Accurate Description of Aqueous Carbonate Ions: An Effective Polarization Model Verified by Neutron Scattering

Ion pairing in aqueous tetramethylammonium-acetate solutions by neutron scattering and molecular dynamics simulations

Tetramethylammonium (TMA) is a ubiquitous cationic motif in biochemistry, found in the charged choline headgroup of membrane phospholipids and in tri-methylated lysine residues, which modulates histone-DNA interactions and impacts epigenetic mechanisms. TMA interactions with anionic species, particularly carboxylate groups of amino acid residues and extracellular sugars, are of substantial biological relevance, as these interactions mediate a wide range of cellular processes. This study investigates the molecular interactions between TMA and acetate, representing carboxylate-containing groups, using neutron scattering experiments complemented by force fields and ab initio molecular dynamics (MD) simulations. Neutron diffraction with isotopic substitution reveals specific ion pairing signatures between TMA and acetate, with simulations providing a detailed interpretation of the ion pairing structures. Force fields, notably CHARMM36 with the electronic continuum correction (ECC) (by a factor of 0.85) and AMBER99SB, capture essential pairing characteristics, but only revPBE-based ab initio MD simulations accurately model specific experimental features such as the low Q peak intensity in reciprocal space. Our study delivers a refined molecular model of TMA-carboxylate interactions, guiding the selection of force fields for complex biological systems where such interactions are of significant importance.

Effective Inclusion of Electronic Polarization Improves the Description of Electrostatic Interactions: The prosECCo75 Biomolecular Force Field

prosECCo75 is an optimized force field effectively incorporating electronic polarization via charge scaling. It aims to enhance the accuracy of nominally nonpolarizable molecular dynamics simulations for interactions in biologically relevant systems involving water, ions, proteins, lipids, and saccharides. Recognizing the inherent limitations of nonpolarizable force fields in precisely modeling electrostatic interactions essential for various biological processes, we mitigate these shortcomings by accounting for electronic polarizability in a physically rigorous mean-field way that does not add to computational costs. With this scaling of (both integer and partial) charges within the CHARMM36 framework, prosECCo75 addresses overbinding artifacts. This improves agreement with experimental ion binding data across a broad spectrum of systems─lipid membranes, proteins (including peptides and amino acids), and saccharides─without compromising their biomolecular structures. prosECCo75 thus emerges as a computationally efficient tool providing enhanced accuracy and broader applicability in simulating the complex interplay of interactions between ions and biomolecules, pivotal for improving our understanding of many biological processes.

Novel Computational Chemistry Infrastructure for Simulating Astatide in Water: From Basis Sets to Force Fields Using Particle Swarm Optimization

Using the example of astatine, the heaviest naturally occurring halogen whose isotope At-211 has promising medical applications, we propose a new infrastructure for large-scale computational models of heavy elements with strong relativistic effects. In particular, we focus on developing an accurate force field for At- in water based on reliable relativistic density functional theory (DFT) calculations. To ensure the reliability of such calculations, we design novel basis sets for relativistic DFT, via the particle swarm optimization algorithm to optimize the coefficients of the new basis sets and the polarization-consistent basis set idea's extension to heavy elements to eliminate the basis set error from DFT calculations. The resulting basis sets enable the well-grounded evaluation of relativistic DFT against "gold-standard" CCSD(T) results. Accounting for strong relativistic effects, including spin-orbit interaction, via our redesigned infrastructure, we elucidate a noticeable dissimilarity between At- and I- in halide-water force field parameters, radial distribution functions, diffusion coefficients, and hydration energies. This work establishes the framework for the systematic development of polarization-consistent basis sets for relativistic DFT and accurate force fields for molecular dynamics simulations to be used in large-scale models of complex molecular systems with elements from the bottom of the periodic table, including actinides and even superheavy elements.

Nonaqueous Ion Pairing Exemplifies the Case for Including Electronic Polarization in Molecular Dynamics Simulations

The inclusion of electronic polarization is of crucial importance in molecular simulations of systems containing charged moieties. When neglected, as often done in force field simulations, charge-charge interactions in solution may become severely overestimated, leading to unrealistically strong bindings of ions to biomolecules. The electronic continuum correction introduces electronic polarization in a mean-field way via scaling of charges by the reciprocal of the square root of the high-frequency dielectric constant of the solvent environment. Here, we use ab initio molecular dynamics simulations to quantify the effect of electronic polarization on pairs of like-charged ions in a model nonaqueous environment where electronic polarization is the only dielectric response. Our findings confirm the conceptual validity of this approach, underlining its applicability to complex aqueous biomolecular systems. Simultaneously, the results presented here justify the potential employment of weaker charge scaling factors in force field development.

Common Cations Are Not Polarizable: Effects of Dispersion Correction on Hydration Structures from Ab Initio Molecular Dynamics

We employed density functional theory-based ab initio molecular dynamics simulations to examine the hydration structure of several common alkali and alkali earth metal cations. We found that the commonly used atom pairwise dispersion correction scheme D3, which assigns dispersion coefficients based on the neutral form of the atom rather than its actual oxidation state, leads to inaccuracies in the hydration structures of these cations. We evaluated this effect for lithium, sodium, potassium, and calcium and found that the inaccuracies are particularly pronounced for sodium and potassium compared to the experiment. To remedy this issue, we propose disabling the D3 correction specifically for all cation-including pairs, which leads to a much better agreement with experimental data.

Ion-Induced Transient Potential Fluctuations Facilitate Pore Formation and Cation Transport through Lipid Membranes

Unassisted ion transport through lipid membranes plays a crucial role in many cell functions without which life would not be possible, yet the precise mechanism behind the process remains unknown due to its molecular complexity. Here, we demonstrate a direct link between membrane potential fluctuations and divalent ion transport. High-throughput wide-field non-resonant second harmonic (SH) microscopy of membrane water shows that membrane potential fluctuations are universally found in lipid bilayer systems. Molecular dynamics simulations reveal that such variations in membrane potential reduce the free energy cost of transient pore formation and increase the ion flux across an open pore. These transient pores can act as conduits for ion transport, which we SH image for a series of divalent cations (Cu2+, Ca2+, Ba2+, Mg2+) passing through giant unilamellar vesicle (GUV) membranes. Combining the experimental and computational results, we show that permeation through pores formed via an ion-induced electrostatic field is a viable mechanism for unassisted ion transport.

Hydration Structure of Na+ and K+ Ions in Solution Predicted by Data-Driven Many-Body Potentials

The hydration structure of Na⁺ and K⁺ ions in solution is systematically investigated using a hierarchy of molecular models that progressively include more accurate representations of many-body interactions. We found that a conventional empirical pairwise additive force field that is commonly used in biomolecular simulations is unable to reproduce the extended X-ray absorption fine structure (EXAFS) spectra for both ions. In contrast, progressive inclusion of many-body effects rigorously derived from the many-body expansion of the energy allows the MB-nrg potential energy functions (PEFs) to achieve nearly quantitative agreement with the experimental EXAFS spectra, thus enabling the development of a molecular-level picture of the hydration structure of both Na⁺ and K⁺ in solution. Since the MB-nrg PEFs have already been shown to accurately describe isomeric equilibria and vibrational spectra of small ion-water clusters in the gas phase, the present study demonstrates that the MB-nrg PEFs effectively represent the long-sought-after models able to correctly predict the properties of ionic aqueous systems from the gas to the liquid phase, which has so far remained elusive.

Resolving the Equal Number Density Puzzle: Molecular Picture from Simulations of LiCl(aq) and NaCl(aq)

The change in number densities of aqueous solutions of alkali chlorides should be qualitatively predictable. Typically, as cations get larger, the number density of the solution decreases. However, aqueous solutions of lithium and sodium chloride exhibit at ambient conditions practically identical number densities at equal molalities despite different ionic sizes. Here, we provide an atomistic interpretation of this experimentally observed anomalous behavior using molecular dynamics simulations. The obtained results show that the rigidity of the Li⁺ first and second solvation shells and the associated compromised hydrogen bonding result in practically equal average water densities in the local hydration regions for Li⁺ and Na⁺ despite different sizes of the cations. In addition, in more distant regions from the cations, the water densities of these two solutions also coincide. These findings thus provide an atomistic interpretation for matching number densities of LiCl and NaCl solutions. In contrast, the number density differences between NaCl and KCl solutions as well as between LiCl and KCl solutions behave in a regular fashion with lower number densities of solutions observed for larger cations.

A practical guide to biologically relevant molecular simulations with charge scaling for electronic polarization

Molecular simulations can elucidate atomistic-level mechanisms of key biological processes, which are often hardly accessible to experiment. However, the results of the simulations can only be as trustworthy as the underlying simulation model. In many of these processes, interactions between charged moieties play a critical role. Current empirical force fields tend to overestimate such interactions, often in a dramatic way, when polyvalent ions are involved. The source of this shortcoming is the missing electronic polarization in these models. Given the importance of such biomolecular systems, there is great interest in fixing this deficiency in a computationally inexpensive way without employing explicitly polarizable force fields. Here, we review the electronic continuum correction approach, which accounts for electronic polarization in a mean-field way, focusing on its charge scaling variant. We show that by pragmatically scaling only the charged molecular groups, we qualitatively improve the charge-charge interactions without extra computational costs and benefit from decades of force field development on biomolecular force fields.

Interfacial and bulk properties of concentrated solutions of ammonium nitrate

We conducted molecular dynamics (MD) simulations to calculate the density and surface tension of concentrated ammonium nitrate (AN) solutions up to the solubility limit of ammonium nitrate in water, by combining the SPC/E, SPCE/F and TIP4P/2005 water models with OPLS model for ammonium and nitrate ions. This is the first time that the properties of concentrated solutions of nitrates, especially AN, have been studied by molecular dynamics. We effectively account for the polarisation effects by the electronic continuum correction (ECC), practically realised via rescaling of the ionic charges. We found that, the full-charge force field MD simulations overestimate the experimental results, as the ions experience repulsion from the interface and prefer to remain in the subsurface layer and the bulk solution. In contrast, reducing the ionic charges results in the behaviour that fits well with the experimental data. The nitrate anions display a greater propensity for the interface than the ammonium cations. We accurately predict both the density and the rise in the surface tension of concentrated solutions of AN, recommending TIP4P/2005 for water and the scaled-charge OPLS model (OPLS/ECC) for the ions in the solutions. We observe that, the adsorption of anions to the interface accompanies their depletion in the subsurface layer, which is preferentially occupied by cations, resulting in the formation of the electric double layer. We demonstrate the ion deficiency for up to 3 Å below the surface and establish the requirement to include the polarisability effects in the OPLS model for AN. While these results confirmed the findings of the previous studies for dilute solutions, they are new in the solubility limit. Concentrated solutions exhibit a strong effect of the abundance of solute on the coordination numbers of ions and on the degree of ion pairing. Surprisingly, ion pairing decreases significantly at the interface compared with the bulk. The present study identifies OPLS/ECC, along with TIP4P/2005, to yield accurate predictions of physical properties of concentrated AN, with precision required for industrial applications, such as a formulation of emulsion and fuel-oil explosives that now predominate the civilian use of AN. An application of this model will allow one to predict the surface properties of supersaturated solutions of AN which fall outside the capability of the present laboratory experiments but are important industrially.

Two-Dimensional Infrared Spectroscopy of Aqueous Solutions of Metal Nitrates: Slowdown of Spectral Diffusion in the Presence of Divalent Cations

The hydrogen-bonded network of water can be affected both structurally and dynamically by the presence of ions. In the present study, we have considered three aqueous solutions of metal nitrates to investigate the effects of divalent cations (Mg²⁺ and Ca²⁺), compared to that of monovalent Na⁺ ions, on hydrogen-bond fluctuations and vibrational spectral diffusion through calculations of linear and two-dimensional infrared spectra of these solutions at room temperature. We have employed the methods of molecular dynamics simulations using effective polarizable models of ions combined with quantum mechanical calculations of transition variables and statistical mechanical calculations of spectral response functions of vibrational spectroscopy. Divalent cations are found to have much stronger and longer-ranged effects on the structure and dynamics of the hydrogen-bonded network than that induced by the monovalent sodium ions. The blue shifts in the calculated linear spectra are found to follow the Hofmeister trend for the cations. The 2D-IR spectral lineshape and intensity corresponding to three-pulse echo peak shift (3PEPS) experiments are calculated. The timescales of these nonlinear spectral responses and also frequency-time correlations show significant slowing down of spectral diffusion for solutions containing divalent Mg²⁺ and Ca²⁺ ions compared to the corresponding dynamics of the solution containing Na⁺ ions. Unlike NaNO₃ solution, the relaxation of frequency and dipole orientational fluctuations of anion-bound water in Mg(NO₃)₂ and Ca(NO₃)₂ solutions are found to be somewhat slower than bulk water, which can be attributed to the presence of divalent cations whose effects go beyond their first solvation shells. This is also seen in the dynamics of bulk water in these solutions which is found to be notably slower for the solutions containing divalent cations than that in the NaNO₃ solution. Unlike Mg²⁺ and Ca²⁺ ions, no specific cationic effect is observed for the Na⁺ ions.

Solvation Shell of the Nitrite Ion in Water: An Ab Initio Molecular Dynamics Study

We performed ab initio molecular dynamics simulation of a nitrite ion in water to investigate the structural and dynamical properties of its hydration shell. The nitrite ion is found to exhibit strong asymmetry toward hydrogen bonding due to its two different types of hydrogen bond acceptor sites. This difference is better captured through further partitioning of the hydration shell into its proximal and distal regions. The frequency shifts of the stretch modes of hydration shell water reveal that the nitrogen site forms a stronger hydrogen bond than its oxygen sites with the latter forming hydrogen bonds, which are similar in strength to that between a pair of water molecules. The escape dynamics of water from the hydration shell is found to be rather slow, which seems to classify the nitrite ion as a structure-maker. However, the dynamics of orientational and hydrogen bond relaxation reveal a faster mobility of water molecules in the hydration shell than bulk water in spite of strong ion-water interactions. It is found that the nitrite ion can hold water molecules in its solvation shell and still make them rotate fast in its vicinity through switching of their hydrogen bonds between its nitrogen and oxygen acceptor sites. The dipole moment of the solute in water is also calculated in the present study.

Molecular simulation of liquid-vapor coexistence for NaCl: Full-charge vs scaled-charge interaction models

Scaled-charge models have been recently introduced for molecular simulations of electrolyte solutions and molten salts to attempt to implicitly represent polarizability. Although these models have been found to accurately predict electrolyte solution dynamic properties, they have not been tested for coexistence properties, such as the vapor pressure of the melt. In this work, we evaluate the vapor pressure of a scaled-charge sodium chloride (NaCl) force field and compare the results against experiments and a non-polarizable full-charge force field. The scaled-charge force field predicts a higher vapor pressure than found in experiments, due to its overprediction of the liquid-phase chemical potential. Reanalyzing the trajectories generated from the scaled-charge model with full charges improves the estimation of the liquid-phase chemical potential but not the vapor pressure.

Proximal charge effects on guest binding to a non-polar pocket

Science still does not have the ability to accurately predict the affinity that ligands have for proteins. In an attempt to address this, the Statistical Assessment of Modeling of Proteins and Ligands (SAMPL) series of blind predictive challenges is a community-wide exercise aimed at advancing computational techniques as standard predictive tools in rational drug design. In each cycle, a range of biologically relevant systems of different levels of complexity are selected to test the latest modeling methods. As part of this on-going exercise, and as a step towards understanding the important factors in context dependent guest binding, we challenged the computational community to determine the affinity of a series of negatively and positively charged guests to two constitutionally isomeric cavitand hosts: octa-acid 1, and exo-octa acid 2. Our affinity determinations, combined with molecular dynamics simulations, reveal asymmetries in affinities between host-guest pairs that cannot alone be explained by simple coulombic interactions, but also point to the importance of host-water interactions. Our work reveals the key facets of molecular recognition in water, emphasizes where improvements need to be made in modelling, and shed light on the complex problem of ligand-protein binding in the aqueous realm.

Properties of Lipid Models of Lung Surfactant Containing Cholesterol and Oxidized Lipids: A Mixed Experimental and Computational Study

We introduce and study a multicomponent lipid film mimicking lipid composition of the human lung surfactant. It consists of phospholipids with various lipid headgroups and tail saturation. Furthermore, it includes cholesterol and oxidized lipids. Langmuir trough and fluorescence microscopy experiments are combined with fully atomistic molecular dynamics simulations. The considered lipid mixtures form complex interfacial films with properties modulated by lateral compression. Cholesterol laterally condenses, and oxidized lipids laterally expand the films; both types of molecules increase film miscibility. Oxidized lipids also alter the lipid-water interface enhancing film hydration; this effect can be partially reversed by cholesterol. Regarding presentation of different chemical moieties toward the aqueous subphase, the zwitterionic phosphatidylcholine groups dominate at the lipid-water interface, while both the negatively charged phosphatidylglycerol and hydroxyl group of cholesterol are less exposed. The investigated synthetic lipid-only mimic of the lung surfactant may serve as a basis for further studies involving nonlipid pulmonary surfactant components.

Accurate Biomolecular Simulations Account for Electronic Polarization

In this perspective, we discuss where and how accounting for electronic many-body polarization affects the accuracy of classical molecular dynamics simulations of biomolecules. While the effects of electronic polarization are highly pronounced for molecules with an opposite total charge, they are also non-negligible for interactions with overall neutral molecules. For instance, neglecting these effects in important biomolecules like amino acids and phospholipids affects the structure of proteins and membranes having a large impact on interpreting experimental data as well as building coarse grained models. With the combined advances in theory, algorithms and computational power it is currently realistic to perform simulations with explicit polarizable dipoles on systems with relevant sizes and complexity. Alternatively, the effects of electronic polarization can also be included at zero additional computational cost compared to standard fixed-charge force fields using the electronic continuum correction, as was recently demonstrated for several classes of biomolecules.

Dielectric Decrement for Aqueous NaCl Solutions: Effect of Ionic Charge Scaling in Nonpolarizable Water Force Fields

We investigate the dielectric constant and the dielectric decrement of aqueous NaCl solutions by means of molecular dynamic simulations. We thereby compare the performance of four different force fields and focus on disentangling the origin of the dielectric decrement and the influence of scaled ionic charges, as often used in nonpolarizable force fields to account for the missing dynamic polarizability in the shielding of electrostatic ion interactions. Three of the force fields showed excessive contact ion pair formation, which correlates with a reduced dielectric decrement. In spite of the fact that the scaling of charges only weakly influenced the average polarization of water molecules around an ion, the rescaling of ionic charges did influence the dielectric decrement, and a close-to-linear relation of the slope of the dielectric constant as a function of concentration with the ionic charge was found.

Modeling of solid–liquid interfaces using scaled charges: rutile (110) surfaces

The first application of the electronic continuum correction model with scaled charges to molecular dynamics simulations of solid–liquid interfaces.

Metal Ion Modeling Using Classical Mechanics

Metal ions play significant roles in numerous fields including chemistry, geochemistry, biochemistry, and materials science. With computational tools increasingly becoming important in chemical research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aqueous, and solid phases. Herein, we review both quantum and classical modeling strategies for metal ion-containing systems that have been developed over the past few decades. This Review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond-based models. Quantum mechanical studies of metal ion-containing systems at the semiempirical, ab initio, and density functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion-containing systems.

Accounting for Electronic Polarization Effects in Aqueous Sodium Chloride via Molecular Dynamics Aided by Neutron Scattering

Modeled ions, described by nonpolarizable force fields, can suffer from unphysical ion pairing and clustering in aqueous solutions well below their solubility limit. The electronic continuum correction takes electronic polarization effects of the solvent into account in an effective way by scaling the charges on the ions, resulting in a much better description of the ionic behavior. Here, we present parameters for the sodium ion consistent with this effective polarizability approach and in agreement with experimental data from neutron scattering, which could be used for simulations of complex aqueous systems where polarization effects are important.

Comparison of structural, thermodynamic, kinetic and mass transport properties of Mg(2+) ion models commonly used in biomolecular simulations

The prevalence of Mg(2+) ions in biology and their essential role in nucleic acid structure and function has motivated the development of various Mg(2+) ion models for use in molecular simulations. Currently, the most widely used models in biomolecular simulations represent a nonbonded metal ion as an ion-centered point charge surrounded by a nonelectrostatic pairwise potential that takes into account dispersion interactions and exchange effects that give rise to the ion's excluded volume. One strategy toward developing improved models for biomolecular simulations is to first identify a Mg(2+) model that is consistent with the simulation force fields that closely reproduces a range of properties in aqueous solution, and then, in a second step, balance the ion-water and ion-solute interactions by tuning parameters in a pairwise fashion where necessary. The present work addresses the first step in which we compare 17 different nonbonded single-site Mg(2+) ion models with respect to their ability to simultaneously reproduce structural, thermodynamic, kinetic and mass transport properties in aqueous solution. None of the models based on a 12-6 nonelectrostatic nonbonded potential was able to reproduce the experimental radial distribution function, solvation free energy, exchange barrier and diffusion constant. The models based on a 12-6-4 potential offered improvement, and one model in particular, in conjunction with the SPC/E water model, performed exceptionally well for all properties. The results reported here establish useful benchmark calculations for Mg(2+) ion models that provide insight into the origin of the behavior in aqueous solution, and may aid in the development of next-generation models that target specific binding sites in biomolecules.

Polarizable molecular interactions in condensed phase and their equivalent nonpolarizable models

Earlier, using phenomenological approach, we showed that in some cases polarizable models of condensed phase systems can be reduced to nonpolarizable equivalent models with scaled charges. Examples of such systems include ionic liquids, TIPnP-type models of water, protein force fields, and others, where interactions and dynamics of inherently polarizable species can be accurately described by nonpolarizable models. To describe electrostatic interactions, the effective charges of simple ionic liquids are obtained by scaling the actual charges of ions by a factor of 1/√(ε(el)), which is due to electronic polarization screening effect; the scaling factor of neutral species is more complicated. Here, using several theoretical models, we examine how exactly the scaling factors appear in theory, and how, and under what conditions, polarizable Hamiltonians are reduced to nonpolarizable ones. These models allow one to trace the origin of the scaling factors, determine their values, and obtain important insights on the nature of polarizable interactions in condensed matter systems.

Exploring Ion-Ion Interactions in Aqueous Solutions by a Combination of Molecular Dynamics and Neutron Scattering

Recent advances in computational and experimental techniques have allowed for accurate description of ion pairing in aqueous solutions. Free energy methods based on ab initio molecular dynamics, as well as on force fields accounting effectively for electronic polarization, can provide quantitative information about the structures and occurrences of individual types of ion pairs. When properly benchmarked against electronic structure calculations for model systems and against structural experiments, in particular neutron scattering, such force field simulations represent a powerful tool for elucidating interactions of salt ions in complex biological aqueous environments.

Calcium Binding to Calmodulin by Molecular Dynamics with Effective Polarization

Calcium represents a key biological signaling ion with the EF-hand loops being its most prevalent binding motif in proteins. We show using molecular dynamics simulations with umbrella sampling that including electronic polarization effects via ionic charge rescaling dramatically improves agreements with experiment in terms of the strength of calcium binding and structures of the calmodulin binding sites. The present study thus opens way to accurate calculations of interactions of calcium and other computationally difficult high-charge-density ions in biological contexts.

Dipeptide Aggregation in Aqueous Solution from Fixed Point-Charge Force Fields

The description of aggregation processes with molecular dynamics simulations is a playground for testing biomolecular force fields, including a new generation of force fields that explicitly describe electronic polarization. In this work, we study a system consisting of 50 glycyl-l-alanine (Gly-Ala) dipeptides in solution with 1001 water molecules. Neutron diffraction experiments have shown that at this concentration, Gly-Ala aggregates into large clusters. However, general-purpose force fields in combination with established water models can fail to correctly describe this aggregation process, highlighting important deficiencies in how solute-solute and solute-solvent interactions are parametrized in these force fields. We found that even for the fully polarizable AMOEBA force field, the degree of association is considerably underestimated. Instead, a fixed point-charge approach based on the newly developed IPolQ scheme [Cerutti et al. J. Phys. Chem.2013, 117, 2328] allows for the correct modeling of the dipeptide aggregation in aqueous solution. This result should stimulate interest in novel fitting schemes that aim to improve the description of the solvent polarization effect within both explicitly polarizable and fixed point-charge frameworks.

Polarizability series of aqueous polyatomic anions revealed by femtosecond Kerr effect spectroscopy

Femtosecond OHD-RIKES measurements show that the hyperpolarizability series of aqueous polyatomic anions increases in the following sequence HPO₄²⁻ < HSO₄⁻ < CO₃²⁻ < AC⁻ < NO₃⁻ < SCN⁻.

Polarizable Mean-Field Model of Water for Biological Simulations with Amber and Charmm force fields

Although a great number of computational models of water are available today, the majority of current biological simulations are done with simple models, such as TIP3P and SPC, developed almost thirty years ago and only slightly modified since then. The reason is that the non-polarizable force fields that are mostly used to describe proteins and other biological molecules are incompatible with more sophisticated modern polarizable models of water. The issue is electronic polarizability: in liquid state, in protein, and in vacuum the water molecule is polarized differently, and therefore has different properties; thus the only way to describe all these different media with the same model is to use a polarizable water model. However, to be compatible with the force field of the rest of the system, e.g. a protein, the latter should be polarizable as well. Here we describe a novel model of water that is in effect polarizable, and yet compatible with the standard non-polarizable force fields such as AMBER, CHARMM, GROMOS, OPLS, etc. Thus the model resolves the outstanding problem of incompatibility.