Chloride ions as integral parts of hydrogen bonded networks in aqueous salt solutions: the appearance of solvent separated anion pairs

Hydrogen bonding to chloride ions in various aqueous environments has been discussed many times over the past more than 5 decades. Still, the possible role of such hydrogen bonds (HB) in networks of HB-s has not been investigated at any detail. Here we consider computer models of concentrated aqueous LiCl solutions and compute usual HB network characteristics, such as distributions of cluster sizes and of cyclic entities, for the models by taking and not taking chloride ions into account. During the analysis of hydrogen bonded rings, a significant amount of 'solvent separated anion pairs' have been detected at high LiCl concentration. It is demonstrated that including the halide anions into the network does make the interpretation of structural details significantly more meaningful than when considering water molecules only. Finally, we compare simulated structures generated by 'good' and 'bad' potential sets on the basis of the tools developed here, and show that this novel concept is, indeed, helpful from this respect, too.


Introduction
The term 'hydrogen bonding' is traditionally connected to water and ice, where oxygen atoms form bonds with hydrogen atoms of neighboring water molecules by enhancing the electronic density between O and (non-bonded) H by the lone electron pairs of the O atoms [1][2][3] . The same mechanism works for many other compounds with hydroxyl (-OH) groups: examples are alcohols, organic acids, sugars, proteins, DNA, etc… However, hydrogen bonding (H-bonding) is responsible for the very strong links between molecules of hydrogen fluoride, HF 4,5 , too: that is, hydrogen bonds (HB-s) may be formed not only by oxygen-, but also, by halogen atoms/halogenide ions (and, in some rare cases, even by nitrogen, c.f. liquid ammonia, NH3) 6 .
The phenomenon of hydrogen bonding with halogen atoms/halogenide ions is, indeed, well documented in the literature: for instance, the crystal structure of hydrogen chloride hydrates has been investigated by diffraction methods already half a century ago 7,8 . A fairly large number of hydrogen bond distances to halogenide ions in crystals have been reported a couple of decades ago 9 . Hydrogen bonding in chloride-water clusters has been considered by Xantheas 10 , and even the dynamics of HBs have been studied, via molecular dynamics (MD) simulations, in aqueous solutions of halide ions 11 . However, quite surprisingly, according to the best of our knowledge, halide ions have never been considered as integral parts of the network of hydrogen bonds in aqueous solutions of, e.g., aqueous solutions of alkali halide salts. Indeed, most of the (faintly) related discussions in earlier papers have been about how ions actually break/disrupt the hydrogen bonding network of water molecules in these solutions (see, e.g., Refs. 12,13). The traditional 'structure making/structure breaking' roles of ions 14 also concern the issue whether the presence of ions enhances or deteriorates of the HB network of water molecules. What happens when hydrogen bonds between halide anions and water molecules are both treated as network formers has not yet been investigated.
There is a notable, qualitative difference between the ways chloride ions and O atoms of water molecules act as (electron) donors while forming hydrogen bonds. Water molecules provide extra electron density by the lone electron pairs of their oxygen atoms, i.e., via localised electrons. The extra electron (providing the 1-negative charge) of the chloride ions, on the other hand, is distributed evenly over the 'surface' of the ion. This difference is the main reason why water oxygens can donate electrons for two (at most three) neighbouring H-atoms, whereas chloride ions can form 6(-7) hydrogen bonds 15,16 (without specific orientations). In other words, the number of H-bonds formed by chloride ions is limited by steric effects only.
Here, we make use of some of the standard hydrogen bonding related analysis tools 17,18 applied recently to water-methanol 19 , water-ethanol 20 and water-isopropanol 21

Results and discussion
We wished to facilitate comparability with literature by taking exactly the same salt concentrations as in previous, related works from our laboratory 15,16,22,23 , namely 3.74 m (mol/kg; corresponding to 6.3 molar %), 8.3 m (13 molar %), 11.37 m (17 molar %) and 19.55 m (26 molar %). In fact, the calculations providing the atomic assemblies ('particle configurations') were identical to those reported recently by one of us 15 . Note that these concentration values are rather high, the highest one representing an ion/water ratio of about 50:75. The reason why such systems have been selected was the expectation that the role of ions in enhancing/disrupting the hydrogen bonded network would be most apparent under such circumstances.
Simulation details, as well as a brief description the geometric definition of hydrogen bonds used here throughout are provided in the 'Computational section' (see below). Most importantly, H-bonded Cl -…H maximum distances are somewhat longer than O…H ones, as it is defined by the first minimum of the Cl --H and O-H partial radial distribution functions (see, e.g., Refs. 15,16,23 ). The potential model called 'JC-S' from Ref. 16 is used just below for demonstrating features of the 'mixed' H-bond network concept.

Cluster size distributions
In order to characterize the extent of the H-bond network, cluster size distributions (as defined in, e.g. Refs. 17,18) have first been determined; these are shown in Figure 1. Robust hydrogen bonded networks, like those in most alcohol-water mixtures, percolate 18,24,25 , i.e. the largest H-bonded cluster is comparable in its size with the system size. From Figure 1 it is obvious that when chloride ions are not considered as 'network formers' then this criterion is fulfilled only for pure water and, to some extent, for the least concentrated LiCl solution. In the more concentrated solutions one can only find isolated water clusters, up to sizes of about 180 (11.37 m) or even only about 20 (19.55 m) molecules.
That is, the H-bonded networks of water molecules are really small in comparison with the system size and also, such a picture would suggest a kind of 'microphase separation', debated quite hotly in the cases of alcohol-water mixtures 26,27 . On the other hand, when chloride ions are taken into account as parts of the network then cluster sizes are equal (within a few percent) with the cumulative number of water molecules and chloride ions. (The vertical lines show the number of (a) water molecules (b) the Clions plus water molecules in the system.) Note that when chloride ions are included, even the most concentrated systems percolate -which makes sense in a homogeneous solution.

Hydrogen bonded rings
Next, the occurrence of H-bonded cyclic entities is scrutinized ( Figure 2). The number or purely water rings decreases dramatically with increasing ion concentration, with hardly any cycles present above 8.3 m. On the other hand, there is a fair amount of 'mixed' cycles even at the highest ion concentration when the anions are also counted (even though the number of H-bonded cycles decreases also here when salt concentration is growing). Interestingly, the size of the rings also decreases with increasing concentration, so much, that the most frequent ring size in the 19  It is also instructive to investigate the ratio of water molecules and chloride ions in the 'mixed' cycles ( Figure 3). Contrary to what was observed in methanol-water liquid mixtures 19 , the participation of ions in the H-bonded rings follows roughly the overall concentration of (an)ions in the solutions. Again, it is the most concentrated solution that exhibits the most spectacular feature: the most frequent cycle is the one that consists of two water molecules and two chloride ions (see Figure 4 for representative parts of the particle configurations).   (blue) 6-membered ring with 1 Clion and 5 water molecules, (magenta) 5-membered ring with 5 water molecules and (yellow) 6-membered ring contains 6 water molecules; on part (b) (blue) 4membered rings with 2 Clion and 2 water molecules, (magenta) 5-membered ring with 2 Clions and 3 water molecules and (yellow) 6-membered ring contains 3 Clions and 3 water molecules.
The commonsense expectation is that no two chloride ions would be connected directly (it would not even be any kind of a 'hydrogen bond'). Indeed, closer inspection reveals (cf. Figure 4, part (b)) that a frequently occurring constellation is where there is one water molecule between two chloride ions: these motifs can be considered as 'solvent separated anion pairs'. Even though, at least once the 'mixed' water/anion H-bonded network concept is introduced, the presence of such particle arrangements is not entirely unexpected, to our best of knowledge, this is the first occasion when this phenomenon is observed and pictured in a very straightforward manner.
So far, it has been shown that there are marked differences between the concepts of considering the 'pure' hydrogen bonded network containing only water molecules and that of a 'mixed' network that includes chloride ions, too. We believe that the latter provides a more sensible characterization of a homogeneous liquid -and since no sign of any small angle scattering could be spotted on either the neutron or the X-ray data 22 we argue that however concentrated the solutions in question are, even the 19.55 m LiCl solution is homogeneous.

Utilization of the concept
Next, we further demonstrate the usefulness of the 'mixed' concept by comparing 'good' and 'bad' potential models for aqueous LiCl solutions (cf. Refs. 15,16). As 'good' force field, the JC-S combination from Ref. 16 was taken, that consists of the SPC/E water model 28   (The x-axes are normalized with the number of (a, c) Clions plus water molecules, (b, d) water molecules in the configurations.) Note that for the RM model, which was found to be one of the worst when comparing simulated and experimental total structure factors, cluster sizes with Clions (part (c)) appear to be smaller than the percolation limit, whereas pure water clusters (part (d)) are large even at high salt concentrations. This indicates non-perfect mixing (i.e., 'microphase-segregation' between water and salt), which is against the observation that all solution considered are homogeneous. water H-bonded clusters are larger, mixed water-anion ones are smaller in the case of the 'bad' RM model. These observations are consistent with the notion that mixing of ions and water is far from perfect when the RM combination of force fields is applied, leading to a kind of (micro-)phase segregation, between water-rich and ion-rich regions. Please remember: the RM model cannot reproduce diffraction data appropriately, i.e. the behavior detected in Figure 5 for this model cannot be related to characteristics of the real system.  When the composition of cyclic entities formed in the JC-S and RM structural models is compared (see Figure 6), an analogous conclusion can be drawn: while in the 'good' JC-S structure H-bonded rings contain a number Clions that is in accord with the overall concentration of ions, cycles in the 'bad' RM structure tend to contain far less anions than it could be expected from the ion concentration in the solutions. In the RM model, the overwhelming majority of the rings is waterdominated even at the highest ion concentration. This, again, is an indication that the RM combination of water and ion force fields does not lead to homogeneous structures.

Conclusions
In summary, it has been demonstrated that the concept of 'mixed' water-anion hydrogen bonded network provides a sensible characterization of highly concentrated chloride salt solutions. It can account for the homogeneity of such systems, contrary to what the 'pure' water network suggests.
The approach has brought about the observation of 'solvent separated anion pairs' that are the dominant motifs in cyclic hydrogen bonded entities at high LiCl concentration (see Figures 3 and 4).
The characterization of, as well as the distinction between, 'good' and 'bad' potential models of aqueous LiCl solutions becomes very natural via the 'mixed' network concept: good models facilitate mixing of ions and water molecules at the atomic scale, whereas inappropriate force fields tend to result in separation of solvent and solute (micro-)phases (cf. Figures 5 and 6).
Further explorations are needed (and underway) for establishing whether the 'mixed' water+halide ion hydrogen bonded network is a useful concept in general for discussing properties of highly concentrated aqueous solutions of (at least) alkali-halides. As a possible next step, we will first look at a situation where the counterion is the largest of alkali cations, namely the case of CsCl solutions (for which experimental data is available from our group 31 ).

Computational section
Classical molecular dynamics (MD) simulations were performed by the GROMACS software package (version 5. Pairwise additive non-polarizable intermolecular potential was applied for the description of interatomic interactions. The non-bonded interactions are described by the Coulomb potential accounting for electrostatics and the 12-6 Lennard-Jones (LJ) potential for the van der Waals interactions: Here rij is the distance between particles i and j, qi and qj are the point charges of the particles, ε0 is the vacuum permittivity, εij and σij are the 12-6 LJ potential parameters. Potential parameters applied in this study were chosen from the collection of Ref. 16, in which paper 29 force field models were compared according to their appropriateness to describe the structure of highly concentrated aqueous  Table 2. During the simulations water molecules were kept together rigidly by the SETTLE algorithm 33 .
Coulomb interactions were treated by the smoothed particle-mesh Ewald (SPME) method 34,35 , using a 10 Å cutoff in direct space. The van der Waals interactions were also truncated at 10 Å, with added long-range corrections to energy and pressure 36 The initial particle configurations were obtained by placing the ions and water molecules randomly into the simulation boxes. Energy minimization was carried out using the steepest descent method.
After that the leap-frog algorithm was applied for integrating Newton's equations of motion, using a

Conflicts of interest
There are no conflicts to declare.

Supporting Information
Chloride ions as integral parts of hydrogen bonded networks in aqueous salt solutions: the appearance of solvent separated anion pairs Six potential models from the collection of Ref.
[S1] were chosen to be applied in this study (see Table S1 and the corresponding water models in Table S2). According to Ref.
[S1] their appropriateness to describe the structure of the highly concentrated aqueous LiCl solutions is more or less proportional to the number of the contact ion pairs predicted by them. Thus they were selected to cover the full range of the numbers of the contact ion pairs found in Ref.