Quantum chemical exploration of the binding motifs and binding energies of neutral molecules, radicals and ions with small water clusters: characterisation and astrochemical implications

ABSTRACT Accurate binding energies of molecules to water clusters are relevant for understanding intermolecular interactions and various chemical applications. They enter models of interstellar chemical processes, as binding to icy grains influences surface reactions and thus affects calculated gas-phase abundances. Unfortunately, many astrochemical molecules (especially radicals and ions) are incompletely characterised in these models. To address this, we report computational searches for optimal structures and benchmark binding and condensation energies for sets of neutral, radical, cationic, and anionic molecules of astrochemical relevance with clusters of $ N=1{\rm -}4 $ N=1−4 water molecules. These calculations utilised reliable density functionals for geometry optimisation, and coupled cluster (CCSD(T)) single point calculations with large basis sets. Four energetic binding motifs (weak, intermediate, strong or covalently bonded) were observed depending on the chemical nature of the guest molecule. Neutral closed and open-shell molecules with strong dipoles and a greater potential for hydrogen bonding are more tightly bound to water clusters compared to non-polar ones. For closed-shell cationic and anionic species, barrier-less reactions with water clusters occur, which reveals radical-free routes to molecular processing in the gas phase and on amorphous ice surfaces. GRAPHICAL ABSTRACT


Introduction
Molecular reactions in the interstellar medium (ISM) range from relatively simple to amazingly elaborate in spite of its extreme physical conditions.Despite low number densities and cold temperatures, it has been known since the 1930's that reactive chemistry in a variety of extraterrestrial environments produces a diverse array of molecules [1][2][3][4][5][6].
of novel and increasingly complex organics can be instigated by the condensation of molecules onto icy grain surfaces, where processing via stellar radiation or impact activation can promote reactions that yield interesting products, including pre-biotic molecules such as nucleobases [10,11].
Icy grains are prevalent in the frigid, dense ISM, and can originate from multiple sources -a few relevant examples include dense molecular clouds, inside the snowline of the proto-planetary disks, in planetary atmospheres, and in the gaseous plumes of Enceladus.Most grains from the former sources, particularly molecular clouds, are particles of interstellar dust containing other atomic and molecular species coated in an icy mantle.The water condensation process in particular influences the composition of the amorphous ice particles and thus the reactions that occur on them [12].The H 2 O matrix plays an important role in instigating reactions and shaping the molecular composition of the ices by acting as a catalyst, lowering energetic barriers for a given reaction, and more [13][14][15].Analysis of ejecta from vents at the surface of Enceladus, an icy moon of Saturn, has shown evidence of macromolecular material that may have been produced from hydrothermal activity in the sub-surface ocean, or possibly formed by reactions on the icy grain surfaces from deposited precursors [16][17][18].
Grain surface chemistry is dependent on elementary processes including molecular binding, diffusion, surface reaction, dissociation, and impact activation.These processes are typically included in gas-grain chemical models, and are critically important for understanding phenomena from core collapse to planetesimal formation.The binding energy of a molecule directly influences its desorption efficiency, which in turn affects its gasphase abundance and reaction potential after cold grain production.Diffusion coefficients, for example, are often calculated as a fraction of the binding energy; however, the diffusion behaviour of molecules can vary greatly and should be evaluated on a case-by-case basis (as will be demonstrated by the results presented here).While several of the most important molecular binding energies with one or two water molecules and some experimentally obtained data for neutral molecules are included in gas-grain chemical models, many of these values (especially for radicals and ions on ice) are not available, and are either assumed from literature values of similar species or not considered at all.Inclusion of the binding energies of such species to amorphous ice analogs is expected to result in a significant improvement in the outcomes of gas-grain chemical models.
Experimentally, binding energies are usually determined using techniques such as temperature programmed desorption (TPD), where target species are adsorbed to and desorbed from a particular substrate in a controlled fashion [19].Condensation and vaporisation temperatures of H 2 O and CO ice, and associated binding energies, have also been investigated using infrared spectroscopy [20].Although this method can provide useful data, it is highly dependent on the reactivity of the target species and the nature of the substrate among other experimental parameters.Experimental data for reactive species (i.e.radicals as well as ions) are limited since these typically have fairly short lifetimes in the laboratory.Finite water clusters with a dopant molecule, ion or radical represent the small particle limit and there has been a tremendous amount of experimental work to generate and spectroscopically characterise such species.It is beyond our present scope to adequately review this large literature, but a number of major reviews provide an entry point for the interested reader [21][22][23][24][25][26][27].
Computationally, the same challenges of modelling reactive species and building a suitable grain surface remain.Periodic density functional theory (DFT), molecular dynamics and mixed QM/MM approaches have been used to describe amorphous water surfaces and compute molecular binding energies, which give insight into the range of binding sites available on an ice grain [28,29].A small but growing set of data is available for the binding energies of molecules with smaller water clusters, usually in the range of one to ten waters [30]; calculations of this size are tractable at a modest level of theory [31][32][33].Wakelam et al. have performed fitting procedures between computed and experimental binding energies to bootstrap their way to larger water clusters [34].Recently, Bovolenta et al. have made Python libraries available for the reliable, systemic calculation of binding energies based upon DFT and other methods [35].Despite these efforts, as well as a tremendous amount of work on the computational modelling of clusters in general, [36] systematic binding energies calculated using highly accurate methods are not widely available even for relatively 'simple' species, and even less information is available when it comes to ionic and radical species.
In this work, we aim to present the results of a computational exploration of the binding motifs (i.e.preferred mode of binding) and the associated binding and condensation energies for sets of neutral, radical, cationic, and anionic molecules relevant for reactions occurring on icy grains.We aim to explore: (1) How does the binding energy and the preferred mode of binding of a molecule to water change between open and closed-shell molecules?(2) How do the binding energies and associated structures of closed-shell cations and anions compare to their neutral counterparts?(3) What electronic structure-, stereochemical, or functional group-dependent trends are apparent in the binding energies of these species to small water clusters, and how do they affect the potential reactivity of the molecules in question?(4) How do the binding energies change during the water condensation process, i.e. for successively larger water clusters?Using high-level ab initio density functional theory (DFT) and Coupled-Cluster (CCSD(T)) methods, we have identified low-lying cluster geometries for molecules bound to N = 1−4 waters, and compared the trends in binding energies that result from changes in functional groups, ionisation, and other electronic structure modifications.Our results expand the existing data for binding energies of small neutral and radicals in a meaningful and systematic way and for the first time introduce these data for the ions.These results provide insight into how electronic structure influences the binding energies and therefore the reactivity of these species during the water freeze-out process.

Methods
Water cluster structures have been well described in the existing literature [37][38][39][40]; the structural geometries for bare water clusters of varying size were selected and subjected to geometry optimisation, frequency evaluations, and single point energy analyses as described below.In order to sample the conformers associated with multiple binding sites on a given water cluster in an effective way, we utilised automated conformer generation with Grimme's Conformer-Rotamer Ensemble Sampling Tool (CREST) [41], which is supported by Grimme's GFN2-xTB tight-binding software [42], and provides a rapid avenue for conformer generation.
For neutral and open-shell guest molecules with N = 1−4 molecules, 50-100 conformer geometries were computed with CREST, and the 10 with lowest energy were selected for further analysis and optimisation.Additional structures were explored and validated using conformer searches informed by chemical intuition.For open-shell and ionic guest molecules, CREST was not used due to the observation of poor results for these types; the structures that were generated deviated from those one would expect based on a general understanding of chemical interactions.These results depicted several instances of unusual chemistry, for example, with attractive forces between protons.Such discrepancies likely stem from limitations associated with the underlying GFN2-xTB framework, such as the minimal basis set and high levels of element-wise parameterisation used in this theory.Instead, starting structures were generated using a chemically intuitive starting point or inspired by literature structures if available.
Unique conformers established during pre-screening for each molecule were selected for geometry optimisation using DFT at the ωB97X-V/def2-svpd level of theory [43].Vibrational frequency calculations were performed using the same basis and functional to ensure that minima were found successfully.Single point energies for the conformers that were found to be the energetic minima for a given guest molecule-water complex were refined with the same functional in the larger def2qzvppd basis set to reduce basis set incompleteness error (BSIE) as well as to mitigate basis set superposition error (BSSE) [44].All DFT calculations were performed using the Q-Chem software package [45].Zero Point Vibrational Energy (ZPVE) corrections were included at the ωB97X-V/def2-svpd level.These were calculated using the following scheme: Here, To achieve a high level of computational accuracy and provide very accurate binding energies for binding to small water clusters, optimised geometries at the ωB97X-V/def2-svpd level were used to calculate single-point energies at the CCSD(T)/aug-cc-pVTZ level of theory.All the coupled cluster energies were evaluated using the MOLPRO quantum chemistry package [46].DFT calculated zero-point vibrational energies were used for the ZPVE corrections of the CCSD(T) energies.We shall subsequently see that there is excellent agreement between the DFT and coupled-cluster binding energies, which serves to validate the DFT protocols which will be the primary workhorse for larger clusters.

Results
Representative neutral, radical, cationic, and anionic molecules were chosen with consideration to 1. species that have been detected in cold molecular clouds or planetary atmospheres, 2. species that are postulated to be present in such environments, and 3. species that have been indicated as important for astrochemical modelling that display a good range of functional groups, and thus varied chemical properties.Binding energies were computed for a total of 25 distinct species with water clusters containing N = 1−4 water molecules as discussed below.
In the following sections, the binding energies of the closed shell neutral molecules, neutral radicals, cations, and anions with one to four water molecules are presented.A discussion of the observed trends in structures and binding energies and their implications for various astrophysical environments are presented sequentially.For each molecule, radical, or ion, many low-lying conformers or isomers were identified with (N = 1−4) water clusters.Only the lowest-lying cluster is presented here for comparison.All the other structures and their interaction energies are presented in the Supplementary Information, available in electronic form only.

Neutrals
Figure 1 shows the trends in (a) condensation energies (Equation (2)) and (b) binding energies (Equation ( 1)) between neutral molecules and water clusters of up to four water molecules.As can be seen from Figure 1(a), the condensation energy increases monotonically with number of waters, reflecting growing numbers of interactions.By contrast, the binding energy (Figure 1(b)) of the guest to the cluster does not necessarily increase monotonically as the water cluster grows.With a large enough number of molecules, water interacts most strongly with itself, forming well-documented structures from the monomer to the pentamer [38,39,47].For guest species that do not interact too strongly with water, such as the neutral molecules presented here, the most powerful interactive forces are hydrogen bonds optimised for the maximum amount of H 2 O • • • H-OH interaction, leading to tightly bound structures and a peripherally attached guest molecule.Since the guest species is in large part adapting to the water cluster rather than viceversa, the binding energy need not increase with cluster size.
Hydrocarbons are the least tightly bound group, here modelled by CH 4 , C 2 H 2 , and C 2 H 4 .CH 4 , without any π-system, barely interacts with the water at all, leading to only weakly bound complexes for all water cluster sizes.In these cases, the water complex is bound in its lowestenergy configuration (that is, the structure observed in the presence of no guest molecule), adjacent to the guest molecule.Notably, despite being linear hydrocarbons without means for strong hydrogen bonding networks, C 2 H 2 and C 2 H 4 do bind more strongly than their saturated cousin CH 4 .For the N = 3 and N = 4 water cases, the water mostly interacts with itself, forming only weak interactions between water's oxygen and H-C bonds in the hydrocarbon.Interactions are most obvious in the N = 2 water case, where there is some attraction between the hydrogen atoms of the water and the double or triple C-C bonds of each hydrocarbon, i.e. interaction with the π system (π • • • H-OH).A similarly weak binding is seen for N 2 ; while the nitrogen can interact with the O-H of water, the molecule has no dipole moment, and thus interactions are weak with individual water molecules.
The polar molecules H 2 CO, HCN, and NH 3 are are more tightly bound to the water clusters.H 2 CO and HCN have two sites that can interact via hydrogen bonding with water, with electron deficient H atoms at one end and electron rich O and N atoms respectively at the other.For HCN, the NCH−OH 2 interaction is dominant, as has been documented in previous literature [48][49][50].
Notably, the curves for NH 3 and H 2 O are quite similar in shape and magnitude.The chemical structure and potential for hydrogen bonding of NH 3 is somewhat akin to that of H 2 O, with an electron rich nitrogen atom in place of oxygen; as evidenced by the cluster structures with N = 1−3 waters, the structural formations of NH 3 and water clusters are analogous to water with itself, leading to similar general trends in binding energies and maximising hydrogen bonding.In previous literature, the global minimum of NH 3 with four waters was found to be a cyclic structure; while we have included this conformer and a number of other documented low-lying isomers in our analysis [51,52], we have identified an alternative lower energy structure where NH 3 interacts with the water cluster through hydrogen bonding without forming a pentamer-like complex.The minimum used here, with NH 3 bonded to the water tetramer by a HO-H••• NH 3 hydrogen bond but not incorporated into the cluster, is also used by Das et al. [30].The latter is more representative of a guest molecule approaching an existing water cluster structure, while the hydrogen-bonded pentamer (analogous to the 5-water cluster) is more indicative of a structure where the guest molecule has integrated fully into the cluster, or where waters are added sequentially and relaxed.
Table 1 compares the binding energies calculated with DFT to those acquired with CCSD(T).In general, the agreement between the two is very good.For the guest molecule bound to a single water molecule, discrepencies between DFT and CCSD(T) are less than 0.4 kcal/mol for all the guest molecules investigated here, with N 2 binding showing the largest deviations.As the water cluster size increases, errors in DFT compared to CCSD(T) scarcely change, indicating that the DFT numbers were well converged near accurate values.Indeed, BSIE is smaller for the DFT calculations than the CCSD(T) calculations, while correlation errors are smaller for CCSD(T) than for ωB97X-V.The generally very good agreement can be considered as a cross-validation of both sets of results.In all cases, DFT slightly overbinds in comparison to CCSD(T).

Radicals
Somewhat surprisingly, many open-shell neutral radicals (Figure 2) have (a) condensation and (b) binding energies very similar to those of their closed-shell counterparts.Despite their reputation as highly reactive species, none of the radicals studied here spontaneously reacted with members of the water cluster.Of course, there are other minima separated by energetic barriers from the structures characterised here that appear reacted (i.e.covalently bonded): for instance, the H 2 O • • • H • cluster has another local minimum corresponding to HO • • • • H 2 , but we did not consider these highly activated rearrangements.Structurally, the radicals tend to bind peripherally to the H 2 O clusters.In agreement with previous literature, H • is the weakest binder and interacts remotely with the water cluster for all structures via dispersion forces; even at cluster sizes of four waters, H • binds at a magnitude of only ∼ 1 kcal/mol.Structures of H • bound to clusters of N = 3 and N = 4 waters are shown in Figure 3. Previously calculated binding energies for H • with four waters are even lower, significantly less than 1 kcal/mol -this discrepancy could be accounted for by the inclusion of crucial zero point corrections in our study, which were neglected by Das et al. [30].The NO • radical also behaves only as a spectator to the water clusters, especially as they grow in size, and is bound with a strength of ∼ 2.5 kcal/mol at the largest cluster size.Chemically, this lack of interaction is easily explainable due to the lack of a strong dipole in NO • , which leaves hydrogen bonding interactions between the waters of the cluster itself as the strongest forces at play.
Similarly, open-shell hydrocarbon species are bound to water clusters through weak dispersion forces (Table 2).CH 3 • , the dehydrogenated analogue of CH 4 , binds only slightly stronger than CH 4 to water clusters, and hydrogen bonding amongst the waters prevails over any interaction from the guest molecule.The pattern of binding between the dehydrogenated radical CH 3 • and neutral CH 4 for water clusters of increasing size is strikingly similar.While CH 3 • binds with a slightly greater strength to all clusters (by approx.0.5-1 kcal/mol), the binding strengths for both CH 4 and CH 3 • increase from cluster sizes of 1-2 waters, decrease slightly for interactions with 3 waters, then increase slightly for 4 waters.The magnitudes of these interactions scale similarly as well -for the largest cluster, CH 3 • is bound by approx.3 kcal/mol (only ∼ 0.1 kcal/mol stronger than CH 4 ), indicating that these are van der Waals clusters.These analogous trends for molecules of similar functional groups between the open and closedshell molecule sets are apparent for several species, including several that bind with greater strength.
Stronger binders HCO • and NH 2 • also exhibit patterns in binding that are similar to their neutral cousins H 2 CO and NH 3 .NH 2 • (like NH 3 ) acts as a hydrogen bond acceptor and actively participates in the water cluster.In the lowest-lying tetramer geometry, NH 2 forms a complex nearly identical to the lowest-lying geometry of the water pentamer, a structure that has also been observed as a minimum for NH 3 [49,52].The O-H••• N distance in this structure is quite short at ∼ 1.8 Å, while usual O-H−N hydrogen bonding distances are slightly longer [53].Similar hydrogen bonding patterns shown in clusters containing guest molecules with N-H and O-H functional groups lead to binding strengths that are quite similar for NH 2 • , NH 3 , and H 2 O, both in magnitude and curve shape with increasing numbers of water.The hydroxyl radical OH • also binds in a similar pattern to water with itself (with a nearly identical magnitude of binding energy), and has been investigated more thoroughly in previous literature [54].Xie and Schaefer found the ground state dissociation energy of OH-H 2 O complex to be 5.6 kcal/mol at the CISD/TZ2P level of theory.We find the binding energy (as opposed to Xie's dissociation) of this complex to be −3.82kcal/mol.The binding energies of OH radical to H 2 O dimer, trimer and tetramers are −7.75, −8.45, and −7.30 kcal/mol, respectively.
Comparatively, HCO • is an interesting case.Like NH 2 • , HCO • maximises hydrogen bonding with water molecules to form cyclic structures for N = 2 waters and above (shown bound to the water trimer and tetramer in Figure 4).However, while the binding strengths for nitrogenated guest molecules such as NH 2 • generally increase as the water cluster size grows, HCO • experiences a dramatic decrease after N = 2 waters.The hydrogen bonding interactions for the C = O bond of HCO • are notable -however, they are still not as strong as those of the H--O-H bond of H 2 O with water or the H--N-H bond of NH 2 • ; so, despite similarities in structure, the interactions between this molecule and water clusters are not as robust.The strength of hydrogen bonding tracks well with X--H bond distances, where X is the atom acting as a hydrogen bond acceptor on the guest molecule.Hydrogen bonds for NH 2 • , OH • , and HCO • are indicated in Figure 4 for the water trimer and tetramer.For both NH 2 • and OH • , X--H hydrogen bond distances shorten notably upon addition of a water molecule to the cluster.Previous work on species such as the peroxy radical supports the observation that an unpaired electron can influence hydrogen bonding of radicals to water, with hydrogen bonding effects strengthened or diminished depending on the bonding angle and relative positioning of the unpaired electron [55,56].
Overall, many the neutral open-shell molecules behave similarly to the neutral closed-shell ones; despite having an unpaired electron, hydrogen-bonding interactions between water molecules generally win out over interactions with the guest molecule, unless the guest has a significant ability to act as a hydrogen bond donor or acceptor.

Cations
Charged water clusters have been and are currently a highly active area of research [57][58][59], as are hydrated alkali ions [60][61][62][63][64] and other molecules [65][66][67][68].There are many careful, benchmark-level studies of the complexes formed by simple cations, such as the alkali metal ions, hydronium, and ammonium, with small water clusters.Cations are considered to be major contributors to interstellar chemistry, but their inclusion in astrochemical models has been limited.From a chemical viewpoint, cations of the AH n+1 + form considered here can be viewed as acids whose conjugate base is a neutral AH n molecule.Such acids can be very strong, and can in some cases initiate barrier-less chemical reactions, as discussed below.with one water molecule.The binding of water with itself, which to this point has been the strongest guest binder, is the weakest binder here compared to the ions.As the water cluster size grows from N = 1−4 water molecules, binding energies with all cationic guest molecules smoothly increase and begin to plateau between N = 3 and 4 waters.The substantial binding energies observed in these cations can be attributed to intense electrostatic interactions (both permanent and induced), as well as partial charge-transfer to the electrophilic cation.All these factors promote reactivity with water and, in some cases, initiate barrier-less acid-base chemistry (Table 3).
The weakest binders from this set of cationic molecu les (NH 4 + and H 3 O + ) still have binding energies at least twice that of their non-protonated counterparts NH 3 and H 2 O.The dramatic effect of even modest acid/base chemistry on binding energies for a given cation is immediately apparent in H 3 O + -this molecule effectively shares a proton with the other H 2 O in the cluster.NH 4 + is the only molecule of this set that undergoes no further reaction when solvated; the lowest energy structures of NH 4 + with water clusters maximise hydrogen bonding interactions between the protons of NH 4 + and the oxygen molecules of H 2 O, but no protons are lost to the water cluster, and no new chemical bonds are formed.This lack of reactivity has been noted in previous studies of solvated NH 4 + in clusters containing up to six waters [69].Four unique conformers within 3. 25   + and H 2 O produces protonated hydroxylamine spontaneously; as the water cluster size grows, the potential for proton sharing increases, and hydroxylamine is deprotonated.
As the number of waters in the cluster increases, the N-O bond distance in this hydroxylamine moiety decreases to 1.43, 1.42, and 1.40 Å for N = 2, 3, and 4 waters, respectively.As a proton from the bonded O-H is pulled away to interact with other free H 2 O, the new N-O bond starts to form.At N = 4 waters, hydroxylamine is fully realised; the three remaining waters interact through hydrogen bonding and a proton is shared between the nitrogen of hydroxylamine (formerly NH 2 + ) and a water molecule.The difference in binding energy magnitudes between the two NH cations (NH 2 + and NH 4 + ) is quite striking -by contrast, NH 4 + is non-reactive with water molecules in the cluster.For interactions of NH 4 + with water trimer and tetramer, the H 3 N-H••• OH 2 bonds are slightly lengthened (by 0.02-0.04Å), but not at lengths long enough to break the N-H bond and donate a proton into the water cluster.Unlike NH 2 + , no N-O bond is formed to create a new species.
A rather strong binder is CH 3 + , which reacts with water molecules to form protonated methanol, CH 3 OH 2 + , or a composite closely resembling methanol with H 3 O + (shown in Figure 7).In a similar trend to NH 2 + , bond distances between the closest interacting water molecule and the carbon atom of CH 3 + decrease to 1.50, 1.47, and 1.44 Å with N = 1−3 waters, respectively.In the case of the water tetramer, the C-O bond length again increases slightly to 1.45 Å; another lowlying conformer where methanol is fully realised in the tetramer case lies approx.3 kcal/mol higher in energy.The water molecules assist with solvation of the proton and make the formation of CH 3 OH possible.This indicates the spontaneous formation of NH 2 OH and CH 3 OH from cations in water clusters.Ion-molecule reactions are known to produce important prebiotic molecules in astrophysical environments [70,71].Recently, the CH 3 + ion was detected in the Orion nebula in a protoplanetary disk d203-506 where H 2 O was not detected [72].
Our results indicate that the methyl cation may have been detected because the disk lacked water.Had water been around even in small quantities in the disk it would have depleted CH 3 + by reactions with H 2 O to make CH 3 OH.

Anions
We have also explored binding motifs and computed binding energies for selection of closed-shell anionic species to water clusters (Table 4).Generally, anions exhibit stronger binding energies compared to neutral molecules with similar formula, but do not bind as strongly to the water clusters as cations do.Broadly, one can view the anions in a simple model with A − as the deprotonated conjugate base of a neutral molecule, AH.In some cases these bases are strong enough to barrierlessly deprotonate water.
Figure 8 shows trends in the (a) condensation and (b) binding energies of seven selected anionic species.Weaker binders amongst the anions include NO − , CN − , and HCO 3 − .NO − is a relatively weak binder to just one water (compared to CN − and HCO 3 − ), but binds more strongly to dimer, trimer, and tetramer water clusters in its lowest energy conformations.For one water, the OH 2 • • • N or OH 2 • • • O hydrogen bonds occur at similar distances (1.74, 1.7, and 1.72 Å) for CN − , HCO 3 − , and NO − , respectively, and at direct angles.Increased binding energies in CN − and HCO 3 − are likely due to the stronger dipole of the C-N and C-O bonds.Binding energies with the water dimer are fairly similar for the three molecules, but divergences occur when binding to the water trimer.At N = 3 waters, both HCO 3 − and NO − bind far more strongly to the waters than CN − , as they maintain a higher count of hydrogen bonds (Table 4).
CN − interacts with H 2 O through only one 'true' hydrogen bond, as indicated in Figure 9 − are part of a group that makes water-cluster bound anions that keeps its anionic nature intact.
Anions (CH 3 − , NH 2 − ) and HCO − are stronger binders and make a group that undergoes structural changes.Figure 10 shows the result of NH 2 − binding to clusters of N = 1−4 waters.In all cases, NH 2 − acts as a strong base to spontaneously deprotonate water to form NH 3 and OH − , resulting in the smoothly increasing binding energies exhibited in Figure 8.In the complexes, the water structures (with OH − now replacing one water) mimic their minima configurations with NH 3 spectating or weakly interacting.The OH − -H 2 O cluster structures are similar to the "tree" pattern structures found earlier by [73].CH 3 − follows a nearly identical trend, deprotonating water to form CH 4 and OH − in very similar structures with the exception of the water trimer.In almost all cases anions produce OH − after exchanging a hydrogen and charge with water cluster.This leaves a neutral hydride and an active OH − in the water cluster to take part in further reactions.
HCO − has an interesting pattern of reactivity, as shown in Figure 11.With just one water, HCO − has a similar binding energy to its functional group cousin HCO 3 − ( ∼ 19 versus ∼ 15 kcal/mol, respectively).Unlike NH 2 − and CH 3 − , HCO − does not react with the water monomer; the hydrogen of H 2 O interacts with the negatively charged carbon atom of HCO − at a distance of 1.69 Å, but the attraction is not strong enough to barrierlessly deprotonate H 2 O.However, when interacting instead with the water dimer, one H 2 O molecule reacts with HCO − to form hydroxymethanolate after undergoing a H-transfer to carbon from oxygen.The relatively electronegative carbon atom of HCO − deprotonates one water of the dimer to form formaldehyde (H 2 CO), leaving OH − .This hydroxyl anion then reacts with newly formed formaldehyde to form a C-O bond In the trimer and tetramer structures, HCO − again deprotonates one water molecule to form formaldehyde and OH − .Here however, the OH − is recaptured by the water cluster, which is large enough to form cyclic structures close to those of the water minima with strong Table 4. Comparison of (zero-point corrected) ωB97X-V/def2-qzvppd and CCSD(T)/aug-cc-pVTZ binding energy values for select anionic structures, reported in kcal/mol.For several molecules, alternative low-lying conformers are available in addition to the global minima presented here.The number of low-energy conformers rise with the size of the water cluster.The final structure obtained upon minimisation depends largely on (1) the initial approach of the guest molecule relative to the cluster, and (2) interaction with an existing cluster versus sequential addition of dispersed water.

Discussions and conclusions
The binding energies presented here indicate, as expec ted, that previous estimates of binding energies of a guest molecule to one water, i.e. purely gas phase energy, do not give the full picture of binding or condensation, and that binding to a few water molecules should be considered.Binding energies, however, converge quickly as the available sites for attachment of H 2 O on a guest molecule are occupied, and after the first few H 2 O molecules, water-water interactions become the primary source of additional binding energy.The structures of the guest molecule bound to the water cluster, the binding energies and the condensation energies are dependent on the nature of the species; properties such as polarity, charge, and the ability to make hydrogen bonds are the most important factors.
For closed-shell neutral molecules and radicals, binding energies span a relatively small range of values, generally no more than approximately 10 kcal/mol for the strongest binders; predictably, polar molecules with stronger dipoles and the molecules with greater capacity for hydrogen bonding have the largest binding energies.The binding energy values computed for radicals show similar trends as closed-shell nuetrals.The strongest (non-water) open-shell binders HCO • and NH 2 • exhibit short hydrogen bonds with surrounding water molecules that may be a precursor to dehydrogenation reactions.Cationic and anionic species' interaction with water clusters are particularly intriguing.Many, but not all, of the ions investigated here bind with exceptional strength, especially the cations (some with binding energies above 100 kcal/mol).The most striking examples are NH 2 + , CH 3 + , HCO + , NH 2 − , CH 3 − , and HCO − .Each of these molecules undergo barrierless acid-base chemistry in the cluster to form new species (formaldehyde, methanol, hydroxylamine and more) and release H + or OH − into the surrounding water molecules.These reactions occur spontaneously without additional energetic input, indicating radical-free synthetic routes to important astrobiological precursors (especially oxides) in ice grains without the need for energetic processing.
Four The third is a strong binding motif found in the ion-water complexes marked with ion-dipole bound water clusters.The strength of the ionwater interactions means that they control the structure of clusters with small numbers of water molecules.The fourth category is one in which the ion has reacted with the water to make new covalent bonds and the parent ion is non-existent.This type is very important for creating new molecules in cold icy grains.
Several noteworthy examples arise from ionic species, for which reactivity and interactions with water are more dramatic.Of the cations, NH 2 + and HCO + are two that have interesting low-lying, unique conformers arising from varied starting structures.Figure 12 shows two conformers arising from two different starting structures of NH 2 + with water tetramer.The lowest-energy conformer arises from nitrogen-forward approach by NH 2 + ; another conformer approx.9.8 kcal/mol above the minimum arises from hydrogen-forward approach of the guest.For the first, the approaching nitrogen immediately binds with the oxygen atom of a water molecule in the cluster, and the positive charge shifts to this H 2 O, causing proton release as the N-O bond and hydroxylamine forms.Further rearrangement occurs as new hydrogen bonds form and the free proton is shuttled around the complex.In the second case, a similar process occurs, but the extra reorganisation needed to orient NH 2 + to form the new N-O bond leads to an alternative arrangement of waters and proton.
Similarly, approach from either the oxygen or hydrogen end of HCO + (Figure 13) influences the final structure, shown here most plainly for binding to water dimer and tetramer.Approach from the proton end appears to result in fast deprotonation by the water cluster, and conformers 12.4 and 11.8 kcal/mol above the minimum for water dimer and tetramer respectively.These alternative conformers form CO and a proton shared amongst the water molecules, in contrast to the more dramatic reactions that occur in alternative approaches.The proton reversion channel is only a minor component of the competing reaction channels.
The examples shown above are a small sample illustrating the effects of starting structure on final conformer.Additional examples may be found in the Supplementary Information.The alternative conformers resulting from varied angles of approach by the guest molecule, in addition to having different structures than the minimal energy conformer, bind to water clusters with strengths that can vary from those of the minima anywhere from less than 1 kcal/mol to 10's of kcal/mol depending on the interactions at play.This is especially important to note when considering astrochemical models, as alternative conformers found by reactive molecules may have a wide variety of binding strengths, which thus influence desorption and other surface reaction processes.
Grain-surface chemistry, especially involving grains that are covered with a thin layer of H 2 O ice, are important sites for reactive chemistry within the dense interstellar medium, proto-planetary disks, exo-planetary atmospheres, and the plumes of Enceladus.The first step of condensation of molecules on grains may be the formation of molecular complexes by binding to H 2 O or CO ice surfaces, which are the astrophysically dominant ice species in protoplanetary disks.Binding energies (BEs), and other parameters that depend on them, e.g.diffusion energies (DEs), are important input parameters for the gas-grain chemical simulations of interstellar molecular clouds and protoplanetary disks.The BEs calculated here will have significant usage, as BEs were previously only available for a limited number of molecules.In some cases, while the gas phase BEs for species with individual H 2 O molecules are available, binding energies with dimers, trimers, and clusters of water molecules adhering to the surface were not available.Even though binding energies of some major ices have been obtained from laboratory experiments, the binding and diffusion energies of key radicals and ions are largely missing because it is difficult to study them in the laboratory due to their high reactivity.Knowing the diffusion energy barriers is critical (particularly for radical species) because they control the reactivity in the ice in disk chemical models.Additionally, at present, the DE of a given molecule is considered as a fixed fraction of its BE in disk models, [34] owing to a lack of experimental and computed DE data for a large number of molecules.However, not all molecules bind equally as we have seen above.Binding energies of molecules as shown here vary significantly during the water condensation process.Some interactions are weak, that may result in those molecules diffusing easily on the surface of icy grains, while others are more strongly bound, resulting in slower diffusion.Accurate binding energy results during water condensation process presented here indicate that the DEs of molecules containing different species will vary widely given that their BEs with the H 2 O surface have strong species dependence.While the radicals and neutral species bind less strongly than water binds to itself, the binding energies of ions are significantly larger.The ions, therefore, bind permanently or change their nature altogether by reacting with the water cluster.For some ions, contact with H 2 O surface leads to a spontaneous reaction even at low temperatures.Some of these ions therefore are not likely to diffuse on water surface, though others may still be able to do so.The spontaneous reactions of some ions also indicate that these ions (NH 2 + .CH 3 + , HCO + , NH 2 − , CH 3 − , HCO − ) are less likely to be detected in the ice phase as they will have changed their nature in the ice.Other ions (NH 4 + , H 3 O + , HCO 3 − , and CN − ) will be possible to be detected in the ice.
Polar closed-shell neutrals and polar open-shell radicals e.g.NH 3 , HCN and H 2 CO, that bind almost as strongly with H 2 O surface as H 2 O itself, will sublimate at similar temperatures as water does.Hydrocarbons will sublimate at much lower temperatures.In the context of Enceladus' southern plumes, once some of these ions come in contact with the icy grains, they will react and evolve into newer species, leaving behind a proton or a hydride.
Overall, our computations provide binding energies data at the DFT and coupled cluster CCSD(T) levels for neutral closed-shell molecules, and include neutral radical and ionic species, which have received less attention in previous literature.We have identified important trends in reactivity and a variety of conformers for ionic species bound to water clusters, which are particularly important to include in models of astrochemical reactions, as ions are important synthetic drivers in environments where energetic stimulus is sparse.The binding energies computed here may be included in gas-grain astrochemical models to improve their quality, will inform us about the potential detectability of some ions, and the conformer geometries we have generated should be considered when investigating molecular binding to amorphous ice.We hope that these results will prompt more investigation into the role and fate of ions and other species in cold grains, and how the binding of these species influences the production of prebiotic molecules.

Figure 1 .
Figure 1.Zero point corrected DFT condensation energies (a), and binding energies (b) calculated for a set of closed-shell neutral molecules.As expected, non-polar molecules such as hydrocarbons exhibit weaker binding to water clusters, while molecules with a stronger dipole such as NH 3 and H 2 CO have binding energies that are nearly on par with water-water interactions.

Figure 2 .
Figure 2. Zero point corrected condensation energies (a), and binding energies (b) calculated using DFT for a set of neutral, open-shell molecules.Despite their reactive unpaired electrons, most open-shell species do not exhibit binding energies stronger than their neutral counterparts, nor do they spontaneously react in a significant way with H 2 O in the water cluster.

Figure 3 .
Figure 3. Minima for H • , NO • , and CH 3 • bound to water clusters of size N = 3 and 4.These three molecules bind only weakly to the clusters.The strongest hydrogen bonding interactions are still between water molecules, and minima configurations of these are undisturbed by the guest.

Figure 4 .
Figure 4. Minima for structures of NH 2 • , OH • , and HCO • bound to water clusters of size N = 3 and 4 waters.Hydrogen bonding interactions between the heavy atom of the guest molecule and hydrogen atoms of water are indicated by dashed lines.These guest molecules bind strongly and exhibit similar structures -hydrogen bond interactions generally become closer in distance as the number of waters in the cluster increases, resulting in steadily increasing binding strengths for NH 2 • and OH • .

Figure 5 .
Figure 5. Zero point corrected condensation energies (a), and binding energies (b) for cationic closed-shell molecules with water calculated using DFT.All ions tested here bind to water clusters significantly more strongly than neutral or radical molecules.The molecules with the strongest binding energies (NH 2 + , CH 3 + , HCO + ) react with water as the cluster size increases to form new solvated products and a free proton.Neutral H 2 O is included as a reference point.A larger negative number indicates stronger binding.

Figure 6 .
Figure 6.Optimized geometries for the lowest-energy conformers of NH 2 + bound to water monomer, dimer, trimer, and tetramer.Close interaction between NH 2+ and H 2 O produces protonated hydroxylamine spontaneously; as the water cluster size grows, the potential for proton sharing increases, and hydroxylamine is deprotonated.

Figure 7 .
Figure 7. Optimized minima CH 3 + bound to clusters of N = 1−4 water molecules.Like NH 2 + , CH 3 + reacts with one of the water molecules to form a new species (methanol).
: CN••• HOH between CN − and H 2 O, and one additional hydrogen bond exists between the additional two water molecules, which form a dimer structure.This dimer interacts with C through a weaker HOH••• CN − attraction.In contrast, HCO 3 − and NO − form five hydrogen bonds both between the water molecules themselves and the guest molecule.Upon complexation with an additional water (N = 4 H 2 O), the minimum energy conformer of HCO 3 − with four waters now forms one extra hydrogen bond than those in the complexes of CN − and NO − , giving HCO 3 − a slight edge in binding once again.These three anions, CN − and NO − , and HCO 3

Figure 8 .
Figure 8. Zero point corrected condensation energies (a), and binding energies (b) for a set of anionic molecules calculated using DFT.The magnitude of binding energies exhibited by anions is greater than closed and open-shell neutrals, but less than that of cationic molecules in the previous section.Analogous to the cations, the strongest binders are CH 3 − , NH 2 − , and HCO − .Neutral H 2 O is included as a reference point.

Figure 9 .
Figure 9. Hydrogen bonding (marked with dashed lines) for anionic conformers of CN − , HCO 3 − , and NO − , from left to right, with N = 3 waters.NO − and HCO 3 − maximise the number of hydrogen bonds formed between guest and water molecules, and thus have larger binding energies than CN − .

Figure 10 .
Figure 10.NH 2 − reactivity with water clusters of size N = 1−4.NH 2 − acts as a strong base to spontaneously deprotonate water, forming NH 3 and OH − .The resulting hydroxyl anion clusters with the remaining water molecules in familiar structures, while newly formed NH 3 interacts less strongly.

Figure 11 .
Figure 11.Minima geometries of HCO − interacting and reacting with N = 1−4 water molecules.Different reactions occur with differing numbers of H 2 O; in the case of N = 2 waters, HCO − reacts with one water to form hydroxymethanolate, H 2 COH(O) − , which is the conjugate base of methane diol, H 2 C(OH) 2 .For N > 3 waters however, HCO − deprotonates a water molecule to form formaldehyde and OH − .

Figure 12 .
Figure 12.Starting structures versus and their resulting optimised geometries for two conformers of NH 2+ bound to water tetramer.Initial approach of the guest molecule via N results in a different configuration than approach via the H atoms of NH 2+ .Both conformers form hydroxylamine, but form different composite structures with the remaining waters and shared proton.Energy differences are indicated with respect to the global minimum in kcal/mol.

Figure 13 .
Figure 13.Minima and next-lowest conformers of HCO + bound to water dimer and tetramer shown in conjunction with their respective starting structures.Energy differences are indicated with respect to the minima in kcal/mol.
complex is the energy of the bound guest/water complex, E molecule the energy of the guest molecule, and E water the energy of the water cluster minima for a given number of water molecules.E condensation is the total condensation energy of the constituent molecules of the guest-water cluster, and E bind is the binding energy of the guest to the water cluster.nE (H 2 O) is number (n) times the energy of an H 2 O molecule.

Table 1 .
Comparison of (zero-point corrected) ωB97X-V/def2-qzvppd and CCSD(T)/aug-cc-pVTZ binding energy values for most stable structures binding the closed shell molecule given in the left-hand column with N = 1−4 water molecules, reported in kcal/mol.
Note: General agreement is observed between the methods, and trends are preserved.A larger negative number indicates stronger binding.
In both cases the global minimum is one in which 3 and 4 H 2 O molecules, respectively, make strong hydrogen bonded quasi-planar structures on which the NH 4+ binds as a guest.Other structures where the NH 4 kcal/mol are found for NH 4 + with N = 3 H 2 O clusters, and four unique conformers within 3.1 kcal/mol of global minimum are found for NH 4 + with N = 4 H 2 O clusters.
key binding regimes are evident from the binding motifs and the binding energies of representative groups of guest molecule to water complexes.The first is a 'weak' guest-water binding regime in which the guest molecule is typically externally bound with the water cluster (which is itself bound by H-bonds) by weak dispersion and dipole-induced dipole type interactions.Neutral molecules such as N 2 and hydrocarbons such as CH 4 , C 2 H 2 and C 2 H 4 , and H, NO, CH 3 radical complexes are examples of this binding regime.One can say that the overall cluster structure is controlled by optimising the water-water interactions, leading to structures similar to the corresponding pure water clusters.The second is an 'intermediate' binding regime in which the guest molecule or radical is able to make hydrogen bonds with one or more H 2 O molecules in the cluster.This category of complexes is marked by slightly stronger binding energies and structures in which guest molecules are assimilated into the cluster.The neutral molecules NH 3 , HCN, H 2 CO and the open-shell NH 2 , HCO, and OH are examples of this category.