On the temperature dependence of liquid structure

Neural-network-based molecular dynamics simulations reveal that proton transport in water is doubly gated by sequential hydrogen-bond exchange

The transport of excess protons in water is central to acid-base chemistry, biochemistry and energy production. However, elucidating its mechanism has been challenging. Recent nonlinear vibrational spectroscopy experiments could not be explained by existing models. Here we use both vibrational spectroscopy calculations and neural-network-based molecular dynamics simulations that account for nuclear quantum effects for all atoms to determine the proton transport mechanism. Our simulations reveal an equilibrium between two stable proton-localized structures with distinct Eigen-like and Zundel-like hydrogen-bond motifs. Proton transport follows a three-step mechanism gated by two successive hydrogen-bond exchanges: the first reduces the proton-acceptor water coordination, leading to proton transfer, and the second, the rate-limiting step, prevents rapid back-transfer by increasing the proton-donor coordination. This sequential mechanism is consistent with experimental characterizations of proton diffusion, explaining the low activation energy and the prolonged intermediate lifetimes in vibrational spectroscopy. These results are crucial for understanding proton dynamics in biochemical and technological systems.

Energetics of water expulsion from intervening space between two particles during aggregation

Solvent expulsion away from an intervening region between two approaching particles plays important roles in particle aggregation yet remains poorly understood. In this work, we use metadynamics molecular simulations to study the free energy landscape of removing water molecules from gibbsite and pyrophyllite slit pores representing the confined spaces between two approaching particles. For gibbsite, removing water from the intervening region is both entropically and enthalpically unfavorable. The closer the particles approach each other, the harder it is to expel water molecules. For pyrophyllite, water expulsion is spontaneous, which is different from the gibbsite system. A smaller pore makes the water removal more favorable. When water is being drained from the intervening region, single chains of water molecules are observed in gibbsite pore, while in pyrophyllite pore water cluster is usually observed. Water-gibbsite hydrogen bonds help stabilize water chains, while water forms clusters in pyrophyllite pore to maximize the number of hydrogen bonds among themselves. This work provides the first assessment into the energetics and structure of water being drained from the intervening region between two approaching particles during oriented attachment and aggregation.

Accelerated Bayesian Inference for Molecular Simulations using Local Gaussian Process Surrogate Models

While Bayesian inference is the gold standard for uncertainty quantification and propagation, its use within physical chemistry encounters formidable computational barriers. These bottlenecks are magnified for modeling data with many independent variables, such as X-ray/neutron scattering patterns and electromagnetic spectra. To address this challenge, we employ local Gaussian process (LGP) surrogate models to accelerate Bayesian optimization over these complex thermophysical properties. The time-complexity of the LGPs scales linearly in the number of independent variables, in stark contrast to the computationally expensive cubic scaling of conventional Gaussian processes. To illustrate the method, we trained a LGP surrogate model on the radial distribution function of liquid neon and observed a 1,760,000-fold speed-up compared to molecular dynamics simulation, beating a conventional GP by three orders-of-magnitude. We conclude that LGPs are robust and efficient surrogate models poised to expand the application of Bayesian inference in molecular simulations to a broad spectrum of experimental data.

A structure-dynamics relationship enables prediction of the water hydrogen bond exchange activation energy from experimental data

It has long been understood that the structural features of water are determined by hydrogen bonding (H-bonding) and that the exchange of, or "jumps" between, H-bond partners underlies many of the dynamical processes in water. Despite the importance of H-bond exchanges there is, as yet, no direct method for experimentally measuring the timescale of the process or its associated activation energy. Here, we identify and exploit relationships between water's structural and dynamical properties that provide an indirect route for determining the H-bond exchange activation energy from experimental data. Specifically, we show that the enthalpy and entropy determining the radial distribution function in liquid water are linearly correlated with the activation energies for H-bond jumps, OH reorientation, and diffusion. Using temperature-dependent measurements of the radial distribution function from the literature, we demonstrate how these correlations allow us to infer the value of the jump activation energy, Ea,0, from experimental results. This analysis gives Ea,0 = 3.43 kcal mol-1, which is in good agreement with that predicted by the TIP4P/2005 water model. We also illustrate other approaches for estimating this activation energy consistent with these estimates.

Effects of polarizability and charge transfer on water dynamics and the underlying activation energies

A large number of force fields have been proposed for describing the behavior of liquid water within classical atomistic simulations, particularly molecular dynamics. In the past two decades, models that incorporate molecular polarizability and even charge transfer have become more prevalent, in attempts to develop more accurate descriptions. These are frequently parameterized to reproduce the measured thermodynamics, phase behavior, and structure of water. On the other hand, the dynamics of water is rarely considered in the construction of these models, despite its importance in their ultimate applications. In this paper, we explore the structure and dynamics of polarizable and charge-transfer water models, with a focus on timescales that directly or indirectly relate to hydrogen bond (H-bond) making and breaking. Moreover, we use the recently developed fluctuation theory for dynamics to determine the temperature dependence of these properties to shed light on the driving forces. This approach provides key insight into the timescale activation energies through a rigorous decomposition into contributions from the different interactions, including polarization and charge transfer. The results show that charge transfer effects have a negligible effect on the activation energies. Furthermore, the same tension between electrostatic and van der Waals interactions that is found in fixed-charge water models also governs the behavior of polarizable models. The models are found to involve significant energy-entropy compensation, pointing to the importance of developing water models that accurately describe the temperature dependence of water structure and dynamics.

Departures from perfect isomorph behavior in Lennard-Jones fluids and solids

Isomorphs are lines on a fluid or solid phase diagram along which the microstructure is invariant on affine density scaling of the molecular coordinates. Only inverse power (IP) and hard sphere potential systems are perfectly isomorphic. This work provides new theoretical tools and criteria to determine the extent of deviation from perfect isomorphicity for other pair potentials using the Lennard-Jones (LJ) system as a test case. A simple prescription for predicting isomorphs in the fluid range using the freezing line as a reference is shown to be quite accurate for the LJ system. The shear viscosity and self-diffusion coefficient scale well are calculated using this method, which enables comments on the physical significance of the correlations found previously in the literature to be made. The virial–potential energy fluctuation and the concept of an effective IPL system and exponent, n′, are investigated, particularly with reference to the LJ freezing and melting lines. It is shown that the exponent, n′, converges to the value 12 at a high temperature as ∼ T−1/2, where T is the temperature. Analytic expressions are derived for the density, temperature, and radius derivatives of the radial distribution function along an isomorph that can be used in molecular simulation. The variance of the radial distribution function and radial fluctuation function are shown to be isomorph invariant.

Interaction of guanidinium and ammonium cations with phosphatidylcholine and phosphatidylserine lipid bilayers - Calorimetric, spectroscopic and molecular dynamics simulations study

The ability of arginine-rich peptides to cross the lipid bilayer and enter cytoplasm, unlike their lysine-based analogues, is intensively studied in the context of cell-penetrating peptides. Although the experiments have not yet reconstructed their internalization mechanism, the computational studies have shown that the type or charge of lipid polar groups is one of the crucial factors in their translocation. In order to gain more detailed insight into the interaction of guanidinium (Gdm⁺) and ammonium (NH₄⁺) cations, as important building blocks in arginine and lysine amino acids, with lipid bilayers, we conducted the experimental and computational study that tackles this phenomenon. The adsorption of Gdm⁺ and NH₄⁺ on lipid bilayers prepared from a zwitterionic (DPPC) and an anionic (DPPS) lipid was examined by thermoanalytic and spectroscopic techniques. Using temperature-dependent UV-Vis spectroscopy and DSC calorimetry we determined the impact of Gdm⁺ and NH₄⁺ on the thermotropic properties of lipid bilayers. FTIR data, along with molecular dynamics simulations, unraveled the molecular-level details on the nature of their interactions, showing the proton transfer between NH₄⁺ and DPPS, but not between Gdm⁺ and DPPS. The findings originated from this work imply that Gdm⁺ and NH₄⁺ form qualitatively different interactions with lipids of different charge which is reflected in the physico-chemical interactions that arginine-and lysine-based peptides establish at a complex and chemically heterogeneous environment such as the biological membrane.

Direct calculation of the temperature dependence of 2D-IR spectra: Urea in water

A method for directly calculating the temperature derivative of two-dimensional infrared (2D-IR) spectra from simulations at a single temperature is presented. The approach is demonstrated by application to the OD stretching spectrum of isotopically dilute aqueous (HOD in H₂O) solutions of urea as a function of concentration. Urea is an important osmolyte because of its ability to denature proteins, which has motivated significant interest in its effect on the structure and dynamics of water. The present results show that the temperature dependence of both the linear IR and 2D-IR spectra, which report on the underlying energetic driving forces, is more sensitive to urea concentration than the spectra themselves. Additional physical insight is provided by calculation of the contributions to the temperature derivative from different interactions, e.g., water-water, water-urea, and urea-urea, present in the system. Finally, it is demonstrated how 2D-IR spectra at other temperatures can be obtained from only room temperature simulations.

Triplet States Reveal Slow Local Dynamics in the Solvation Shell of Biomolecules

Protein hydration shell dynamics plays a pivotal role in biochemical processes such as protein folding, enzyme function, molecular recognition and interaction with biological membranes. Thus, it is crucial to understand the mobility of the solvation shell at the surface of biomolecules. Triplet state solvation dynamics can reveal the slow dynamics of the solvation shell. This is done in the present work without adding separate dye molecules but instead by using a phosphorescent subgroup of the biomolecule itself. In particular, we study a small heptapeptide in a glycerol-water mixture under cryoconservation conditions so that the system can be supercooled without crystallization. We find a significant slowing of molecules in the solvation shell in the millisecond range compared to the bulk. This opens up the possibility to unravel the nature of relaxation processes in the solvation shell usually overlapping at room temperature.

Interpretation of the X-Ray Emission Spectra of Liquid Water through Temperature and Isotope Dependence

The interpretation of x-ray emission spectroscopy (XES) spectra in terms of their sensitivity to the hydrogen bonding and the consequent microheterogeneity in liquid water has been debated over a decade. To shed a light on this problem, we report the theoretical reproduction of the debated 1b_{1} peaks observed in the XES spectra of liquid water using semiclassical Kramers-Heisenberg formula. The essence of the temperature and isotope dependence of the 1b_{1} double peaks is explained by molecular dynamics simulations including full vibrational (O─H stretching, bending, and) modes, rotational combined with the density functional theory and core-hole induced dynamics. Some inconsistencies exist with the experimental XES profile, which illustrates the need to employ a more precise theoretical calculations for both geometry sampling and electronic structure using a more sophisticated procedure.

Using Activation Energies to Elucidate Mechanisms of Water Dynamics

Recent advances in the calculation of activation energies are shedding new light on the dynamical time scales of liquid water. In this Perspective, we examine how activation energies elucidate the central, but not singular, role of the exchange of hydrogen-bond (H-bond) partners that rearrange the H-bond network of water. The contributions of other motions to dynamical time scales and their associated activation energies are discussed along with one case, vibrational spectral diffusion, where H-bond exchanges are not mechanistically significant. Nascent progress on outstanding challenges, including descriptions of non-Arrhenius effects and activation volumes, are detailed along with some directions for future investigations.

Molecular Simulations of Phase Equilibria and Transport Properties in a Model CO2-Expanded Lithium Perchlorate Electrolyte

Carbon-dioxide (CO₂)-expanded liquids, in which a significant mole fraction of CO₂ is dissolved into an organic solvent, have been of significant interest, especially as catalytic support media. Because the CO₂ mole fraction and density can be controlled over a significant range by changing the CO₂ partial pressure, the transport properties of these solvents are highly tunable. Recently, these liquids have garnered interest as potential electrolyte solutions for catalytic electrochemistry; however, little is currently known about the influence of the electrolyte on CO₂ expansion. In the present work, we use molecular-dynamics simulations to study diffusion and viscosity in a model lithium perchlorate electrolyte in CO₂-expanded acetonitrile and demonstrate that these properties are highly dependent on the concentration of the electrolyte. Our present results indicate that the electrolyte slows down diffusion of both CO₂ and MeCN, and that the slowed diffusion in the former is driven by changes in the activation entropy, whereas slowed diffusion in the latter is driven by changes in the activation energy.

Examining the Role of Different Molecular Interactions on Activation Energies and Activation Volumes in Liquid Water

There are a large number of force fields available to model water in molecular dynamics simulations, which each have their own strengths and weaknesses in describing the behavior of the liquid. One particular weakness in many of these models is their description of dynamics away from ambient conditions, where their ability to reproduce measurements is mixed. To investigate this issue, we use the recently developed fluctuation theory for dynamics to directly evaluate measures of the local temperature and pressure dependence: the activation energy and the activation volume. We examine these activation parameters for hydrogen-bond jump exchange times, OH reorientation times, and diffusion coefficients calculated from the SPC/E, SPC/Fw, TIP3P-PME, TIP3P-PME/Fw, OPC3, TIP4P/2005, TIP4P/Ew, E3B2, and E3B3 water models. Activation energy decompositions available through the fluctuation theory approach provide mechanistic insight into the origins of different temperature dependences between the various models, as well as the influence of three-body effects and flexibility.

Temperature Dependence of Peptide Conformational Equilibria from Simulations at a Single Temperature

Understanding the structure of proteins is key to unraveling their function in biological processes. Thus, significant attention has been paid to the calculation of conformational free energies. In this paper, we demonstrate a simple extension of fluctuation theory that permits the calculation of the temperature derivative of the conformational free energy, and hence the internal energy and entropy, from single-temperature simulations. The method further enables the decomposition into the contribution of different interactions present in the system to the internal energy surface. We illustrate the method for the canonical test system of alanine dipeptide in aqueous solution, for which we examine the free energy as a function of two dihedral angles. This system, like many, is most effectively treated using accelerated sampling methods and we show how the present approach is compatible with an important class of these, those that introduce a bias potential, by implementing it within metadynamics.

On the role of hydrogen-bond exchanges in the spectral diffusion of water

The dynamics of a vibrational frequency in a condensed phase environment, i.e., the spectral diffusion, has attracted considerable interest over the last two decades. A significant impetus has been the development of two-dimensional infrared (2D-IR) photon-echo spectroscopy that represents a direct experimental probe of spectral diffusion, as measured by the frequency-frequency time correlation function (FFCF). In isotopically dilute water, which is perhaps the most thoroughly studied system, the standard interpretation of the longest timescale observed in the FFCF is that it is associated with hydrogen-bond exchange dynamics. Here, we investigate this connection by detailed analysis of both the spectral diffusion timescales and their associated activation energies. The latter are obtained from the recently developed fluctuation theory for the dynamics approach. The results show that the longest timescale of spectral diffusion obtained by the typical analysis used cannot be directly associated with hydrogen-bond exchanges. The hydrogen-bond exchange time does appear in the decay of the water FFCF, but only as an additional, small-amplitude (<3%) timescale. The dominant contribution to the long-time spectral diffusion dynamics is considerably shorter than the hydrogen-bond exchange time and exhibits a significantly smaller activation energy. It thus arises from hydrogen-bond rearrangements, which occur in between successful hydrogen-bond partner exchanges, and particularly from hydrogen bonds that transiently break before returning to the same acceptor.

Examining the Hofmeister Series through Activation Energies: Water Diffusion in Aqueous Alkali-Halide Solutions

The effect of ions on the properties of aqueous solutions is often categorized in terms of the Hofmeister series that ranks them from chaotropes ("structure-breakers"), which weaken the surrounding hydrogen-bond network to kosmotropes ("structure-makers"), which enhance it. Here, we investigate the Hofmeister series in ∼1 M sodium-halide solutions using molecular dynamics simulations to calculate the effect of the identity and proximity of the halide anion on both the water diffusion coefficient and its activation energy. A recently developed method for calculating the activation energy from a single-temperature simulation is used, which also permits a rigorous decomposition into contributions from different interactions and motions. The mechanisms of the salt effects on the water dynamics are explored by separately considering water molecules based on their location relative to the ions. The results show that water diffusion is accelerated moving down the halide group from F^- to I^-. The behavior of the diffusion activation energy, E_a, is more complex, indicating a significant role for entropic effects. However, water molecules in the first or second solvation shell of an ion exhibit a decrease in E_a moving down the halide series and Na⁺ exhibits a larger effect than any of the anions. The E_a for water molecules within the second solvation shell of an ion are modest, indicating a short-ranged nature of the ion influence.

Structure of the Lennard-Jones liquid estimated from a single simulation

Combining the recent Piskulich-Thompson approach [Z. A. Piskulich and W. H. Thompson, J. Chem. Phys. 152, 011102 (2020)JCPSA60021-960610.1063/1.5135932] with isomorph theory, from a single simulation the structure of a single-component Lennard-Jones (LJ) system is obtained at an arbitrary state point in almost the whole liquid region of the temperature-density phase diagram. The LJ system exhibits two temperature ranges where the van't Hoff assumption that energetic and entropic forces are temperature independent is valid to a good approximation. A method to evaluate the structure at an arbitrary state point along an isochore from the knowledge of structures at two temperatures on the isochore is also discussed. We argue that, in general, the structure of any hidden scale-invariant system obeying the van't Hoff assumption in the whole range of temperatures can be determined in the whole liquid region of the phase diagram from a single simulation.

Extrapolation and interpolation strategies for efficiently estimating structural observables as a function of temperature and density

Thermodynamic extrapolation has previously been used to predict arbitrary structural observables in molecular simulations at temperatures (or relative chemical potentials in open-system mixtures) different from those at which the simulation was performed. This greatly reduces the computational cost in mapping out phase and structural transitions. In this work, we explore the limitations and accuracy of thermodynamic extrapolation applied to water, where qualitative shifts from anomalous to simple-fluid-like behavior are manifested through shifts in the liquid structure that occur as a function of both temperature and density. We present formulas for extrapolating in volume for canonical ensembles and demonstrate that linear extrapolations of water's structural properties are only accurate over a limited density range. On the other hand, linear extrapolation in temperature can be accurate across the entire liquid state. We contrast these extrapolations with classical perturbation theory techniques, which are more conservative and slowly converging. Indeed, we show that such behavior is expected by demonstrating exact relationships between extrapolation of free energies and well-known techniques to predict free energy differences. An ideal gas in an external field is also studied to more clearly explain these results for a toy system with fully analytical solutions. We also present a recursive interpolation strategy for predicting arbitrary structural properties of molecular fluids over a predefined range of state conditions, demonstrating its success in mapping qualitative shifts in water structure with density.

Temperature Dependence of the Water Infrared Spectrum: Driving Forces, Isosbestic Points, and Predictions

The temperature derivative of the infrared (IR) spectrum of HOD/D₂O is directly calculated from simulations at a single temperature using a fluctuation theory approach. It is demonstrated, on the basis of an energetic decomposition of the derivative, that the blue shift with increasing temperature is associated with the competition between electrostatic and Lennard-Jones interactions. The same competition gives rise, where their contributions cancel, to a near isosbestic point. The derivative is further used to define an effective internal energy (and entropy) associated with the IR spectrum, and it is shown how a van't Hoff relation can be used to accurately predict the spectrum over a wide range of temperatures. These predictions also explain why a precise isosbestic point is not observed.