A molecular theory of liquid interfaces

AmberTools

AmberTools is a free and open-source collection of programs used to set up, run, and analyze molecular simulations. The newer features contained within AmberTools23 are briefly described in this Application note.

EPISOL: A software package with expanded functions to perform 3D-RISM calculations for the solvation of chemical and biological molecules

Integral equation theory (IET) provides an effective solvation model for chemical and biological systems that balances computational efficiency and accuracy. We present a new software package, the expanded package for IET-based solvation (EPISOL), that performs 3D-reference interaction site model (3D-RISM) calculations to obtain the solvation structure and free energies of solute molecules in different solvents. In EPISOL, we have implemented 22 different closures, multiple free energy functionals, and new variations of 3D-RISM theory, including the recent hydrophobicity-induced density inhomogeneity (HI) theory for hydrophobic solutes and ion-dipole correction (IDC) theory for negatively charged solutes. To speed up the convergence and enhance the stability of the self-consistent iterations, we have introduced several numerical schemes in EPISOL, including a newly developed dynamic mixing approach. We show that these schemes have significantly reduced the failure rate of 3D-RISM calculations compared to AMBER-RISM software. EPISOL consists of both a user-friendly graphic interface and a kernel library that allows users to call its routines and adapt them to other programs. EPISOL is compatible with the force-field and coordinate files from both AMBER and GROMACS simulation packages. Moreover, EPISOL is equipped with an internal memory control to efficiently manage the use of physical memory, making it suitable for performing calculations on large biomolecules. We demonstrate that EPISOL can efficiently and accurately calculate solvation density distributions around various solute molecules (including a protein chaperone consisting of 120,715 atoms) and obtain solvent free energy for a wide range of organic compounds. We expect that EPISOL can be widely applied as a solvation model for chemical and biological systems. EPISOL is available at https://github.com/EPISOLrelease/EPISOL.

Explainable Solvation Free Energy Prediction Combining Graph Neural Networks with Chemical Intuition

The prediction of a molecule's solvation Gibbs free (ΔG_solv) energy in a given solvent is an important task which has traditionally been carried out via quantum chemical continuum methods or force field-based molecular simulations. Machine learning (ML) and graph neural networks in particular have emerged as powerful techniques for elucidating structure-property relationships. This work presents a graph neural network (GNN) for the prediction of ΔG_solv which, in addition to encoding typical atom and bond-level features, incorporates chemically intuitive, solvation-relevant parameters into the featurization process: semiempirical partial atomic charges and solvent dielectric constant. Solute-solvent interactions are included via an interaction map layer which can be visualized to examine solubility-enhancing or -decreasing interactions learnt by the model. On a test set of small organic molecules, our GNN predicts ΔG_solv in water and cyclohexane with an accuracy comparable to polarizable and ab initio generated force field methods [mean absolute error (MAE) = 0.4 and 0.2 kcal mol^-1, respectively], without the need for any molecular simulation. For the FreeSolv data set of hydration free energies, the test MAE is 0.7 kcal mol^-1. Interpretability and applicability of the model is highlighted through several examples including rationalizing the increased solubility of modified diaminoanthraquinones in organic solvents. The clear explanations afforded by our GNN allow for easy understanding of the model's predictions, giving the experimental chemist confidence in employing ML models toward more optimized synthetic routes.

The Ion-Dipole Correction of the 3DRISM Solvation Model to Accurately Compute Water Distributions around Negatively Charged Biomolecules

The 3D reference interaction site model (3DRISM) provides an efficient grid-based solvation model to compute the structural and thermodynamic properties of biomolecules in aqueous solutions. However, it remains challenging for existing 3DRISM methods to correctly predict water distributions around negatively charged solute molecules. In this paper, we first show that this challenge is mainly due to the orientation of water molecules in the first solvation shell of the negatively charged solute molecules. To properly consider this orientational preference, position-dependent two-body intramolecular correlations of solvent need to be included in the 3DRISM theory, but direct evaluations of these position-dependent two-body intramolecular correlations remain numerically intractable. To address this challenge, we introduce the Ion-Dipole Correction (IDC) to the 3DRISM theory, in which we incorporate the orientation preference of water molecules via an additional solute-solvent interaction term (i.e., the ion-dipole interaction) while keeping the formulism of the 3DRISM equation unchanged. We prove that this newly introduced IDC term is equivalent to an effective direct correlation function which can effectively consider the orientation effect that arises from position dependent two-body correlations. We first quantitatively validate our 3DRISM-IDC theory combined with the PSE3 closure on Cl^-, [ClO]^- (a two-site anion), and [NO₂]^- (a three-site anion). For all three anions, we show that our 3DRISM-IDC theory significantly outperforms the 3DRISM theory in accurately predicting the solvation structures in comparison to MD simulations, including RDFs and 3D water distributions. Furthermore, we have also demonstrated that the 3DRISM-IDC can improve the accuracy of hydration free-energy calculation for Cl^-. We further demonstrate that our 3DRISM-IDC theory yields significant improvements over the 3DRISM theory when applied to compute the solvation structures for various negatively charged solute molecules, including adenosine triphosphate (ATP), a short peptide containing 19 residues, a DNA hairpin containing 24 nucleotides, and a riboswitch RNA molecule with 77 nucleotides. We expect that our 3DRISM-IDC-PSE3 solvation model holds great promise to be widely applied to study solvation properties for nucleic acids and other biomolecules containing negatively charged functional groups.

Understanding the Liquid States of Cyclic Hydrocarbons Containing N, O, and S Atoms via the 3D-RISM-KH Molecular Solvation Theory

The 3D-reference interaction site model (3D-RISM) molecular solvation theory in combination with the Kovalenko-Hirata (KH) closure is extended to seven heterocyclic liquids to understand their liquid states and to test the performance of the theory in solvation free energy (SFE) calculations of solutes in select solvents. The computed solvent site distribution profiles were compared with the all-atom molecular dynamics (MD) simulations, showing comparable performances. The computational results were compared against the structural parameters for liquids, whenever available, as well as against the experimental SFEs. The liquids are found to have local ordered structures held together via weak interactions in both the RISM and MD simulations. The 3D-RISM-KH computed SFEs are in good agreement with the benchmark values for the tetrahydrothiophene-S,S-dioxide, and showed comparatively larger deviations in the case of the SFEs in the tetrahydrofuran continuum.

Benchmarking Free Energy Calculations in Liquid Aliphatic Ketone Solvents Using the 3D-RISM-KH Molecular Solvation Theory

The three-dimensional reference interaction site model of the molecular solvation theory with the Kovalenko–Hirata closure is used to calculate the free energy of solvation of organic solutes in liquid aliphatic ketones. The ketone solvent sites were modeled using a modified united-atom force field. The successful application of these solvation models in calculating ketone–water partition coefficients of a large number of solutes supports the validation and benchmarking reported here.

Predicting PAMPA permeability using the 3D-RISM-KH theory: are we there yet?

The parallel artificial membrane permeability assay (PAMPA), a non-cellular lab-based assay, is extensively used to measure the permeability of pharmaceutical compounds. PAMPA experiments provide a working mimic of a molecule passing through cells and PAMPA values are widely used to estimate drug absorption parameters. There is an increased interest in developing computational methods to predict PAMPA permeability values. We developed an in silico model to predict the permeability of compounds based on the PAMPA assay. We used the three-dimensional reference interaction site model (3D-RISM) theory with the Kovalenko-Hirata (KH) closure to calculate the excess chemical potentials of a large set of compounds and predicted their apparent permeability with good accuracy (mean absolute error or MAE = 0.69 units) when compared to a published experimental data set. Furthermore, our in silico PAMPA protocol performed very well in the binary prediction of 288 compounds as being permeable or impermeable (precision = 94%, accuracy = 93%). This suggests that our in silico protocol can mimic the PAMPA assay and could aid in the rapid discovery or screening of potentially therapeutic drug leads that can be delivered to a desired tissue.

First-principles modeling of chemistry in mixed solvents: Where to go from here?

Mixed solvents (i.e., binary or higher order mixtures of ionic or nonionic liquids) play crucial roles in chemical syntheses, separations, and electrochemical devices because they can be tuned for specific reactions and applications. Apart from fully explicit solvation treatments that can be difficult to parameterize or computationally expensive, there is currently no well-established first-principles regimen for reliably modeling atomic-scale chemistry in mixed solvent environments. We offer our perspective on how this process could be achieved in the near future as mixed solvent systems become more explored using theoretical and computational chemistry. We first outline what makes mixed solvent systems far more complex compared to single-component solvents. An overview of current and promising techniques for modeling mixed solvent environments is provided. We focus on so-called hybrid solvation treatments such as the conductor-like screening model for real solvents and the reference interaction site model, which are far less computationally demanding than explicit simulations. We also propose that cluster-continuum approaches rooted in physically rigorous quasi-chemical theory provide a robust, yet practical, route for studying chemical processes in mixed solvents.

Statistical field theory of ion–molecular solutions

Schematic representation of the multipolar molecule surrounded by salt ions in a dielectric solvent medium.

Application of the 3D-RISM-KH molecular solvation theory for DMSO as solvent

The molecular solvation theory in the form of the Three-Dimensional Reference Interaction Site Model (3D-RISM) with Kovalenko-Hirata (KH) closure relation is benchmarked for use with dimethyl sulfoxide (DMSO) as solvent for (bio)-chemical simulation within the framework of integral equation formalism. Several force field parameters have been tested to correctly reproduce solvation free energy in DMSO, ion solvation in DMSO, and DMSO coordination prediction. Our findings establish a united atom (UA) type parameterization as the best model of DMSO for use in 3D-RISM-KH theory based calculations.

To Pass or Not To Pass: Predicting the Blood-Brain Barrier Permeability with the 3D-RISM-KH Molecular Solvation Theory

Predicting the ability of chemical species to cross the blood-brain barrier (BBB) is an active field of research for development and mechanistic understanding in the pharmaceutical industry. Here, we report the BBB permeability of a large data set of compounds by incorporating molecular solvation energy descriptors computed by the 3D-RISM-KH molecular solvation theory. We have been able to show, for the first time, that the computed excess chemical potential in different solvents can be successfully used to predict permeability of compounds in a binary manner (yes/no) via a minimum-descriptor-based model. Our findings successfully combine the molecular solvation theory with the machine learning approach to address one of the most daunting challenges in predictive structure-activity relationship modeling. The workflow presented in this work is simple enough to be used by nonexperts with ease.

Predicting skin permeability using the 3D-RISM-KH theory based solvation energy descriptors for a diverse class of compounds

The state-of-the-art molecular solvation theory is used to predict skin permeability of a large set of compounds with available experimental skin permeability coefficient (logK_P). Encouraging results are obtained pointing to applicability of a novel quantitative structure activity model that uses statistical physics based 3D-RISM-KH theory for solvation free energy calculations as a primary descriptor for the prediction of logK_P with relative mean square error of 0.77 units.

Performance of 3D-RISM-KH in Predicting Hydration Free Energy: Effect of Solute Parameters

The three-dimensional reference interaction site model molecular solvation theory with the Kovalenko-Hirata closure relation has been shown to produce excellent solvation characteristics for a large class of (bio)chemical systems in solution. Correct calculation of hydration free energy is central to successful application of any solvation model. In order to find out the best possible force-field parameters to be used for hydration free energy calculation with the aforementioned theory, we have developed an extended database containing a large number of experimental solvation free energies available in the current literature and used a plethora of theoretical models for assessment. The general Amber force field was found to perform satisfactorily, whereas special care should be taken in solute charge assignment with the universal force field.

Active hole generation in a liquid droplet dissolving into a binary solvent

In liquid-liquid dissolution, the critical point of phase separation is determined by the temperature. When the solvent consists of multi-components, in contrast, the mole fractions in the solvent also take on the role of control parameter. In this study an ionic liquid dissolves into a binary solvent composed of ethanol and water. It is found in this system that, near the critical point, a hole is spontaneously created in the droplet of the ionic liquid. The creation of the hole is initiated by a mutual interaction between the concentrations of the ionic liquid and the binary solvent via their affinity. A spatial inhomogeneity of the interfacial tension is induced through an amplification of fluctuation in the concentration due to an instability mechanism, and causes the Marangoni effect to create the hole. The hole moves inside the droplet and consequently leads to the motion of the droplet. The present system provides not only a new type of dissolution process but also a peculiar example of active matter realized in a liquid droplet.

Multiple time step molecular dynamics in the optimized isokinetic ensemble steered with the molecular theory of solvation: accelerating with advanced extrapolation of effective solvation forces

We develop efficient handling of solvation forces in the multiscale method of multiple time step molecular dynamics (MTS-MD) of a biomolecule steered by the solvation free energy (effective solvation forces) obtained from the 3D-RISM-KH molecular theory of solvation (three-dimensional reference interaction site model complemented with the Kovalenko-Hirata closure approximation). To reduce the computational expenses, we calculate the effective solvation forces acting on the biomolecule by using advanced solvation force extrapolation (ASFE) at inner time steps while converging the 3D-RISM-KH integral equations only at large outer time steps. The idea of ASFE consists in developing a discrete non-Eckart rotational transformation of atomic coordinates that minimizes the distances between the atomic positions of the biomolecule at different time moments. The effective solvation forces for the biomolecule in a current conformation at an inner time step are then extrapolated in the transformed subspace of those at outer time steps by using a modified least square fit approach applied to a relatively small number of the best force-coordinate pairs. The latter are selected from an extended set collecting the effective solvation forces obtained from 3D-RISM-KH at outer time steps over a broad time interval. The MTS-MD integration with effective solvation forces obtained by converging 3D-RISM-KH at outer time steps and applying ASFE at inner time steps is stabilized by employing the optimized isokinetic Nosé-Hoover chain (OIN) ensemble. Compared to the previous extrapolation schemes used in combination with the Langevin thermostat, the ASFE approach substantially improves the accuracy of evaluation of effective solvation forces and in combination with the OIN thermostat enables a dramatic increase of outer time steps. We demonstrate on a fully flexible model of alanine dipeptide in aqueous solution that the MTS-MD/OIN/ASFE/3D-RISM-KH multiscale method of molecular dynamics steered by effective solvation forces allows huge outer time steps up to tens of picoseconds without affecting the equilibrium and conformational properties, and thus provides a 100- to 500-fold effective speedup in comparison to conventional MD with explicit solvent. With the statistical-mechanical 3D-RISM-KH account for effective solvation forces, the method provides efficient sampling of biomolecular processes with slow and/or rare solvation events such as conformational transitions of hydrated alanine dipeptide with the mean life times ranging from 30 ps up to 10 ns for "flip-flop" conformations, and is particularly beneficial for biomolecular systems with exchange and localization of solvent and ions, ligand binding, and molecular recognition.

Multiscale modeling of solvation in chemical and biological nanosystems and in nanoporous materials

Statistical–mechanical, 3D-RISM-KH molecular theory of solvation (3D reference interaction site model with the Kovalenko–Hirata closure) is promising as an essential part of multiscale methodology for chemical and biomolecular nanosystems in solution. 3D-RISM-KH explains the molecular mechanisms of self-assembly and conformational stability of synthetic organic rosette nanotubes (RNTs), aggregation of prion proteins and β-sheet amyloid oligomers, protein-ligand binding, and function-related solvation properties of complexes as large as the Gloeobacter violaceus pentameric ligand-gated ion channel (GLIC) and GroEL/ES chaperone. Molecular mechanics/Poisson–Boltzmann (generalized Born) surface area [MM/PB(GB)SA] post-processing of molecular dynamics (MD) trajectories involving SA empirical nonpolar terms is replaced with MM/3D-RISM-KH statistical–mechanical evaluation of the solvation thermodynamics. 3D-RISM-KH has been coupled with multiple time-step (MTS) MD of the solute biomolecule driven by effective solvation forces, which are obtained analytically by converging the 3D-RISM-KH integral equations at outer time-steps and are calculated in between by using solvation force coordinate extrapolation (SFCE) in the subspace of previous solutions to 3D-RISM-KH. The procedure is stabilized by the optimized isokinetic Nosé–Hoover (OIN) chain thermostatting, which enables gigantic outer time-steps up to picoseconds to accurately calculate equilibrium properties. The multiscale OIN/SFCE/3D-RISM-KH algorithm is implemented in the Amber package and illustrated on a fully flexible model of alanine dipeptide in aqueous solution, exhibiting the computational rate of solvent sampling 20 times faster than standard MD with explicit solvent. Further substantial acceleration can be achieved with 3D-RISM-KH efficiently sampling essential events with rare statistics such as exchange and localization of solvent, ions, and ligands at binding sites and pockets of the biomolecule. 3D-RISM-KH was coupled with ab initio complete active space self-consistent field (CASSCF) and orbital-free embedding (OFE) Kohn–Sham (KS) density functional theory (DFT) quantum chemistry methods in an SCF description of electronic structure, optimized geometry, and chemical reactions in solution. The (OFE)KS-DFT/3D-RISM-KH multi-scale method is implemented in the Amsterdam Density Functional (ADF) package and extensively validated against experiment for solvation thermochemistry, photochemistry, conformational equilibria, and activation barriers of various nanosystems in solvents and ionic liquids (ILs). Finally, the replica RISM-KH-VM molecular theory for the solvation structure, thermodynamics, and electrochemistry of electrolyte solutions sorbed in nanoporous materials reveals the molecular mechanisms of sorption and supercapacitance in nanoporous carbon electrodes, which is drastically different from a planar electrical double layer.

Integral equations in the study of polar and ionic interaction site fluids

In this review article we consider some of the current integral equation approaches and application to model polar liquid mixtures. We consider the use of multidimensional integral equations and in particular progress on the theory and applications of three dimensional integral equations. The IEs we consider may be derived from equilibrium statistical mechanical expressions incorporating a classical Hamiltonian description of the system. We give example including salt solutions, inhomogeneous solutions and systems including proteins and nucleic acids.

Liquid-vapor interfaces in XY -spin fluids: an inhomogeneous anisotropic integral-equation approach

An integral-equation approach is developed to study interfacial properties of anisotropic fluids with planar spins in the presence of an external magnetic field. The approach is based on the coupled set of the Lovett-Mou-Buff-Wertheim integro-differential equation for the inhomogeneous anisotropic one-particle density and the Ornstein-Zernike equation for the orientationally dependent two-particle correlation functions. Using the proposed inhomogeneous angle-harmonics expansion formalism we show that these integral equations can be reduced to a much simpler form similar to that inherent for a system of isotropic fluids. The interfacial orientationally dependent direct correlation function can be consistently constructed by means of a nonlinear interpolation via its values obtained in the coexisting anisotropic bulk phases. A soft mean spherical approximation is employed for the closure relation. This has allowed us to solve the complicated integral equations in the situation when both spatial inhomogeneity and orientational anisotropy are present simultaneously. The approach introduced is applied to an XY fluid model with ferromagnetic spin interactions. As a result, the density-orientation and magnetization profiles at the liquid-vapor interfaces are calculated in a wide range of temperatures up to subcritical regions. The influence of the external field on the microscopic structure of the interfaces and the surface tension is also analyzed in detail.

An integral equation theory for inhomogeneous molecular fluids: the reference interaction site model approach

An integral equation theory which is applicable to inhomogeneous molecular liquids is proposed. The "inhomogeneous reference interaction site model (RISM)" equation derived here is a natural extension of the RISM equation to inhomogeneous systems. This theory makes it possible to calculate the pair correlation function between two molecules which are located at different density regions. We also propose approximations concerning the closure relation and the intramolecular susceptibility of inhomogeneous molecular liquids. As a preliminary application of the theory, the hydration structure around an ion is investigated. Lithium, sodium, and potassium cations are chosen as the solute. Using the Percus trick, the local density of solvent around an ion is expressed in terms of the solute-solvent pair correlation function calculated from the RISM theory. We then analyze the hydration structure around an ion through the triplet correlation function which is defined with the inhomogeneous pair correlation function and the local density of the solvent. The results of the triplet correlation functions for cations indicate that the thermal fluctuation of the hydration shell is closely related to the size of the solute ion. The triplet correlation function from the present theory is also compared with that from the Kirkwood superposition approximation, which substitutes the inhomogeneous pair correlation by the homogeneous one. For the lithium ion, the behavior of the triplet correlation functions from the present theory shows marked differences from the one calculated within the Kirkwood approximation.

Hydronium ion motion in nanometer 3-methyl-pentane films

An ion soft-landing approach was applied to study the motion of hydronium (D(3)O(+)) and cesium (Cs(+)) ions from 84 to 104 K in glassy 3-methyl-pentane (3MP) films vapor deposited on Pt(111). Both ions were found to have very similar mobilities in 3MP. The span of ion mobilities probed is from approximately 10(-18) to approximately 10(-13) m(2) V(-1) s(-1). Ion transport in these films was studied as a function of film thickness and electric field strength. The drift velocity was found to be linear with applied field below about 2 x 10(8) Vm and deviated from linearity above this. To a large extent, D(3)O(+) and Cs(+) motion in 3MP was well predicted by a simple continuum-based ion mobility model in films from 25 to 20,000 ML thick (including pronounced perturbations 7 ML from both the vacuum and Pt interfaces). The mobility varied with temperature more slowly than predicted by Stokes' law, which may be due to extended inhomogeneous structures in the 3MP near its glass transition at 77 K.

Liquid-vapor and liquid-liquid interfaces in Ising fluids: An integral equation approach

The microscopic structure and thermodynamic properties of liquid-vapor and liquid-liquid interfaces in Ising fluids are studied using an integral equation approach. The calculations are performed in the absence and presence of an external magnetic field by solving the corresponding set of Lovett-Mou-Buff-Wertheim integrodifferential equations for the one-particle density distribution functions. The two-particle inhomogeneous direct correlation functions are consistently constructed by nonlinear interpolation between the bulk ones. The bulk correlation functions of the coexisting phases are obtained from the Ornstein-Zernike equations with a modified soft mean spherical approximation for the closure relation. As a result, the density and magnetization profiles at liquid-vapor and liquid-liquid interfaces as well as the surface tension and adsorption coefficients are evaluated in a wide temperature range including subcritical regions. The influence of an external magnetic field on the liquid-vapor interfaces is also considered.

Importance of boundary conditions for fluctuation-induced forces between colloids at interfaces

We calculate the effective fluctuation-induced force between spherical or disklike colloids trapped at a flat, fluid interface mediated by thermally excited capillary waves. This Casimir-type force is determined by the partition function of the system which in turn is calculated in a functional integral approach, where the restrictions on the capillary waves imposed by the colloids are incorporated by auxiliary fields. In the long-range regime the fluctuation-induced force is shown to depend sensitively on the boundary conditions imposed at the three-phase contact line between the colloids and the two fluid phases. Separating the colloid fluctuations from the fluctuations of the capillary wave field leads to competing repulsive and attractive contributions, respectively, which give rise to cancellations of the leading terms. In a second approach based on a multipole expansion of the Casimir interaction, these cancellations can be understood from the vanishing of certain multipole moments enforced by the boundary conditions. We also discuss the connection of the different types of boundary conditions to certain external fields acting on the colloids which appear to be realizable by experimental techniques such as the laser tweezer method.