the (NH₃)₁₄ and (NH₃)₂₃ clusters were analysed in the crystalline (only single point calculations, see below) as well as the amorphous state obtained by minimization, [(NH₃)₁₄] and AIMD simulation, [(NH₃)₂₃] (see ESI). Observing Fig. 2, the comparison between the neutral and radical-anionic cluster geometries shows quite substantial differences with the exceptions of the (NH₃)₄ and (NH₃)₈ clusters. In the (NH₃)₈ case, a slight rotation between the two (NH₃)₄ planes is observed. The spin density is always localized outside the clusters, re-confirming the external electron stabilization found in other studies (Baranyi & Turi 2020) seemingly not dependent on the geometric order (see ESI for further analysis on how the level of theory affects the spin density distributions). In Table 3, values of VAE, EA, and VDE together with the ΔG of cluster formation (relative to monomer free energies), are listed.

When T = 100 K, the computed ΔG of formation predicts stable clusters for both the neutral and radical-anion forms with the exception of n = 4. At T = 300 K, all clusters are unstable, in agreement with experimental findings where small cluster stabilization is reached at T ≈ 90 K (Marchi et al. 1988).

Regarding the VAE, EA, and VDE values, (NH₃)_nn = 4, 5 clusters do not show stable radical-anion character (EA < 0) though (NH₃)₅ reports a positive VDE, denoting its meta-stability (if formed) limited by the cluster relaxation time. The EA of the (NH₃)₄ cluster was further scrutinized by adding a second set of diffuse functions to the basis sets (d-aug-cc-pVDZ and d-aug-cc-pVTZ). The additional diffuse functions serve to stabilize the radical anion and accelerate convergence of energies to a CBS limit. An EA determined by treating the d-aug-cc-pVTZ contribution additively to the aug-cc-pVQZ value is +0.6 kcal/mol (see ESI for more details). The EA of the (NH₃)₅ cluster is also likely close to zero when approaching the CBS limit. Qualitatively previous results will not affect the EA values of larger clusters and probably all of the (NH₃)_x radical anions are likely to be more stable at better (and intractable) levels of theory.

All bigger clusters show VAE, EA, and VDE values suggesting a stable electron capture. However, VAE, EA, and VDE values are somewhat erratic, exhibiting no correlation with the number of ammonia molecules in the clusters. Again, it is likely that a macroscopic relation relies on a representative statistical ensemble (Zho et al. 2018; Park & Schwartz 2022) instead of a single conformer (Herbert & Head-Gordon 2005).

To better understand how cluster isomers affect the VAE, eight (NH₃)₂₃ conformers along the AIMD trajectory (T = 210 K, NVT) were extracted (see ESI) with a considerable range of VAE values, −5.6 to +1.0 kcal/mol. Such behaviour underlines the importance of dynamical effects which are associated with molecular translational and librational motions and are extremely important in electron relaxation (Yang et al. 2001; Lee et al. 2008). The values reported in Table 3 represent single conformers lying on the PES cluster. The correlation to macroscopic variables/relations should consider phase space exploration by sophisticated AIMD methods especially if phase transitions are involved (Sun & Cheng 2019).

However, crystalline ices or amorphous solids with reduced phase space; i.e. negligible translational motion with limited rotational degrees of freedom, should demonstrate a better correlation between single conformer(s) and VDE values. To test, single point calculations are performed on (NH₃)_n, n = 14, 23, 38 clusters based on 1 × 1 ×1, 1 × 1 ×2, and 1 × 2 ×2 unit cells of solid ammonia (Olovsson & Templeton 1959) in both the neutral and radical-anionic states (Fig. 3). As can be seen in Fig. 3, the spin density is again localized externally to the cluster.

Figure 3.

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Single point calculations on crystalline (NH|$_3)_{14}^{-\cdot }$| (upper panel, left), (NH|$_3)_{23}^{-\cdot }$| (upper panel, right), and (NH|$_3)_{38}^{-\cdot }$| (lower panel). For clarity, the (NH|$_3)_{23}^{-\cdot }$| and (NH|$_3)_{38}^{-\cdot }$| clusters are depicted in perspective. Isosurface value: 0.0001 a.u.

Plotting the calculated VDE values against the inverse number of NH₃ molecules in the solid cluster model (Barnett et al. 1988a, b; Sarkas et al. 2002; Park & Schwartz 2022) (Fig. 4), a clear linear relation is obtained (for further details, see ESI). The VDE intercepts the axis at 24.43 kcal/mol (1.06 eV), which gives a prediction of the crystalline ammonia VDE. Our value is lower compared to the experimentally measured VDE of 1.25–1.47 eV in the bulk liquid (Haesing 1940; Aulich et al. 2003).

Figure 4.

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Plot of the calculated VDE (kcal/mol) versus n^−1/3; (n = 14, 23, 38) based on a CBS extrapolation method using the DLPNO-CCSD(T)/aug-cc-pVT(Q)Z and DPNO-CCSD(T)/aug-cc-pVD(T)Z levels of theory. The intercept approximates the VDE in the bulk. Solid line: CBS aug-cc-pVT(Q)Z; dashed line: CBS aug-cc-pVD(T)Z. Fitting equations are depicted. See ESI for details.

The results indicate that a crystalline (NH₃)_x cluster or ammonia ice (T ≤ 195 K) can trap and stabilize low-energy electrons. Furthermore, the external state of the radical-anion (see Fig. 3) can be correlated to the experimental finding where low-energy electrons ‘injected’ in an NH₃ thin porous amorphous or crystalline ice layer are mainly displaced on the surface (Sagi et al. 2021). In Section 3.3, the ammonia clusters and solid surfaces reactivities with astrochemically relevant molecules will be analysed.

3.3 (NH₃)_n clusters interacting with H₂O, CH₃OH, HCN, and CO molecules

Once primary or secondary electrons are trapped by an ammonia cluster or solid surface, an electron transfer to a hetero-molecule physically absorbed on the cluster or surface can be hypothesized. Ammonia (melting point T_mp = 195.42 K, boiling point T_bp = 239.81 K) is in the solid state at T = 100 K considered by our computations. Crystalline or amorphous structures with a solid/solid or solid/gas interface can be present. As case studies, four different astrochemically relevant molecules were considered: H₂O, CH₃OH, HCN, and CO selected by their abundances, involvement in formation of complex organic matter (COM), and hydrogen bond donor-acceptor character. In Fig. 5, the (NH|$_3)_{14}^{-\cdot }$| cluster is shown in contact with H₂O, CH₃OH, HCN, or CO.

Figure 5.

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Optimized H₂O-(NH|$_3)_{14}^{-\cdot }$|⁠, CH₃OH-(NH|$_3)_{14}^{-\cdot }$|⁠, HCN-(NH|$_3)_{14}^{-\cdot }$| CO-(NH|$_3)_{14}^{-\cdot }$| are depicted. Isosurface value: 0.0002 a.u.

Inline with previous results, the spin density is almost always localized externally to the cluster with no qualitatively relevant density on any atoms of the hetero-molecules. The same trend is displayed by the (NH|$_3)_{8}^{-\cdot }$| cluster in presence of CO, HCN, and CH₃OH where no apparent electron transfer was found (see ESI) with the exception of water. In fact, under certain geometrical conditions, the spin density of the excess electron can be mainly localized on the water and methanol molecules forming very reactive H₂O^−· and CH₃OH^−· radical-anion species (see Fig. 6). From interpretation of spin densities, no CO^−· or HCN^−· species are observed.

Figure 6.

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Optimized H₂O-(NH₃)_n and CH₃OH-(NH₃)_n (n = 4, 8, 14), are depicted. In the first line, the (NH₃)₄ neutral cluster is reported to better illustrate the common H-bond geometry involved in the electron transfer where both ‘lone pairs’ of H₂O and CH₃OH interact with two Hs of two different ammonia molecules in a perfect tetrahedral rearrangement. Isosurface value: 0.0002 a.u.

The absence of electron transfer between the analysed ammonia clusters and HCN or CO molecules could originate from a limited sampling of conformations and by interactions between the frontier orbitals where energy difference, symmetry, and overlap play a major role. This idea is reinforced by the computed EAs of the neutral molecules, based on the computational scheme reported in Section 2.1, the obtained values (kcal/mol) are: EA|$_{H_2O}$| = −5.7, EA|$_{CH_3OH}$| = −0.3, EA_HCN = −29.1, and EA_CO = −22.6. Although all molecules provide a negative EA, CO and HCN have much larger negative values compared to H₂O and CH₃OH, pointing to an important correlation between the EA of the heteromolecule and electron transfer with the ammonia cluster.

In Table 4, the EA, ΔG of formation, and relative stability of the analysed clusters are reported. Three general trends can be extracted from Table 4:

• The EA values with only few exceptions are always positive. Interestingly, EAs associated with clusters involved in electron transfer are higher than those with no apparent electron transfer, favouring the formation of the radical-anionic forms of water and methanol with the exceptions of H₂O-(NH|$_3)_{8,14}^{tr}$|⁠.

• The ΔG|$_{A^0}$| values always favour cluster formation. However, the conformers involved in electron transfer show a slightly less favourable formation energy, with the highest value belonging to the CH₃OH-(NH|$_3)_{14}^{tr}$| cluster (G|$_{A_0^{tr}}$|-G_A = 7.3 kcal/mol);

• Cluster radical anions are always more stable than the corresponding neutral clusters, with the exception of the H₂O-(NH₃)₈ cluster reporting ΔG|$_{A^{-\cdot }-A_0}$| = 0.4 kcal/mol. Furthermore, the radical-anionic conformers reporting an electron transfer are less stable than the corresponding neutral clusters, with the most unfavourable case represented by the CH₃OH-(NH|$_3)_{14}^{tr}$| cluster (G|$_{A^{-\cdot }}^{tr}$|-G|$_{A^{-\cdot }}$| = 8.2 kcal/mol).

The formation of the very reactive H₂O^−· and CH₃OH^−· radical-anion species initiates complex organic chemistry at low T. For example, (H₂O)^−· decomposition results in a series of highly reactive products such as H⁻ + OH, H₂ + O⁻, and H + OH⁻ (Garrett et al. 2005). Experimentally, water radical anions were indirectly observed in micro-droplet chemistry (Qiu & Cooks 2022), playing a main role in the water/air interface (Liang, Zhu & Yang 2023).

Methanol irradiation by electrons of different energies is experimentally well known due to its importance as a starter in COM formation (Torres-Díaz et al. 2023). For example, from a dissociative electron attachment centred at ≈5.5 eV or a neutral dissociation mechanism ≥7 eV, CH₃O^· and H^· radicals are formed that lead to the formation of methyl formate upon CO addition (Schmidt et al. 2021).

Although the extrapolation of cluster properties to solid surfaces must be made with caution, experimental findings where electrons are trapped and accumulated on the surface of ammonia ice (like in a capacitor) (Sagi et al. 2021) can support the hypotheses: (i) the electron external state on the surface of a cluster is valid for a solid surface (an expected phenomenon due to surface charge accumulation in a conductor-like material); (ii) if water and methanol interact with the solid surface, an electron transfer to such molecules is possible. In such a case, the polarized interface between the two chemical phases plays an important role working similarly to an astrochemical ‘electrode’ where water, ammonia, and methanol are involved in the formation of COM with electrons captured and donated by solid NH₃ at low T.

4 CONCLUSIONS

NH₃ and a few low molecular weight primary amines in the liquid state are known to stabilize e⁻ by forming ammoniated electrons. As such, due to the presence of solid ammonia in or on a great variety of astrophysical bodies, the existence of ammoniated e⁻ in the solid state would open new pathways to low temperature astrochemistry. The aim of this work is to analyse two main problems: (i) is it possible for ammonia clusters and solid ammonia in both the amorphous and crystalline states to capture and stabilize e⁻ similarly to liquid ammonia?; (ii) once the e⁻ is captured and stabilized, is it possible for the e⁻ to be transferred to molecules of astrochemical interest such as H₂O, CH₃OH, HCN, and CO?

• The ability of ammonia clusters (NH₃)_n (n = 4, 5, 6, 8, 24, 34) to trap and stabilize e⁻ was analysed by computational methods (DFT, DLPNO-CCSD(T), AIMD) and an extrapolation to the solid state in both the amorphous and crystalline state was analysed. With the exception of the smallest cluster (n = 4), the radical-anions are stable with the e⁻ localized externally to the clusters (T = 100 K). The extrapolation to the bulk amorphous state was challenging due to the dependence of EA/VDE/VAE values on conformational and isomeric statistical ensembles. The results underline the necessity to explore meaningful portions of the phase space to extract macroscopic values of the considered variables using enhanced sampling AIMD techniques. The crystalline bulk VDE was extrapolated by a series of different cluster dimensions to find a VDE = 1.06 eV, indicating that a low-energy electron could be captured and stabilized in ammonia ices.

• NH₃ is an important nitrogen donor in astrochemistry and its abundant presence in the Kuiper belt planetoids, comets, and giant planets can initiate the formation of N-based complex organic chemistry. As such, if molecules of astrochemical interest (H₂O, CH₃OH, HCN, and CO) are adsorbed on ammonia clusters or on solid ammonia surfaces in both the crystalline or amorphous states, an electron transfer from ammonia to a heteromolecule is possible under opportune conditions. The electron transfer from the radical-anion ammonia cluster was found favourable to water and methanol under a precise geometric arrangement of the hydrogen bond network. No electron transfer to HCN and CO was found. The formation of water and methanol radical-anions, due to their extreme reactivity, develop a complex organic chemistry at low T. Formally, the overall process, in the presence of a polarized surface, can be defined as an astro-electrochemical reaction based on the sequence: flux of free e⁻ →e⁻ capture/stabilization/surface polarization → transfer to the heteromolecule, where the ammonia works as an electron trap or ‘cathode’.

Furthermore, the use of AIMD is essential if macroscopic values such as EA, VDE, and VAE are to be estimated, especially if liquid/amorphous states are to be considered. In fact, clusters can undergo different phase transitions at different temperatures compared to the macroscopic states, as such, such transitions should be taken into account and analysed. Future analysis of the cluster phase space in selected ensembles will be performed. In conclusion, the ability of clusters and crystalline solid NH₃ to capture and stabilize low-energy/secondary electrons suggests a fascinating aspect of astro-electrochemistry where extremely reactive chemical species (radical anions) are formed at low T. This work demonstrates that theoretical studies of astrochemical reactions can also lead to new directions in terrestrial electrochemistry or surface science.

ACKNOWLEDGEMENTS

We thank the Department of Chemistry at the University of Memphis and the University of Memphis High Performance Computing Facility for support. Prof. Dr NJDY and Dr MF acknowledge funding from the National Science Foundation (NSF CAREER BIO-1846408 and NSF CHE-2154121). Prof. Dr ROR acknowledges funding from Department of Science and Technology (DST), the Science and Engineering Board (SERB), and ECR/2016000041.

DATA AVAILABILITY

The data underlying this article are available in the article and in its online supplementary material.

References