Exploiting graph theory in MD simulations for extracting chemical and physical properties of materials

Some of our recent developments and applications of algorithmic graph theory for extracting the physical and chemical properties of materials from molecular dynamics simulations are presented. From the chemical viewpoint, the power of graph theory is illustrated in the search for a catalyst's active sites at a silica solid surface. From the physical viewpoint, we present graph algorithms that recognize the structural motifs that exist at the silica/liquid water interface. Statistical analyses of the instances of these surface-water motifs provide a detailed understanding of the structures and dynamics at the aqueous interface.

Structural Properties of [N1888][TFSI] Ionic Liquid: A Small Angle Neutron Scattering and Polarizable Molecular Dynamics Study

In this study, we investigate the quaternary ammonium-based ionic liquid (QAIL), methyltrioctylammonium bis(trifluoromethylsulfonyl)imide, [N1888][TFSI], utilizing small angle neutron scattering (SANS) measurements and polarizable molecular dynamics (MD) simulations to characterize the short- and long-range liquid structure. Scattering structure factors show signatures of three length scales in reciprocal space indicative of alternating polarity (k ∼ 0.44 Å-1), charge (k ∼ 0.75 Å-1), and neighboring or adjacent (k ∼ 1.46 Å-1) domains. Excellent agreement between simulation and experimental scattering structure factors validates various simulation analyses that provide detailed atomistic characterization of the different length scale correlations. The first solvation shell structure is illustrated by obtaining radial, angular, dihedral, and combined distribution functions, where two dominant spatial motifs, N+···N- and N+···O-, compete for optimal packing around the polar head of the [N1888]+ cation. Intermediate and long-range structures are governed by the balance between local electroneutrality and octyl chain networking, respectively. By computing the charge-correlation structure factor, SZZ, and the spatial extent of the octyl chain network using graph theory, the bulk-phase structure of [N1888][TFSI] is characterized in terms of electrostatic screening and apolar domain formation length scales.

Effects of Hydrogen Bond Networks on Viscosity in Aqueous Solutions

In aqueous solutions, the impact of ions on hydrogen bond networks plays a crucial role in transport properties. We used molecular dynamics simulations to explain how ions affect viscosity through structural changes. We developed a quantitative model to describe the effect of ions on viscosity. The model comprises two parts: the addition of ions alters hydrogen bond networks, and changes in hydrogen bond networks exponentially lead to changes in viscosity. The influence of ions on hydrogen bond networks involves the following mechanisms: first, ions can disrupt the tetrahedral structures within the first solvation shell into three-coordinated structures through substitution; second, structural changes within the first shells affect the global hydrogen bond network through electrostatic forces and the hindrance of ionic volumes. By analyzing the mechanisms of how hydrogen bond networks determine viscosity through the decomposition of viscosity, we found that the proportion of potential viscosity in aqueous solutions primarily increases due to the enhancement of non-hydrogen bonding interactions, and the proportion of hydrogen bonding viscosity decreases accordingly. Our results demonstrate that hydrogen bond networks are crucial for describing the changes in transport phenomena affected by external factors.

Graph Theoretical Description of Phase Transitions in Complex Multiscale Phases with Supramolecular Assemblies

Phase transitions are typically quantified using order parameters, such as crystal lattice distances and radial distribution functions, which can identify subtle changes in crystalline materials or high-contrast phases with large structural differences. However, the identification of phases with high complexity, multiscale organization and of complex patterns during the structural fluctuations preceding phase transitions, which are essential for understanding the system pathways between phases, is challenging for those traditional analyses. Here, it is shown that for two model systems- thermotropic liquid crystals and a lyotropic water/surfactant mixtures-graph theoretical (GT) descriptors can successfully identify complex phases combining molecular and nanoscale levels of organization that are hard to characterize with traditional methodologies. Furthermore, the GT descriptors also reveal the pathways between the different phases. Specifically, centrality parameters and node-based fractal dimension quantify the system behavior preceding the transitions, capturing fluctuation-induced breakup of aggregates and their long-range cooperative interactions. GT parameterization can be generalized for a wide range of chemical systems and be instrumental for the growth mechanisms of complex nanostructures.

Interfacial Enrichment of Lauric Acid Assisted by Long-Chain Fatty Acids, Acidity and Salinity at Sea Spray Aerosol Surfaces

Surfactant monolayers at sea spray aerosol (SSA) surfaces regulate various atmospheric processes including gas transfer, cloud interactions, and radiative properties. Most experimental studies of SSA employ a simplified surfactant mixture of long-chain fatty acids (LCFAs) as a proxy for the sea surface microlayer or SSA surface. However, medium-chain fatty acids (MCFAs) make up nearly 30% of the FA fraction in nascent SSA. Given that LCFA monolayers are easily disrupted upon the introduction of chemical heterogeneity (such as mixed chain lengths), simple FA proxies are unlikely to represent realistic SSA interfaces. Integrating experimental and computational techniques, we characterize the impact that partially soluble MCFAs have on the properties of atmospherically relevant LCFA mixtures. We explore the extent to which the MCFA lauric acid (LA) is surface stabilized by varying acidity, salinity, and monolayer composition. We also discuss the impacts of pH on LCFA-assisted LA retention, where the presence of LCFAs may shift the surface-adsorption equilibria of laurate─the conjugate base─toward higher surface activities. Molecular dynamic simulations suggest a mechanism for the enhanced surface retention of laurate. We conclude that increased FA heterogeneity at SSA surfaces promotes surface activity of soluble FA species, altering monolayer phase behavior and impacting climate-relevant atmospheric processes.

Unraveling the interplay of temperature with molecular aggregation and miscibility in TEA-water mixtures

In the phase diagram of binary liquid mixtures, a miscibility gap is found with the concomitant liquid-liquid phase separation, wherein temperature is a key parameter in modulating the phase behavior. This includes critical temperatures such as the lower critical solution temperature (LCST) and upper critical solution temperature (UCST). Using a comprehensive approach including molecular dynamics (MD) simulation, graph theoretical analysis and spatial inhomogeneity measurement in an LCST-type mixture, we attempt to establish the relationship between the molecular aggregation pattern and phase behavior in TEA-water mixtures. At lower temperatures of binary liquid mixtures, TEA molecules tend to aggregate while simultaneously interacting with water forming a homogeneous solution. As the temperature increases, these TEA aggregates tend to self-associate by minimizing the interaction with water, which facilitates formation of two distinct liquid phases in the binary liquid. The spatial distribution analysis also reveals that the TEA aggregates compatible with water promote uniform distribution of water molecules, maintaining a homogeneous solution, while the water-incompatible ones generate isolation of water H-bond aggregates, leading to liquid-liquid phase separation in the binary system. This current study on temperature-induced molecular aggregation behavior is anticipated to contribute to a critical understanding of the phase behavior in binary liquid mixtures, including UCST, LCST, and reentrant phase behavior.

Biomolecular condensates form spatially inhomogeneous network fluids

The functions of biomolecular condensates are thought to be influenced by their material properties, and these will be determined by the internal organization of molecules within condensates. However, structural characterizations of condensates are challenging, and rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that are formed by macromolecules from nucleolar granular components (GCs). We show that these minimal facsimiles of GCs form condensates that are network fluids featuring spatial inhomogeneities across different length scales that reflect the contributions of distinct protein and peptide domains. The network-like inhomogeneous organization is characterized by a coexistence of liquid- and gas-like macromolecular densities that engenders bimodality of internal molecular dynamics. These insights suggest that condensates formed by multivalent proteins share features with network fluids formed by systems such as patchy or hairy colloids.

Water-Ion Interaction Determines the Mobility of Ions in Highly Concentrated Aqueous Electrolytes

Solvation engineering plays a critical role in tailoring the performance of batteries, particularly through the use of highly concentrated electrolytes, which offer heterogeneous solvation structures of mobile ions with distinct electrochemical properties. In this study, we employed spectroscopic techniques and molecular dynamics simulations to investigate mixed-cation (Li+/K+) acetate aqueous electrolytes. Our research unravels the pivotal role of water in facilitating ion transport within a highly viscous medium. Notably, Li+ cations primarily form ion aggregates, predominantly interacting with acetate anions, while K+ cations emerge as the principal charge carriers, which is attributed to their strong interaction with water molecules. Intriguingly, even at a concentration as high as 40 m, a substantial amount of water molecules persistently engages in hydrogen bonding with one another, creating mobile regions rich in K+ ions. Our observations of a redshift of the OH stretching band of water suggest that the strength of the hydrogen bond alone cannot account for the expansion of the electrochemical stability window. These findings offer valuable insights into the cation transfer mechanism, shedding light on the contribution of water-bound cations to both the ion conductivity and the electrochemical stability window of aqueous electrolytes for rechargeable batteries. Our comprehensive molecular-level understanding of the interplay between cations and water provides a foundation for future advances in solvation engineering, leading to the development of high-performance batteries with improved energy storage and safety profiles.

Biomolecular condensates form spatially inhomogeneous network fluids

The functions of biomolecular condensates are thought to be influenced by their material properties, and these will be determined by the internal organization of molecules within condensates. However, structural characterizations of condensates are challenging, and rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that are formed by macromolecules from nucleolar granular components (GCs). We show that these minimal facsimiles of GCs form condensates that are network fluids featuring spatial inhomogeneities across different length scales that reflect the contributions of distinct protein and peptide domains. The network-like inhomogeneous organization is characterized by a coexistence of liquid- and gas-like macromolecular densities that engenders bimodality of internal molecular dynamics. These insights suggest that condensates formed by multivalent proteins share features with network fluids formed by systems such as patchy or hairy colloids.

Molecular Aggregation Behavior and Microscopic Heterogeneity in Binary Osmolyte-Water Solutions

Osmolytes, small organic compounds, play a key role in modulating the protein stability in aqueous solutions, but the operating mechanism of the osmolyte remains inconclusive. Here, we attempt to clarify the mode of osmolyte action by quantitatively estimating the microheterogeneity of osmolyte-water mixtures with the aid of molecular dynamics simulation, graph theoretical analysis, and spatial distribution measurement in the four osmolyte solutions of trimethylamine-N-oxide (TMAO), tetramethylurea (TMU), dimethyl sulfoxide, and urea. TMAO, acting as a protecting osmolyte, tends to remain isolated with no formation of osmolyte aggregates while preferentially interacting with water, but there is a strong aggregation propensity in the denaturant TMU solution, characterized by favored hydrophobic interactions between TMU molecules. Taken together, the mechanism of osmolyte action on protein stability is proposed as a comprehensive one that encompasses the direct interactions between osmolytes and proteins and indirect interactions through the regulation of water properties in the osmolyte-water mixtures.

Observing ion diffusion and reciprocating hopping motion in water

When an ionic crystal dissolves in solvent, the positive and negative ions associated with solvent molecules release from the crystal. However, the existing form, interaction, and dynamics of ions in real solution are poorly understood because of the substantial experimental challenge. We observed the diffusion and aggregation of polyoxometalate (POM) ions in water by using liquid phase transmission electron microscopy. Real-time observation reveals an unexpected local reciprocating hopping motion of the ions in water, which may be caused by the short-range polymerized bridge of water molecules. We find that ion oligomers, existing as highly active clusters, undergo frequent splitting, aggregation, and rearrangement in dilute solution. The formation and dissociation of ion oligomers indicate a weak counterion-mediated interaction. Furthermore, POM ions with tetrahedral geometry show directional interaction compared with spherical ions, which presents structure-dependent dynamics.

Ionic conduction mechanism in high concentration lithium ion electrolytes

The conduction mechanism of a family of high concentration lithium electrolytes (HCEs) is investigated. It is found in all HCEs that the molecular motions are regulated by the anion size and correlated to the HCE ionic resistivity. From the results, a mechanism involving highly correlated ionic networks is derived.

Spatially resolved structural order in low-temperature liquid electrolyte

Determining the degree and the spatial extent of structural order in liquids is a grand challenge. Here, we are able to resolve the structural order in a model organic electrolyte of 1 M lithium hexafluorophosphate (LiPF₆) dissolved in 1:1 (v/v) ethylene carbonate:diethylcarbonate by developing an integrated method of liquid-phase transmission electron microscopy (TEM), cryo-TEM operated at -30°C, four-dimensional scanning TEM, and data analysis based on deep learning. This study reveals the presence of short-range order (SRO) in the high-salt concentration domains of the liquid electrolyte from liquid phase separation at the low temperature. Molecular dynamics simulations suggest the SRO originates from the Li⁺-(PF₆^-)_n (n > 2) local structural order induced by high LiPF₆ salt concentration.

ReNeGate: A Reaction Network Graph-Theoretical Tool for Automated Mechanistic Studies in Computational Homogeneous Catalysis

Exploration of the chemical reaction space of chemical transformations in multicomponent mixtures is one of the main challenges in contemporary computational chemistry. To remove expert bias from mechanistic studies and to discover new chemistries, an automated graph-theoretical methodology is proposed, which puts forward a network formalism of homogeneous catalysis reactions and utilizes a network analysis tool for mechanistic studies. The method can be used for analyzing trajectories with single and multiple catalytic species and can provide unique conformers of catalysts including multinuclear catalyst clusters along with other catalytic mixture components. The presented three-step approach has the integrated ability to handle multicomponent catalytic systems of arbitrary complexity (mixtures of reactants, catalyst precursors, ligands, additives, and solvents). It is not limited to predefined chemical rules, does not require prealignment of reaction mixture components consistent with a reaction coordinate, and is not agnostic to the chemical nature of transformations. Conformer exploration, reactive event identification, and reaction network analysis are the main steps taken for identifying the pathways in catalytic systems given the starting precatalytic reaction mixture as the input. Such a methodology allows us to efficiently explore catalytic systems in realistic conditions for either previously observed or completely unknown reactive events in the context of a network representing different intermediates. Our workflow for the catalytic reaction space exploration exclusively focuses on the identification of thermodynamically feasible conversion channels, representative of the (secondary) catalyst deactivation or inhibition paths, which are usually most difficult to anticipate based solely on expert chemical knowledge. Thus, the expert bias is sought to be removed at all steps, and the chemical intuition is limited to the choice of the thermodynamic constraint imposed by the applicable experimental conditions in terms of threshold energy values for allowed transformations. The capabilities of the proposed methodology have been tested by exploring the reactivity of Mn complexes relevant for catalytic hydrogenation chemistry to verify previously postulated activation mechanisms and unravel unexpected reaction channels relevant to rare deactivation events.

Distinct Hydrogen Bonding Dynamics Underlies the Microheterogeneity in DMF-Water Mixtures

The hydrogen bonding interaction between the amide functional group and water is fundamental to understanding the liquid-liquid heterogeneity in biological systems. Herein, the structure and dynamics of the N,N-dimethylformamide (DMF)-water mixtures have been investigated by linear and nonlinear IR spectroscopies, using the hydroxyl stretch and extrinsic probe of thiocyanate as local vibrational reporters. According to vibrational relaxation dynamics measurements, the orientational dynamics of water is not directly tied to those of DMF molecules. Wobbling-in-a-cone analysis demonstrates that the water molecules have varying degrees of angular restriction depending on their composition due to the formation of specific water-DMF networks. Because of the preferential solvation by DMF molecules, the rotational dynamics of the extrinsic probe is slowed significantly, and its rotational time constants are correlated to the change of solution viscosity. The unique structural dynamics observed in the DMF-water mixtures is expected to provide important insights into the underlying mechanism of microscopic heterogeneity in binary mixtures.

Gelation, Clustering and Crowding in the Electrical Double Layer of Ionic Liquids

Understanding the bulk and interfacial properties of super-concentrated electrolytes, such as ionic liquids (ILs), has attracted significant attention lately for their promising applications in supercapacitors and batteries. Recently, McEldrew et al. developed a theory for reversible ion associations in bulk ILs, which accounted for the formation of all possible Cayley tree clusters and a percolating ionic network (gel). Here we adopt and develop this approach to understand the associations of ILs in the electrical double layer at electrified interfaces. With increasing charge of the electrode, the theory predicts a transition from a regime dominated by a gelled or clustered state to a crowding regime dominated by free ions. This transition from gelation to crowding is conceptually similar to the overscreening to crowding transition.

From Networked to Isolated: Observing Water Hydrogen Bonds in Concentrated Electrolytes with Two-Dimensional Infrared Spectroscopy

Superconcentrated electrolytes have emerged as a promising class of materials for energy storage devices, with evidence that high voltage performance is possible even with water as the solvent. Here, we study the changes in the water hydrogen bonding network induced by the dissolution of lithium bis(trifluoromethane sulfonyl)imide (LiTFSI) in concentrations ranging from the dilute to the superconcentrated regimes. Using time-resolved two-dimensional infrared spectroscopy, we observe the progressive disruption of the water-water hydrogen bond network and the appearance of isolated water molecules interacting only with ions, which can be identified and spectroscopically isolated through the intermolecular cross-peaks between the water and the TFSI^- ions. Analyzing the vibrational relaxation of excitations of the H₂O stretching mode, we observe a transition in the dominant relaxation path as the bulk-like water vanishes and is replaced by ion-solvation water with the rapid single-step relaxation of delocalized stretching vibrations into the low frequency modes being replaced by multistep relaxation through the intramolecular H₂O bend and into the TFSI^- high frequency modes prior to relaxing to the low frequency structural degrees of freedom. These results definitively demonstrate the absence of vibrationally bulk-like water in the presence of high concentrations of LiTFSI and especially in the superconcentrated regime, while additionally revealing aspects of the water hydrogen bond network that have been difficult to discern from the vibrational spectroscopy of the neat liquid.

Water clusters and density fluctuations in liquid water based on extended hierarchical clustering methods

The microscopic structures of liquid water at ambient temperatures remain a hot debate, which relates with structural and density fluctuations in the hydrogen bond network. Here, we use molecular dynamics simulations of liquid water to study the properties of three-dimensional cage-like water clusters, which we investigate using extended graph-based hierarchical clustering methods. The water clusters can cover over 95% of hydrogen bond network, among which some clusters maximally encompass thousands of molecules extending beyond 3.0 nm. The clusters imply fractal behaviors forming percolating networks and the morphologies of small and large clusters show different scaling rules. The local favored clusters and the preferred connections between adjacent clusters correspond to lower energy and conformational entropy depending on cluster topologies. Temperature can destroy large clusters into small ones. We show further that the interior of clusters favors high-density patches. The water molecules in the small clusters, inside which are the void regarded as hydrophobic objects, have a preference for being more tetrahedral. Our results highlight the properties and changes of water clusters as the fundamental building blocks of hydrogen bond networks. In addition, the water clusters can elucidate structural and density fluctuations on different length scales in liquid water.

Hierarchical clustering analysis of hydrogen bond networks in aqueous solutions

To understand the relation between the macroscopic properties and microscopic structure of hydrogen bond networks in solutions, we introduced a hierarchical clustering method to analyze the typical configurations of water clusters in this type of network. Regarding hydrogen bonds as frames, the rings, fragments and clusters are defined and analyzed to provide a comprehensive perspective for the distributional and dynamic characteristics of the hydrogen-bonding network in NaCl solution at different concentrations. The properties of the radial distribution function and hydrogen bonds are first analyzed. Destruction and shorter lifetimes of hydrogen bonds are observed in solutions. In further analysis of the two-dimensional configuration, i.e., ring, and three-dimensional configuration, i.e., fragment, the average number, size and lifetime of these structures consistently decrease as the concentration increases. Ionic effects on disrupting rings and fragments are significant in the first hydration shell, especially with sodium cations, and these effects weaken beyond the first hydration shell. Regarding the clusters obtained using the Louvain algorithm, our results indicate that clusters break and become smaller as the NaCl concentration increases. The presence of ions also leads to the isolation of clusters and therefore the inhibition of changes. The lifetime of clusters increases with NaCl concentration, indicating the slowed breakage and reformation of clusters in NaCl solutions. This method can be further applied to quantitatively characterize hydrogen bond networks to elucidate more properties of aqueous solutions.

Some opinions on MD-based vibrational spectroscopy of gas phase molecules and their assembly: An overview of what has been achieved and where to go

We hereby review molecular dynamics simulations for anharmonic gas phase spectroscopy and provide some of our opinions of where the field is heading. With these new directions, the theoretical IR/Raman spectroscopy of large (bio)-molecular systems will be more easily achievable over longer time-scale MD trajectories for an increase in accuracy of the MD-IR and MD-Raman calculated spectra. With the new directions presented here, the high throughput 'decoding' of experimental IR/Raman spectra into 3D-structures should thus be possible, hence advancing e.g. the field of MS-IR for structural characterization by spectroscopy. We also review the assignment of vibrational spectra in terms of anharmonic molecular modes from the MD trajectories, and especially introduce our recent developments based on Graph Theory algorithms. Graph Theory algorithmic is also introduced in this review for the identification of the molecular 3D-structures sampled over MD trajectories.

Unraveling the Influence of Osmolytes on Water Hydrogen-Bond Network: From Local Structure to Graph Theory Analysis

Water structure in aqueous osmolyte solutions, deduced from the slight alteration in the water-water radial distribution function, the decrease in water-water hydrogen bonding, and tetrahedral ordering based only on the orientation of nearest water molecules derived from the molecular dynamics simulations, appears to have been perturbed. A careful analysis, however, reveals that the hydrogen bonding and the tetrahedral ordering around a water molecule in binary solutions remain intact as in neat water when the contribution of osmolyte-water interactions is appropriately incorporated. Furthermore, the distribution of the water binding energies and the water excess chemical potential of solvation in solutions are also pretty much the same as in neat water. Osmolytes are, therefore, well integrated into the hydrogen-bond network of water. Indeed, osmolytes tend to preferentially hydrogen bond with water molecules and their interaction energies are strongly correlated to their hydrogen-bonding capability. The graph network analysis, further, illustrates that osmolytes act as hubs in the percolated hydrogen-bond network of solutions. The degree of hydrogen bonding of osmolytes predominantly determines all of the network properties. Osmolytes like ethanol that form fewer hydrogen bonds than a water molecule disrupt the water hydrogen-bond network, while other osmolytes that form more hydrogen bonds effectively increase the connectivity among water molecules. Our observation of minimal variation in the local structure and the vitality of osmolyte-water hydrogen bonds on the solution network properties clearly imply that the direct interaction between protein and osmolytes is solely responsible for the protein stability. Further, the relevance of hydrogen bonds on solution properties suggests that the hydrogen-bonding interaction among protein, water, and osmolyte could be the key determinant of the protein conformation in solutions.

Figures of Graph Partitioning by Counting, Sequence and Layer Matrices

A series of counting, sequence and layer matrices are considered precursors of classifiers capable of providing the partitions of the vertices of graphs. Classifiers are given to provide different degrees of distinctiveness for the vertices of the graphs. Any partition can be represented with colors. Following this fundamental idea, it was proposed to color the graphs according to the partitions of the graph vertices. Two alternative cases were identified: when the order of the sets in the partition is relevant (the sets are distinguished by their positions) and when the order of the sets in the partition is not relevant (the sets are not distinguished by their positions). The two isomers of C28 fullerenes were colored to test the ability of classifiers to generate different partitions and colorings, thereby providing a useful visual tool for scientists working on the functionalization of various highly symmetrical chemical structures.

Effects of molecular shape on alcohol aggregation and water hydrogen bond network behavior in butanol isomer solutions

Despite butanol isomers such as n-butanol, sec-butanol, isobutanol and tert-butanol having the same chemical formula, their liquid-liquid phase diagrams are distinct. That is, tert-butanol is miscible in water at all concentrations, while the other three butanol isomers are partially miscible under ambient conditions. The molecular shape of tert-butanol is close to globular and differs from the other three butanol molecules with a relatively long carbon chain. By performing molecular dynamics simulations and graph theoretical analysis of the four water-butanol isomer mixtures at varying concentrations, we show how distinct butanol aggregates are formed which depend upon the molecular shape and affect the water H-bond network structure and phase diagram in the binary liquid. The three butanol isomers of n-butanol, sec-butanol and isobutanol at concentrated solutions form chain-like alcohol aggregates, but tert-butanol forms small aggregates due to the distinct packing behavior caused by its globular molecular shape. By employing the graph theoretical analysis such as the degree distribution and the eigenvalue spectrum from the adjacency matrix in the graphical representation of the alcohol H-bond network, we show that the tert-butanol aggregates have a different morphological structure from that of the other three butanol isomers in aqueous solution. The graph theoretically distinct butanol aggregates are categorized into two groups, water-compatible and water-incompatible, depending upon the interaction between the alcohol and water molecules. Based upon our observations, we propose that the water-incompatible networks of n-butanol, sec-butanol and isobutanol aggregates do not change the water structure significantly, forming two separate liquid phases that are alcohol-rich and water-rich. However, the water-compatible network of tert-butanol aggregates has a considerable interaction with the water molecules and causes significant disruption of the water H-bond network, forming a homogeneous solution. Understanding the alcohol aggregation behavior and water structure in butanol-water mixtures provides a critical clue in appreciating fundamental issues such as miscibility and phase separation in aqueous solution systems.

A hierarchical clustering method of hydrogen bond networks in liquid water undergoing shear flow

Many properties of water, such as turbulent flow, are closely related to water clusters, whereas how water clusters form and transform in bulk water remains unclear. A hierarchical clustering method is introduced to search out water clusters in hydrogen bonded network based on modified Louvain algorithm of graph community. Hydrogen bonds, rings and fragments are considered as 1st-, 2nd-, and 3rd-level structures, respectively. The distribution, dynamics and structural characteristics of 4th- and 5th-level clusters undergoing non-shear- and shear-driven flow are also analyzed at various temperatures. At low temperatures, nearly 50% of water molecules are included in clusters. Over 60% of clusters remain unchanged between neighboring configurations. Obvious collective translational motion of clusters is observed. The topological difference for clusters is elucidated between the inner layer, which favors 6-membered rings, and the external surface layer, which contains more 5-membered rings. Temperature and shearing can not only accelerate the transformation or destruction of clusters at all levels but also change cluster structures. The assembly of large clusters can be used to discretize continuous liquid water to elucidate the properties of liquid water.

Correlated Ion Transport and the Gel Phase in Room Temperature Ionic Liquids

Here we present a theory of ion aggregation and gelation of room temperature ionic liquids (RTILs). Based on it, we investigate the effect of ion aggregation on correlated ion transport-ionic conductivity and transference numbers-obtaining closed-form expressions for these quantities. The theory depends on the maximum number of associations a cation and anion can form and the strength of their association. To validate the presented theory, we perform molecular dynamics simulations on several RTILs and a range of temperatures for one RTIL. The simulations indicate the formation of large clusters, even percolating through the system under certain circumstances, thus forming a gel, with the theory accurately describing the obtained cluster distributions in all cases. However, based on the strength and lifetime of associations in the simulated RTILs, we expect free ions to dominate ionic conductivity despite the presence of clusters, and we do not expect the percolating cluster to trigger structural arrest in the RTIL.

Molecular heterogeneity in aqueous cosolvent systems

Aqueous cosolvent systems (ACoSs) are mixtures of small polar molecules such as amides, alcohols, dimethyl sulfoxide, or ions in water. These liquids have been the focus of fundamental studies due to their complex intermolecular interactions as well as their broad applications in chemistry, medicine, and materials science. ACoSs are fully miscible at the macroscopic level but exhibit nanometer-scale spatial heterogeneity. ACoSs have recently received renewed attention within the chemical physics community as model systems to explore the relationship between intermolecular interactions and microscopic liquid-liquid phase separation. In this perspective, we provide an overview of ACoS spatial segregation, dynamic heterogeneity, and multiscale relaxation dynamics. We describe emerging approaches to characterize liquid microstructure, H-bond networks, and dynamics using modern experimental tools combined with molecular dynamics simulations and network-based analysis techniques.

Insights into the hydrogen bond network topology of phosphoric acid and water systems

Phosphoric acid and its mixtures with water are some of the best proton conducting materials known to science. Although the proton conductivity in pure phosphoric acid decreases upon external doping with excess H+ or OH-, the addition of water improves it substantially. A number of experimental and theoretical studies indicate that these systems form a very special case of hydrogen bond networks which not only facilitate fast proton transport but also show a number of other interesting properties such as glass forming ability. In this work, we present the molecular dynamics simulation results of the H3PO4-H2O system over the entire concentration range. The hydrogen bond networks were analyzed in terms of conventional microscopic as well as topological properties based on graph and network theory. The results show that the hydrogen bond network of H3PO4 is fundamentally different from that of H2O. On average, each phosphoric acid molecule tends to form more and stronger hydrogen bonds than water which leads to a much more connected and clustered network showing small-world properties which are absent in pure water. Moreover, these hydrogen bond network properties persist in the H3PO4-H2O mixtures as well, even at relatively high water contents. Finally, many of the physical properties such as molecular diffusion coefficients seem to be also intimately related to the network topological properties and follow similar trends with respect to system content. These results strongly indicate that many important properties such as proton transport in phosphoric acid and its aqueous systems are fundamentally related to their hydrogen bond network topology and might hold the key for their ultimate molecular understanding.

Hopping in High Concentration Electrolytes - Long Time Bulk and Single-Particle Signatures, Free Energy Barriers, and Structural Insights

Although ion-hopping is believed to be a significant mode of transport for small ions in liquid high concentration electrolytes (HCE), its bulk signatures over sufficiently long time intervals are yet to be shown. We computationally establish the long and short time imprints of hopping in HCEs using LiBF₄-in-sulfolane mixtures as models. The high viscosity of this electrolyte leads to significant dynamic heterogeneity in Li-ion transport. Li-ions exhibit a preference to transit to previously occupied Li-ion-sites, bridged through anion or solvent molecules. Hopping in the liquid matrix was found to be an activated process, whose free energy barrier and transition state structure have been determined. Evidence for nanoscale compositional heterogeneity at high salt concentrations is also presented. The simulations shed light on the composition, stiffness, and lifetime of the solvation shell of Li ions. The understanding of HCEs gleaned from this study will spearhead the choice, engineering and applicability of this class of electrolytes.

Competitive Pi-Stacking and H-Bond Piling Increase Solubility of Heterocyclic Redoxmers

Redoxmers are organic molecules that carry electric charge in flow batteries. In many instances, they consist of heteroaromatic moieties modified with appended groups to prevent stacking of the planar cores and increase solubility in liquid electrolytes. This higher solubility is desired as it potentially allows achieving greater energy density in the battery. However, the present synthetic strategies often yield bulky molecules with low molarity even when they are neat and still lower molarity in liquid solutions. Fortunately, there are exceptions to this rule. Here, we examine one well-studied redoxmer, 2,1,3-benzothiadiazole, which has solubility ∼5.7 M in acetonitrile at 25 °C. We show computationally and prove experimentally that the competition between two packing motifs, face-to-face π-stacking and random N-H bond piling, introduces frustration that confounds nucleation in crowded solutions. Our findings and examples from related systems suggest a complementary strategy for the molecular design of redoxmers for high energy density redox flow cells.

Self-Assembled Solute Networks in Crowded Electrolyte Solutions and Nanoconfinement of Charged Redoxmer Molecules

Redoxmers are electrochemically active organic molecules storing charge and energy in electrolyte fluids circulating through redox flow batteries (RFBs). Such molecules typically have solvent-repelling cores and solvent-attracting pendant groups introduced to increase solubility in liquid electrolytes. These two features can facilitate nanoscale aggregation of the redoxmer molecules in crowded solutions. In some cases, this aggregation leads to the emergence of continuous networks of solute molecules in contact, and the solution becomes microscopically heterogeneous. Here, we use small-angle X-ray scattering (SAXS) and molecular dynamics modeling to demonstrate formation of such networks and examine structural factors controlling this self-assembly. We also show that salt ions become excluded from these solute aggregates into small pockets of electrolytes, where these ions strongly associate. This confinement by exclusion is also likely to occur to charged redoxmer molecules in a "sea" of neutral precursors coexisting in the same solution. Here, we demonstrate that the decay lifetime of the confined charged molecules in such solutions can increase several fold compared to dilute solutions. We attribute this behavior to a "microreactor effect" on reverse reactions of the confined species during their decomposition.

Understanding alcohol aggregates and the water hydrogen bond network towards miscibility in alcohol solutions: graph theoretical analysis

Under ambient conditions, methanol and ethanol are miscible in water at all concentrations, while n-butanol is partially miscible. This is the first study to quantitatively examine the miscibility of butanol and compare with miscible alcohols by employing molecular dynamics simulations and graph theoretical analysis of three water-alcohol mixtures at various concentrations. We show how distinct alcohol aggregates are formed, thereby affecting the water structure, which established the relationship between the morphological structure of the aggregates and the miscibility of the alcohol in aqueous solution. The aggregates of methanol and ethanol in highly concentrated solutions form an extended H-bond network that intertwines well with the H-bond network of water. n-Butanol tends to self-associate and form large aggregates, while such aggregates are segregated from water. Graph theoretical analysis revealed that the alcohol aggregates of methanol and ethanol solutions have a morphological structure different from that of n-butanol, although there is no significant difference in morphology between the three pure alcohols. These two distinct alcohol aggregates are classified as water-compatible and water-incompatible depending upon their interaction with the water H-bond network, and their effect on the water structure was investigated. Our study reveals that the water-compatible network of alcohol aggregates in methanol and ethanol solutions disrupts the water H-bond networks, while the water-incompatible network of n-butanol aggregates does not considerably alter the water structure, which is consistent with the experimental results. Furthermore, we propose that miscible alcohols form water-compatible networks in binary aqueous systems while partially miscible alcohols form water-incompatible networks. The bifurcating hypothesis on the alcohol aggregation behavior in liquid water is of critical use to understand the fundamental issues such as solubility and phase separation in solution systems.

Weighted persistent homology for osmolyte molecular aggregation and hydrogen-bonding network analysis

It has long been observed that trimethylamine N-oxide (TMAO) and urea demonstrate dramatically different properties in a protein folding process. Even with the enormous theoretical and experimental research work on these two osmolytes, various aspects of their underlying mechanisms still remain largely elusive. In this paper, we propose to use the weighted persistent homology to systematically study the osmolytes molecular aggregation and their hydrogen-bonding network from a local topological perspective. We consider two weighted models, i.e., localized persistent homology (LPH) and interactive persistent homology (IPH). Boltzmann persistent entropy (BPE) is proposed to quantitatively characterize the topological features from LPH and IPH, together with persistent Betti number (PBN). More specifically, from the localized persistent homology models, we have found that TMAO and urea have very different local topology. TMAO is found to exhibit a local network structure. With the concentration increase, the circle elements in these networks show a clear increase in their total numbers and a decrease in their relative sizes. In contrast, urea shows two types of local topological patterns, i.e., local clusters around 6 Å and a few global circle elements at around 12 Å. From the interactive persistent homology models, it has been found that our persistent radial distribution function (PRDF) from the global-scale IPH has same physical properties as the traditional radial distribution function. Moreover, PRDFs from the local-scale IPH can also be generated and used to characterize the local interaction information. Other than the clear difference of the first peak value of PRDFs at filtration size 4 Å, TMAO and urea also shows very different behaviors at the second peak region from filtration size 5 Å to 10 Å. These differences are also reflected in the PBNs and BPEs of the local-scale IPH. These localized topological information has never been revealed before. Since graphs can be transferred into simplicial complexes by the clique complex, our weighted persistent homology models can be used in the analysis of various networks and graphs from any molecular structures and aggregation systems.

Liquid-Liquid Phase Separation Produces Fast H-Bond Dynamics in DMSO-Water Mixtures

Liquid-liquid phase separation is common in complex mixtures, but the behavior of nanoconfined liquids is poorly understood from a physical perspective. Dimethyl sulfoxide (DMSO) is an amphiphilic molecule with unique concentration-dependent bulk properties in mixtures with water. Here, we use ultrafast two-dimensional infrared (2D IR) spectroscopy to measure the H-bond dynamics of two probe molecules with different polarities: formamide (FA) and dimethylformamide (DMF). Picosecond H-bond dynamics are fastest in the intermediate concentration regime (20-50 mol % DMSO), because such confined water exhibits bulk-like dynamics. Each vibrational probe experiences a unique microscopic environment as a result of nanoscale phase separation. Molecular dynamics simulations show that the dynamics span multiple time scales, from femtoseconds to nanoseconds. Our studies suggest a previously unknown liquid environment, which we label "local bulk", in which despite the local heterogeneity, the ultrafast H-bond dynamics are similar to bulk water.

Persistent homology analysis of osmolyte molecular aggregation and their hydrogen-bonding networks

Dramatically different patterns can be observed in the topological fingerprints for hydrogen-bonding networks from two types of osmolyte systems.

How Molecular Crowding Differs from Macromolecular Crowding: A Femtosecond Mid-Infrared Pump-Probe Study

Crowding is an inherent property of living systems in which biochemical processes occur in highly concentrated solutions of various finite-sized species of both low (molecular crowding) and high (macromolecular crowding) molecular weights. Is molecular crowding fundamentally different from macromolecular crowding? To answer this question, we use a femtosecond mid-infrared pump-probe technique with three vibrational probes in molecular (diethylene glycol) and macromolecular (polyethylene glycol) solutions. In less crowded media, both molecular and macromolecular crowders fail to affect the dynamics of interstitial bulk-like water molecules and those at the crowder/water interface. In highly crowded media, interstitial water dynamics strongly depends on molecular crowding, but macromolecular crowding does not alter the bulk-like hydration dynamics and has a modest crowding effect on water at the crowder/water interface. The results of this study provide a molecular level understanding of the structural and dynamic changes to water and the water-mediated cross-linking of crowders.