Orientational correlation function for molecular liquids: The case of liquid water

Interfacial local field and surface response coefficients

The interfacial local field is of critical importance in data analysis to deduce intrinsic surface responses from optical measurements of interfaces of condensed media but has not yet been well interrogated. We present here a simple approach to find local fields approximately at various interfaces of isotropic or nearly isotropic media. We divide a medium into atomic planes or molecular layers. It is found that the dipolar field contribution to the local field in a plane or layer from induced dipoles residing in planes beyond the nearest neighbor planes or layers is negligible; in many cases, the contribution is dominated by in-plane dipoles and the local field has a simple expression very much like that for an isotropic bulk. This finding allows us to calculate approximate local field variation at various interfaces. With the interfacial local field known, intrinsic surface response coefficients can be extracted from the optically measured surface responses.

Structure and dynamics of liquid water from ab initio simulations: adding Minnesota density functionals to Jacob's ladder

The accurate representation of the structural and dynamical properties of water is essential for simulating the unique behavior of this ubiquitous solvent. Here we assess the current status of describing liquid water using ab initio molecular dynamics, with a special focus on the performance of all the later generation Minnesota functionals. Findings are contextualized within the current knowledge on DFT for describing bulk water under ambient conditions and compared to experimental data. We find that, contrary to the prevalent idea that local and semilocal functionals overstructure water and underestimate dynamical properties, M06-L, revM06-L, and M11-L understructure water, while MN12-L and MN15-L overdistance water molecules due to weak cohesive effects. This can be attributed to a weakening of the hydrogen bond network, which leads to dynamical fingerprints that are over fast. While most of the hybrid Minnesota functionals (M06, M08-HX, M08-SO, M11, MN12-SX, and MN15) also yield understructured water, their dynamical properties generally improve over their semilocal counterparts. It emerges that exact exchange is a crucial component for accurately describing hydrogen bonds, which ultimately leads to corrections in both the dynamical and structural properties. However, an excessive amount of exact exchange strengthens hydrogen bonds and causes overstructuring and slow dynamics (M06-HF). As a compromise, M06-2X is the best performing Minnesota functional for water, and its D3 corrected variant shows very good structural agreement. From previous studies considering nuclear quantum effects (NQEs), the hybrid revPBE0-D3, and the rung-5 RPA (RPA@PBE) have been identified as the only two approximations that closely agree with experiments. Our results suggest that the M06-2X(-D3) functionals have the potential to further improve the reproduction of experimental properties when incorporating NQEs through path integral approaches. This work provides further proof that accurate modeling of water interactions requires the inclusion of both exact exchange and balanced (non-local) correlation, highlighting the need for higher rungs on Jacob's ladder to achieve predictive simulations of complex biological systems in aqueous environments.

Understanding dynamics in coarse-grained models. I. Universal excess entropy scaling relationship

Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural properties, assessing dynamic properties in CG modeling is often unfeasible due to the accelerated dynamics of the CG models, which allows for more efficient structural sampling. Therefore, the ultimate goal of the present series of articles is to establish a better correspondence between the FG and CG dynamics. To assess and compare dynamical properties in the FG and the corresponding CG models, we utilize the excess entropy scaling relationship. For Paper I of this series, we provide evidence that the FG and the corresponding CG counterpart follow the same universal scaling relationship. By carefully reviewing and examining the literature, we develop a new theory to calculate excess entropies for the FG and CG systems while accounting for entropy representability. We demonstrate that the excess entropy scaling idea can be readily applied to liquid water and methanol systems at both the FG and CG resolutions. For both liquids, we reveal that the scaling exponents remain unchanged from the coarse-graining process, indicating that the scaling behavior is universal for the same underlying molecular systems. Combining this finding with the concept of mapping entropy in CG models, we show that the missing entropy plays an important role in accelerating the CG dynamics.

Nonlocal Dielectric Response of Water in Nanoconfinement

Recent experiments reporting a very low dielectric permittivity for nanoconfined water have renewed the interest in the structure and dielectric properties of water in narrow gaps. Here, we describe such systems with a minimal Landau-Ginzburg field theory composed of a nonlocal bulk-determined term and a local water-surface interaction term. We show how the interplay between the boundary conditions and intrinsic bulk correlations encodes the dielectric properties of confined water. Our theoretical analysis is supported by molecular dynamics simulations and comparison with the experimental data.

Deconstructing the Local Intermolecular Ordering and Dynamics of Liquid Chloroform and Bromoform

Local intermolecular structure and dynamics of the polar molecular liquids chloroform and bromoform are studied by molecular dynamics simulation. Structural distribution functions, including 1- and 2-D pair correlations and dipole contour plots allow direct comparison and show agreement with recent analyses of diffraction experiments. Studies of the haloforms' reorientational dynamics and longevity of structural features resulting from intermolecular interaction extend previous work toward deeper understanding of the factors controlling these features. Analyses of ensemble average structures and dynamical properties isolate mass, electrostatics, and steric packing as driving forces or contributing factors for the observed ordering and dynamics.

A new one-site coarse-grained model for water: Bottom-up many-body projected water (BUMPer). I. General theory and model

Water is undoubtedly one of the most important molecules for a variety of chemical and physical systems, and constructing precise yet effective coarse-grained (CG) water models has been a high priority for computer simulations. To recapitulate important local correlations in the CG water model, explicit higher-order interactions are often included. However, the advantages of coarse-graining may then be offset by the larger computational cost in the model parameterization and simulation execution. To leverage both the computational efficiency of the CG simulation and the inclusion of higher-order interactions, we propose a new statistical mechanical theory that effectively projects many-body interactions onto pairwise basis sets. The many-body projection theory presented in this work shares similar physics from liquid state theory, providing an efficient approach to account for higher-order interactions within the reduced model. We apply this theory to project the widely used Stillinger-Weber three-body interaction onto a pairwise (two-body) interaction for water. Based on the projected interaction with the correct long-range behavior, we denote the new CG water model as the Bottom-Up Many-Body Projected Water (BUMPer) model, where the resultant CG interaction corresponds to a prior model, the iteratively force-matched model. Unlike other pairwise CG models, BUMPer provides high-fidelity recapitulation of pair correlation functions and three-body distributions, as well as N-body correlation functions. BUMPer extensively improves upon the existing bottom-up CG water models by extending the accuracy and applicability of such models while maintaining a reduced computational cost.

Dihydrogen Bonds in Aqueous NaBD4 Solution by Neutron and X-ray Diffraction

Neutron diffraction, X-ray diffraction, and empirical potential structure refinement modeling were employed to study the structure of alkaline aqueous NaBD₄ solutions at different NaBD₄ concentrations and temperatures. In 1.0 mol·dm^-3 NaBD₄ aqueous solutions, about 5.6 ± 1.6 water molecules bond to BD₄^- via tetrahedral edges or tetrahedral corners without a very specific hydration geometry; that is, each hydrogen atom of BD₄^- bonds to 2.2 ± 1.0 water molecules through dihydrogen bonds with the D(B)···D(W) distance of 1.95 Å. The number of dihydrogen bonds decreases with increasing concentration and increases with temperature. Dihydrogen bonding is a predominantly electrostatic interaction which shows relatively lower directionality and saturability in comparison with the regular hydrogen bonds between water molecules. The water orientation around BD₄^- shows that the proportion of tetrahedral-edge dihydrogen bonds increases with temperature and decreases with concentration.

Assimilating Radial Distribution Functions To Build Water Models with Improved Structural Properties

The structural properties of three- and four-site water models are improved by extending the ForceBalance parametrization code to include a new methodology allowing for the targeting of any radial distribution function (RDF) during the parametrization of a force field. The mean squared difference (MSD) between the experimental and simulated RDFs contributes to an objective function, allowing for the systematic optimization of force field parameters to reach closer overall agreement with experiment. RDF fitting is applied to develop modified versions of the TIP3P and TIP4P/2005 water models in which the Lennard-Jones potential is replaced by a Buckingham potential. The optimized TIP3P-Buckingham and TIP4P-Buckingham potentials feature 93 and 98% lower MSDs in the OO RDF compared to the TIP3P and TIP4P/2005 models respectively, with marked decreases in the height of the first peak. Additionally, these Buckingham models predict the entropy of water more accurately, reducing the error in the entropy of TIP3P from 11 to 3% and the error in the entropy of TIP4P/2005 from 11 to 2%. These new Buckingham models have improved predictive power for many nonfitted properties particularly in the case of TIP3P. Our work directly demonstrates how the Buckingham potential can improve the description of water's structural properties beyond the Lennard-Jones potential. Moreover, adding a Buckingham potential is a favorable alternative to adding interaction sites in terms of computational speed on modern GPU hardware.

Interstitial Voids and Resultant Density of Liquid Water: A First-Principles Molecular Dynamics Study

Many anomalous properties of water can be explained on the basis of the coexistence of more than one density states: high-density water (HDW) and low-density water (LDW). We investigated these two phases of water molecules through first-principles molecular dynamics simulations using density functional theory (DFT) in conjunction with various van der Waals-corrected exchange and correlation functionals. Different density regions were found to exist due to the difference in short-range and long-range forces present in DFT potentials. These density regions were identified and analyzed on the basis of the distribution of molecules and voids present. We defined a local structure index to distinguish and find the probability of occurrence of these different states. HDW and LDW arise due to the presence of "interstitial water" molecules in between the first and second coordination shells. The population of interstitial water molecules is found to affect the overall dynamics of the system as they change the hydrogen bond pattern.

Characterizing Hydration Properties Based on the Orientational Structure of Interfacial Water Molecules

In this work, we present a general computational method for characterizing the molecular structure of liquid water interfaces as sampled from atomistic simulations. With this method, the interfacial structure is quantified based on the statistical analysis of the orientational configurations of interfacial water molecules. The method can be applied to generate position dependent maps of the hydration properties of heterogeneous surfaces. We present an application to the characterization of surface hydrophobicity, which we use to analyze simulations of a hydrated protein. We demonstrate that this approach is capable of revealing microscopic details of the collective dynamics of a protein hydration shell.

B(OH)4- hydration and association in sodium metaborate solutions by X-ray diffraction and empirical potential structure refinement

X-ray diffraction is used to study the structure of aqueous sodium metaborate solutions at salt concentrations of 1, 3, and 5 (oversaturated) mol dm^-3. The X-ray structure factors are subjected to empirical potential structure refinement (EPSR) modelling to extract the individual site-site pair correlation functions, the coordination numbers, and the spatial density functions (three-dimensional structure) of ion hydration and association as well as solvent water in the borate solutions. The sodium ion is surrounded on average by (5.4 ± 0.7), (4.6 ± 1.0), and (3.7 ± 1.2) water molecules at 1, 3, and 5 mol dm^-3, respectively, with the Na-O (H₂O) distance of 2.34 Å. The decrease in hydration number of the sodium ion is compensated by direct binding of the oxygen atom of the borate ion, B(OH)₄^-, with the average coordination number of (0.2 ± 0.5), (1.0 ± 0.8), and (2.1 ± 1.3) at the Na-O(B) distance of 2.34 Å to keep the octahedral hydration shell of the sodium ion. The average number of water molecules around the borate ion is (13.9 ± 1.8), (14.2 ± 1.8), and (16.1 ± 2.4) per borate ion with increasing salt concentration with the B-O(H₂O) distance of 3.72 Å. The number of nearest-neighbour water molecules around a central water molecule in a solvent decreases as (4.8 ± 1.2), (3.8 ± 1.1), and (2.8 ± 1.1) with an increase in salt concentration with the O(H₂O)-O(H₂O) distance of 2.79 Å. The Na⁺-B(OH)₄^- ion association is characterized by the Na-O(B) and Na-B pair correlation functions. The Na-B interactions are observed at 3.00 Å as a shoulder and 3.57 Å as a main peak in the site-site pair correlation function, suggesting two occupancy sites of Na⁺ with one for the edge-shared bidentate bonding and the other for the corner-shared monodentate bonding. The total number of Na-B interactions at 3.00 and 3.57 Å is consistent with that of the Na-O(B) interactions. The detailed three-dimensional structure of the ion hydration and association is visualized as a function of salt concentration. The structure and stability of [NaB(OH)₄(H₂O)₆]⁰ clusters are further investigated by DFT calculations, and the most likely structure is proposed and cross-checked.

Pair Correlation Function of a 2D Molecular Gas Directly Visualized by Scanning Tunneling Microscopy

The state of matter in fluid phases, determined by the interactions between particles, can be characterized by a pair correlation function (PCF). At the nanoscale, the PCF has been so far obtained experimentally only by means of reciprocal-space techniques. We use scanning tunneling microscopy (STM) at room temperature in combination with lattice-gas kinetic Monte Carlo (KMC) simulations to study a two-dimensional gas of highly mobile molecules of fluorinated copper phthalocyanine on a Si(111)/Tl-(1×1) surface. A relatively slow mechanism of STM image acquisition results in time-averaging of molecular occurrence under the STM tip. We prove by the KMC simulations that in the proximity of fixed molecules STM images represent the PCF. We demonstrate that STM is capable of visualizing directly the pair correlation function in real space.

Probing the triplet correlation function in liquid water by experiments and molecular simulations

Three-body information of liquid water is extracted using X-ray diffraction experiment as well as in molecular simulations via isothermal pressure derivative of structure factor term.

Systematic Parameterization of Monovalent Ions Employing the Nonbonded Model

Monovalent ions play fundamental roles in many biological processes in organisms. Modeling these ions in molecular simulations continues to be a challenging problem. The 12-6 Lennard-Jones (LJ) nonbonded model is widely used to model monovalent ions in classical molecular dynamics simulations. A lot of parameterization efforts have been reported for these ions with a number of experimental end points. However, some reported parameter sets do not have a good balance between the two Lennard-Jones parameters (the van der Waals (VDW) radius and potential well depth), which affects their transferability. In the present work, via the use of a noble gas curve we fitted in former work (J. Chem. Theory Comput. 2013, 9, 2733), we reoptimized the 12-6 LJ parameters for 15 monovalent ions (11 positive and 4 negative ions) for three extensively used water models (TIP3P, SPC/E, and TIP4P(EW)). Since the 12-6 LJ nonbonded model performs poorly in some instances for these ions, we have also parameterized the 12-6-4 LJ-type nonbonded model (J. Chem. Theory Comput. 2014, 10, 289) using the same three water models. The three derived parameter sets focused on reproducing the hydration free energies (the HFE set) and the ion-oxygen distance (the IOD set) using the 12-6 LJ nonbonded model and the 12-6-4 LJ-type nonbonded model (the 12-6-4 set) overall give improved results. In particular, the final parameter sets showed better agreement with quantum mechanically calculated VDW radii and improved transferability to ion-pair solutions when compared to previous parameter sets.

Experimental triplet and quadruplet fluctuation densities and spatial distribution function integrals for pure liquids

Fluctuation solution theory has provided an alternative view of many liquid mixture properties in terms of particle number fluctuations. The particle number fluctuations can also be related to integrals of the corresponding two body distribution functions between molecular pairs in order to provide a more physical picture of solution behavior and molecule affinities. Here, we extend this type of approach to provide expressions for higher order triplet and quadruplet fluctuations, and thereby integrals over the corresponding distribution functions, all of which can be obtained from available experimental thermodynamic data. The fluctuations and integrals are then determined using the International Association for the Properties of Water and Steam Formulation 1995 (IAPWS-95) equation of state for the liquid phase of pure water. The results indicate small, but significant, deviations from a Gaussian distribution for the molecules in this system. The pressure and temperature dependence of the fluctuations and integrals, as well as the limiting behavior as one approaches both the triple point and the critical point, are also examined.

Polar stacking of molecules in liquid chloroform

‘Super-dipole’ aggregates in liquid chloroform may explain its outstanding solvent properties and highlight a route to designing new high-performance solvents.

A continuous mixture of two different dimers in liquid water

Liquid water is formed by a continuous mixture of two different dimers (cis and trans) with distinct energies related to different relative water molecule orientations.

The Radial Distribution Functions of Water as Derived from Radiation Total Scattering Experiments: Is There Anything We Can Say for Sure?

The present paper reviews the investigation of ambient water structure and focusses in particular on the determination of the radial distribution functions of water from total experimental radiation scattering experiments. A novel method for removing the inelastic scattering from neutron data is introduced, and the effect of Compton scattering on X-ray data is discussed. In addition the extent to which quantum effects can be discerned between heavy and light water is analysed against these more recent data. It is concluded that, with the help of modern data analysis and computer simulation tools to interrogate the scattering data, a considerable degree of consistency can be obtained between recent and past scattering experiments on water. That consistency also gives a realistic estimate of the likely uncertainties in the extracted radial distribution functions, as well as offering a benchmark against which future experiments can be judged.

Computing free energy hypersurfaces for anisotropic intermolecular associations

We previously used an adaptive reaction coordinate force biasing method for calculating the free energy of conformation (Naidoo and Brady, J Am Chem Soc 1999, 121, 2244) and chemical reactions (Rajamani et al., J Comput Chem 2003, 24, 1775) amongst others. Here, we describe a generalized version able to produce free energies in multiple dimensions, descriptively named the free energies from adaptive reaction coordinate forces method. To illustrate it, we describe how we calculate a multidimensional intermolecular orientational free energy, which can be used to investigate complex systems such as protein conformation and liquids. This multidimensional intermolecular free energy W(r, theta(1), theta(2), phi) provides a measure of orientationally dependent interactions that are appropriate for applications in systems that inherently have molecular anisotropic features. It is a highly informative free energy volume, which can be used to parameterize key terms such as the Gay-Berne intermolecular potential in coarse grain simulations. To demonstrate the value of the information gained from the W(r, theta(1), theta(2), phi) hypersurfaces we calculated them for TIP3P, TIP4P, and TIP5P dimer water models in vacuum. A comparison with a commonly used one-dimensional distance free energy profile is made to illustrate the significant increase in configurational information. The W(r) plots show little difference between the three models while the W(r, theta(1), theta(2), phi) hypersurfaces reveal the underlying energetic reasons why these potentials reproduce tetrahedrality in the condensed phase so differently from each.