Topological hydrogen-bond definition to characterize the structure and dynamics of liquid water

Experimental and computational study of binary mixture ethanolamine and 2-amino-2-methyl-1-propanol

The present work involves experimental and computational investigations into the density of pure and mixed states of ethanolamine (ET) and 2-amino-2-methyl-1-propanol (AMP) under a pressure of 1 atm and temperatures ranging from 293.15 K to 333.15 K The density data were used to derive the excess molar volume, thermal expansion coefficient, and isothermal coefficient of pressure excess molar enthalpy. The Redlich-Kister equation was employed to calculate the excess molar and its accompanying coefficients. In the gas phase, density functional theory (DFT) was utilized to explore the most stable structures of ET … ET, AMP … AMP, and the ET … AMP mixture. Molecular dynamics simulation (MD) was used to calculate the structural properties of these mixtures in the liquid phase. Radial distribution function (RDFs) combined distribution function (CDF) and spatial distribution function (SDF) in different mole fractions calculated in the liquid phase. The intramolecular and intermolecular interactions of ethanolamine and AMP were obtained using the radial distribution function in different molar fractions. It was found that the ethanolamine molecule has a greater tendency to form intramolecular hydrogen bonds, while the AMP molecule has a greater tendency to form intermolecular hydrogen bonds.

ZundEig: The Structure of the Proton in Liquid Water from Unsupervised Learning

The structure of the excess proton in liquid water has been the subject of lively debate on both experimental and theoretical fronts for the last century. Fluctuations of the proton are typically interpreted in terms of limiting states referred to as the Eigen and Zundel species. Here, we put these ideas under the microscope, taking advantage of recent advances in unsupervised learning that use local atomic descriptors to characterize environments of acidic water combined with advanced clustering techniques. Our agnostic approach leads to the observation of only one charged cluster and two neutral ones. We demonstrate that the charged cluster involving the excess proton is best seen as an ionic topological defect in water's hydrogen bond network, forming a single local minimum on the global free-energy landscape. This charged defect is a highly fluxional moiety, where the idealized Eigen and Zundel species are neither limiting configurations nor distinct thermodynamic states. Instead, the ionic defect enhances the presence of neutral water defects through strong interactions with the network. We dub the combination of the charged and neutral defect clusters as ZundEig, demonstrating that the fluctuations between these local environments provide a general framework for rationalizing more descriptive notions of the proton in the existing literature.

Characterization of the Hydrogen-Bond Network in High-Pressure Water by Deep Potential Molecular Dynamics

The hydrogen-bond (H-bond) network of high-pressure water is investigated by neural-network-based molecular dynamics (MD) simulations with first-principles accuracy. The static structure factors (SSFs) of water at three densities, i.e., 1, 1.115, and 1.24 g/cm3, are directly evaluated from 512 water MD trajectories, which are in quantitative agreement with the experiments. We propose a new method to decompose the computed SSF and identify the changes in the SSF with respect to the changes in H-bond structures. We find that a larger water density results in a higher probability for one or two non-H-bonded water molecules to be inserted into the inner shell, explaining the changes in the tetrahedrality of water under pressure. We predict that the structure of the accepting end of water molecules is more easily influenced by the pressure than by the donating end. Our work sheds new light on explaining the SSF and H-bond properties in related fields.

Temperature Dependence of Hydrogen Bond Networks of Liquid Water: Thermodynamic Properties and Structural Heterogeneity from Topological Descriptors

Topological analyses of hydrogen bond networks were performed based on the complex network and island statistics of liquid water at different temperatures. The influence of temperature on the liquid water structures and the topological properties of the hydrogen bond networks was investigated by Metropolis Monte Carlo simulations with the TIP4P/2005 potential model. The bilinear behavior of the second peak in the radial distribution function with the temperature was properly reproduced by these simulations. The average connectivity also displayed a bilinear behavior consistent with being a local descriptor. The semiglobal average path length (or geodesic distance) descriptor showed an unprecedented trimodal distribution, whose areas were dependent on the temperature. Considering equilibrium between these three sets of networks, standard enthalpy and entropy of equilibrium were determined for the first time, providing new insights into the structural heterogeneities of liquid water with interesting perspectives for modeling these quantitative properties of hydrogen bond networks.

The collective burst mechanism of angular jumps in liquid water

Understanding the microscopic origins of collective reorientational motions in aqueous systems requires techniques that allow us to reach beyond our chemical imagination. Herein, we elucidate a mechanism using a protocol that automatically detects abrupt motions in reorientational dynamics, showing that large angular jumps in liquid water involve highly cooperative orchestrated motions. Our automatized detection of angular fluctuations, unravels a heterogeneity in the type of angular jumps occurring concertedly in the system. We show that large orientational motions require a highly collective dynamical process involving correlated motion of many water molecules in the hydrogen-bond network that form spatially connected clusters going beyond the local angular jump mechanism. This phenomenon is rooted in the collective fluctuations of the network topology which results in the creation of defects in waves on the THz timescale. The mechanism we propose involves a cascade of hydrogen-bond fluctuations underlying angular jumps and provides new insights into the current localized picture of angular jumps, and its wide use in the interpretations of numerous spectroscopies as well in reorientational dynamics of water near biological and inorganic systems. The role of finite size effects, as well as of the chosen water model, on the collective reorientation is also elucidated.

Total free energy analysis of fully hydrated proteins

The total free energy of a hydrated biomolecule and its corresponding decomposition of energy and entropy provides detailed information about regions of thermodynamic stability or instability. The free energies of four hydrated globular proteins with different net charges are calculated from a molecular dynamics simulation, with the energy coming from the system Hamiltonian and entropy using multiscale cell correlation. Water is found to be most stable around anionic residues, intermediate around cationic and polar residues, and least stable near hydrophobic residues, especially when more buried, with stability displaying moderate entropy-enthalpy compensation. Conversely, anionic residues in the proteins are energetically destabilized relative to singly solvated amino acids, while trends for other residues are less clear-cut. Almost all residues lose intraresidue entropy when in the protein, enthalpy changes are negative on average but may be positive or negative, and the resulting overall stability is moderate for some proteins and negligible for others. The free energy of water around single amino acids is found to closely match existing hydrophobicity scales. Regarding the effect of secondary structure, water is slightly more stable around loops, of intermediate stability around β strands and turns, and least stable around helices. An interesting asymmetry observed is that cationic residues stabilize a residue when bonded to its N-terminal side but destabilize it when on the C-terminal side, with a weaker reversed trend for anionic residues.

Aqueous Electrolytes Reinforced by Mg and Ca Ions for Highly Reversible Fe Metal Batteries

Iron (Fe) metal batteries, such as Fe-ion batteries and all Fe flow batteries, are promising energy storage technologies for grid applications due to the extremely low cost of Fe and Fe salts. Nonetheless, the cycle life of Fe metal batteries is poor primarily due to the low Coulombic efficiency of the Fe deposition/stripping reaction. Current aqueous electrolytes based on Fe chloride or sulfate salts can only operate at a Coulombic efficiency of <91% under mild operation conditions (<5 mA/cm²), largely due to undesired hydrogen evolution reaction (HER). This work reports a series of novel Fe electrolytes, Fe electrolytes reinforced with Mg ions (FERMI) and Ca ions (FERCI), which have remarkably better Coulombic efficiency, higher conductivity, and faster deposition/stripping kinetics. By the addition of 4.5 M MgCl₂ or CaCl₂ into the baseline FeCl₂ electrolyte, the Fe deposition/stripping efficiency can be significantly improved to 99.1%, which greatly boosts the cycling performance of Fe metal batteries in both half-cells and full-cells. Mechanistic studies reveal that the remarkably improved efficiency is due to a reduced amount of "dead Fe" as well as suppressed HER. By the combination of experiments and molecular dynamics and density functional theory computation, the electrolyte structure is revealed, and the mechanism for enhanced water reduction resistance is elucidated. These novel electrolytes not only enable a highly reversible Fe metal anode for low-cost energy storage technologies but also have the potential to address the HER side reaction problem in other electrochemical technologies based on aqueous electrolytes, such as CO₂ reduction, NH₃ synthesis, etc.

High-Dimensional Fluctuations in Liquid Water: Combining Chemical Intuition with Unsupervised Learning

The microscopic description of the local structure of water remains an open challenge. Here, we adopt an agnostic approach to understanding water's hydrogen bond network using data harvested from molecular dynamics simulations of an empirical water model. A battery of state-of-the-art unsupervised data-science techniques are used to characterize the free-energy landscape of water starting from encoding the water environment using local atomic descriptors, through dimensionality reduction and finally the use of advanced clustering techniques. Analysis of the free energy under ambient conditions was found to be consistent with a rough single basin and independent of the choice of the water model. We find that the fluctuations of the water network occur in a high-dimensional space, which we characterize using a combination of both atomic descriptors and chemical-intuition-based coordinates. We demonstrate that a combination of both types of variables is needed in order to adequately capture the complexity of the fluctuations in the hydrogen bond network at different length scales both at room temperature and also close to the critical point of water. Our results provide a general framework for examining fluctuations in water under different conditions.

Identification of Valence Electronic States Reflecting the Hydrogen Bonding in Liquid Ethanol

The temperature-dependent X-ray emission spectra of liquid ethanol were calculated theoretically using a semi-classical approximation to the Kramers-Heisenberg formula, which includes the dynamical effects induced by a core-hole. Soft X-ray emission spectroscopic measurements were performed to discern the changes in the hydrogen bonding (h-bonding) structure of liquid ethanol using a temperature-controlled liquid cell at 241 and 313 K. The relative intensities of the peaks at approximately 526.5 and 527.1 eV varied with temperature, and the corresponding behavior was reproduced theoretically, although the variation with temperature in the calculated spectra were more enhanced than that in the experiment. The two peaks can be attributed to the 3a″ + 10a' mixed state and pure 3a″ state, respectively, depending on the behavior of the local h-bonding structure. The splitting of the 3a″ component occurred because of the h-bonding behavior of liquid ethanol. Furthermore, the size of the ethanol cluster decreased with an increase in temperature, mainly due to the breaking of the one-donor/one-acceptor type h-bonding. Our studies suggest that the electronic state of liquid ethanol reflects several types of h-bonding structures, and the ratios of these h-bonding types vary with temperature.

Transition pathway of hydrogen bond switching in supercooled water analyzed by the Markov state model

In this work, we examine hydrogen-bond (H-bond) switching by employing the Markov State Model (MSM). During the H-bond switching, a water hydrogen initially H-bonded with water oxygen becomes H-bonded to a different water oxygen. MSM analysis was applied to trajectories generated from molecular dynamics simulations of the TIP4P/2005 model from a room-temperature state to a supercooled state. We defined four basis states to characterize the configuration between two water molecules: H-bonded ("H"), unbound ("U"), weakly H-bonded ("w"), and alternative H-bonded ("a") states. A 16 × 16 MSM matrix was constructed, describing the transition probability between states composed of three water molecules. The mean first-passage time of the H-bond switching was estimated by calculating the total flux from the HU to UH states. It is demonstrated that the temperature dependence of the mean first-passage time is in accordance with that of the H-bond lifetime determined from the H-bond correlation function. Furthermore, the flux for the H-bond switching is decomposed into individual pathways that are characterized by different forms of H-bond configurations of trimers. The dominant pathway of the H-bond switching is found to be a direct one without passing through such intermediate states as "w" and "a," the existence of which becomes evident in supercooled water. The pathway through "w" indicates a large reorientation of the donor molecule. In contrast, the pathway through "a" utilizes the tetrahedral H-bond network, which is revealed by the further decomposition based on the H-bond number of the acceptor molecule.

Thermodynamic Origin of Differential Excipient-Lysozyme Interactions

Understanding the intricate interplay of interactions between proteins, excipients, ions and water is important to achieve the effective purification and stable formulation of protein therapeutics. The free energy of lysozyme interacting with two kinds of polyanionic excipients, citrate and tripolyphosphate, together with sodium chloride and TRIS-buffer, are analysed in multiple-walker metadynamics simulations to understand why tripolyphosphate causes lysozyme to precipitate but citrate does not. The resulting multiscale decomposition of energy and entropy components for water, sodium chloride, excipients and lysozyme reveals that lysozyme is more stabilised by the interaction of tripolyphosphate with basic residues. This is accompanied by more sodium ions being released into solution from tripolyphosphate than for citrate, whilst the latter instead has more water molecules released into solution. Even though lysozyme aggregation is not directly probed in this study, these different mechanisms are suspected to drive the cross-linking between lysozyme molecules with vacant basic residues, ultimately leading to precipitation.

Per|Mut: Spatially Resolved Hydration Entropies from Atomistic Simulations

The hydrophobic effect is essential for many biophysical phenomena and processes. It is governed by a fine-tuned balance between enthalpy and entropy contributions from the hydration shell. Whereas enthalpies can in principle be calculated from an atomistic simulation trajectory, calculating solvation entropies by sampling the extremely large configuration space is challenging and often impossible. Furthermore, to qualitatively understand how the balance is affected by individual side chains, chemical groups, or the protein topology, a local description of the hydration entropy is required. In this study, we present and assess the new method “Per|Mut”, which uses a permutation reduction to alleviate the sampling problem by a factor of N! and employs a mutual information expansion to the third order to obtain spatially resolved hydration entropies. We tested the method on an argon system, a series of solvated n-alkanes, and solvated octanol.

Entropy of Proteins Using Multiscale Cell Correlation

A new multiscale method is presented to calculate the entropy of proteins from molecular dynamics simulations. Termed Multiscale Cell Correlation (MCC), the method decomposes the protein into sets of rigid-body units based on their covalent-bond connectivity at three levels of hierarchy: molecule, residue, and united atom. It evaluates the vibrational and topographical entropy from forces, torques, and dihedrals at each level, taking into account correlations between sets of constituent units that together make up a larger unit at the coarser length scale. MCC gives entropies in close agreement with normal-mode analysis and smaller than those using quasiharmonic analysis as well as providing much faster convergence. Moreover, MCC provides an insightful decomposition of entropy at each length scale and for each type of amino acid according to their solvent exposure and whether they are terminal residues. While the residue entropy depends weakly on solvent exposure, there is greater variation in entropy components for larger, more polar amino acids, which have increased conformational entropy but reduced vibrational entropy with greater solvent exposure.

Formation and migration of H3O+ and OH− ions at the water/silica and water/vapor interfaces under the influence of a static electric field: a molecular dynamics study

Water ‘layers’ 1 and 2 in pink; ‘layer’ 3 in blue and green over portion of glass surface (grey). +90° field causes water migration and clustering.

Entropy of Simulated Liquids Using Multiscale Cell Correlation

Accurately calculating the entropy of liquids is an important goal, given that many processes take place in the liquid phase. Of almost equal importance is understanding the values obtained. However, there are few methods that can calculate the entropy of such systems, and fewer still to make sense of the values obtained. We present our multiscale cell correlation (MCC) method to calculate the entropy of liquids from molecular dynamics simulations. The method uses forces and torques at the molecule and united-atom levels and probability distributions of molecular coordinations and conformations. The main differences with previous work are the consistent treatment of the mean-field cell approximation to the approriate degrees of freedom, the separation of the force and torque covariance matrices, and the inclusion of conformation correlation for molecules with multiple dihedrals. MCC is applied to a broader set of 56 important industrial liquids modeled using the Generalized AMBER Force Field (GAFF) and Optimized Potentials for Liquid Simulations (OPLS) force fields with 1.14*CM1A charges. Unsigned errors versus experimental entropies are 8.7 J K - 1 mol - 1 for GAFF and 9.8 J K - 1 mol - 1 for OPLS. This is significantly better than the 2-Phase Thermodynamics method for the subset of molecules in common, which is the only other method that has been applied to such systems. MCC makes clear why the entropy has the value it does by providing a decomposition in terms of translational and rotational vibrational entropy and topographical entropy at the molecular and united-atom levels.

Role of the hydrogen bond lifetimes and rotations at the water/amorphous silica interface on proton transport

Using a highly robust and reactive all-atom potential, molecular dynamics computer simulations have been used to provide detailed analysis of the behavior of water and protons at a large-scale amorphous silica surface that offers the heterogeneity of surface sites and water/silica interactions. Structural data of the H-O distances as a function of distance from the glass surface showed variation in hydrogen bond (H-bond) lengths to second and third nearest oxygen neighbors that play an important role in H-bond lifetimes, rotations, and proton transfer, especially at the glass surface. The higher density and inherently closer average spacing between oxygens in the glass surface (2.6 Å) in comparison to that in water (2.8 Å) create a significantly different environment for H-bond lifetimes and proton transfers. Continuous H-bond lifetime autocorrelation functions for water H-bonded to the surface are considerably shorter than those of bulk water, whereas the intermittent lifetime autocorrelation functions are longer. Such results affect proton transfers that are over an order of magnitude higher at the surface than farther from the surface or in bulk water. However, most of these transfers are rattling events between the participating oxygens, one of which is the newly formed H₃O⁺ ion adjacent to the interface. Such a H₃O⁺ ion has an extremely low barrier to proton transfer back to the surface site in comparison to a H₃O⁺ ion in bulk water. Nonetheless, the simulations showed that rotation of the H₃O⁺ ion away from the initial transfer site allowed for structural diffusion of an excess proton away from the surface. Proton conduction from such rotations could be enhanced by external forces.

Carboxylic acids in aqueous solutions: Hydrogen bonds, hydrophobic effects, concentration fluctuations, ionization, and catalysis

In the frequency range between 100 kHz and 2 GHz, ultrasonic absorption spectra have been measured for a series of carboxylic acids from formic to enanthic acid, including constitutional isomers. Also investigated have been the spectra for mixtures with water of short-chain formic, acetic, propionic, butyric, and isobutyric acid, in each case covering the complete composition range. The neat carboxylic acids feature two Debye-type relaxation terms with relaxation times between 5.6 and 260 ns as well as 0.14 and 1.4 ns, respectively, at room temperature. Depending on the composition, mixtures with water reveal an additional Debye relaxation term in the intermediate frequency range (acetic acid) or a term subject to a relaxation time distribution (propionic, butyric, and isobutyric acid). The relaxations of the neat acids are assigned to the equilibrium between monomers and single-hydrogen-bonded linear dimers and between linear and twofold-hydrogen-bonded cyclic dimers. The latter equilibrium is considerably catalyzed by hydronium and carboxylate ions. Several mixtures with water indicate one of the up to three Debye relaxations to reflect the protolysis of the organic acid. The term with underlying relaxation time distribution is due to noncritical fluctuations in the local concentrations. The Debye relaxations are evaluated to yield the parameters of the relevant elementary chemical reactions, such as the rate and equilibrium constants and the isentropic reaction volumes. A comparison of the correlation length of concentration fluctuations with data for other aqueous systems confirms the idea that the hydrophobic part of the organic constituent promotes the formation of a micro-heterogeneous liquid structure, whereas the hydrophilic moiety is of minor importance in this respect. The high-frequency limiting absorption suggests the equilibrium between conformers of linear dimers to contribute to the spectra well above the frequency range of measurements.

Understanding the effect of nanoconfinement on the structure of water hydrogen bond networks

Dynamic hydrogen bond trails in water confined between two phospholipid membranes traced by the information flow model.

Structural aspects of the topological model of the hydrogen bond in water on auto-dissociation via proton transfer

Different H-bond structures of donor and acceptor water molecules significantly affect structure, H-bond lifetimes, and autodissociation via proton transfer.

Water phase transitions from the perspective of hydrogen-bond network analysis

Analysis of the water phase transitions from the perspective of hydrogen bond networks.

Ab initio molecular dynamics simulations of liquid water using high quality meta-GGA functionals

We have used ab initio molecular dynamics (AIMD) to characterize water properties using two meta-generalized gradient approximation (meta-GGA) functionals, M06-L-D3 and B97M-rV, and compared their performance against a standard GGA corrected for dispersion, revPBE-D3, at ambient conditions (298 K, and 1 g cm-3 or 1 atm). Simulations of the equilibrium density, radial distribution functions, self-diffusivity, the infrared spectrum, liquid dipole moments, and characterizations of the hydrogen bond network show that all three functionals have overcome the problem of the early AIMD simulations that erroneously found ambient water to be highly structured, but they differ substantially among themselves in agreement with experiment on this range of water properties. We show directly using water cluster data up through the pentamer that revPBE-D3 benefits from a cancellation of its intrinsic functional error by running classical trajectories, whereas the meta-GGA functionals are demonstrably more accurate and would require the simulation of nuclear quantum effects to realize better agreement with all cluster and condensed phase properties.

Local and Global Effects of Dissolved Sodium Chloride on the Structure of Water

Determining how the structure of water is modified by the presence of salts is instrumental to understanding the solvation of biomolecules and, in general, the role played by salts in biochemical processes. However, the extent of hydrogen bonding disruption induced by salts remains controversial. We performed extensive first-principles simulations of solutions of a simple salt (NaCl) and found that, while the cation does not significantly change the structure of water beyond the first solvation shell, the anion has a further reaching effect, modifying the hydrogen-bond network even outside its second solvation shell. We found that a distinctive fingerprint of hydrogen bonding modification is the change in polarizability of water molecules. Molecular dipole moments are instead insensitive probes of long-range modifications induced by Na⁺ and Cl^- ions. Though noticeable, the long-range effect of Cl^- is expected to be too weak to affect solubility of large biomolecules.

The opposite effects of sodium and potassium cations on water dynamics

Water rotational dynamics in NaSCN and KSCN solutions at a series of concentrations are investigated using femtosecond infrared spectroscopy and theory. Femtosecond infrared measurements, consistent with previous NMR observations, detect that sodium slows down while potassium accelerates the water O-H bond rotation. Results of reported neutron scattering measurements, on the other hand, suggested that these two cations have similar structure-breaking effects on water, and therefore should both accelerate water rotation through the presumably dominating large-amplitude angular jump component. To explain this discrepancy, theoretical studies with both classical and ab initio models were carried out, which indicate that both ions indeed accelerate the large-amplitude angular jump rotation of the water molecules, while the observed cation specific effect originates from the non-negligible opposite impact of the sodium and potassium cations on the diffusive rotation of water molecules.

Locally adaptive method to define coordination shell

An algorithm is presented to define a particle's coordination shell for any collection of particles. It requires only the particles' positions and no pre-existing knowledge or parameters beyond those already in the force field. A particle's shell is taken to be all particles that are not blocked by any other particle and not further away than a blocked particle. Because blocking is based on two distances and an angle for triplets of particles, it is called the relative angular distance (RAD) algorithm. RAD is applied to Lennard-Jones particles in molecular dynamics simulations of crystalline, liquid, and gaseous phases at various temperatures and densities. RAD coordination shells agree well with those from a cut-off in the radial distribution function for the crystals and liquids and are slightly higher for the gas.

Proton Wire Dynamics in the Green Fluorescent Protein

Inside proteins, protons move on proton wires (PWs). Starting from the highest resolution X-ray structure available, we conduct a 306 ns molecular dynamics simulation of the (A-state) wild-type (wt) green fluorescent protein (GFP) to study how its PWs change with time. We find that the PW from the chromophore via Ser205 to Glu222, observed in all X-ray structures, undergoes rapid water molecule insertion between Ser205 and Glu222. Sometimes, an alternate Ser205-bypassing PW exists. Side chain rotations of Thr203 and Ser205 play an important role in shaping the PW network in the chromophore region. Thr203, with its bulkier side chain, exhibits slower transitions between its three rotameric states. Ser205 experiences more frequent rotations, slowing down when the Thr203 methyl group is close by. The combined states of both residues affect the PW probabilities. A random walk search for PWs from the chromophore reveals several exit points to the bulk, one being a direct water wire (WW) from the chromophore to the bulk. A longer WW connects the "bottom" of the GFP barrel with a "water pool" (WP1) situated below Glu222. These two WWs were not observed in X-ray structures of wt-GFP, but their analogues have been reported in related fluorescent proteins. Surprisingly, the high-resolution X-ray structure utilized herein shows that Glu222 is protonated at low temperatures. At higher temperatures, we suggest ion pairing between anionic Glu222 and a proton hosted in WP1. Upon photoexcitation, these two recombine, while a second proton dissociates from the chromophore and either exits the protein using the short WW or migrates along the GFP-barrel axis on the long WW. This mechanism reconciles the conflicting experimental and theoretical data on proton motion within GFP.

Water's dual nature and its continuously changing hydrogen bonds

A model is proposed for liquid water that is a continuum between the ordered state with predominantly tetrahedral coordination, linear hydrogen bonds and activated dynamics and a disordered state with a continuous distribution of multiple coordinations, multiple types of hydrogen bond, and diffusive dynamics, similar to that of normal liquids. Central to water's heterogeneous structure is the ability of hydrogen to donate to either one acceptor in a conventional linear hydrogen bond or to multiple acceptors as a furcated hydrogen. Linear hydrogen bonds are marked by slow, activated kinetics for hydrogen-bond switching to more crowded acceptors and sharp first peaks in the hydrogen-oxygen radial distribution function. Furcated hydrogens, equivalent to free, broken, dangling or distorted hydrogens, have barrierless, rapid kinetics and poorly defined first peaks in their hydrogen-oxygen radial distribution function. They involve the weakest donor in a local excess of donors, such that barrierless whole-molecule vibration rapidly swaps them between the linear and furcated forms. Despite the low number of furcated hydrogens and their transient existence, they are readily created in a single hydrogen-bond switch and free up the dynamics of numerous surrounding molecules, bringing about the disordered state. Hydrogens in the ordered state switch with activated dynamics to make the non-tetrahedral coordinations of the disordered state, which can also combine to make the ordered state. Consequently, the ordered and disordered states are both connected by diffusive dynamics and differentiated by activated dynamics, bringing about water's continuous heterogeneity.

Water: A Tale of Two Liquids

Water is the most abundant liquid on earth and also the substance with the largest number of anomalies in its properties. It is a prerequisite for life and as such a most important subject of current research in chemical physics and physical chemistry. In spite of its simplicity as a liquid, it has an enormously rich phase diagram where different types of ices, amorphous phases, and anomalies disclose a path that points to unique thermodynamics of its supercooled liquid state that still hides many unraveled secrets. In this review we describe the behavior of water in the regime from ambient conditions to the deeply supercooled region. The review describes simulations and experiments on this anomalous liquid. Several scenarios have been proposed to explain the anomalous properties that become strongly enhanced in the supercooled region. Among those, the second critical-point scenario has been investigated extensively, and at present most experimental evidence point to this scenario. Starting from very low temperatures, a coexistence line between a high-density amorphous phase and a low-density amorphous phase would continue in a coexistence line between a high-density and a low-density liquid phase terminating in a liquid–liquid critical point, LLCP. On approaching this LLCP from the one-phase region, a crossover in thermodynamics and dynamics can be found. This is discussed based on a picture of a temperature-dependent balance between a high-density liquid and a low-density liquid favored by, respectively, entropy and enthalpy, leading to a consistent picture of the thermodynamics of bulk water. Ice nucleation is also discussed, since this is what severely impedes experimental investigation of the vicinity of the proposed LLCP. Experimental investigation of stretched water, i.e., water at negative pressure, gives access to a different regime of the complex water diagram. Different ways to inhibit crystallization through confinement and aqueous solutions are discussed through results from experiments and simulations using the most sophisticated and advanced techniques. These findings represent tiles of a global picture that still needs to be completed. Some of the possible experimental lines of research that are essential to complete this picture are explored.

The structure of liquid water beyond the first hydration shell

Distance dependent excess entropy calculations reveal that water is tetrahedrally structured up to long distances.

Macromolecular Entropy Can Be Accurately Computed from Force

A method is presented to evaluate a molecule's entropy from the atomic forces calculated in a molecular dynamics simulation. Specifically, diagonalization of the mass-weighted force covariance matrix produces eigenvalues which in the harmonic approximation can be related to vibrational frequencies. The harmonic oscillator entropies of each vibrational mode may be summed to give the total entropy. The results for a series of hydrocarbons, dialanine and a β hairpin are found to agree much better with values derived from thermodynamic integration than results calculated using quasiharmonic analysis. Forces are found to follow a harmonic distribution more closely than coordinate displacements and better capture the underlying potential energy surface. The method's accuracy, simplicity, and computational similarity to quasiharmonic analysis, requiring as input force trajectories instead of coordinate trajectories, makes it readily applicable to a wide range of problems.

Femtosecond coherent anti-Stokes Raman scattering spectroscopy of hydrogen bonded structure in water and aqueous solutions

Femtosecond coherent anti-Stokes Raman scattering (fsCARS) spectroscopy, together with perturbation theory based numerical calculation, is employed to study OH stretching (υOH) of pure water and aqueous lithium chloride solutions. Vibrational OH stretching (υOH) modes of aqueous solutions are Raman-excited by a pair of ultrashort, femtosecond laser pulses, and then probed through inelastic scattering of a third, time-delayed laser field. In order to overcome limited spectral resolution of fsCARS, numerical evaluation of the CARS signal through vibrational wave packet propagation was employed in order to confirm the position of distinctive OH stretching mode that is complicated by intramolecular and intermolecular vibrational coupling. Moreover, in order to come to a microscopic description of the observed CARS spectra for aqueous solutions, we have performed molecular dynamics simulations of aqueous lithium chloride solutions with varying concentrations at ambient conditions. To this end we have analyzed the equilibrium distributions of hydrogen bonds in the first solvation shells of the ions as well as in bulk water and also computed the average number of hydrogen bonds per water molecule. According to our experimental and theoretical results on time evolution of Raman OH stretching band of water, it can be inferred that the dissolved ions mainly influence hydrogen bond strength and structure of water molecules in the first hydration shell, the addition of lithium chloride primarily breaks the tetrahedral hydrogen bonding, promotes formation of the donor hydrogen bonding in water, and slightly increases the amount of free OH bonds.

Bulk and interfacial liquid water as a transient network

The special macroscopic properties of liquid water stem from its structure as a complex network of molecules connected by hydrogen bonds. While the dynamics of single molecules within this network has been extensively investigated, only little attention has been paid to the closed loops (meshes) of hydrogen-bonded molecules which determine the network topology. Using molecular dynamics simulations we analyze the size, shape, geometrical arrangement, and dynamical stability of loops containing up to 10 hydrogen bonds. We find that six-membered loops in liquid water even at room temperature retain a striking similarity with the well-known structure of ice. Analyzing the network dynamics we find that rings of more than five hydrogen bonds are stabilized compared to a random collection containing the same number of single bonds. We finally show that in the vicinity of hydrophobic and hydrophilic interfaces loops arrange in a preferred orientation.