Water dynamics visited. A comprehensive DFT study of proton transfer in liquid water underscores the pivotal role of ion pairing phenomena

Water dynamics visited. 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A comprehensive DFT study of proton transfer in liquid water underscores the pivotal role of ion pairing phenomena Jose Saa, Antonio Frontera This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8425076/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The core issue standing behind water's unique and extraordinary properties is proton transfer. The extremely fast nature (under the picosecond time scale) of proton transfers taking place in water convinced us to resort to a classic approach: a comprehensive DFT study of neutral, medium-sized water clusters (H 2 O) n (n up to 30). Our main objective was to determine the instantaneous (I) structures of the transition states of proton transfers, which are inaccessible by experimental techniques or molecular dynamics simulations. Subsequent IRC analysis and AIM treatment of the three stationary points thereby available for each transition state structure were fundamental to describing the basics of water dynamics. Actually, our study shows that proton transfers occurring in neutral, liquid water involve a variety of ion-pairing phenomena that operate not only on neutral waters clusters but also on neutral ion-pair clusters. The unveiled properties of water ion-pairs suggest that the long-standing assumption that water's ionic components do not interact with one another -a hypothesis that has remained unchallenged for over a century- may be erroneous. Water ion-pairs are at the center of the new paradigm, shedding light on water electrodynamics and offering plausible suggestions on the abiotic origin of life that are worth exploring. Physical sciences/Chemistry/Physical chemistry/Chemical physics Physical sciences/Chemistry/Theoretical chemistry/Computational chemistry Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Hydrogen transfer and hydrogen ion (proton) transfer are at the heart of chemical reactions. However, as emphasized by A. Zewail in the preface to Hydrogen-Transfer Reactions , 1 hydrogen and proton transfer processes are quite complex in nature and, therefore, in describing the dynamics of both condensed-phase and biological systems undergone by such many-body complex systems, 2 “… it is not perhaps beneficial to consider every atom of a many-body complex system. Instead, the objective is hopefully to project the key electronic and nuclear forces which are responsible for behavior ”. Accordingly, “… computer simulations…should be a tool of guidance to formulate a predictive theory” and, “… similarly for experiments, the most significant ones are those that dissect complexity and provide quite lucid pictures of the key and relevant processes ”. In light of these considerations, the present study focused its attention on liquid water due to its status as a unique chemical system that exhibits distinctive and exceptional properties 3 relevant to life and, most importantly, because these properties result primarily from the extremely rapid proton transfers 4,5 that occur within the extensive, three-dimensional hydrogen bonding network characteristic of liquid water and ice. Indeed, a consensus has emerged among researchers in the field regarding the most crucial question to address to gain a microscopic understanding of water: " what is the structure and dynamics of the hydrogen bonding network in water that gives rise to these unique properties? ". 6 However, despite the considerable time and effort that has been devoted to improving the original Bernal-Fowler paradigm over the course of several decades, 7 the scientific community continues to regard water as an unsolved puzzle of confronting theories. This enigma is, at least in part, due to the temporal and spatial scale constraints imposed on liquid water structural data resulting from experiments and/or computations. In fact, experimental techniques with time scales ranging from 1 to 10 picoseconds may yield vibrational averaged (V) structures exclusively, while those with time scales greater than 10 picoseconds generate solely diffusion averaged (D) structures. Conversely, computer simulations that yield only states of minimum energy on the potential energy surface generate frozen (F) structures with infinite time scales (t -> ∞). Unfortunately, the key instantaneous (I) structures (with time scales << 1 picosecond), whose dynamical behavior would allow us to reach V, D and F structures, have been deemed inaccessible by experimental measurements, 8 though V. Artemov has recently theorized them based on the electrodynamic properties of water. 9 As described below, however, we demonstrate that the key proton transfer transition state structures (I) are available computationally. Methods and protocols In accordance with the aforementioned recommendations and in our pursuit of a lucid picture of these pivotal processes, 10 we planned to tackle water dynamics by studying proton transfer in neutral, liquid water using static ab initio SCF simulations, instead of resorting to a molecular dynamics treatment 11 upon the original water model whose ionic components do not interact with each other. Furthermore, we planned to incorporate solvent effects through a polarizable continuum model (PCM), 12 with the objective of facilitating access to the relevant instantaneous (I) structures of the transition states (whose lifetimes are on the 10-100 femtosecond time scale) of proton transfers, whether concerted and synchronic or otherwise, taking place in liquid water. 13 To this end, we selected from the literature a substantial number of known, neutral, medium-sized water clusters ((H 2 O) n with n up to 30, and up to 25 isomers for each cluster size) as objects of study, 14 as they represent micro-snapshots of liquid water. Despite the strong criticism of applying the classic approach to condensed phases, 15 we anticipated that a subsequent IRC analysis 16 of these (I) structures would provide us with a comprehensive description of the relevant atomic-molecular dynamics of the rearrangements undergone by the hydrogen-bond network triggered by proton transfers operating on factual reaction coordinates. 17 In this regard, it is worth remarking that we did not rely on energetic or geometric criteria for the description of the hydrogen bonding networks. Rather, we projected to analyze the electron density topology provided by theoretical means (see below), as recommended by IUPAC. 18 Specifically, we expected that the programmed IRC analysis of the transition state structures (I) of direct proton transfers to yield the F-structures of both the initial and final clusters. Conversely, when applied to the instantaneous, transition state structures (I) of indirect proton transfers, we anticipated that the analysis would reveal the F-structure of the initial cluster and, most significantly, that of the ion-pair product, 19 presumably displaying vibrational-averaged structures (V), given that ion-pair lifetimes lie on the picosecond timescale. 4,8,9 Over the years, the lack of compelling evidence supporting the association of the ionic components of water and ice has been widely accepted. Consequently, the prevailing notion that still persists in textbooks and scientific literature is that isolated, non-interacting pairs of ions, rather than solvent-separated ion-pairs, are the natural components of water and ice. 20 In fact, a substantial body of scientific literature describes the proton transfer properties of isolated Zündel and Eigen cations, which differ from those of the corresponding isolated anions. It is imperative to note that the properties exhibited by these isolated cations and anions have been attributed to neutral water, thereby perpetuating the original paradigm. However, we posited that the detailed structure and properties of single 21 and multiple water ion-pairs would be paramount in describing the dynamic structure of water and, consequently, its associated dielectric properties. To reach the aforementioned goals, we planned to rely on Kohn-Sham density functional theory (KS-DFT) as the foundational ab initio method. 22 Given our plan to study proton transfers in an extensive range of neutral, medium-sized clusters (H 2 O) n , with n reaching up to 30, Truhlar’s M06-2X hybrid functional, 23 paired with the 6-311++G(d,p) basis set, was selected as the optimal choice for its balance of accuracy and computational efficiency. 24 Results and discussion The initial clusters 14 were subsequently re-optimized employing the Polarizable Continuum Model (PCM) to model solvent effects (solvent=water). 12 Then, hydrogen atoms were precisely positioned at the midpoint of each O…O pair, prior to the transition state searches were launched. The ensuing IRC analysis of the transition state (I) structures, which were identified as stationary points, unveiled two distinct categories of reaction coordinates (see Figure 1). The first category comprises direct proton transfer (DPT) processes involving three stationary points on the reaction coordinate (147 transition states were found, see Table 1). The initial and final clusters are both F structures, with a cyclic transition state (I structure) connecting them. The second category encompasses concerted processes that result in the formation of ion-pair clusters as products (a grand total of 276 transition states were localized). This category is thus designated as ion-pair proton transfers (IPPT). Interestingly, two sub-categories of IPPT processes were distinguished, namely Ion-Pair Collapse (IPC, 152 transition states) and Ion-Pair Walk (IPW, 124 transition states), which involve short- and long-lived ion pairs, respectively. 25 The step-ladder reaction coordinate, which is characteristic of Ion-Pair Collapse (IPC) processes, provides a clear illustration of the evolution of short-lived ion pairs (Figure 1b, first TS). During this process, a specific proton transfer occurs as the ion pair (V structure) passes through a nearby transition state (I-structure), eventually resulting in a collapsed cluster (F structure). Conversely, processes involving ion-pair clusters as both the initial and final products (Figure 1b, subsequent TSs) are designated Ion-Pair Walk (IPW) processes. IPPT processes involving long-lived ion pairs, namely IPW processes, will presumably impact on the nature of the microscopic model of water and, consequently, on its electrodynamic properties. 9 In contrast, IPPT processes involving short-lived ion pairs, specifically IPC processes, as well as all kinds of DPT processes, are expected to have no effect on water dissociation phenomena. 4 A detailed description of the DPT and IPPT processes follows. In this analysis, particular emphasis is placed on the instantaneous (I) structures of proton transfer transition states and their evolution into products that are either frozen (F) or averaged (V and D) structures. Direct Proton Transfers operating on neutral water clusters. - The absence of ion-pair products is the hallmark of the reaction coordinates for all categories of direct proton transfer (DPT) processes. It is worth remarking though that these reactions exhibit ion-pair-like cyclic transition state (I) structures with clear charge separation (Fig. 2), as revealed by the corresponding NBO analysis of the charge distribution. 26 For the efficient operation of these cyclic processes, it is imperative that oxygen atoms possess an ad configuration, as they must act as both a donor ( d ) and an acceptor ( a ) along the reaction coordinate. This distinctive property facilitates recombination into two neutral clusters with slightly different constitutions, due to the fact that proton transfer occurs almost equally clockwise or counterclockwise (as depicted in the transition state models shown in Figure 2). This fact qualifies DPT processes as quite relevant to explain in detail the much-debated molecular mechanism of water reorientation phenomena 27 associated to the Debye relaxation dynamics of water, 28 and ice. 29 The most prevalent DPT processes 30 belong to the internal class, illustrated in Figure 2a as i-DPT, which models the transition structure of three- to eight-membered ring internal, direct proton transfers in which only three, four, five, six, seven, or eight hydrogen atoms of a given neutral water cluster are translocated from their original positions. To date, no evidence has been found to suggest the occurrence of internal DPT (i-DPT) processes involving transition structures with larger cyclic rings. In contrast, the atypical cases depicted in Figure 2, designated as class b (four-membered ring transitions structures in most cases), involve the translocation of five hydrogen atoms. 31 This phenomenon occurs in edge cases b1 and b2 (illustrated as e-DPT in Figure 2), where a water molecule is present at the periphery of the cyclic transition state structure, either as the H 3 O d + (b1), or the OH d - (b2) moiety. A third class of DPT processes, illustrated as c) in Figure 2, namely swing DPT (s-DPT) processes, involves a four-membered ring transition structure in which a single proton (H ab1 ) behaves like the pendulum of a wall clock swinging to the right and to the left to trap a proton in channels a or b. Proton transfers taking place through DPT processes can be regarded as a consequence of the so-called accordion effect, which is defined as the effect of a stopping event on the fluid passage of a body of elements moving along a defined path. 32 In essence, DPT processes involve the compression of a specific hydrogen bond along the proton channel connecting two distant water molecules leading to a halt at the transition state. This is subsequently followed by decompression until fluid passage resumes. The application of Bader's Atoms in Molecules (AIM) theory 33 to the analysis of DPT processes enabled the delineation of the complete connectivity at their cyclic transition states, as well as at the initial and final products. In most cases, the planar transition states (predominantly those with three, four and some with five member rings) of DPT processes exhibit compression at all their O-H…O bonds. The strongest compression (O-O distance ≤ 2.41 Å) occurs at the sites actually involved in the proton transfer process. 30 As illustrated in Table 1, DPT processes found in all (H 2 O) n clusters studied (n = 8–30) exhibited energy barriers (DH*) spanning from 15 to 29 kcal/mol (most common values found at ca. 20 kca/mol; see Table 1 and Supplementary Information). 30 The protons actually being transferred in the transition state are covalently bound to both vicinal oxygen atoms and are therefore detected by AIM which shows negative values of the Laplacian of the electron density at the hydrogen bond critical points (HBCP). 33 Accordingly, it can be said that the majority of DPT processes entail a single, sometimes double, proton transfer in the transition state, with the subsequent transfers occurring after some molecular arrangements have taken place, as revealed by the corresponding IRCs. Consequently, as indicated by Dewar et al. 34 and Houk et al., 35 these processes should be qualified as concerted, albeit asynchronous, proton transfers. 36 Conversely, some DPT processes actually undergo molecular adjustments at the transition state prior to the occurrence of proton transfer. 37 In these cases, the reaction coordinates resulting from the corresponding IRC analysis are not sharp (as illustrated in Fig. 1a) but, instead, rather rounded and irregular (not shown). In such cases, proton transfer is not detected by AIM. Ion-pair Proton Transfer operating on neutral water clusters.- In contrast to the behavior exhibited by DPT processes, the most common proton transfer processes, namely IPPT processes, whether IPC (ion-pair collapse) or IPW (ion-pair walk), involve ion-pair clusters, i.e. clusters comprising pairs of ions, specifically H 3 O + and OH - units, that are not isolated species. Rather, they are interconnected by three "wires", that is, by three proton channels,each channel involving a network of hydrogen bonds of variable length that facilitate the interconnectivity between the proton source and the proton sink. 38,39 A noteworthy observation is that proton transfer in IPPT processes can occur through any of these channels. In the context of ion pair walk (IPW) processes involving long-lived ion pairs, 9,25 the "wire" acting as the actual proton channel for proton transfer undergoes a discernible compression (up to ca. 6% of their length) as the original ion-pair reaches the transition state located nearby. Concurrent with the compression of the active “wire”, the inactive “wires” cooperate by undergoing simultaneous decompression, thereby facilitating the proton transfer process, i.e. proton transfer occurs because the whole system fluctuates. 4 Individual account of this “wiring” interconnectivity, together with the compression and decompression undergone by the active and the inactive “wires” at the transition state of each proton transfer, is provided as Supplementary Information. In the majority of IPW cases, the enthalpy cost (DH*) is in the range of 0.01 to 5 kcal/mol (Table 1), and the O-O distance at the key O--H--O unit undergoing proton transfer in the transition state oscillates between 2.38 and 2.42 angstroms. 40 A detailed, quantitative account of these events is provided as Supplementary Information. 30 The subsequent decompression of the aforementioned active "wire" results in the formation of a new ion-pair, in which either the head (+) or the tail (-) has been displaced from its original position to a nearby one. This is because proton transfer involves protons immediately close to either the source ion (a 0 , b 0 or c 0 ), or the sink ion (a x , b x or c x ), as illustrated in Figure 3. We identify these displacements as ion-pair 'walks', which can drive a single ion-pair into a new position in six different directions. It is also noteworthy that the resulting ion-pair can undergo additional, rapid "walk" displacements involving the head (+) or tail (-) units, thereby creating new ion-pairs at each “walk” step. 30 Since the original proposal by Kohlrausch, 41 and subsequent adoption by Bernal and Fowler, 7 it has been assumed that water ionic components H 3 O + (H 2 O) n and (H 2 O) n OH - move independently, freely, and randomly. 42 However our study shows, instead, that water ion-pairs (with up to 30 water molecules) possess an intrinsic, previously unrecognized, "walking" capacity. In fact, despite Onsager’s assertion that the distinction between free ions and their associated ion-pairs depends on arbitrary conventions, 43 we contend instead that the IRC and AIM of IPPT processes not only provide substantial evidence for the existence of the aforementioned “wiring” interconnection between water constituent ions, but also support the “walking” capabilities of long-lived ion-pairs over large distances (up to 11.9 angstroms in this study). In addition to the aforementioned processes of annihilation (IPC) and rebuilding (IPW) of water ion-pairs, we also explored the inversion of the H 3 O + moieties of non-symmetrical ion-pairs. The results of this analysis with a total of seven transition states, demonstrate for the first time the ability of ion-pairs to undergo the so-called umbrella inversion process (IPI), 44 thereby interconverting concave ion-pairs clusters to convex ion-pairs clusters (F structures) via locally planar (Fig. 4) transition states (I) structures. The enthalpy cost (DH*) of these ion-pair umbrella-inversion processes lies in the range of 0.7 to 2.5 kcal/mol in most cases (see Table 2). As illustrated in Figure 4, we have found that the resulting concave and convex ion-pair clusters, which share identical wiring systems, evolve independently via the aforementioned standard proton transfer mechanisms. Furthermore, water ion-pairs can undergo isomerization processes, whereby a specific water molecule reorients itself within the ion-pair cluster. This reorientation does not involve proton transfer, but rather simple water rotation (see Table 2). Ion-pair collapse (IPC) processes involve short-lived ion-pairs. 9,25,45 There, the initial compression of the active 'wire' of the original ion-pair occurs upon reaching the nearby transition state in cooperation with the decompression of the inactive 'wires' (see below). The majority of cases studied have enthalpy cost values (DH*) in the range of 0.002 to 8 kcal/mol, as shown in Table 1). The subsequent collapsing event, which involves the recombination of the ion-pair constituent ions, takes place by proton hopping through an amplified Grotthuss mechanism, 46 as it can start not only at a proton close to the source ion (a 0 , b 0 or c 0 ), but also at a proton close to the sink ion (a x , b x or c x ), as illustrated in Figure 3. According to the criteria of Dewar, 34 and Houk, 35 all IPC processes examined in this study, as revealed by IRC and AIM, can thus be defined as concerted and asynchronous. Apparently, these observations are in striking contrast to the findings reported by molecular dynamic simulations studies on the recombination events of isolated ions H 3 O + and OH - . These studies report that, after reaching contact distance (c.a. 6 angstroms), a concerted triple jump takes place. 47 Artemov 25,45 showed that long-lived ion pairs are responsible for pH whereas short-lived ion pairs are not. We have tried to learn about the structural reasons underlying this behavior by analyzing the up-to-six proton transfer routes available for single ion pairs operating in all types of IPPT processes. For every proton transfer route, this analysis encompassed not only the number of water molecules (x, y, and z) linking both H 3 O + and OH - units, but also the specific O-H bond constituents a, b, and c of [x,y,z] "wires" of ion pairs IP0011 (Figure 3). Additionally, the "wire" lengths, herein defined as the sum of the O-O distances as they go from the source (O + ) to the sink (O - ) poles, were also taken into account. The most salient conclusion that emerged from this analysis is that "wire" lengths of ion-pairs ranging from 7.3 to 7.7 angstroms, 48 i.e., when either x, y, or z equals 2, promote immediate ion pair collapse through that “wire”. 40 This happens because the optimal geometrical parameters for proton jumping (O-O distance ca. 2.4 angstroms) are reached by even a weak fluctuation involving compression of 0.1-0.3 angstroms of the active "wire", an effort that is counterbalanced by the simultaneous decompression of the two “wires” that remain inactive. Collapse events, however, are not limited to these cases only. In fact, some collapse events occur when x, y or z = 3, though quite unusually when x, y or z = 4. On the other hand, IPW processes involving long-lived ion pairs are common for species having large values (4 and above) for x, y or z. Very often the potential energy surface describing the proton transfer activity of these large ion-pairs is of a mixed type showing both IPC and IPW paths competing. Proton transfers on neutral, ionized water clusters .- Despite being constrained by the space limitations of our clusters (which contain a maximum of 30 water molecules), the programmed dynamic analysis also focused its attention upon water single ion-pairs as a whole, neutral, wired-up systems capable of undergoing further proton transfer processes. To this end, a methodology similar to the one previously described was employed. Among the single ion-pairs previously obtained, some of them were selected and then hydrogen atoms were precisely positioned at the midpoint of some O…O pairs, specifically those far away from the existing ion pair. Subsequent transition state searches revealed the basic proton transfer operations undergone by the single ion-pairs, namely direct proton transfers (DPTs), and IPPT processes involving short- and long-lived bis ion-pairs, respectively, however with several specific subtypes worth being described. A brief description of these interesting species based on IRC and AIM analysis follows. Notably, all these transition states lie at a second-floor energy level, approximately 20-25 kcal/mol above those at the first-floor energy level described above (see Table 3). Figure 5 provides a simplified illustration of the energy building of single, bis and multiple ion pairs, and the energy loss resulting from ion pair collapse (IPC) and ion pair quench (IPQ) processes. Higher floor energy levels, not yet identified, are presumed to be inhabited by multiple ion-pairs. Direct proton transfers (only i-DPT processes, as illustrated in Figure 2a) operating upon single ion-pair clusters entail the translocation of hydrogen atoms through a cyclic transition state, located far away from the original ion-pair. Accordingly, the resulting products PT1 and PT2 (Figure 1) are isomeric ion-pairs as they retain the original ion-pair constitution but differ at some points of their structures. Particular emphasis was placed on IPPT processes of the IPW and IPC types because they should implicate bis ion-pairs. This is exemplified by a generalized bis ion-pair IP1234-IPabcd where the first two digits, or letters, denote the location of the H 3 O + unit, while the final two specify the position of the corresponding OH - unit. The displacement of ions in IPW processes has been shown to induce a shift of either the source (H 3 O + ) or sink (OH - ) unit of each ion pair to a vicinal position, thereby resulting in the formation of a novel bis ion pair (either IP5634-IPabcd when the H 3 O + unit moves from position 12 to 56, or IP1278-IPabcd when the OH - unit moves from position 34 to 78, or IP1234-IPefcd when the H 3 O + unit moves from position ab to ef, or IP1234-IPabgh when the OH - unit moves from position cf to gh). Subsequent IPW displacements on the resulting bis ion-pair may occur, thus contributing to the understanding of the underlying mechanism of long-lived ion-pairs. Moreover, since every source and sink unit is affixed by three “wires”, it follows that such displacements can take place in any of the 2x6 possible space directions. On the other hand, several mechanisms can actually drive bis ion-pairs to a short-lived term. Thus, in addition to the standard collapse (IPC) processes in which the original bis ion-pair collapses, thereby leading to a single ion-pair, either IP1234 (if IPabcd collapses), or IPabcd (if IP1234 collapes), novel IPC subclasses were identified. Specifically, the so-called ion-pair crossed collapse (IPCC) processes drive the original bis ion-pair to either single ion-pair IP12cd or IPab34. 30 This happens because the entangled nature of the original bis ion-pair's wiring system in a constrained space causes the collapse event to affect one ionic unit from each component of the original bis ion-pair. In addition to this partial collapse event, a full collapse event may also take place upon the bis ion-pair system. This phenomenon, termed an ion-pair quench (IPQ) process, leads to the complete quenching of the bis ion-pair system, resulting in the formation of a neutral, non-ionized cluster. As illustrated in Figure 5, and Table 3, IPQs exhibit a complete release of energy over a brief time period, particularly when operating on multiple ion-pairs. 30 Further research is required to elucidate the mechanisms responsible for proton transfers that presumably occur during atmospheric events, such as lightning and thunder. It is recommended that these investigations utilize substantially larger water and ice clusters. Conclusions To sum up, the present DFT-based study of water dynamics, has uncovered the fundamental proton transfer mechanisms that occur in liquid water. Basically, the dynamics of water are contingent on three distinct proton transfer operations. Direct proton transfers (DPT) have been shown to involve ion-pair-like transition states (I structures), i.e, evanescent ion-pairs. Conversely, ion-pair collapse (IPC) and ion pair-walk (IPW) processes operate on ion-pairs (F structures), the former involving ion-on-pairs that can be categorized as short-living and the later as long-living ion-pairs. This conclusion is supported by IRC analysis of the instantaneous (I) structures obtained for their transition states, combined with AIM studies upon the three stationary points coming from IRC analysis. DPT processes, which induce the translocation of protons undergoing transfer through cyclic transition states, have been shown to operate on both non-ionized and ion-pair clusters. Proton transfer processes involving single ion-pairs, namely IPC and IPW, and bis ion-pairs, namely IPC, IPCC, IPQ and IPW, are facilitated by the cooperative fluctuations undergone by the wiring system of ion-pairs. Two salient properties of ion-pairs are: 1) their capacity to undergo umbrella inversion (IPI) processes with negligible energy cost, thereby augmenting the number of operative proton transfers, and 2) their ability of some constituent water molecules to suffer isomerization. It is imperative though to recognize that collapse (IPC and IPCC) and quench (IPQ) processes limit the lifetime of ion-pairs, whereas those undergoing walk (IPW) processes i.e., long-lived ion-pairs, hold relevance in the context of pH, as pointed out by Artemov’s “ionic model of water”. 9 In this regard, it is worth recognizing that the almost costless capacity of long-lived ion-pairs to “walk” in nx6 space directions (herein demonstrated for n=1 and 2), clearly indicates that there may be no necessity to invoke the existence of free, non-interacting ions resulting from autoionization. The new paradigm not only recognizes the prevailing role of long-lived ion pairs in the electrodynamic properties of water, as Artemov has suggested,⁹ but also points to the plausible role of multiple ion pairs, due to their chiral nature, in the genesis of chirality 49 and the abiotic origin of life on Earth. 50 Declarations Acknowledgments. - A.F. is grateful to Project PID2023-148453NB-I00 funded by the Ministerio de Ciencia, Innovación y Universidades of Spain, MCIU/AEI/ 10.13039/501100011033 and FEDER, UE References Hydrogen-Transfer Reactions . Edited by Hynes, J. T., Klinman, J. P., Limbach, H.-H., Schowen, R. L., Wiley-VCH Verlag GmbH&Co. KGaA, Weinheim (2007). Proton Transfer in Hydrogen-Bonded Systems . Edited by T. Bountis, NATO ASI series, Vol. 291, Springer (1992). Chaplin, M. F., Water Structure and Science , (2001). https://water.lsbu.ac.uk/water/ . 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Treating high dimensional systems such as condensed phases with a classic approach is “ likely irrelevant ” due to the uncountable number of saddle points in their PES. See: Bolhuis, P.G., Chandler, D., Dellago, C., Geissler, D.L. Transition path sampling: throwing ropes over rough mountain passes, in the dark Annu. Rev. Phys. Chem. , 53, 291–318, (2002). Fukui, K. The path of chemical reactions-The IRC approach Acc. Chem. Res. 14 , 363–368, (1981). Methodologies using the “ transition path sample ” approach do not require the identification of a reaction coordinate to describe a chemical reaction. See: Dellago, C., Bolhuis, P.G., Csajka, F.S., Chandler, D. Transition path sampling and the calculation of rate constants J. Chem. Phys. 108, 1964–1977, (1998); Dellago, C., Bolhuis, P.G., Chandler, D. Efficient transition path sampling: Application to Lennard-Jones cluster rearrangements J. Chem. Phys. 108, 9236–9245, (1988); Bolhuis, P.G., Dellago, C., Chandler, D. Sampling ensembles of deterministic transition pathways Faraday Discuss. 110, 421–436, (1998); Geissler, D.L., Dellago, C., Chandler, D., Hutter, D., Parrinello, M. Ab initio analysis of proton transfer dynamics in (H 2 O) 3 H + Chem. Phys. Lett. 321, 225–230, (2000). Arunan, E., Desiraju, G. R., Klein, R. A., Sadlej, J., Scheiner, S., Alkorta, I., Clary, D.C., Crabtree, R. H., Dannenberg, J. J., Hobza, P., Kjaergaard, H. G., Legon, A. C., Mennucci, B., Nesbitt, D. J. Defining the hydrogen bond: An account (IUPAC technical report) Pure & Appl. Chem . 83, 1619–1636, (2011); Definition of the hydrogen bond (IUPAC recommendations 2011) ibid . 83, 1637–1641, (2011). Markus, Y., Hefter, G. Ion pairing Chem. Rev. 106, 4585–4621, (2006). Robinson, R. A., Stokes, R. H. Electrolyte Solutions , 2nd ed. revised; Butterworth: London, 1965. A few small, highly symmetric, three-dimensional water ion-pair clusters (not unfrequently abbreviated by linear formulas of the type H 3 O + --(H 2 O) n–2 --OH – , with n = 5, 8, 10) have been described in the realm of gas-phase ab-initio SCF calculations. See: a) Lee, C., Sosa, C., Novoa, J. J. Evidence of the existence of dissociated water molecules in water clusters J. Chem. Phys . 103, 4360–4362, (1995); b) Tozer, D.J., Lee, C., Fitzgerald, D. An investigation of hydrogen transfer in water clusters J. Chem. Phys . 104, 5555–5557, (1996); c) Jensen, J. O., Samuels, A. C., Krishnan, L. A., Burke, P. N. Ion pair formation in water clusters: a theoretical study Chem. Phys. Lett. 276, 145–151, (1997); d) Cárdenas, R., Lagúnez-Otero, J., Flores-Rivero, A. Ab initio study of the reaction mechanism of water dissociation into the ionic species OH – and H 3 O + Int. J. Quantum Chem. 68, 253–259, (1998); e) Smith, A., Vincent, M.A., Hillier, I.H. Mechanism of acid dissociation in water clusters: electronic structure studies of (H 2 O) n HX (n = 4, 7: X = OH, F, SH, HSO3, OOSO 2 H, OOH.SO 2 ) J. Phys. Chem. A 103, 1132–1139, (1999); f) Svocil, D., Jungwirth, P. Cluster model of the ionic product of water: accuracy and limitations of common density functional methods J. Phys. Chem. A 110, 9194–9199 (2006); g) Perlt, E., von Domaros, M., Kirchner, B., Ludwig, R., Weinhold, F. Predicting the ionic product of water Sci. Rep. 7, 10244–10253, (2017); h) Turi, L., Rodrigues, J. Laria, D. Combined effects from solvation and nuclear quantum fluctuations on autoionization mechanisms in aqueous clusters J. Phys. Chem. B 124, 2198–2208, (2020). See You, H.S., Li, S.L., Truhlar D.G. Perspective: Kohn-Sham density functional theory descending a staircase J. Chem. Phys. 145, 130901-23, (2016), and references therein. Y. Zhao, D.G. Truhlar, The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, non-covalent interactions, excited states, and transition elements: two new functional sans systematic testing of four M06-class functionals and 12 other functionals Theor. Chem. Acc. 120, 215–241, (2008). Gillan, M.J., Alfè, D., Michaelides, A. How good is DFT for water? J. Chem. Phys. 144, 130901–33 (2016). By examining the range of water conductivity values measured at high frequencies, which essentially reflect the net proton dynamics of water, Volkov, Artemov, and Pronin came to the provocative conclusion that, in addition to the long-lived ion pairs that are responsible for the autoionization event, there must be a substantial number of short-lived ions. See Volkov, A.A., Artemov, V.G., Pronin, A.V. A radical new suggestion about the electrodynamics of water: can the pH index and the Debye relaxation be of a common origin? EPL 106, 46004-p6, (2014). See also Artemov, V.G., Volkov Jr., A.A., Sysoev, N.N., Volkov, A.A. On autoionization and pH of liquid water Doklady Physics 61, 1–4, (2016). Reed, A.E., Curtis, L.A., Weinhold, F. Intermolecular interactions from a natural bond orbital, donor-acceptor viewpoint Chem. Rev. 88, 899–926, (1988). See Laage, D., Stirnemann, G., Sterpone, F., Rey, R., Hynes, J.T. Reorientation and allied dynamics in water and aqueous solutions Annu. Rev. Phys. Chem. 62, 395 –416, (2011), and references cited therein. The Debye diffusion model was described almost a hundred years ago. See Debye, P. J. W. Polar Molecules , The Chemical Catalog Company, New York, 1929. Bjerrum recognized the necessary operation of DPT processes in ice. See Bjerrum, N. Structure and properties of ice Science , 115, 385–390, (1952). A full account, as well as detailed information, is available as Supporting Information. A seven membered ring transition state has also been found, associated though with the translocation of eight hydrogen atoms. Sugiyama, Y., Fukui, M., Kikuchi, M., Hasebe, K., Nakayama, A., Nishinari, K., Tadaki, S., Yukawa, S. Traffic jams without bottlenecks-experimental evidence for the physical mechanism of the formation of a jam New J. Physics 10, 33001–7, (2008). Bader, R.F.W. Atoms in Molecules: A Quantum Theory , Oxford, Clarendon, 1990; Bader, R.F.W. Atoms in molecules Acc. Chem. Res. 18, 9–15, (1985); Bader, R.F.W. A quantum theory of molecular structure and its applications Chem. Rev. 91, 893–928, (1990). Dewar, M. J. S. Multibond reactions cannot normally be synchronous J. Am. Chem. Soc. 106 , 209–219, (1984). Borden, W. T., Loncharich, R. J., Houk, K. N. Synchronicity in multibond reactions Ann. Rev. Phys. Chem. 39 , 213–236, (1988). In a negligible number of instances (involving small, highly symmetric clusters at the transition state), the migration of all protons occurs synchronously, resulting in a high imaginary frequency associated with the transition state (greater than – 1500 cm – 1 ), where all O-O distances are similar and shorter than 2.39 Å. Actually, only a single direct-proton-transfer (DPT) case was found (11W6-iDPT3) where a proton triple jump takes place through a cyclic transition state (AIM shows that the three protons are covalently bound to the corresponding vicinal oxygens). 30 According to Eigen, most proton transfers undergone by [(H 2 O) n H + ] species in water occur after some structural rearrangement (structural diffusion). See Eigen, M. Proton transfer, acid-base catalysis, and enzymatic hydrolysis. Part 1: Elementary processes Angew. Chem. Int. Ed. 3, 1–9, (1964). It should be noted that the term “proton wire”, first coined by Morowitz to describe likely mechanisms for proton transport across biomembranes, did not address the mechanism of proton injection into the chain. See Nagle, J.F., Morowitz, H.J. Molecular mechanisms for proton transport in membranes Proc. Natl. Acad. Sci. USA 75, 298–302, (1978). Instead, our definition of “wire” includes both the proton source (H 3 O + ) and the proton sink (OH – ). The occurrence of ion pairs with only two proton channels (“wires”) is rare but real, as detected in this study. Herzfeld recognized the role of “special pairs” (characterized by having ultrashort hydrogen bonds) as transition states for proton transfers. See Bai, C., Herzfeld, J. Special pairs are decisive in the autoionization and recombination of water J. Phys. Chem. B 121, 4213–4219, (2017). Kohlrausch, F., Heydweiller, Ad. Über reines wasser Ann.d.Phys.u.Chem. (neue folge ) 53 , 209–235, (1894). A quite large number of publications have examined the properties of water constituent ions H + (H 2 O) n and (H 2 O) n OH – as isolated, independent entities. For a comprehensive review, see Agmon, N., Bakker, H. J., Campen, R. K., Henchman, R. H., Pohl, P., Roke, S., Thämer, M., Hassanali, A. Protons and hydroxide ions in aqueous systems Chem. Rev. 116, 7642–7672, (2016) and references therein. L. Onsager, J. Chim. Phys. , Special Issue on the 19th Meeting of the Société de Chimie Physique at Montpellier, September 1968, p. 86. Bühl, M., Wipff, G. Hydronium ion complex of 18-crown-6: where are the protons?.A density functional study of static and dynamic properties J. Am. Chem. Soc. 124, 4473–4480, (2002). -Experimental evidence for the presence short-living ions (in up to 2% of the content of water molecules) coexisting with long-lived pH-active ions, has recently been reported. See Artemov, V.G., Uykur, E., Roh, S., Pronin, A.V., Houerdane, E., Dressel, M. Revealing excess protons in the infrared spectrum of liquid water Scientific Reports , 10, 11320-9, (2020). de Grotthuss, C. J. T., Sur la decomposition de l’eau e des corps qu’elle tient en dissolution à l’aide de l’electricité galvanique Ann. Chim. (Paris) 1806, LVIII, 54–7. English translation: Philos. Mag. (London) 1806, 25 , 330–339. Hassanali, A., Prakash, M. K., Eshet, H., Parrinello, M. On the recombination of hydronium and hydroxide ions in water Proc. Natl. Acad. Sci. 108, 20410–20415, (2011). The contact distance reported in the literature for a H + -to-OH – collapse event (ca. 6 angstroms) does not include the proton source. Full agreement with our data is however observed when the H-O distance is added (assuming H 3 O + is the donor). See Natzle, W.C., Moore, C.B. Recombination of hydrogen ion (H + ) and hydroxide in pure liquid water J. Phys. Chem. 89, 2605–2612, (1985). Blackmond, D.G. The origin of biological homochirality Cold Spring Harb. Perspect. Biol. 11:a032540 1–10, (2019). See also, Devinsky, F. Chirality and the origin of life Symmetry 13, 2277–2292, (2021). Abiogenesis . Edited by K. Rogers, (2025, August 14). Encyclopedia Britannica . https://www.britannica.com/science/abiogenesis . Tables Table 1. Cluster size, Number of isomers (# isomers) studied, number of TSs localized (# TSs), number of Direct Proton Transfers (# DPTs), Ion-Pair Collapse (# IPC) and on-Pair Walk (# IPW). For each TS type, the range of activation energies (AE) are given in parenthesis (kcal/mol) for clusters formed from 8 to 30 water molecules Cluster # isomers # TSs # DPTs (AE) # IPCs (AE) # IPW (AE) 8 14 14 13 (16-26) 1 (23 & 0.3) ------------- 9 14 19 12 (15-21) 7 (22-24 & 0.04-1.4) ------------- 10 14 33 9 (17-29) 24 (20-26 & 0.006-2.6) ------------- 11 14 18 13 (16-26) 5 (30-32 & 0.07-1.1) ------------- 12 7 12 4 (17-20) 4 (19-26 & 0.14-6) 4 (0.09-5.8) 13 9 17 6 (18-25) 8 (22-29 & 0.002-4.2) 3 (0.05-1.7) 14 11 11 9 (18-25) 2 (18-22 & 0.28-0.96) ------------- 15 14 19 8 (17-26) 9 (16-31 & 0.05-3.3) 2 (0.05-1.4) 16 25 26 22 (17-26) 3 (26-29 & 0.8-3.8) 1 (1.2-1.5) 17 21 54 9 (18-21) 25 (19-29 & 0.03-3.5) 20 (0.1-5.4) 18 17 33 8 (18-25) 11 (19-33 & 0.05-3.3) 14 (0.04-3.3) 19 9 12 4 (20-23) 6 (18-31 & 0.07-3.9) 2 (0.08-11.6) 20 21 93 13 (18-27) 22 (18-31 & 0.02-4) 58 (0.01-9.5) 21 17 43 10 (18-27) 22 (21-28 & 0.08-8) 11 (0.07-4) 22 10 4 1 (19-21) 1 (29.4 & 4.8) 2 (0.47-1.34) 23 12 1 ------------- ---------------------------- 1 (0.6-1.4) 24 14 1 ------------- ---------------------------- 1 (0.7-1.7) 25 10 1 1 (24-25) ---------------------------- ------------- 26 12 1 ------------- 1 (26.1 & 3.4) ------------- 27 12 0 ------------- ---------------------------- ------------- 28 9 1 1 (26-28) ---------------------------- ------------- 29 7 1 ------------- 1 (27.4 & 2.1) ------------- 30 9 9 4 (21-23) ---------------------------- 5 (0.01-5.5) Total 302 423 147 152 124 Table 2. Number Ion-Pair Inversion and Ion-Pair Isomerization TSs localized (# TSs). For each TS type, the (negative) frequency (cm -1 ), as well as the range of activation energies are given in parenthesis (kcal/mol). Cluster # TSs # TS-Inversion # TS-Isomerization 17W1 1 f = -119 (0.70 - 2.34) ---------------------------- 17W5 1 f = -91 (1.42 - 4.93) ---------------------------- 17W7 1 f = -112 (0.91 – 2.55) ---------------------------- 18W2 1 f = -137 (0.75 – 2.75) ---------------------------- 18W16 1 f = -95 (0.67 - 1.84) ---------------------------- 20W4 1 f = -120 (0.97 - 1.86) ---------------------------- 20W22 1 f = -113 (0.90 - 8.36) ---------------------------- 18W2 1 -------------------------- f = -161 1.23 – 1.82 Table 3. Clusters, Number of TSs localized (# TSs), number of Direct Proton Transfers (#DPTs), Ion-Pair Collapse (# IPC), Ion-Pair Cross-Collapse (# IPCC), Ion-Pair Quench (# IPQ) and on-Pair Walk (IPW) in bis ion-pairs. For each TS type, the range of activation energies (AE) is given in parenthesis (kcal/mol). Cluster # TSs # DPTs # IPCs (AE) # IPCCs (AE) # IPQ (AE) # IPW (AE) 20 10 1 (18-19) 4 (18-28 & 0.3-2.9) 4 (23.5 & 0.1) 1 (42.9-0.3) --------------- 21 10 ----------- 8 (22-25 & 0.1-0.7) 1 (24.7 & 2.1) --------------- 1 (0.02-2.7) 21 1 1 (23.1 &0.2) 30 3 1 (17-18) 1 (27 & 0.5) ------------------ ---------------- 1 (0.3-1.7) Total 24 2 13 6 1 2 Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryinformationlistingandguidelinesAll.docx Water proton transfer processes and their potential energy surfaces Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8425076","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":584286154,"identity":"e850e690-ae62-4e4d-9021-b60e99a2339f","order_by":0,"name":"Jose Saa","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAm0lEQVRIiWNgGAWjYBACxgYQWcHAY0CiljOkaIHoa2NgIF4L87TjDz/8nHdYxpyB+fAH4iyYnWMs2bvtMI9lA1uaBLFaGCR4gVoMDvCYEecwxtnpj3/+nQPSwv+ZWIclmEnzNoBtYSDaYWbWMsfSeSyb2cyI02IIdNjNNzXW9ubszY+Jc5hhA4zFTJR6IJAnVuEoGAWjYBSMYAAA9bArjY0xjwMAAAAASUVORK5CYII=","orcid":"https://orcid.org/0000-0001-7365-6690","institution":"Universitat de les Illes Balears","correspondingAuthor":true,"prefix":"","firstName":"Jose","middleName":"","lastName":"Saa","suffix":""},{"id":584286155,"identity":"d451d95a-833a-4f0f-b792-3a5acdfe6654","order_by":1,"name":"Antonio Frontera","email":"","orcid":"https://orcid.org/0000-0001-7840-2139","institution":"Universitat de les Illes Balears","correspondingAuthor":false,"prefix":"","firstName":"Antonio","middleName":"","lastName":"Frontera","suffix":""}],"badges":[],"createdAt":"2025-12-22 12:48:21","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8425076/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8425076/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101833502,"identity":"e52d3cfa-f3e1-4ead-9d39-4c4d98d8afb5","added_by":"auto","created_at":"2026-02-04 06:59:34","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":86085,"visible":true,"origin":"","legend":"\u003cp\u003eStandard reaction coordinates resulting from IRC analysis of transition state (I) structures: a) Direct Proton Transfer (DPT) processes; b) Ion-Pair Proton Transfer (IPPT) processes, namely Ion-Pair Collapse (IPC) and Ion-Pair Walk (IPW) processes.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-8425076/v1/05f2f85a719afcd93a9c6c00.png"},{"id":101833504,"identity":"2f0f6668-8ec3-4b23-88a6-3b7366c0bf52","added_by":"auto","created_at":"2026-02-04 06:59:34","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":65491,"visible":true,"origin":"","legend":"\u003cp\u003eTransition state models for Direct Proton Transfers: a) internal Direct Proton Transfers (i-DPT), b) edge Direct Proton Transfers (e-DPT) and c) swing Direct Proton Transfers (s-DPT) processes.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-8425076/v1/e275510c7fd55968402704a2.png"},{"id":101881477,"identity":"0c4b228c-d82d-4579-9a2f-95ab256bc075","added_by":"auto","created_at":"2026-02-04 15:12:25","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":24088,"visible":true,"origin":"","legend":"\u003cp\u003e“Wires” [x,y,z] of ion-pair IP0011, where “00” is the number of the positive O-atom and the “11” is the number of the negative O-atom. This numbering is used in the supplementary information\u003csup\u003e30\u003c/sup\u003e to identify the IPs.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-8425076/v1/09a792c107334d60f59080c8.png"},{"id":101833507,"identity":"05661117-154b-4d23-91dc-989985440629","added_by":"auto","created_at":"2026-02-04 06:59:35","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":86052,"visible":true,"origin":"","legend":"\u003cp\u003eGeneral scheme for umbrella-inversion processes undergone by water ion-pairs (IPI).\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-8425076/v1/d141c39c87262ec1e8872b50.png"},{"id":101833505,"identity":"cdd2f2b8-a084-4380-9cc3-726ba3b9ae79","added_by":"auto","created_at":"2026-02-04 06:59:35","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":112904,"visible":true,"origin":"","legend":"\u003cp\u003eSimplified (only IPC and IPQ processes shown) reaction coordinate of single, bis and, presumably multiple ion-pairs.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-8425076/v1/89610e1df0ed4fb1920ebc8c.png"},{"id":101882530,"identity":"58ac8453-5bfc-4b3d-b272-0e95bf904434","added_by":"auto","created_at":"2026-02-04 15:23:38","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":982192,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8425076/v1/e3371924-b94b-41f0-b211-e5f36a6c3045.pdf"},{"id":101833503,"identity":"5e5108e5-ffed-4d42-8d90-32677b552b32","added_by":"auto","created_at":"2026-02-04 06:59:34","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":63418,"visible":true,"origin":"","legend":"Water proton transfer processes and their potential energy surfaces","description":"","filename":"SupplementaryinformationlistingandguidelinesAll.docx","url":"https://assets-eu.researchsquare.com/files/rs-8425076/v1/e26a225ae6ce5263b28cb2ab.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"\u003cp\u003eWater dynamics visited. A comprehensive DFT study of proton transfer in liquid water underscores the pivotal role of ion pairing phenomena\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eHydrogen transfer and hydrogen ion (proton) transfer are at the heart of chemical reactions. However, as emphasized by A. Zewail in the preface to\u0026nbsp;\u003cem\u003eHydrogen-Transfer Reactions\u003c/em\u003e,\u003csup\u003e1\u003c/sup\u003e hydrogen and proton transfer processes are quite complex in nature and, therefore, in describing the dynamics of both condensed-phase and biological systems undergone by such many-body complex systems,\u003csup\u003e2\u003c/sup\u003e \u0026ldquo;\u0026hellip; \u003cem\u003eit is not perhaps beneficial to consider every atom of a many-body complex system. Instead, the objective is hopefully to project the key electronic and nuclear forces which are responsible for behavior\u003c/em\u003e\u0026rdquo;. Accordingly, \u0026ldquo;\u0026hellip;\u003cem\u003ecomputer simulations\u0026hellip;should be a tool of guidance to formulate a predictive theory\u0026rdquo;\u003c/em\u003e and, \u0026ldquo;\u0026hellip;\u003cem\u003esimilarly for experiments, the most significant ones are those that\u003c/em\u003e \u003cem\u003edissect complexity and provide quite lucid pictures of the key and relevant processes\u003c/em\u003e\u0026rdquo;. In light of these considerations, the present study focused its attention on liquid water due to its status as a unique chemical system that exhibits distinctive and exceptional properties\u003csup\u003e3\u003c/sup\u003e relevant to life\u0026nbsp;and, most importantly, because these properties result primarily from the extremely rapid proton transfers\u003csup\u003e4,5\u003c/sup\u003e that occur within the extensive, three-dimensional hydrogen bonding network characteristic of liquid water and ice. Indeed, a consensus has emerged among researchers in the field regarding the most crucial question to address to gain a microscopic understanding of water: \u0026quot;\u003cem\u003ewhat is the structure and dynamics of the hydrogen bonding network in water that gives rise to these unique properties?\u003c/em\u003e\u0026quot;.\u003csup\u003e6\u003c/sup\u003e However, despite the considerable time and effort that has been devoted to improving the original Bernal-Fowler paradigm over the course of several decades,\u003csup\u003e7\u003c/sup\u003e the scientific community continues to regard water as an unsolved puzzle of confronting theories. This enigma is, at least in part, due to the temporal and spatial scale constraints imposed on liquid water structural data resulting from experiments and/or computations. In fact, experimental techniques with time scales ranging from 1 to 10 picoseconds may yield vibrational averaged (V) structures exclusively, while those with time scales greater than 10 picoseconds generate solely diffusion averaged (D) structures. Conversely, computer simulations that yield only states of minimum energy on the potential energy surface\u0026nbsp;generate\u0026nbsp;frozen (F) structures with infinite time scales (t -\u0026gt;\u0026nbsp;\u0026infin;). Unfortunately, the key instantaneous (I) structures (with time scales \u0026lt;\u0026lt; 1 picosecond), whose dynamical behavior would allow us to reach V, D and F structures, have been deemed inaccessible by experimental measurements,\u003csup\u003e8\u003c/sup\u003e though V. Artemov has recently theorized them based on the electrodynamic properties of water.\u003csup\u003e9\u003c/sup\u003e As described below, however, we demonstrate that the key proton transfer transition state structures (I) are available computationally.\u003c/p\u003e"},{"header":"Methods and protocols","content":"\u003cp\u003eIn accordance with the aforementioned recommendations and in our pursuit of a lucid picture of these pivotal processes,\u003csup\u003e10\u003c/sup\u003e we planned to tackle water dynamics by studying proton transfer in neutral, liquid water using static \u003cem\u003eab initio\u003c/em\u003e SCF simulations, instead of resorting to a molecular dynamics treatment\u003csup\u003e11\u003c/sup\u003e upon the original water model whose ionic components do not interact with each other. Furthermore, we planned to incorporate solvent effects through a polarizable continuum model (PCM),\u003csup\u003e12\u003c/sup\u003e with the objective of facilitating access to the relevant instantaneous (I) structures of the transition states (whose lifetimes are on the 10-100 femtosecond time scale) of proton transfers, whether concerted and synchronic or otherwise, taking place in liquid water.\u003csup\u003e13\u003c/sup\u003e To this end, we selected from the literature a substantial number of known, neutral, medium-sized water clusters ((H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003en\u003c/sub\u003e with n up to 30, and up to 25 isomers for each cluster size) as objects of study,\u003csup\u003e14\u003c/sup\u003e as they represent micro-snapshots of liquid water. Despite the strong criticism of applying the classic approach to condensed phases,\u003csup\u003e15\u003c/sup\u003e we anticipated that a subsequent IRC analysis\u003csup\u003e16\u003c/sup\u003e of these (I) structures would provide us with a comprehensive description of the relevant atomic-molecular dynamics of the rearrangements undergone by the hydrogen-bond network triggered by proton transfers operating on factual reaction coordinates.\u003csup\u003e17\u003c/sup\u003e In this regard, it is worth remarking that we did not rely on energetic or geometric criteria for the description of the hydrogen bonding networks. Rather, we projected to analyze the electron density topology provided by theoretical means (see below), as recommended by IUPAC.\u003csup\u003e18\u0026nbsp;\u003c/sup\u003eSpecifically, we expected that the programmed IRC analysis of the transition state structures (I) of direct proton transfers to yield the F-structures of both the initial and final clusters. Conversely, when applied to the instantaneous, transition state structures (I) of indirect proton transfers, we anticipated that the analysis would reveal the F-structure of the initial cluster and, most significantly, that of the ion-pair product,\u003csup\u003e19\u003c/sup\u003e presumably displaying vibrational-averaged structures (V), given that ion-pair lifetimes lie on the picosecond timescale.\u003csup\u003e4,8,9\u003c/sup\u003e Over the years, the lack of compelling evidence supporting the association of the ionic components of water and ice has been widely accepted. Consequently, the prevailing notion that still persists in textbooks and scientific literature is that isolated, non-interacting pairs of ions, rather than solvent-separated ion-pairs, are the natural components of water and ice.\u003csup\u003e20\u003c/sup\u003e In fact, a substantial body of scientific literature describes the proton transfer properties of isolated Z\u0026uuml;ndel and Eigen cations, which differ from those of the corresponding isolated anions. It is imperative to note that the properties exhibited by these isolated cations and anions have been attributed to neutral water, thereby perpetuating the original paradigm. However, we posited that the detailed structure and properties of single\u003csup\u003e21\u003c/sup\u003e and multiple water ion-pairs would be paramount in describing the dynamic structure of water and, consequently, its associated dielectric properties.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo reach the aforementioned goals, we planned to rely on Kohn-Sham density functional theory (KS-DFT) as the foundational ab initio method.\u003csup\u003e22\u003c/sup\u003e Given our plan to study proton transfers in an extensive range of neutral, medium-sized clusters (H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003en\u003c/sub\u003e, with n reaching up to 30, Truhlar\u0026rsquo;s M06-2X hybrid functional,\u003csup\u003e23\u003c/sup\u003e paired with the 6-311++G(d,p) basis set, was selected as the optimal choice for its balance of accuracy and computational efficiency.\u003csup\u003e24\u003c/sup\u003e\u003c/p\u003e"},{"header":"Results and discussion","content":"\u003cp\u003eThe initial clusters\u003csup\u003e14\u003c/sup\u003e were subsequently re-optimized employing the Polarizable Continuum Model (PCM) to model solvent effects (solvent=water).\u003csup\u003e12\u003c/sup\u003e Then, hydrogen atoms were precisely positioned at the midpoint of each O…O pair, prior to the transition state searches were launched. The ensuing IRC analysis of the transition state (I) structures, which were identified as stationary points, unveiled two distinct categories of reaction coordinates (see Figure 1). The first category comprises direct proton transfer (DPT) processes involving three stationary points on the reaction coordinate (147 transition states were found, see Table 1). The initial and final clusters are both F structures, with a cyclic transition state (I structure) connecting them. The second category encompasses concerted processes that result in the formation of ion-pair clusters as products (a grand total of 276 transition states were localized). This category is thus designated as ion-pair proton transfers (IPPT). Interestingly, two sub-categories of IPPT processes were distinguished, namely Ion-Pair Collapse (IPC, 152 transition states) and Ion-Pair Walk (IPW, 124 transition states), which involve short- and long-lived ion pairs, respectively.\u003csup\u003e25\u003c/sup\u003e The step-ladder reaction coordinate, which is characteristic of Ion-Pair Collapse (IPC) processes, provides a clear illustration of the evolution of short-lived ion pairs (Figure 1b, first TS). During this process, a specific proton transfer occurs as the ion pair (V structure) passes through a nearby transition state (I-structure), eventually resulting in a collapsed cluster (F structure). Conversely, processes involving ion-pair clusters as both the initial and final products (Figure 1b, subsequent TSs) are designated Ion-Pair Walk (IPW) processes.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIPPT processes involving long-lived ion pairs, namely IPW processes, will presumably impact on the nature of the microscopic model of water and, consequently, on its electrodynamic properties.\u003csup\u003e9\u003c/sup\u003e In contrast, IPPT processes involving short-lived ion pairs, specifically IPC processes, as well as all kinds of DPT processes, are expected to have no effect on water dissociation phenomena.\u003csup\u003e4\u003c/sup\u003e A detailed description of the DPT and IPPT processes follows. In this analysis, particular emphasis is placed on the instantaneous (I) structures of proton transfer transition states and their evolution into products that are either frozen (F) or averaged (V and D) structures.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDirect Proton Transfers operating on neutral water clusters.\u003c/strong\u003e- The absence of ion-pair products is the hallmark of the reaction coordinates for all categories of direct proton transfer (DPT) processes. It is worth remarking though that these reactions exhibit ion-pair-like cyclic transition state (I) structures with clear charge separation (Fig. 2), as revealed by the corresponding NBO analysis of the charge distribution.\u003csup\u003e26\u003c/sup\u003e For the efficient operation of these cyclic processes, it is imperative that oxygen atoms possess an \u003cem\u003ead\u003c/em\u003e configuration, as they must act as both a donor (\u003cem\u003ed\u003c/em\u003e) and an acceptor (\u003cem\u003ea\u003c/em\u003e) along the reaction coordinate. This distinctive property facilitates recombination into two neutral clusters with slightly different constitutions, due to the fact that proton transfer occurs almost equally clockwise or counterclockwise (as depicted in the transition state models shown in Figure 2). This fact qualifies DPT processes as quite relevant to explain in detail the much-debated molecular mechanism of water reorientation phenomena\u003csup\u003e27\u003c/sup\u003e associated to the Debye relaxation dynamics of water,\u003csup\u003e28\u003c/sup\u003e and ice.\u003csup\u003e29\u003c/sup\u003e The most prevalent DPT processes\u003csup\u003e30\u003c/sup\u003e belong to the internal class, illustrated in Figure 2a as i-DPT, which models the transition structure of three- to eight-membered ring internal, direct proton transfers in which only three, four, five, six, seven, or eight hydrogen atoms of a given neutral water cluster are translocated from their original positions. To date, no evidence has been found to suggest the occurrence of internal DPT (i-DPT) processes involving transition structures with larger cyclic rings. In contrast, the atypical cases depicted in Figure 2, designated as class b (four-membered ring transitions structures in most cases), involve the translocation of five hydrogen atoms.\u003csup\u003e31\u003c/sup\u003e This phenomenon occurs in edge cases b1 and b2 (illustrated as e-DPT in Figure 2), where a water molecule is present at the periphery of the cyclic transition state structure, either as the H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003ed\u003c/sup\u003e\u003csup\u003e+\u003c/sup\u003e (b1), or the OH\u003csup\u003e\u0026nbsp;d\u003c/sup\u003e\u003csup\u003e-\u003c/sup\u003e (b2) moiety. A third class of DPT processes, illustrated as c) in Figure 2, namely swing DPT (s-DPT) processes, involves a four-membered ring transition structure in which a single proton (H\u003csub\u003eab1\u003c/sub\u003e) behaves like the pendulum of a wall clock swinging to the right and to the left to trap a proton in channels a or b.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eProton transfers taking place through DPT processes can be regarded as a consequence of the so-called accordion effect, which is defined as the effect of a stopping event on the fluid passage of a body of elements moving along a defined path.\u003csup\u003e32\u003c/sup\u003e In essence, DPT processes involve the compression of a specific hydrogen bond along the proton channel connecting two distant water molecules leading to a halt at the transition state. This is subsequently followed by decompression until fluid passage resumes. The application of Bader's Atoms in Molecules (AIM) theory\u003csup\u003e33\u003c/sup\u003e to the analysis of DPT processes enabled the delineation of the complete connectivity at their cyclic transition states, as well as at the initial and final products. In most cases, the planar transition states (predominantly those with three, four and some with five member rings) of DPT processes exhibit compression at all their O-H…O bonds. The strongest compression (O-O distance ≤ 2.41 Å) occurs at the sites actually involved in the proton transfer process.\u003csup\u003e30\u003c/sup\u003e As illustrated in Table 1, DPT processes found in all (H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003en\u003c/sub\u003e clusters studied (n = 8–30) \u0026nbsp;exhibited energy barriers (DH*) spanning from 15 to 29 kcal/mol (most common values found at ca. 20 kca/mol; see Table 1 and Supplementary Information).\u003csup\u003e30\u003c/sup\u003e The protons actually being transferred in the transition state are covalently bound to both vicinal oxygen atoms and are therefore detected by AIM which shows negative values of the Laplacian of the electron density at the hydrogen bond critical points (HBCP).\u003csup\u003e33\u003c/sup\u003e Accordingly, it can be said that the majority of DPT processes entail a single, sometimes double, proton transfer in the transition state, with the subsequent transfers occurring after some molecular arrangements have taken place, as revealed by the corresponding IRCs. Consequently, as indicated by Dewar et al.\u003csup\u003e34\u003c/sup\u003e and Houk et al.,\u003csup\u003e35\u003c/sup\u003e these processes should be qualified as concerted, albeit asynchronous, proton transfers.\u003csup\u003e36\u003c/sup\u003e Conversely, some DPT processes actually undergo molecular adjustments at the transition state prior to the occurrence of proton transfer.\u003csup\u003e37\u003c/sup\u003e In these cases, the reaction coordinates resulting from the corresponding IRC analysis are not sharp (as illustrated in Fig. 1a) but, instead, rather rounded and irregular (not shown). In such cases, proton transfer is not detected by AIM.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eIon-pair Proton Transfer operating on neutral water clusters.-\u003c/strong\u003e In contrast to the behavior exhibited by DPT processes, the most common proton transfer processes, namely IPPT processes, whether IPC (ion-pair collapse) or IPW (ion-pair walk), involve ion-pair clusters, i.e. clusters comprising pairs of ions, specifically H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e and OH\u003csup\u003e-\u003c/sup\u003e units, that are not isolated species. Rather, they are interconnected by three \"wires\", that is, by three proton channels,each channel involving a network of hydrogen bonds of variable length that facilitate the interconnectivity between the proton source and the proton sink.\u003csup\u003e38,39\u003c/sup\u003e A noteworthy observation is that proton transfer in IPPT processes can occur through any of these channels. In the context of ion pair walk (IPW) processes involving long-lived ion pairs,\u003csup\u003e9,25\u003c/sup\u003e the \"wire\" acting as the actual proton channel for proton transfer undergoes a discernible compression (up to ca. 6% of their length) as the original ion-pair reaches the transition state located nearby. Concurrent with the compression of the active “wire”, the inactive “wires” cooperate by undergoing simultaneous decompression, thereby facilitating the proton transfer process, i.e. proton transfer occurs because the whole system fluctuates.\u003csup\u003e4\u003c/sup\u003e Individual account of this “wiring” interconnectivity, together with the compression and decompression undergone by the active and the inactive “wires” at the transition state of each proton transfer, is provided as Supplementary Information. In the majority of IPW cases, the enthalpy cost (DH*) is in the range of 0.01 to 5 kcal/mol (Table 1), and the O-O distance at the key O--H--O unit undergoing proton transfer in the transition state oscillates between 2.38 and 2.42 angstroms.\u003csup\u003e40\u003c/sup\u003e A detailed, quantitative account of these events is provided as Supplementary Information.\u003csup\u003e30\u003c/sup\u003e The subsequent decompression of the aforementioned active \"wire\" results in the formation of a new ion-pair, in which either the head (+) or the tail (-) has been displaced from its original position to a nearby one. This is because proton transfer involves protons immediately close to either the source ion (a\u003csub\u003e0\u003c/sub\u003e, b\u003csub\u003e0\u003c/sub\u003e or c\u003csub\u003e0\u003c/sub\u003e), or the sink ion (a\u003csub\u003ex\u003c/sub\u003e, b\u003csub\u003ex\u003c/sub\u003e or c\u003csub\u003ex\u003c/sub\u003e), as illustrated in Figure 3. We identify these displacements as ion-pair 'walks', which can drive a single ion-pair into a new position in six different directions. It is also noteworthy that the resulting ion-pair can undergo additional, rapid \"walk\" displacements involving the head (+) or tail (-) units, thereby creating new ion-pairs at each “walk” step.\u003csup\u003e30\u003c/sup\u003e Since the original proposal by Kohlrausch,\u003csup\u003e41\u003c/sup\u003e and subsequent adoption by Bernal and Fowler,\u003csup\u003e7\u003c/sup\u003e it has been assumed that water ionic components H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003en\u003c/sub\u003e and (H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003en\u003c/sub\u003eOH\u003csup\u003e-\u003c/sup\u003e move independently, freely, and randomly.\u003csup\u003e42\u003c/sup\u003e However our study shows, instead, that water ion-pairs (with up to 30 water molecules) possess an intrinsic, previously unrecognized, \"walking\" capacity. In fact, despite Onsager’s assertion that the distinction between free ions and their associated ion-pairs depends on arbitrary conventions,\u003csup\u003e43\u003c/sup\u003e we contend instead that the IRC and AIM of IPPT processes not only provide substantial evidence for the existence of the aforementioned “wiring” interconnection between water constituent ions, but also support the “walking” capabilities of long-lived ion-pairs over large distances (up to 11.9 angstroms in this study).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIn addition to the aforementioned processes of annihilation (IPC) and rebuilding (IPW) of water ion-pairs, we also explored the inversion of the H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e moieties of non-symmetrical ion-pairs. The results of this analysis with a total of seven transition states, demonstrate for the first time the ability of ion-pairs to undergo the so-called umbrella inversion process (IPI),\u003csup\u003e44\u003c/sup\u003e thereby interconverting concave ion-pairs clusters to convex ion-pairs clusters (F structures) via locally planar (Fig. 4) transition states (I) structures. The enthalpy cost (DH*) of these ion-pair umbrella-inversion processes lies in the range of 0.7 to 2.5 kcal/mol in most cases (see Table 2). As illustrated in Figure 4, we have found that the resulting concave and convex ion-pair clusters, which share identical wiring systems, evolve independently via the aforementioned standard proton transfer mechanisms.\u003c/p\u003e\n\u003cp\u003eFurthermore, water ion-pairs can undergo isomerization processes, whereby a specific water molecule reorients itself within the ion-pair cluster. This reorientation does not involve proton transfer, but rather simple water rotation (see Table 2).\u003c/p\u003e\n\u003cp\u003eIon-pair collapse (IPC) processes involve short-lived ion-pairs.\u003csup\u003e9,25,45\u003c/sup\u003e There, the initial compression of the active 'wire' of the original ion-pair occurs upon reaching the nearby transition state in cooperation with the decompression of the inactive 'wires' (see below). The majority of cases studied have enthalpy cost values (DH*) in the range of 0.002 to 8 kcal/mol, as shown in Table 1). The subsequent collapsing event, which involves the recombination of the ion-pair constituent ions, takes place by proton hopping through an amplified Grotthuss mechanism,\u003csup\u003e46\u003c/sup\u003e as it can start not only at a proton close to the source ion (a\u003csub\u003e0\u003c/sub\u003e, b\u003csub\u003e0\u003c/sub\u003e or c\u003csub\u003e0\u003c/sub\u003e), but also at a proton close to the sink ion (a\u003csub\u003ex\u003c/sub\u003e, b\u003csub\u003ex\u003c/sub\u003e or c\u003csub\u003ex\u003c/sub\u003e), as illustrated in Figure 3. According to the criteria of Dewar,\u003csup\u003e34\u003c/sup\u003e and Houk,\u003csup\u003e35\u003c/sup\u003e all IPC processes examined in this study, as revealed by IRC and AIM, can thus be defined as concerted and asynchronous. Apparently, these observations are in striking contrast to the findings reported by molecular dynamic simulations studies on the recombination events of isolated ions H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e and OH\u003csup\u003e-\u003c/sup\u003e. These studies report that, after reaching contact distance (c.a. 6 angstroms), a concerted triple jump takes place.\u003csup\u003e47\u003c/sup\u003e\u0026nbsp; \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eArtemov\u003csup\u003e25,45\u003c/sup\u003e showed that long-lived ion pairs are responsible for pH whereas short-lived ion pairs are not. We have tried to learn about the structural reasons underlying this behavior by analyzing the up-to-six proton transfer routes available for single ion pairs operating in all types of IPPT processes. For every proton transfer route, this analysis encompassed not only the number of water molecules (x, y, and z) linking both H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e and OH\u003csup\u003e-\u003c/sup\u003e units, but also the specific O-H bond constituents a, b, and c of [x,y,z] \"wires\" of ion pairs IP0011 (Figure 3). Additionally, the \"wire\" lengths, herein defined as the sum of the O-O distances as they go from the source (O\u003csup\u003e+\u003c/sup\u003e) to the sink (O\u003csup\u003e-\u003c/sup\u003e) poles, were also taken into account. The most salient conclusion that emerged from this analysis is that \"wire\" lengths of ion-pairs ranging from 7.3 to 7.7 angstroms,\u003csup\u003e48\u003c/sup\u003e i.e., when either x, y, or z equals 2, promote immediate ion pair collapse through that “wire”.\u003csup\u003e40\u003c/sup\u003e This happens because the optimal geometrical parameters for proton jumping (O-O distance ca. 2.4 angstroms) are reached by even a weak fluctuation involving compression of 0.1-0.3 angstroms of the active \"wire\", an effort that is counterbalanced by the simultaneous decompression of the two “wires” that remain inactive. Collapse events, however, are not limited to these cases only. In fact, some collapse events occur when x, y or z = 3, though quite unusually when x, y or z = 4. On the other hand, IPW processes involving long-lived ion pairs are common for species having large values (4 and above) for x, y or z. Very often the potential energy surface describing the proton transfer activity of these large ion-pairs is of a mixed type showing both IPC and IPW paths competing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eProton transfers on neutral, ionized water clusters\u003c/strong\u003e.- Despite being constrained by the space limitations of our clusters (which contain a maximum of 30 water molecules), the programmed dynamic analysis also focused its attention upon water single ion-pairs as a whole, neutral, wired-up systems capable of undergoing further proton transfer processes. To this end, a methodology similar to the one previously described was employed. Among the single ion-pairs previously obtained, some of them were selected and then hydrogen atoms were precisely positioned at the midpoint of some O…O pairs, specifically those far away from the existing ion pair. Subsequent transition state searches revealed the basic proton transfer operations undergone by the single ion-pairs, namely direct proton transfers (DPTs), and IPPT processes involving short- and long-lived bis ion-pairs, respectively, however with several specific subtypes worth being described. A brief description of these interesting species based on IRC and AIM analysis follows. Notably, all these transition states lie at a second-floor energy level, approximately 20-25 kcal/mol above those at the first-floor energy level described above (see Table 3). Figure 5 provides a simplified illustration of the energy building of single, bis and multiple ion pairs, and the energy loss resulting from ion pair collapse (IPC) and ion pair quench (IPQ) processes. Higher floor energy levels, not yet identified, are presumed to be inhabited by multiple ion-pairs.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eDirect proton transfers (only i-DPT processes, as illustrated in Figure 2a) operating upon single ion-pair clusters entail the translocation of hydrogen atoms through a cyclic transition state, located far away from the original ion-pair. Accordingly, the resulting products PT1 and PT2 (Figure 1) are isomeric ion-pairs as they retain the original ion-pair constitution but differ at some points of their structures.\u003c/p\u003e\n\u003cp\u003eParticular emphasis was placed on IPPT processes of the IPW and IPC types because they should implicate bis ion-pairs. This is exemplified by a generalized bis ion-pair IP1234-IPabcd where the first two digits, or letters, denote the location of the H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e unit, while the final two specify the position of the corresponding OH\u003csup\u003e-\u003c/sup\u003e unit. The displacement of ions in IPW processes has been shown to induce a shift of either the source (H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e) or sink (OH\u003csup\u003e-\u003c/sup\u003e) unit of each ion pair to a vicinal position, thereby resulting in the formation of a novel bis ion pair (either IP5634-IPabcd when the H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e unit moves from position 12 to 56, or IP1278-IPabcd when the OH\u003csup\u003e-\u003c/sup\u003e unit moves from position 34 to 78, or IP1234-IPefcd when the H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e unit moves from position ab to ef, or IP1234-IPabgh when the OH\u003csup\u003e-\u003c/sup\u003e unit moves from position cf to gh). Subsequent IPW displacements on the resulting bis ion-pair may occur, thus contributing to the understanding of the underlying mechanism of long-lived ion-pairs. Moreover, since every source and sink unit is affixed by three “wires”, it follows that such displacements can take place in any of the 2x6 possible space directions. On the other hand, several mechanisms can actually drive bis ion-pairs to a short-lived term. Thus, in addition to the standard collapse (IPC) processes in which the original bis ion-pair collapses, thereby leading to a single ion-pair, either IP1234 (if IPabcd collapses), or IPabcd (if IP1234 collapes), novel IPC subclasses were identified. Specifically, the so-called ion-pair crossed collapse (IPCC) processes drive the original bis ion-pair to either single ion-pair IP12cd or IPab34.\u003csup\u003e30\u003c/sup\u003e This happens because the entangled nature of the original bis ion-pair's wiring system in a constrained space causes the collapse event to affect one ionic unit from each component of the original bis ion-pair. In addition to this partial collapse event, a full collapse event may also take place upon the bis ion-pair system. This phenomenon, termed an ion-pair quench (IPQ) process, leads to the complete quenching of the bis ion-pair system, resulting in the formation of a neutral, non-ionized cluster. As illustrated in Figure 5, and Table 3, IPQs exhibit a complete release of energy over a brief time period, particularly when operating on multiple ion-pairs.\u003csup\u003e30\u003c/sup\u003e Further research is required to elucidate the mechanisms responsible for proton transfers that presumably occur during atmospheric events, such as lightning and thunder. It is recommended that these investigations utilize substantially larger water and ice clusters.\u003c/p\u003e"},{"header":"Conclusions","content":"\u003cp\u003eTo sum up, the present DFT-based study of water dynamics, has uncovered the fundamental proton transfer mechanisms that occur in liquid water. Basically, the dynamics of water are contingent on three distinct proton transfer operations. Direct proton transfers (DPT) have been shown to involve ion-pair-like transition states (I structures), i.e, evanescent ion-pairs. Conversely, ion-pair collapse (IPC) and ion pair-walk (IPW) processes operate on ion-pairs (F structures), the former involving ion-on-pairs that can be categorized as short-living and the later as long-living ion-pairs. This conclusion is supported by IRC analysis of the instantaneous (I) structures obtained for their transition states, combined with AIM studies upon the three stationary points coming from IRC analysis. DPT processes, which induce the translocation of protons undergoing transfer through cyclic transition states, have been shown to operate on both non-ionized and ion-pair clusters. Proton transfer processes involving single ion-pairs, namely IPC and IPW, and bis ion-pairs, namely IPC, IPCC, IPQ and IPW, are facilitated by the cooperative fluctuations undergone by the wiring system of ion-pairs. Two salient properties of ion-pairs are: 1) their capacity to undergo umbrella inversion (IPI) processes with negligible energy cost, thereby augmenting the number of operative proton transfers, and 2) their ability of some constituent water molecules to suffer isomerization. It is imperative though to recognize that collapse (IPC and IPCC) and quench (IPQ) processes limit the lifetime of ion-pairs, whereas those undergoing walk (IPW) processes i.e., long-lived ion-pairs, hold relevance in the context of pH, as pointed out by Artemov\u0026rsquo;s \u0026ldquo;ionic model of water\u0026rdquo;.\u003csup\u003e9\u003c/sup\u003e In this regard, it is worth recognizing that the almost costless capacity of long-lived ion-pairs to \u0026ldquo;walk\u0026rdquo; in nx6 space directions (herein demonstrated for n=1 and 2), clearly indicates that there may be no necessity to invoke the existence of free, non-interacting ions resulting from autoionization. The new paradigm not only recognizes the prevailing role of long-lived ion pairs in the electrodynamic properties of water, as Artemov has suggested,⁹ but also points to the plausible role of multiple ion pairs, due to their chiral nature, in the genesis of chirality\u003csup\u003e49\u003c/sup\u003e and the abiotic origin of life on Earth.\u003csup\u003e50\u003c/sup\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAcknowledgments.\u003c/h2\u003e \u003cp\u003e- A.F. is grateful to Project PID2023-148453NB-I00 funded by the Ministerio de Ciencia, Innovaci\u0026oacute;n y Universidades of Spain, MCIU/AEI/\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.13039/501100011033\u003c/span\u003e\u003cspan address=\"10.13039/501100011033\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e and FEDER, UE\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003e\u003cem\u003eHydrogen-Transfer Reactions\u003c/em\u003e. Edited by Hynes, J. T., Klinman, J. P., Limbach, H.-H., Schowen, R. L., Wiley-VCH Verlag GmbH\u0026amp;Co. KGaA, Weinheim (2007).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003e\u003cem\u003eProton Transfer in Hydrogen-Bonded Systems\u003c/em\u003e. Edited by T. Bountis, NATO ASI series, Vol. 291, Springer (1992).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eChaplin, M. F., \u003cem\u003eWater Structure and Science\u003c/em\u003e, (2001). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://water.lsbu.ac.uk/water/\u003c/span\u003e\u003cspan address=\"https://water.lsbu.ac.uk/water/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMolecular dynamics studies combined with a \u0026ldquo;transition path sampling\u0026rdquo; approach have shown that hydrogen transfer occurs in the subpicosecond time scale. See Geissler, P. L., Dellago, C., Chandler, D., Hutter, J., Parrinello, M. Autoionization in liquid water \u003cem\u003eScience\u003c/em\u003e 291, 2121\u0026ndash;2124. (2001).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHassanali, A., Prakash, M.P., Eshet, H., Parrinello, M. On the recombination of hydronium and hydoxyde ions in water \u003cem\u003eProc. Natl. Acad. Sci. U.S.A.\u003c/em\u003e 108, 20410\u0026ndash;20415, (2011).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eA full \u003cem\u003eChemical Reviews\u003c/em\u003e issue has been dedicated to expose most-relevant water issues. Edited by Petterson, L. G. M., Henchman, R. H., Nilsson, A. \u003cem\u003eChem. Rev.\u003c/em\u003e 116, issue 13, 7459\u0026ndash;7726, (2016).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBernal, J.D., Fowler, R.H. A theory of water and ionic solutions, with particular reference to hydrogen and hydroxyl ions \u003cem\u003eJ. Chem. 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Proton transfer 200 years after von Grotthuss: insights from ab initio simulations \u003cem\u003eChemPhysChem\u003c/em\u003e 7, 1848\u0026ndash;1870, (2006), and references therein.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSee Tomasi, J., Cammi, R., Mennucci, B., Cappelli, C., Corni, S. Molecular properties in solution described with a continuum solvation model \u003cem\u003ePhys. Chem. Chem. Phys\u003c/em\u003e. 4, 5697\u0026ndash;5712, (2002), and references therein.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eM\u0026uuml;ller, K. Reaction paths on multidimensional energy hypersurfaces \u003cem\u003eAngew. Chem. Int. Ed. Engl\u003c/em\u003e. 19, 1\u0026ndash;13, (1980).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMalloum, A., Fifen, J.J., Dhauoadi, Z., Engo, S. G. N., Conradie, J. Structure, relative stability and binding energies of neutral water clusters, (H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e2\u0026ndash;30\u003c/sub\u003e \u003cem\u003eNew J. Chem.\u003c/em\u003e, \u003cem\u003e43\u003c/em\u003e, 13020\u0026ndash;13037, (2019).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eTreating high dimensional systems such as condensed phases with a classic approach is \u0026ldquo;\u003cem\u003elikely irrelevant\u003c/em\u003e\u0026rdquo; due to the uncountable number of saddle points in their PES. See: Bolhuis, P.G., Chandler, D., Dellago, C., Geissler, D.L. Transition path sampling: throwing ropes over rough mountain passes, in the dark \u003cem\u003eAnnu. Rev. Phys. Chem.\u003c/em\u003e, 53, 291\u0026ndash;318, (2002).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFukui, K. The path of chemical reactions-The IRC approach \u003cem\u003eAcc. Chem. Res. 14\u003c/em\u003e, 363\u0026ndash;368, (1981).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMethodologies using the \u0026ldquo;\u003cem\u003etransition path sample\u003c/em\u003e\u0026rdquo; approach do not require the identification of a reaction coordinate to describe a chemical reaction. See: Dellago, C., Bolhuis, P.G., Csajka, F.S., Chandler, D. Transition path sampling and the calculation of rate constants \u003cem\u003eJ. Chem. Phys.\u003c/em\u003e 108, 1964\u0026ndash;1977, (1998); Dellago, C., Bolhuis, P.G., Chandler, D. Efficient transition path sampling: Application to Lennard-Jones cluster rearrangements \u003cem\u003eJ. Chem. Phys.\u003c/em\u003e 108, 9236\u0026ndash;9245, (1988); Bolhuis, P.G., Dellago, C., Chandler, D. Sampling ensembles of deterministic transition pathways \u003cem\u003eFaraday Discuss.\u003c/em\u003e 110, 421\u0026ndash;436, (1998); Geissler, D.L., Dellago, C., Chandler, D., Hutter, D., Parrinello, M. Ab initio analysis of proton transfer dynamics in (H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003e3\u003c/sub\u003eH\u003csup\u003e+\u003c/sup\u003e \u003cem\u003eChem. Phys. Lett.\u003c/em\u003e 321, 225\u0026ndash;230, (2000).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eArunan, E., Desiraju, G. R., Klein, R. A., Sadlej, J., Scheiner, S., Alkorta, I., Clary, D.C., Crabtree, R. H., Dannenberg, J. J., Hobza, P., Kjaergaard, H. G., Legon, A. C., Mennucci, B., Nesbitt, D. J. Defining the hydrogen bond: An account (IUPAC technical report) \u003cem\u003ePure \u0026amp; Appl. Chem\u003c/em\u003e. 83, 1619\u0026ndash;1636, (2011); Definition of the hydrogen bond (IUPAC recommendations 2011) \u003cem\u003eibid\u003c/em\u003e. 83, 1637\u0026ndash;1641, (2011).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMarkus, Y., Hefter, G. Ion pairing \u003cem\u003eChem. Rev.\u003c/em\u003e 106, 4585\u0026ndash;4621, (2006).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRobinson, R. A., Stokes, R. H. \u003cem\u003eElectrolyte Solutions\u003c/em\u003e, 2nd ed. revised; Butterworth: London, 1965.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eA few small, highly symmetric, three-dimensional water ion-pair clusters (not unfrequently abbreviated by linear formulas of the type H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e--(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003en\u0026ndash;2\u003c/sub\u003e--OH\u003csup\u003e\u0026ndash;\u003c/sup\u003e, with n\u0026thinsp;=\u0026thinsp;5, 8, 10) have been described in the realm of gas-phase \u003cem\u003eab-initio\u003c/em\u003e SCF calculations. See: a) Lee, C., Sosa, C., Novoa, J. J. Evidence of the existence of dissociated water molecules in water clusters \u003cem\u003eJ. Chem. Phys\u003c/em\u003e. 103, 4360\u0026ndash;4362, (1995); b) Tozer, D.J., Lee, C., Fitzgerald, D. An investigation of hydrogen transfer in water clusters \u003cem\u003eJ. Chem. Phys\u003c/em\u003e. 104, 5555\u0026ndash;5557, (1996); c) Jensen, J. O., Samuels, A. C., Krishnan, L. A., Burke, P. N. Ion pair formation in water clusters: a theoretical study \u003cem\u003eChem. Phys. Lett.\u003c/em\u003e 276, 145\u0026ndash;151, (1997); d) C\u0026aacute;rdenas, R., Lag\u0026uacute;nez-Otero, J., Flores-Rivero, A. Ab initio study of the reaction mechanism of water dissociation into the ionic species OH\u003csup\u003e\u0026ndash;\u003c/sup\u003e and H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e \u003cem\u003eInt. J. Quantum Chem.\u003c/em\u003e 68, 253\u0026ndash;259, (1998); e) Smith, A., Vincent, M.A., Hillier, I.H. Mechanism of acid dissociation in water clusters: electronic structure studies of (H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003en\u003c/sub\u003eHX (n\u0026thinsp;=\u0026thinsp;4, 7: X\u0026thinsp;=\u0026thinsp;OH, F, SH, HSO3, OOSO\u003csub\u003e2\u003c/sub\u003eH, OOH.SO\u003csub\u003e2\u003c/sub\u003e) \u003cem\u003eJ. Phys. Chem. A\u003c/em\u003e 103, 1132\u0026ndash;1139, (1999); f) Svocil, D., Jungwirth, P. Cluster model of the ionic product of water: accuracy and limitations of common density functional methods \u003cem\u003eJ. Phys. Chem. A\u003c/em\u003e 110, 9194\u0026ndash;9199 (2006); g) Perlt, E., von Domaros, M., Kirchner, B., Ludwig, R., Weinhold, F. Predicting the ionic product of water \u003cem\u003eSci. Rep.\u003c/em\u003e 7, 10244\u0026ndash;10253, (2017); h) Turi, L., Rodrigues, J. Laria, D. Combined effects from solvation and nuclear quantum fluctuations on autoionization mechanisms in aqueous clusters \u003cem\u003eJ. Phys. Chem. B\u003c/em\u003e 124, 2198\u0026ndash;2208, (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSee You, H.S., Li, S.L., Truhlar D.G. Perspective: Kohn-Sham density functional theory descending a staircase \u003cem\u003eJ. Chem. Phys.\u003c/em\u003e 145, 130901-23, (2016), and references therein.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eY. Zhao, D.G. Truhlar, The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, non-covalent interactions, excited states, and transition elements: two new functional sans systematic testing of four M06-class functionals and 12 other functionals \u003cem\u003eTheor. Chem. Acc.\u003c/em\u003e 120, 215\u0026ndash;241, (2008).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGillan, M.J., Alf\u0026egrave;, D., Michaelides, A. How good is DFT for water? \u003cem\u003eJ. Chem. Phys.\u003c/em\u003e 144, 130901\u0026ndash;33 (2016).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBy examining the range of water conductivity values measured at high frequencies, which essentially reflect the net proton dynamics of water, Volkov, Artemov, and Pronin came to the provocative conclusion that, in addition to the long-lived ion pairs that are responsible for the autoionization event, there must be a substantial number of short-lived ions. See Volkov, A.A., Artemov, V.G., Pronin, A.V. A radical new suggestion about the electrodynamics of water: can the pH index and the Debye relaxation be of a common origin? \u003cem\u003eEPL\u003c/em\u003e 106, 46004-p6, (2014). See also Artemov, V.G., Volkov Jr., A.A., Sysoev, N.N., Volkov, A.A. On autoionization and pH of liquid water \u003cem\u003eDoklady Physics\u003c/em\u003e 61, 1\u0026ndash;4, (2016).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eReed, A.E., Curtis, L.A., Weinhold, F. Intermolecular interactions from a natural bond orbital, donor-acceptor viewpoint \u003cem\u003eChem. Rev.\u003c/em\u003e 88, 899\u0026ndash;926, (1988).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSee Laage, D., Stirnemann, G., Sterpone, F., Rey, R., Hynes, J.T. Reorientation and allied dynamics in water and aqueous solutions \u003cem\u003eAnnu. Rev. Phys. Chem.\u003c/em\u003e 62, \u003cem\u003e395\u003c/em\u003e\u0026ndash;416, (2011), and references cited therein.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eThe Debye diffusion model was described almost a hundred years ago. See Debye, P. J. W. \u003cem\u003ePolar Molecules\u003c/em\u003e, The Chemical Catalog Company, New York, 1929.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBjerrum recognized the necessary operation of DPT processes in ice. See Bjerrum, N. Structure and properties of ice \u003cem\u003eScience\u003c/em\u003e, 115, 385\u0026ndash;390, (1952).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eA full account, as well as detailed information, is available as Supporting Information.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eA seven membered ring transition state has also been found, associated though with the translocation of eight hydrogen atoms.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSugiyama, Y., Fukui, M., Kikuchi, M., Hasebe, K., Nakayama, A., Nishinari, K., Tadaki, S., Yukawa, S. Traffic jams without bottlenecks-experimental evidence for the physical mechanism of the formation of a jam \u003cem\u003eNew J. Physics\u003c/em\u003e 10, 33001\u0026ndash;7, (2008).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBader, R.F.W. \u003cem\u003eAtoms in Molecules: A Quantum Theory\u003c/em\u003e, Oxford, Clarendon, 1990; Bader, R.F.W. Atoms in molecules \u003cem\u003eAcc. Chem. Res.\u003c/em\u003e 18, 9\u0026ndash;15, (1985); Bader, R.F.W. A quantum theory of molecular structure and its applications \u003cem\u003eChem. Rev.\u003c/em\u003e 91, 893\u0026ndash;928, (1990).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDewar, M. J. S. Multibond reactions cannot normally be synchronous \u003cem\u003eJ. Am. Chem. Soc. 106\u003c/em\u003e, 209\u0026ndash;219, (1984).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBorden, W. T., Loncharich, R. J., Houk, K. N. Synchronicity in multibond reactions \u003cem\u003eAnn. Rev. Phys. Chem. 39\u003c/em\u003e, 213\u0026ndash;236, (1988).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIn a negligible number of instances (involving small, highly symmetric clusters at the transition state), the migration of all protons occurs synchronously, resulting in a high imaginary frequency associated with the transition state (greater than \u0026ndash;\u0026thinsp;1500 cm\u003csup\u003e\u0026ndash;\u0026thinsp;1\u003c/sup\u003e), where all O-O distances are similar and shorter than 2.39 \u0026Aring;. Actually, only a single direct-proton-transfer (DPT) case was found (11W6-iDPT3) where a proton triple jump takes place through a cyclic transition state (AIM shows that the three protons are covalently bound to the corresponding vicinal oxygens).\u003csup\u003e30\u003c/sup\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAccording to Eigen, most proton transfers undergone by [(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003en\u003c/sub\u003eH\u003csup\u003e+\u003c/sup\u003e] species in water occur after some structural rearrangement (structural diffusion). See Eigen, M. Proton transfer, acid-base catalysis, and enzymatic hydrolysis. Part 1: Elementary processes \u003cem\u003eAngew. Chem. Int. Ed.\u003c/em\u003e 3, 1\u0026ndash;9, (1964).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eIt should be noted that the term \u0026ldquo;proton wire\u0026rdquo;, first coined by Morowitz to describe likely mechanisms for proton transport across biomembranes, did not address the mechanism of proton injection into the chain. See Nagle, J.F., Morowitz, H.J. Molecular mechanisms for proton transport in membranes \u003cem\u003eProc. Natl. Acad. Sci. USA\u003c/em\u003e 75, 298\u0026ndash;302, (1978). Instead, our definition of \u0026ldquo;wire\u0026rdquo; includes both the proton source (H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e) and the proton sink (OH\u003csup\u003e\u0026ndash;\u003c/sup\u003e).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eThe occurrence of ion pairs with only two proton channels (\u0026ldquo;wires\u0026rdquo;) is rare but real, as detected in this study.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHerzfeld recognized the role of \u0026ldquo;special pairs\u0026rdquo; (characterized by having ultrashort hydrogen bonds) as transition states for proton transfers. See Bai, C., Herzfeld, J. Special pairs are decisive in the autoionization and recombination of water \u003cem\u003eJ. Phys. Chem. B\u003c/em\u003e 121, 4213\u0026ndash;4219, (2017).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKohlrausch, F., Heydweiller, Ad. \u0026Uuml;ber reines wasser \u003cem\u003eAnn.d.Phys.u.Chem. (neue folge\u003c/em\u003e) \u003cem\u003e53\u003c/em\u003e, 209\u0026ndash;235, (1894).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eA quite large number of publications have examined the properties of water constituent ions H\u003csup\u003e+\u003c/sup\u003e(H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003en\u003c/sub\u003e and (H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003en\u003c/sub\u003eOH\u003csup\u003e\u0026ndash;\u003c/sup\u003e as isolated, independent entities. For a comprehensive review, see Agmon, N., Bakker, H. J., Campen, R. K., Henchman, R. H., Pohl, P., Roke, S., Th\u0026auml;mer, M., Hassanali, A. Protons and hydroxide ions in aqueous systems \u003cem\u003eChem. Rev.\u003c/em\u003e 116, 7642\u0026ndash;7672, (2016) and references therein.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eL. Onsager, \u003cem\u003eJ. Chim. Phys.\u003c/em\u003e, Special Issue on the 19th Meeting of the Soci\u0026eacute;t\u0026eacute; de Chimie Physique at Montpellier, September 1968, p. 86.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eB\u0026uuml;hl, M., Wipff, G. Hydronium ion complex of 18-crown-6: where are the protons?.A density functional study of static and dynamic properties \u003cem\u003eJ. Am. Chem. Soc.\u003c/em\u003e 124, 4473\u0026ndash;4480, (2002).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003e-Experimental evidence for the presence short-living ions (in up to 2% of the content of water molecules) coexisting with long-lived pH-active ions, has recently been reported. See Artemov, V.G., Uykur, E., Roh, S., Pronin, A.V., Houerdane, E., Dressel, M. Revealing excess protons in the infrared spectrum of liquid water \u003cem\u003eScientific Reports\u003c/em\u003e, 10, 11320-9, (2020).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ede Grotthuss, C. J. T., Sur la decomposition de l\u0026rsquo;eau e des corps qu\u0026rsquo;elle tient en dissolution \u0026agrave; l\u0026rsquo;aide de l\u0026rsquo;electricit\u0026eacute; galvanique \u003cem\u003eAnn. Chim.\u003c/em\u003e (Paris) 1806, LVIII, 54\u0026ndash;7. English translation: \u003cem\u003ePhilos. Mag.\u003c/em\u003e (London) 1806, \u003cem\u003e25\u003c/em\u003e, 330\u0026ndash;339.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHassanali, A., Prakash, M. K., Eshet, H., Parrinello, M. On the recombination of hydronium and hydroxide ions in water \u003cem\u003eProc. Natl. Acad. Sci.\u003c/em\u003e 108, 20410\u0026ndash;20415, (2011).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eThe contact distance reported in the literature for a H\u003csup\u003e+\u003c/sup\u003e-to-OH\u003csup\u003e\u0026ndash;\u003c/sup\u003e collapse event (ca. 6 angstroms) does not include the proton source. Full agreement with our data is however observed when the H-O distance is added (assuming H\u003csub\u003e3\u003c/sub\u003eO\u003csup\u003e+\u003c/sup\u003e is the donor). See Natzle, W.C., Moore, C.B. Recombination of hydrogen ion (H\u003csup\u003e+\u003c/sup\u003e) and hydroxide in pure liquid water \u003cem\u003eJ. Phys. Chem.\u003c/em\u003e 89, 2605\u0026ndash;2612, (1985).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBlackmond, D.G. The origin of biological homochirality \u003cem\u003eCold Spring Harb. Perspect. Biol.\u003c/em\u003e 11:a032540 1\u0026ndash;10, (2019). See also, Devinsky, F. Chirality and the origin of life \u003cem\u003eSymmetry\u003c/em\u003e 13, 2277\u0026ndash;2292, (2021).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003e\u003cem\u003eAbiogenesis\u003c/em\u003e. Edited by K. Rogers, (2025, August 14). \u003cem\u003eEncyclopedia Britannica\u003c/em\u003e. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.britannica.com/science/abiogenesis\u003c/span\u003e\u003cspan address=\"https://www.britannica.com/science/abiogenesis\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003eTable 1. Cluster size, Number of isomers (# isomers) studied, number of TSs localized (# TSs), number of Direct Proton Transfers (# DPTs), Ion-Pair Collapse (# IPC) and on-Pair Walk (# IPW). For each TS type, the range of activation energies (AE) are given in parenthesis (kcal/mol) for clusters formed from 8 to 30 water molecules\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003eCluster\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e# isomers\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e# TSs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e# DPTs (AE)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e# IPCs (AE)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e# IPW (AE)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e8\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e13 (16-26)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e1 (23 \u0026amp; 0.3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e-------------\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e9\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e12 (15-21)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e7 (22-24 \u0026amp; 0.04-1.4)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e-------------\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e10\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e9 (17-29)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e24 (20-26 \u0026amp; 0.006-2.6)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e-------------\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e11\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e18\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e13 (16-26)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e5 (30-32 \u0026amp; 0.07-1.1)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e-------------\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e12\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e4 (17-20)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e4 (19-26 \u0026amp; 0.14-6)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e4 (0.09-5.8)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e13\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e6 (18-25)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e8 (22-29 \u0026amp; 0.002-4.2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e3 (0.05-1.7)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e14\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e11\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e9 (18-25)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e2 (18-22 \u0026amp; 0.28-0.96)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e-------------\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e15\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e19\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e8 (17-26)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e9 (16-31 \u0026amp; 0.05-3.3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e2 (0.05-1.4)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e16\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e26\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e22 (17-26)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e3 (26-29 \u0026amp; 0.8-3.8)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e1 (1.2-1.5)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e17\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e54\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e9 (18-21)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e25 (19-29 \u0026amp; 0.03-3.5)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e20 (0.1-5.4)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e18\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e33\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e8 (18-25)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e11 (19-33 \u0026amp; 0.05-3.3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e14 (0.04-3.3)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e19\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e4 (20-23)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e6 (18-31 \u0026amp; 0.07-3.9)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e2 (0.08-11.6)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e20\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e93\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e13 (18-27)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e22 (18-31 \u0026amp; 0.02-4)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e58 (0.01-9.5)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e21\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e17\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e43\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e10 (18-27)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e22 (21-28 \u0026amp; 0.08-8)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e11 (0.07-4)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e22\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e1 (19-21)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e1 (29.4 \u0026amp; 4.8)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e2 (0.47-1.34)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e23\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e-------------\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e----------------------------\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e1 (0.6-1.4)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e24\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e14\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e-------------\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e----------------------------\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e1 (0.7-1.7)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e25\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e1 (24-25)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e----------------------------\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e-------------\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e26\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e-------------\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e1 (26.1 \u0026amp; 3.4)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e-------------\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e27\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e12\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e-------------\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e----------------------------\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e-------------\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e28\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e1 (26-28)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e----------------------------\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e-------------\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e29\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e-------------\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e1 (27.4 \u0026amp; 2.1)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e-------------\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e30\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e4 (21-23)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e----------------------------\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e5 (0.01-5.5)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 9.43953%;\"\u003e\n \u003cp\u003e\u003cstrong\u003eTotal\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 12.5369%;\"\u003e\n \u003cp\u003e302\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 8.55457%;\"\u003e\n \u003cp\u003e423\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 17.8466%;\"\u003e\n \u003cp\u003e147\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.8761%;\"\u003e\n \u003cp\u003e152\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 23.7463%;\"\u003e\n \u003cp\u003e124\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eTable 2. Number Ion-Pair Inversion and Ion-Pair Isomerization TSs localized (# TSs). For each TS type, the (negative) frequency (cm\u003csup\u003e-1\u003c/sup\u003e), as well as the range of activation energies are given in parenthesis (kcal/mol).\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 13.9925%;\"\u003e\n \u003cp\u003eCluster\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.7985%;\"\u003e\n \u003cp\u003e# TSs\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 28.1716%;\"\u003e\n \u003cp\u003e# TS-Inversion\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 30.0373%;\"\u003e\n \u003cp\u003e# TS-Isomerization\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 13.9925%;\"\u003e\n \u003cp\u003e17W1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.7985%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 28.1716%;\"\u003e\n \u003cp\u003ef = -119\u0026nbsp;\u003c/p\u003e\n \u003cp\u003e(0.70 - 2.34)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 30.0373%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e----------------------------\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 13.9925%;\"\u003e\n \u003cp\u003e17W5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.7985%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 28.1716%;\"\u003e\n \u003cp\u003ef = -91\u003c/p\u003e\n \u003cp\u003e(1.42 - 4.93)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 30.0373%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e----------------------------\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 13.9925%;\"\u003e\n \u003cp\u003e17W7\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.7985%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 28.1716%;\"\u003e\n \u003cp\u003ef = -112\u003c/p\u003e\n \u003cp\u003e(0.91 \u0026ndash; 2.55)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 30.0373%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e----------------------------\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 13.9925%;\"\u003e\n \u003cp\u003e18W2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.7985%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 28.1716%;\"\u003e\n \u003cp\u003ef = -137\u003c/p\u003e\n \u003cp\u003e(0.75 \u0026ndash; 2.75)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 30.0373%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e----------------------------\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 13.9925%;\"\u003e\n \u003cp\u003e18W16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.7985%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 28.1716%;\"\u003e\n \u003cp\u003ef = -95\u003c/p\u003e\n \u003cp\u003e(0.67 - 1.84)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 30.0373%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e----------------------------\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 13.9925%;\"\u003e\n \u003cp\u003e20W4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.7985%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 28.1716%;\"\u003e\n \u003cp\u003ef = -120\u003c/p\u003e\n \u003cp\u003e(0.97 - 1.86)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 30.0373%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e----------------------------\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 13.9925%;\"\u003e\n \u003cp\u003e20W22\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.7985%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 28.1716%;\"\u003e\n \u003cp\u003ef = -113\u003c/p\u003e\n \u003cp\u003e(0.90 - 8.36)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 30.0373%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e----------------------------\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 13.9925%;\"\u003e\n \u003cp\u003e18W2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 27.7985%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 28.1716%;\"\u003e\n \u003cp\u003e\u003cstrong\u003e--------------------------\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 30.0373%;\"\u003e\n \u003cp\u003ef = -161\u003c/p\u003e\n \u003cp\u003e1.23 \u0026ndash; 1.82\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eTable 3. Clusters, Number of TSs localized (# TSs), number of Direct Proton Transfers (#DPTs), Ion-Pair Collapse (# IPC), Ion-Pair Cross-Collapse (# IPCC), \u0026nbsp;Ion-Pair Quench \u0026nbsp;(# IPQ) and on-Pair Walk (IPW) in bis ion-pairs. For each TS type, the range of activation energies (AE) is given in parenthesis (kcal/mol).\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"631\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10.1426%;\"\u003e\n \u003cp\u003eCluster\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.03328%;\"\u003e\n \u003cp\u003e# TSs\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.8859%;\"\u003e\n \u003cp\u003e# DPTs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 22.504%;\"\u003e\n \u003cp\u003e# IPCs (AE)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16.4818%;\"\u003e\n \u003cp\u003e# IPCCs (AE)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 14.897%;\"\u003e\n \u003cp\u003e# IPQ (AE)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15.0555%;\"\u003e\n \u003cp\u003e# IPW (AE)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10.1426%;\"\u003e\n \u003cp\u003e20\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.03328%;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.8859%;\"\u003e\n \u003cp\u003e1 (18-19)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 22.504%;\"\u003e\n \u003cp\u003e4 (18-28 \u0026amp; 0.3-2.9)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16.4818%;\"\u003e\n \u003cp\u003e4 (23.5 \u0026amp; 0.1)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 14.897%;\"\u003e\n \u003cp\u003e1 (42.9-0.3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15.0555%;\"\u003e\n \u003cp\u003e---------------\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10.1426%;\"\u003e\n \u003cp\u003e21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.03328%;\"\u003e\n \u003cp\u003e10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.8859%;\"\u003e\n \u003cp\u003e-----------\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 22.504%;\"\u003e\n \u003cp\u003e8 (22-25 \u0026amp; 0.1-0.7)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16.4818%;\"\u003e\n \u003cp\u003e1 (24.7 \u0026amp; 2.1)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 14.897%;\"\u003e\n \u003cp\u003e---------------\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15.0555%;\"\u003e\n \u003cp\u003e1 (0.02-2.7)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10.1426%;\"\u003e\n \u003cp\u003e21\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.03328%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.8859%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 22.504%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16.4818%;\"\u003e\n \u003cp\u003e1 (23.1 \u0026amp;0.2)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 14.897%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15.0555%;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10.1426%;\"\u003e\n \u003cp\u003e30\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.03328%;\"\u003e\n \u003cp\u003e\u0026nbsp;3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.8859%;\"\u003e\n \u003cp\u003e1 (17-18)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 22.504%;\"\u003e\n \u003cp\u003e1 (27 \u0026amp; 0.5)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16.4818%;\"\u003e\n \u003cp\u003e------------------\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 14.897%;\"\u003e\n \u003cp\u003e----------------\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15.0555%;\"\u003e\n \u003cp\u003e1 (0.3-1.7)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 10.1426%;\"\u003e\n \u003cp\u003eTotal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 9.03328%;\"\u003e\n \u003cp\u003e24\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 11.8859%;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 22.504%;\"\u003e\n \u003cp\u003e13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 16.4818%;\"\u003e\n \u003cp\u003e6\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 14.897%;\"\u003e\n \u003cp\u003e1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 15.0555%;\"\u003e\n \u003cp\u003e2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-8425076/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8425076/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe core issue standing behind water's unique and extraordinary properties is proton transfer. The extremely fast nature (under the picosecond time scale) of proton transfers taking place in water convinced us to resort to a classic approach: a comprehensive DFT study of neutral, medium-sized water clusters (H\u003csub\u003e2\u003c/sub\u003eO)\u003csub\u003en\u003c/sub\u003e (n up to 30). Our main objective was to determine the instantaneous (I) structures of the transition states of proton transfers, which are inaccessible by experimental techniques or molecular dynamics simulations. Subsequent IRC analysis and AIM treatment of the three stationary points thereby available for each transition state structure were fundamental to describing the basics of water dynamics. Actually, our study shows that proton transfers occurring in neutral, liquid water involve a variety of ion-pairing phenomena that operate not only on neutral waters clusters but also on neutral ion-pair clusters. The unveiled properties of water ion-pairs suggest that the long-standing assumption that water's ionic components do not interact with one another -a hypothesis that has remained unchallenged for over a century- may be erroneous. Water ion-pairs are at the center of the new paradigm, shedding light on water electrodynamics and offering plausible suggestions on the abiotic origin of life that are worth exploring.\u003c/p\u003e","manuscriptTitle":"Water dynamics visited. A comprehensive DFT study of proton transfer in liquid water underscores the pivotal role of ion pairing phenomena","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-04 06:59:30","doi":"10.21203/rs.3.rs-8425076/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"eff7ba48-bced-441b-8ae9-e26df1dfb907","owner":[],"postedDate":"February 4th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":62286663,"name":"Physical sciences/Chemistry/Physical chemistry/Chemical physics"},{"id":62286664,"name":"Physical sciences/Chemistry/Theoretical chemistry/Computational chemistry"}],"tags":[],"updatedAt":"2026-02-04T06:59:30+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-04 06:59:30","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8425076","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8425076","identity":"rs-8425076","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}